Multimodal RoBERTa-based Classification

Multimodal RoBERTa-based Classification (Text + Non-Text Fusion with RoBERTa Encoder)

Multimodal RoBERTa
RoBERTa multimodal classifier
cross-modal RoBERTa classification
MM-RoBERTa

Liu et al. (RoBERTa); multimodal extension by community

Multimodal RoBERTa-based Classification combines the RoBERTa transformer encoder — a robustly optimised variant of BERT — with auxiliary modalities such as images, structured metadata, or tabular features. The fused representation is passed to a classification head, allowing the model to leverage both rich language understanding and non-textual signals simultaneously.

Multimodal text + auxiliary feature classification

Text (tokenized sequences) + structured/image/tabular auxiliary features

Liu, Y., Ott, M., Goyal, N., Du, J., Joshi, M., Chen, D., Levy, O., Lewis, M., Zettlemoyer, L., & Stoyanov, V. (2019). RoBERTa: A Robustly Optimized BERT Pretraining Approach. arXiv preprint arXiv:1907.11692.

Kiela, D., Grave, E., Joulin, A., & Mikolov, T. (2018). Efficient Large-Scale Multi-Modal Classification. Proceedings of the AAAI Conference on Artificial Intelligence, 32(1).

bert-based-classification roberta-based-classification multimodal-transformer multimodal-bert-based-classification sentence-embeddings multimodal-sentence-embeddings


Multimodal Semantic Segmentation

Multimodal Semantic Segmentation (Multi-Sensor Pixel-Level Scene Understanding)

multimodal scene parsing
multi-sensor semantic segmentation
RGB-D semantic segmentation
cross-modal semantic segmentation

Multiple contributors (Hazirbas et al., Long et al., and others)

Multimodal semantic segmentation assigns a semantic class label to every pixel in a scene by fusing information from two or more sensor modalities — most commonly RGB images paired with depth maps (RGB-D), LiDAR point clouds, thermal cameras, or text descriptions. Deep encoder-decoder networks learn to align and fuse complementary cues from each modality, producing denser and more accurate segmentation than any single-modality approach.

Pixel-level classification with multi-sensor fusion

RGB images paired with depth, LiDAR, thermal, or text modalities

Hazirbas, C., Ma, L., Domokos, C., & Cremers, D. (2016). FuseNet: Incorporating Depth into Semantic Segmentation via Fusion-based CNN Architecture. In Proceedings of the Asian Conference on Computer Vision (ACCV). Springer.

Zhang, J., Liu, H., Yang, K., Hu, X., Liu, R., & Stiefelhagen, R. (2023). CMX: Cross-Modal Fusion for RGB-X Semantic Segmentation with Transformers. IEEE Transactions on Intelligent Transportation Systems, 24(12), 14801–14813.

semantic-segmentation panoptic-segmentation instance-segmentation rgb-d-depth-estimation vision-transformer encoder-decoder-network


Multimodal Sentence Embeddings

Multimodal Sentence Embeddings (Joint Vision-Language Representation Learning)

multimodal embeddings
cross-modal sentence embeddings
vision-language embeddings
joint image-text embeddings

Frome et al. (DeViSE, 2013); popularized by Radford et al. (CLIP, 2021)

Multimodal sentence embeddings map text and images (and sometimes audio or video) into a shared continuous vector space, so that semantically related pairs from different modalities land close together. Trained by contrastive objectives on large paired corpora, these representations power cross-modal retrieval, zero-shot classification, and vision-language reasoning.

Paired image-text data; text corpora; image datasets

Radford, A., Kim, J. W., Hallacy, C., Ramesh, A., Goh, G., Agarwal, S., ... & Sutskever, I. (2021). Learning transferable visual models from natural language supervision. In Proceedings of the 38th International Conference on Machine Learning (ICML), pp. 8748–8763. PMLR.

Frome, A., Corrado, G. S., Shlens, J., Bengio, S., Dean, J., Ranzato, M., & Mikolov, T. (2013). DeViSE: A deep visual-semantic embedding model. In Advances in Neural Information Processing Systems (NeurIPS), Vol. 26.

clip contrastive-learning sentence-transformers image-captioning visual-question-answering cross-modal-retrieval


Multimodal Text Summarization

Multimodal Text Summarization (Cross-Modal Abstractive and Extractive Summarization)

MMS
multimodal summarization
cross-modal summarization
vision-language summarization

Multimodal text summarization generates a concise textual summary by jointly processing multiple input modalities — most commonly text and images, but also video frames or audio — using deep learning models that align visual and linguistic representations. The output is a natural-language summary that captures salient content from all available modalities.

Generative / extractive NLP with visual input

Text + images (and optionally audio/video)

Zhu, J., Li, H., Liu, T., Zhou, Y., Zhang, J., & Zong, C. (2018). MSMO: Multimodal Summarization with Multimodal Output. Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing (EMNLP), 4154–4164.

Zhu, J., Zhou, Y., Zhang, J., Li, H., Zong, C., & Li, C. (2020). Multimodal Summarization with Guidance of Multimodal Reference. Proceedings of the AAAI Conference on Artificial Intelligence, 34(05), 9749–9756.

multimodal-transformer multimodal-bert-based-classification fine-tuned-text-summarization multimodal-question-answering transformer bert-based-classification


Multimodal Topic Modeling

Multimodal Topic Modeling (Joint Probabilistic Topic Discovery across Multiple Modalities)

Multimodal LDA
multi-modal topic model
cross-modal topic modeling
MM-TM

Blei, D. M. & Jordan, M. I. (foundational corr-LDA); extended by many authors

Multimodal topic modeling discovers latent thematic structure shared across multiple data modalities — for example, co-occurring words and images — by learning a joint probabilistic representation that aligns topics across modalities. It extends classical text-only approaches such as LDA to settings where each document or observation consists of heterogeneous data types.

Text paired with images, audio, video, or other modalities

Blei, D. M., & Jordan, M. I. (2003). Modeling annotated data. Proceedings of the 26th Annual International ACM SIGIR Conference on Research and Development in Information Retrieval, 127–134.

Ramage, D., Dumais, S., & Liebling, D. (2010). Characterizing microblogs with topic models. Proceedings of the Fourth International AAAI Conference on Weblogs and Social Media, 130–137.

lda-topic-model nmf-topic-model multimodal-bert-based-classification multimodal-sentence-embeddings multimodal-transformer topic-modeling


Multimodal Transformer

Multimodal Transformer (Cross-Modal Attention-Based Architecture)

multimodal attention model
cross-modal transformer
vision-language transformer
multi-modal fusion transformer

Lu et al. (ViLBERT); Radford et al. (CLIP)

A Multimodal Transformer extends the standard Transformer architecture to process and jointly reason over two or more input modalities — most commonly text and images, but also audio, video, or structured data. Cross-modal attention layers allow information from one modality to inform representations in another, enabling tasks such as visual question answering, image captioning, and multimodal sentiment analysis.

Cross-modal attention-based deep learning model

Paired or unpaired multimodal data (text, image, audio, video)

Lu, J., Batra, D., Parikh, D., & Lee, S. (2019). ViLBERT: Pretraining Task-Agnostic Visiolinguistic Representations for Vision-and-Language Tasks. Advances in Neural Information Processing Systems (NeurIPS), 32.

Radford, A., Kim, J. W., Hallacy, C., Ramesh, A., Goh, G., Agarwal, S., ... & Sutskever, I. (2021). Learning Transferable Visual Models From Natural Language Supervision. Proceedings of the 38th International Conference on Machine Learning (ICML), PMLR 139.

transformer bert-based-classification vision-transformer multimodal-bert-based-classification sentence-embeddings image-classification


Multimodal Variational Autoencoder

MVAE
multimodal VAE
multi-modal variational autoencoder
multimodal generative model

The Multimodal Variational Autoencoder (MVAE) is a deep generative model that learns a shared latent representation across two or more data modalities — such as images and captions — using a product-of-experts fusion of modality-specific encoders, enabling generation and inference even when only a subset of modalities is observed at test time.

Multiple modalities (image, text, audio, etc.)

Wu, M., & Goodman, N. (2018). Multimodal Generative Models for Scalable Weakly-Supervised Learning. Advances in Neural Information Processing Systems (NeurIPS), 31.

Kingma, D. P., & Welling, M. (2014). Auto-Encoding Variational Bayes. International Conference on Learning Representations (ICLR).

variational-autoencoder conditional-vae generative-adversarial-network multimodal-learning product-of-experts mixture-of-experts


Multimodal Vision Transformer

Multimodal ViT
vision-language transformer
cross-modal vision transformer
multi-modal ViT

Dosovitskiy et al. (ViT); Radford et al. (CLIP multimodal ViT)

Multimodal Vision Transformer (Multimodal ViT) extends the Vision Transformer architecture to jointly process and align representations from multiple modalities — typically images and text — using self-attention and cross-attention mechanisms. By learning shared or aligned embedding spaces across modalities, it enables tasks such as visual question answering, image-text retrieval, visual grounding, and image captioning.

Images + text (and optionally audio or other modalities)

Dosovitskiy, A., Beyer, L., Kolesnikov, A., Weissenborn, D., Zhai, X., Unterthiner, T., Dehghani, M., Minderer, M., Heigold, G., Gelly, S., Uszkoreit, J., & Houlsby, N. (2021). An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale. In International Conference on Learning Representations (ICLR).

Radford, A., Kim, J. W., Hallacy, C., Ramesh, A., Goh, G., Agarwal, S., Sastry, G., Askell, A., Mishkin, P., Clark, J., Krueger, G., & Sutskever, I. (2021). Learning Transferable Visual Models From Natural Language Supervision. In Proceedings of the 38th International Conference on Machine Learning (ICML), PMLR 139.

vision-transformer transformer bert-based-classification multimodal-bert-based-classification image-classification fine-tuned-vision-transformer


Multimodal Word2Vec

Multimodal Word2Vec (Cross-Modal Distributional Semantics)

multimodal word embeddings
visual-linguistic Word2Vec
cross-modal Word2Vec
MM-W2V

Bruni, E., Tran, N.-K., & Baroni, M. (building on Mikolov et al.)

Multimodal Word2Vec extends the classic Word2Vec framework by grounding word representations in perceptual signals — typically image features — alongside distributional text statistics. The result is word vectors that capture both linguistic co-occurrence patterns and visual meaning, enabling richer semantic similarity judgements and better performance on concept-level tasks where purely text-based embeddings fall short.

Text corpora + image feature vectors (or other modality features)

Bruni, E., Tran, N.-K., & Baroni, M. (2014). Multimodal Distributional Semantics. Journal of Artificial Intelligence Research, 49, 1–47.

Mikolov, T., Sutskever, I., Chen, K., Corrado, G., & Dean, J. (2013). Distributed Representations of Words and Phrases and their Compositionality. Advances in Neural Information Processing Systems (NIPS), 26.

sentence-embeddings multimodal-transformer multimodal-bert-based-classification multimodal-sentence-embeddings multimodal-doc2vec convolutional-neural-network


MULTIMOORA

MULTIMOORA (Multi-Objective Optimisation by Ratio Analysis plus Full Multiplicative Form) is a ranking multi-criteria decision-making (MCDM) method introduced by Brauers, W. K. M., Zavadskas, E. K. in 2010. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Dominance aggregation of three sub-rankings (RS + RP + FMF)

Brauers, W. K. M., Zavadskas, E. K. (2010). Project management by MULTIMOORA as an instrument for transition economies. Technological and Economic Development of Economy

ahp anp bwm bwm-bayesian ccsd cilos cimas critic


Multinomial Logistic Regression

polytomous logistic regression
softmax regression
multinomial logit
nominal logistic regression

Cox (1966); Theil (1969); formalized by McFadden (1974)

Multinomial logistic regression extends binary logistic regression to outcomes with three or more unordered categories. It models the log-odds of each category relative to a chosen reference category as a linear function of the predictors, and estimates all parameters simultaneously via maximum likelihood. It is the standard choice when the dependent variable is nominal with multiple levels.

Nominal categorical outcome (3+ unordered classes), continuous or categorical predictors

Agresti, A. (2002). Categorical Data Analysis (2nd ed.). Wiley-Interscience.

Hosmer, D. W., Lemeshow, S., & Sturdivant, R. X. (2013). Applied Logistic Regression (3rd ed.). Wiley.

ordinal-logistic-regression logistic-regression binary-logistic-regression discriminant-analysis random-forest naive-bayes-classifier


Multinomial Logit

multinomial logistic regression
polytomous logistic regression
softmax regression
Çok Kategorili Lojistik Regresyon

Multinomial logistic regression is a maximum-likelihood method for a nominal (unordered) dependent variable with more than two categories. Building on McFadden's 1974 treatment of qualitative choice, it gives each category its own set of coefficients relative to a reference category.

Independence of irrelevant alternatives (IIA)

McFadden, D. (1974). Conditional Logit Analysis of Qualitative Choice Behavior. In P. Zarembka (Ed.), Frontiers in Econometrics (pp. 105-142). Academic Press.

logistic-regression ordered-logit negative-binomial-regression poisson-regression ols-regression


Multiphase Mixed Methods Design

Multiphase Mixed Methods Research Design

multiphase design
multiproject mixed methods
programmatic mixed methods
multistage mixed methods

2007 (first edition of Designing and Conducting Mixed Methods Research)

The multiphase mixed methods design is a sustained research program in which quantitative and qualitative strands are combined across three or more sequential phases — or across multiple related projects — to address a central program objective. Each phase builds on the prior phase's findings, making the design well-suited to long-term evaluation, intervention development, and large-scale program assessment where a single data-collection cycle cannot fully address the complexity of the research problem.

Quantitative data, qualitative data, or both — collected and integrated across multiple sequential phases or projects

Creswell, J. W., & Plano Clark, V. L. (2018). Designing and Conducting Mixed Methods Research (3rd ed.). Sage.

Tashakkori, A., & Teddlie, C. (Eds.). (2010). SAGE Handbook of Mixed Methods in Social and Behavioral Research (2nd ed.). Sage.


Multiple Baseline Design

Multiple Baseline Single-Subject Experimental Design

MBD
multiple-baseline single-case design
staggered baseline design
multiple-probe design

Donald M. Baer, Montrose M. Wolf, Todd R. Risley

The multiple baseline design is a single-subject experimental design that demonstrates functional control by introducing an intervention at staggered time points across two or more baselines — typically across different behaviors, individuals, or settings. Because no withdrawal of treatment is required, it is especially suitable when the target behavior is irreversible or when removing an effective intervention would be unethical.

Repeated measures of a target behavior over time (continuous observation data)

Baer, D. M., Wolf, M. M., & Risley, T. R. (1968). Some current dimensions of applied behavior analysis. Journal of Applied Behavior Analysis, 1(1), 91–97.

Cooper, J. O., Heron, T. E., & Heward, W. L. (2020). Applied Behavior Analysis (3rd ed.). Pearson.

ab-design aba-design abab-design single-subject-experimental-design changing-criterion-design alternating-treatments-design


Multiple case-based autoethnography

Multiple Case-Based Autoethnographic Research

collective autoethnography
multi-case autoethnography
collaborative autoethnography
multi-site autoethnography

Heewon Chang, Faith Ngunjiri, Kathy-Ann Hernandez (collaborative autoethnography); broader tradition from Carolyn Ellis and Arthur Bochner

Multiple case-based autoethnography is a qualitative design that extends autoethnographic inquiry across two or more researcher-participants or cases, enabling systematic comparison of personal lived experiences within a shared cultural or social phenomenon. By generating rich first-person narratives from each case and then conducting a structured cross-case analysis, the approach combines the depth and reflexivity of autoethnography with the comparative analytical power of multiple case design.

Personal narratives, field notes, reflective journals, interviews across multiple researcher-participants

Chang, H., Ngunjiri, F. W., & Hernandez, K. A. C. (2013). Collaborative Autoethnography. Left Coast Press.

Ellis, C. (2004). The Ethnographic I: A Methodological Novel about Autoethnography. AltaMira Press.

autoethnography collective-autoethnography multiple-case-study narrative-inquiry participatory-autoethnography comparative-autoethnography


Multiple Case-Based Biographical Research

multi-case biographical study
cross-case biography
comparative biographical case study
multiple biographical case analysis

1990s–2000s (cross-case biographical designs consolidated in qualitative methodology literature)

Synthesised from Robert K. Yin (multiple case logic) and biographical research traditions (Roberts, Chamberlayne, Bornat)

Multiple case-based biographical research combines the cross-case replication logic of multiple case study design with the in-depth life-history orientation of biographical research. Each individual biography is treated as a bounded case, examined first on its own terms, and then analysed comparatively across cases to identify patterns, contrasts, and transferable insights about how lives are shaped by social, historical, and structural forces.

In-depth biographical interviews, life-history narratives, personal documents, diaries

Yin, R. K. (2018). Case Study Research and Applications: Design and Methods (6th ed.). Sage.

Roberts, B. (2002). Biographical Research. Open University Press.

biographical-research multiple-case-study life-history-research comparative-biographical-research narrative-inquiry longitudinal-biographical-research


Multiple case-based case study

multiple-case design
collective case study
multi-site case study
multi-case study

1984 (Yin); 2006 (Stake's collective case study formalization)

Robert K. Yin; Robert E. Stake (parallel traditions)

A multiple case study (also called a multiple-case design or collective case study) is a qualitative research design in which two or more bounded cases are examined together to pursue a common research question. By studying several instances of a phenomenon in parallel, the researcher can compare patterns, identify convergences and divergences, and build more robust, transferable conclusions than a single case could support. The design draws principally from Robert Yin's case-study methodology and Robert Stake's collective case study tradition.

Documents, interviews, observations, archival records (across multiple sites/cases)

Stake, R. E. (2006). Multiple Case Study Analysis. Guilford Press.

single-case-study comparative-case-study grounded-theory ethnography cross-case-analysis phenomenology


Multiple Case-Based Classic Grounded Theory

multi-case CGT
classic GT with multiple cases
comparative grounded theory
Glaserian multi-case grounded theory

1967 (foundational); multi-case adaptation developed through 1970s–1990s

Barney G. Glaser and Anselm L. Strauss (foundational); Glaser extended for comparative multi-case contexts

Multiple case-based classic grounded theory (CGT) extends Glaser and Strauss's original inductive framework by grounding theory development simultaneously across two or more purposefully selected cases. Rather than studying a single site or participant group, the researcher treats each case as a distinct analytic unit while using the constant comparative method to draw cross-case theoretical insights. The goal is the same as in all classic GT: emergence of a substantive theory that explains the main concern of participants — but the multi-case structure broadens the conceptual base and supports more robust theoretical abstraction.

Qualitative inductive theory-generation design

Interviews, field notes, documents, and observations across multiple bounded cases

Glaser, B. G., & Strauss, A. L. (1967). The Discovery of Grounded Theory: Strategies for Qualitative Research. Aldine.

Glaser, B. G. (1978). Theoretical Sensitivity: Advances in the Methodology of Grounded Theory. Sociology Press.

grounded-theory constructivist-grounded-theory case-study comparative-case-study constant-comparative-method thematic-analysis


Multiple Case-Based Constructivist Grounded Theory

constructivist grounded theory with multiple cases

2006 (Charmaz's CGT); multi-case applications prominent from 2010s onward

Kathy Charmaz (constructivist grounded theory); multi-case extension developed through methodological elaboration by Charmaz and subsequent scholars

Multiple case-based constructivist grounded theory (CGT) combines Kathy Charmaz's constructivist grounded theory framework with a deliberate multi-case design. The researcher collects and analyzes data from two or more purposively selected cases simultaneously, applying iterative coding, constant comparison, and theoretical sampling across cases to build a grounded theory that accounts for both within-case depth and cross-case variation. The resulting theory is understood as jointly constructed by researcher and participants rather than objectively discovered.

Qualitative research design and analytic approach

Interviews, observations, documents, field notes across multiple bounded cases

Charmaz, K. (2006). Constructing Grounded Theory: A Practical Guide Through Qualitative Analysis. Sage.

Charmaz, K. (2014). Constructing Grounded Theory (2nd ed.). Sage.

grounded-theory constructivist-grounded-theory case-study comparative-case-study thematic-analysis narrative-analysis


Multiple Case-Based Conversation Analysis

multi-case CA
cross-case conversation analysis
comparative conversation analysis
multiple-instance CA

CA founded ~1960s–1970s; multi-case extension adopted from late 1990s onward

Harvey Sacks, Emanuel Schegloff, Gail Jefferson (CA); multiple-case design from Robert Yin

Multiple case-based conversation analysis applies the fine-grained sequential methods of Conversation Analysis (CA) across two or more distinct cases — settings, groups, or interactions — to identify both case-specific patterns and cross-case regularities in naturally occurring talk. By examining how participants organise turn-taking, repair, and action sequences in multiple contexts, the approach strengthens claims about interactional phenomena beyond what a single-case study can establish.

Audio or video recordings of naturally occurring talk, transcribed with CA notation

Sacks, H., Schegloff, E. A., & Jefferson, G. (1974). A simplest systematics for the organization of turn-taking for conversation. Language, 50(4), 696–735.

ten Have, P. (2007). Doing Conversation Analysis: A Practical Guide (2nd ed.). Sage.

conversation-analysis discourse-analysis multiple-case-study comparative-conversation-analysis longitudinal-conversation-analysis critical-discourse-analysis


Multiple Case-Based Critical Discourse Analysis

multi-case CDA
comparative critical discourse analysis
cross-case CDA
multiple case CDA

1990s–2000s (CDA foundations ~1989–1995; multiple case integration in applied discourse research)

Norman Fairclough (CDA); Robert K. Yin (multiple case design)

Multiple case-based critical discourse analysis (multi-case CDA) combines the comparative logic of multiple case study design with the ideological and power-focused analytic apparatus of critical discourse analysis. The researcher selects two or more purposefully chosen cases, collects relevant texts or spoken discourse within each, applies CDA to reveal how language constructs power relations and ideologies within each case, and then synthesises findings across cases to identify patterns, contrasts, and broader sociocritical insights that a single-case design could not yield.

Qualitative research design and analytic method

Texts, documents, transcripts, media artifacts across multiple cases

Fairclough, N. (1995). Critical Discourse Analysis: The Critical Study of Language. Longman.

Yin, R. K. (2014). Case Study Research: Design and Methods (5th ed.). Sage.


Multiple case-based digital ethnography

multi-case digital ethnography
comparative digital ethnography
cross-case digital ethnography
multi-site digital ethnography

Christine Hine (virtual ethnography); Sarah Pink et al. (digital ethnography); cross-case logic from Robert Yin

Multiple case-based digital ethnography is a qualitative research design that conducts ethnographic fieldwork across two or more purposefully selected digital sites or communities, then systematically compares findings across cases. Rooted in digital ethnography's immersive, interpretive tradition and in multiple case study logic, it reveals both site-specific practices and cross-cutting patterns in online social life. It is especially suited to questions about how similar phenomena are enacted differently across digital platforms, communities, or cultural contexts.

Online field observations, digital artifacts, chat logs, social media content, interviews

Hine, C. (2000). Virtual Ethnography. Sage.

Pink, S., Horst, H., Postill, J., Hjorth, L., Lewis, T., & Tacchi, J. (2016). Digital Ethnography: Principles and Practice. Sage.

digital-ethnography comparative-digital-ethnography multiple-case-study netnography comparative-ethnography digital-discourse-analysis


Multiple Case-Based Discourse Analysis

multi-case discourse analysis
comparative discourse analysis
cross-case discourse analysis
MCDA

1990s–2000s (integration formalized in qualitative methodology literature)

Synthesized from Yin's multiple case study design and discourse analysis traditions (van Dijk, Fairclough)

Multiple case-based discourse analysis is a qualitative research design that applies systematic discourse analysis within each of two or more purposively selected cases, then compares the discursive patterns, themes, and power relations across those cases. It combines the replication logic of Yin's multiple case study methodology with the text- and talk-centred analytical tools of discourse analysis traditions such as critical discourse analysis or conversation analysis, enabling researchers to build comparative, theoretically grounded accounts of how language constructs social reality across different contexts.

Textual and verbal data (interviews, documents, media texts, institutional records) across multiple bounded cases

van Dijk, T. A. (Ed.). (1997). Discourse as Social Interaction. Sage.

discourse-analysis case-study critical-discourse-analysis comparative-qualitative-analysis narrative-analysis thematic-analysis


Multiple case-based ethnography

Multiple Case-Based Ethnographic Research

multi-site ethnography
comparative ethnography
multi-case ethnographic design
cross-case ethnography

Robert E. Stake (multiple case study logic); George E. Marcus (multi-sited ethnography)

Multiple case-based ethnography is a qualitative research design that applies sustained ethnographic fieldwork across two or more purposefully selected cases or sites and then compares the resulting thick descriptions to identify patterns, contrasts, and theoretical insights that would be invisible in a single-site study. It combines the contextual depth of ethnography with the comparative logic of multiple case study analysis.

Fieldwork observations, interviews, documents, artefacts across multiple sites or cases

Marcus, G. E. (1995). Ethnography in/of the world system: The emergence of multi-sited ethnography. Annual Review of Anthropology, 24, 95–117.

case-study ethnography comparative-case-study multi-sited-ethnography thematic-analysis grounded-theory


Multiple Case-Based Grounded Theory

multi-case grounded theory
MCGT
comparative case grounded theory
cross-case grounded theory

Synthesised from Kathleen Eisenhardt (multiple-case logic) and Barney Glaser & Anselm Strauss (grounded theory)

Multiple case-based grounded theory is a qualitative research design that embeds grounded theory's inductive coding logic inside a structured multiple-case framework. Rather than generating theory from a single site or interview pool, researchers iteratively collect and analyze data across two or more purposefully selected cases, using constant comparison both within and across cases until theoretical saturation is reached. The result is a substantive theory grounded in rich, cross-site empirical evidence.

Qualitative research design combining case study and grounded theory

Interviews, documents, observations across multiple bounded cases

Eisenhardt, K. M. (1989). Building theories from case study research. Academy of Management Review, 14(4), 532–550.

case-study grounded-theory comparative-case-study thematic-analysis narrative-analysis ethnography


Multiple Case-Based Hermeneutic Phenomenology

Multiple Case-Based Hermeneutic Phenomenological Research

multi-case hermeneutic phenomenology
cross-case hermeneutic phenomenology
interpretive multi-case phenomenology
MCBHP

Max van Manen (hermeneutic phenomenology); Robert Yin (multiple-case logic)

Multiple case-based hermeneutic phenomenology combines the interpretive depth of van Manen's hermeneutic phenomenology with the structured cross-case logic of multiple-case study design. Each case — a bounded individual, group, or site — is analysed for the lived meaning of a shared phenomenon; findings are then compared across cases to reveal both unique contextual textures and common hermeneutic themes. The approach is favoured when context shapes experience in ways that a single case cannot fully illuminate.

In-depth interviews, field notes, documents across multiple bounded cases

van Manen, M. (1990). Researching Lived Experience: Human Science for an Action Sensitive Pedagogy. State University of New York Press.

Lopez, K. A., & Willis, D. G. (2004). Descriptive versus interpretive phenomenology: Their contributions to nursing knowledge. Qualitative Health Research, 14(5), 726–735.

hermeneutic-phenomenology phenomenology multiple-case-study interpretive-phenomenological-analysis narrative-inquiry thematic-analysis


Multiple Case-Based Institutional Ethnography

multi-site institutional ethnography
comparative institutional ethnography
multi-case IE
multiple-site IE

1987 (IE foundation); multi-case application developed through 1990s–2000s

Dorothy E. Smith (institutional ethnography); multi-site adaptation by IE practitioners

Multiple case-based institutional ethnography combines Dorothy E. Smith's institutional ethnography with a multi-site case structure, enabling researchers to trace how the same ruling relations, texts, and institutional processes operate across two or more distinct organizational or community settings. By holding the analytical framework constant while varying the site, this design reveals both the trans-local reach of ruling apparatus and the locally specific ways people navigate institutional coordination.

Interviews, texts/documents, observations across multiple institutional settings

Smith, D. E. (2005). Institutional Ethnography: A Sociology for People. AltaMira Press.

DeVault, M. L., & McCoy, L. (2006). Institutional ethnography: Using interviews to investigate ruling relations. In D. E. Smith (Ed.), Institutional Ethnography as Practice (pp. 15–44). Rowman & Littlefield.

institutional-ethnography comparative-ethnography multiple-case-study critical-institutional-ethnography participatory-institutional-ethnography longitudinal-institutional-ethnography


Multiple Case-Based Interpretive Phenomenological Analysis

cross-case interpretive phenomenological analysis

1996 (IPA); multi-case design consolidated circa 2009

Jonathan A. Smith (IPA); multi-case extension elaborated by Smith, Flowers & Larkin

Multiple case-based interpretive phenomenological analysis (multi-case IPA) applies the close, idiographic reading of IPA to a set of purposively selected cases, conducting detailed within-case analysis before systematically comparing themes across cases. The approach retains IPA's commitment to understanding individual lived experience in depth while allowing the researcher to identify convergent and divergent patterns across structurally similar situations or participant groups.

Qualitative interpretive research design

In-depth interview transcripts; personal accounts across multiple bounded cases

Smith, J. A., Flowers, P., & Larkin, M. (2009). Interpretive Phenomenological Analysis: Theory, Method and Research. Sage.

Smith, J. A. (1996). Beyond the divide between cognition and discourse: Using interpretive phenomenological analysis in health psychology. Psychology and Health, 11(2), 261–271.


Multiple Case-Based Life History Research

multi-case life history
comparative life history
multiple life history study
cross-case life history

1980s–2000s (life history tradition; multiple-case extension)

Ivor Goodson; Robert Stake (multiple-case framing)

Multiple case-based life history research is a qualitative design that collects full biographical accounts from several purposively selected individuals and then compares those life histories across cases to identify shared patterns, divergences, and contextual influences. By treating each person's life story as one analytic case, the approach blends the depth of life history methodology with the comparative rigor of multiple case study logic, producing findings that are both individually rich and cross-case meaningful.

Qualitative comparative biographical design

In-depth biographical interviews, personal documents, field notes

Goodson, I. F., & Sikes, P. (2001). Life History Research in Educational Settings: Learning from Lives. Open University Press.

Stake, R. E. (2006). Multiple Case Study Analysis. Guilford Press.

life-history-research narrative-inquiry case-study biographical-research oral-history cross-case-synthesis


Multiple Case-Based Metaphor Analysis

cross-case metaphor analysis
comparative metaphor analysis
multi-case metaphor study
MCBMA

1980s–2000s (synthesis emerged in qualitative case research)

Building on Lakoff & Johnson (1980) conceptual metaphor theory and Yin's multiple-case logic

Multiple case-based metaphor analysis is a qualitative comparative method that systematically identifies and interprets metaphorical language across two or more bounded cases — such as schools, organisations, or participant groups — to reveal how people in different contexts conceptualise a shared phenomenon. It integrates Lakoff and Johnson's conceptual metaphor theory with Yin's multiple-case logic, enabling both within-case depth and cross-case breadth.

Texts, interviews, documents from multiple bounded cases

Lakoff, G., & Johnson, M. (1980). Metaphors We Live By. University of Chicago Press.

Yin, R. K. (2014). Case Study Research: Design and Methods (5th ed.). Sage Publications.

metaphor-analysis case-study thematic-analysis narrative-analysis content-analysis discourse-analysis


Multiple case-based narrative inquiry

multi-case narrative inquiry
cross-case narrative research
comparative narrative inquiry
multi-site narrative inquiry

2000s (synthesis of Clandinin & Connelly 2000 with multiple case study design)

D. Jean Clandinin & F. Michael Connelly (narrative inquiry); Robert K. Yin (multiple case logic)

Multiple case-based narrative inquiry is a qualitative research design that applies narrative inquiry — the study of human experience through story — across two or more purposively selected cases. Each case is treated as a bounded narrative unit, enabling both within-case depth and cross-case comparison. The approach draws on Clandinin and Connelly's narrative inquiry tradition while adopting the replication logic of multiple case design to build richer, more transferable understandings of how people narrate and make meaning of their experiences.

Interview narratives, life stories, field texts, documents from multiple bounded cases

Clandinin, D. J., & Connelly, F. M. (2000). Narrative inquiry: Experience and story in qualitative research. Jossey-Bass.

Yin, R. K. (2018). Case study research and applications: Design and methods (6th ed.). Sage.

narrative-inquiry comparative-case-study multiple-case-study longitudinal-narrative-research cross-case-analysis interpretive-narrative-inquiry


Multiple case-based netnography

multi-site netnography
comparative netnography
multiple case netnography
multi-community netnography

Robert V. Kozinets (netnography); multiple-case extension draws on Yin's case study logic

Multiple case-based netnography combines Kozinets's netnographic method — an ethnographic adaptation for online communities — with Yin's multiple case study logic. The researcher systematically collects and interprets naturalistic digital data from two or more distinct online communities or platforms, then conducts within-case analyses and a structured cross-case comparison to identify both shared patterns and context-specific differences. The design is especially powerful for understanding how cultural meanings, consumer practices, or social dynamics vary across different digital contexts.

Online community data (posts, threads, profiles, user-generated content) from two or more distinct digital communities or platforms

Kozinets, R. V. (2010). Netnography: Doing Ethnographic Research Online. Sage.

Yin, R. K. (2014). Case Study Research: Design and Methods (5th ed.). Sage.

netnography case-study ethnography virtual-ethnography comparative-qualitative-analysis thematic-analysis


Multiple case-based oral history

Multiple Case-Based Oral History Research

multi-case oral history
comparative oral history
cross-case oral history
multi-site oral history

1970s–1990s (convergence of oral history and case study traditions)

Alessandro Portelli (oral history theory); Robert K. Yin (multiple case logic)

Multiple case-based oral history is a qualitative research design that embeds oral history interviews within a multiple-case framework. Rather than collecting testimonies from a single community or site, the researcher deliberately selects two or more distinct cases — communities, cohorts, organisations, or geographic sites — gathers in-depth oral testimonies within each, and then conducts systematic cross-case comparison to identify both shared and divergent historical experiences.

In-depth oral history interviews, recorded testimonies, archival documents

Portelli, A. (1997). The Battle of Valle Giulia: Oral History and the Art of Dialogue. University of Wisconsin Press.

oral-history comparative-oral-history multiple-case-study longitudinal-oral-history narrative-inquiry life-history-research


Multiple case-based phenomenology

Multiple Case-Based Phenomenological Research

comparative phenomenological case inquiry

Synthesis drawing on Robert Stake (multiple case study) and Edmund Husserl / Clark Moustakas (phenomenology)

Multiple case-based phenomenology combines the bounded, comparative logic of multiple case study design with the lived-experience focus of phenomenological inquiry. The researcher selects two or more distinct cases — individuals, sites, or groups — who share the same target phenomenon, conducts phenomenological analysis within each case, and then synthesises findings across cases to identify both shared essential structures and case-specific variations. The result is richer and more transferable than a single-case phenomenological study while remaining grounded in the depth that phenomenology demands.

In-depth interviews, focus groups, reflective accounts across multiple bounded cases

Moustakas, C. (1994). Phenomenological Research Methods. Sage.

phenomenology multiple-case-study comparative-phenomenology hermeneutic-phenomenology interpretive-phenomenological-analysis longitudinal-phenomenology


Multiple Case-Based Reflexive Thematic Analysis

MC-RTA
multi-case reflexive thematic analysis
cross-case reflexive thematic analysis
multiple case RTA

2006 (RTA origins); 2010s onward (combined application)

Braun & Clarke (reflexive thematic analysis); Yin (multiple case study framework)

Multiple case-based reflexive thematic analysis integrates Braun and Clarke's reflexive thematic analysis (RTA) with a multiple case study framework. Qualitative data are collected from two or more bounded cases, RTA is applied within each case to generate case-specific themes, and the themes are then compared and synthesised across cases. The approach preserves the depth and interpretive richness of RTA while enabling cross-case pattern recognition that single-case designs cannot provide.

Qualitative research design and analysis approach

Qualitative text data (interviews, documents, field notes) from two or more bounded cases

Braun, V., & Clarke, V. (2021). Thematic Analysis: A Practical Guide. Sage.

Yin, R. K. (2018). Case Study Research and Applications: Design and Methods (6th ed.). Sage.

reflexive-thematic-analysis thematic-analysis multiple-case-study case-study narrative-analysis grounded-theory


Multiple Case-Based Semiotic Analysis

multi-case semiotic analysis
comparative semiotic case study
cross-case semiotic inquiry
MCSA

1980s–1990s (consolidation in communication and marketing research)

Synthesised from Peircean/Saussurean semiotics and Yin's multiple case study logic; Floch (1990) is a key applied exemplar

Multiple case-based semiotic analysis is a qualitative research design that applies semiotic frameworks — the systematic study of signs, codes, and meaning-making — across two or more purposively selected cases. By combining the comparative logic of multiple case study research with the interpretive tools of semiotics (structural, Peircean, or Greimasian), it enables researchers to uncover how meaning is constructed and varied across distinct cultural, organisational, or communicative contexts.

Texts, images, advertisements, artefacts, media outputs (sign systems)

Floch, J.-M. (1990). Semiotique, marketing et communication: sous les signes, les strategies. Presses Universitaires de France. [English translation: Semiotics, Marketing and Communication, Palgrave Macmillan, 2001.]

case-study semiotic-analysis discourse-analysis content-analysis narrative-analysis comparative-qualitative-analysis


Multiple Case-Based Single Case Study

Multiple Case-Based Single Case Study (Embedded Single-Case Design)

single case with multiple units of analysis

Robert K. Yin (embedded case design); Robert E. Stake (case study methodology)

A multiple case-based single case study — also called an embedded single-case design — is a qualitative strategy in which a researcher investigates one bounded case (the primary unit of analysis) by systematically examining multiple embedded sub-units within it. Rather than studying several separate cases for comparison, the design focuses all analytical attention on one overarching case while using variation across its internal sub-units to build a richer, more robust understanding of that single case.

Documents, interviews, observations, archival records

Stake, R. E. (1995). The Art of Case Study Research. Sage.

case-study multiple-case-study ethnography phenomenology narrative-inquiry grounded-theory


Multiple Case-Based Straussian Grounded Theory

Strauss-Corbin grounded theory across cases

multiple-site Straussian grounded theory

1990s (synthesis of Strauss & Corbin 1990 and multi-case design conventions)

Anselm Strauss & Juliet Corbin (Straussian GT); multiple-case design formalized by Robert K. Yin and Kathleen Eisenhardt

Multiple case-based Straussian grounded theory combines Strauss and Corbin's systematic coding procedures — open, axial, and selective coding — with a multiple case design in which the same grounded theory analysis is conducted across two or more purposively selected cases. The approach aims to generate a mid-range theory grounded in rich, cross-case qualitative data while capitalizing on the comparative leverage offered by multiple sites or units, ultimately producing a theory with broader scope and stronger transferability than a single-case grounded theory study.

Qualitative research design and analytic strategy

Interviews, observations, documents collected across two or more purposively selected cases

Strauss, A., & Corbin, J. (1990). Basics of Qualitative Research: Grounded Theory Procedures and Techniques. Sage.

Eisenhardt, K. M. (1989). Building theories from case study research. Academy of Management Review, 14(4), 532-550.

straussian-grounded-theory constructivist-grounded-theory multiple-case-study comparative-grounded-theory classic-grounded-theory longitudinal-grounded-theory


Multiple Case-Based Thematic Analysis

cross-case thematic analysis
multi-case thematic analysis
comparative thematic analysis
MCBTA

Synthesized from Braun & Clarke (thematic analysis) and Yin (multiple case study design)

Multiple case-based thematic analysis (MCBTA) is a qualitative design that applies thematic analysis sequentially within each case and then comparatively across cases. It combines the bounded, contextual focus of multiple case study methodology with the systematic coding and theme-development procedures of Braun and Clarke's thematic analysis, enabling researchers to identify both case-specific patterns and shared themes that hold across contexts.

Interview transcripts, documents, field notes across multiple bounded cases

Braun, V., & Clarke, V. (2006). Using thematic analysis in psychology. Qualitative Research in Psychology, 3(2), 77–101.

thematic-analysis case-study comparative-qualitative-analysis cross-case-synthesis narrative-analysis grounded-theory


Multiple Case-Based Visual Analysis

multi-case visual analysis
comparative visual case study
cross-case image analysis
MCVA

2000s–2010s (convergence of case study and visual research traditions)

Synthesised from Robert E. Stake (multiple case design) and Gillian Rose / visual methodologies scholars

Multiple case-based visual analysis is a qualitative design that systematically examines visual materials — photographs, drawings, maps, video stills, or image-rich documents — across two or more purposefully selected cases. By combining Robert Stake's multiple case study logic with visual analysis frameworks, it enables researchers to identify both case-specific visual meanings and cross-case patterns, producing richer comparative insights than either method yields alone.

Visual materials (photographs, drawings, video stills, maps, documents with images) across two or more bounded cases

Rose, G. (2016). Visual Methodologies: An Introduction to Researching with Visual Materials (4th ed.). Sage.

case-study visual-analysis multimodal-analysis comparative-case-study content-analysis ethnography


Multiple-case design-based research

multi-site DBR
multi-case design experiment
multiple-site design research
MCDBR

1992 (DBR); multiple-case variant codified through 2000s–2010s

Ann Brown and Allan Collins (DBR origins); multiple-case extension developed by the DBR Collective and scholars such as Jan Herrington and Thomas Reeves

Multiple-case design-based research (MCDBR) is an interventionist methodology drawn from the learning sciences and education research. It extends single-site design-based research by implementing and iteratively refining an educational intervention across two or more distinct sites, contexts, or participant groups simultaneously or sequentially. The cross-case structure strengthens theoretical transferability and exposes context-dependent variations that a single site could never reveal.

Observations, interviews, artefacts, iterative implementation records from multiple sites

Brown, A. L. (1992). Design experiments: Theoretical and methodological challenges in creating complex interventions in classroom settings. Journal of the Learning Sciences, 2(2), 141–178.

Herrington, J., McKenney, S., Reeves, T., & Oliver, R. (2011). Design-based research and doctoral students: Guidelines for preparing a dissertation proposal. In Proceedings of EdMedia 2007: World Conference on Educational Multimedia, Hypermedia and Telecommunications. Association for the Advancement of Computing in Education (AACE).

design-based-research case-study action-research participatory-action-research mixed-methods-research comparative-case-study


Multiple-case Lesson Study

collaborative lesson research (multi-case)

1999–2002 (Western formalization); Japanese origins 19th century

Japanese education tradition; systematized in Western research by Catherine Lewis, James Stigler, and James Hiebert

Multiple-case lesson study extends the Japanese lesson study cycle — collaborative planning, live observation, and structured debrief of a single research lesson — across two or more independent cases (schools, classrooms, or teacher teams). By replicating and comparing the cycle at multiple sites, researchers can distinguish context-specific findings from those that generalize across settings, producing richer evidence about effective instructional practices in humanities and social science domains.

Collaborative qualitative research design

Observation notes, video recordings, student work samples, teacher reflective logs

Lewis, C. C. (2002). Lesson Study: A Handbook of Teacher-Led Instructional Change. Research for Better Schools.

Stigler, J. W., & Hiebert, J. (1999). The Teaching Gap: Best Ideas from the World's Teachers for Improving Education in the Classroom. Free Press.

lesson-study case-study action-research design-based-research participatory-action-research comparative-case-study


Multiple-Case Study

Multiple-Case (Comparative) Study Design

comparative case study
multi-site case study
collective case study
cross-case analysis

1980s–1990s (Yin's first edition 1984; Stake's collective case study concept 1995)

Robert K. Yin (systematic replication logic); Robert E. Stake (naturalistic/collective case tradition)

Multiple-case study design investigates two or more bounded real-world cases using the same research protocol, then compares findings across cases to identify patterns, contrasts, and explanatory insights that a single case could not produce. Developed primarily through Robert Yin's replication logic and Robert Stake's collective case tradition, the approach is particularly powerful when a researcher needs to determine whether a phenomenon occurs under varied conditions or to test an emerging theoretical explanation against rival contexts.

Interviews, documents, observations, archival records (multiple sources per case)

2–10 cases (each case may involve multiple participants or sites)

Stake, R. E. (2006). Multiple Case Study Analysis. Guilford Press.

case-study ethnography grounded-theory action-research mixed-methods thematic-analysis


Multiple Comparisons Problem

The Multiple Comparisons Problem and Statistical Correction Methods

multiple testing
family-wise error
p-value adjustment
false discovery rate

When conducting multiple statistical tests, the probability of obtaining at least one false positive by chance increases with the number of tests. The multiple comparisons problem (also called the multiplicity problem) occurs because if you conduct 100 hypothesis tests at α = 0.05, you expect ~5 false positives by chance alone, even if all null hypotheses are true. Correction methods—Bonferroni, Benjamini-Hochberg false discovery rate (FDR), and others—adjust the significance threshold or p-values to control error rates. This concept is critical for research integrity and has profound implications for exploratory science.

Bonferroni, C. E. (1935). Il calcolo dei coefficienti di correlazione nel caso di variabilità di gruppi. Instituto Italiano di Statistica.

Benjamini, Y., & Hochberg, Y. (1995). Controlling the false discovery rate: A practical and powerful approach to multiple testing. Journal of the Royal Statistical Society Series B, 57(1), 289–300.

Ioannidis, J. P. A. (2005). Why most published research findings are false. PLoS Medicine, 2(8), e124.

p-value-significance type-i-type-ii-error null-hypothesis publication-bias


Multiple Correspondence Analysis

MCA
Homogeneity Analysis
Multiple Nominal Component Analysis
Çoklu Uyum Analizi

Multiple Correspondence Analysis (MCA) is a multivariate ordination technique designed to explore and visualize associations among three or more categorical variables simultaneously. By mapping both observations and variable categories onto a shared low-dimensional space, MCA reveals hidden structure in nominal or ordinal survey data. The method was comprehensively systematized and extended by Michael Greenacre and Jorg Blasius in their 2006 edited volume, building on earlier geometric data analysis traditions developed in France by Jean-Paul Benzecri during the 1960s and 1970s.

Input: Categorical (nominal/ordinal) variables

Output: Low-dimensional map of categories and observations

Greenacre, M., & Blasius, J. (Eds.). (2006). Multiple Correspondence Analysis and Related Methods. Chapman & Hall/CRC.


Multiple Factor Analysis

Multiple Factor Analysis (MFA) is a dimension reduction technique developed by Escofier and Pagès (1985) for analyzing multiple groups of variables measured on the same observations. MFA balances the influence of each variable group to provide a unified view of how observations relate across multiple perspectives.

Escofier, B., & Pagès, J. (1985). Analyses factorielles simples et multiples : Objectifs, méthodes et interprétation. Dunod.

Pagès, J. (2004). Multiple Factor Analysis by Example Using R. Chapman and Hall/CRC.

Abdi, H., & Valentin, D. (2013). Multiple Factor Analysis. John Wiley & Sons.


Multiple Imputation

Multiple Imputation by Chained Equations (MICE)

Çoklu Atama (Multiple Imputation — MICE)

Multiple Imputation (MI), formally introduced by Donald B. Rubin in 1987, is a principled statistical procedure for handling missing data. Rather than replacing each missing value once, MI fills the gaps m times — each time drawing plausible values from the posterior predictive distribution of the missing data — producing m complete datasets. Each dataset is analysed independently, and the results are combined into a single set of estimates using Rubin's pooling rules. The MICE variant (Multivariate Imputation by Chained Equations), popularised by van Buuren and Groothuis-Oudshoorn (2011), extends the approach to mixed variable types by imputing each variable in turn through a sequence of conditional regression models.

MAR or MCAR required; MNAR requires sensitivity analysis

m ≥ 5 datasets (commonly m ≥ 100 × missing fraction)

Rubin, D.B. (1987). Multiple Imputation for Nonresponse in Surveys. Wiley.

van Buuren, S. & Groothuis-Oudshoorn, K. (2011). mice: Multivariate Imputation by Chained Equations in R. Journal of Statistical Software, 45(3), 1–67.

listwise-deletion single-imputation expectation-maximization missing-data-analysis propensity-score-matching


Multiple Linear Regression

Multiple Linear Regression (Ordinary Least Squares)

linear regression with multiple predictors

Francis Galton; formalized by Karl Pearson

Multiple linear regression (MLR) is a parametric regression model that expresses a continuous outcome as a weighted linear combination of two or more predictor variables plus a random error term. The unknown weights (regression coefficients) are estimated by ordinary least squares (OLS), which minimises the sum of squared residuals. The method traces to Francis Galton's 1886 work on hereditary stature and was placed on firm mathematical footing by Karl Pearson; Draper and Smith's 1966 textbook established it as the standard framework for applied regression.

linearity, independence, homoscedasticity, normality of residuals, no perfect multicollinearity

Galton, F. (1886). Regression towards mediocrity in hereditary stature. Journal of the Anthropological Institute of Great Britain and Ireland, 15, 246–263.

Pearson, K., & Lee, A. (1908). On the generalised probable error in multiple normal correlation. Biometrika, 6(1), 59–68.

Draper, N. R., & Smith, H. (1966). Applied Regression Analysis (1st ed.). John Wiley & Sons.

Montgomery, D. C., Peck, E. A., & Vining, G. G. (2012). Introduction to Linear Regression Analysis (5th ed.). John Wiley & Sons.

simple-linear-regression logistic-regression ridge-regression lasso-regression polynomial-regression stepwise-regression one-way-anova ancova principal-component-regression


Multiple Regression Analysis

MLR
multivariate regression
linear regression

Multiple regression analysis is a statistical method for modeling the relationship between a continuous dependent variable and two or more independent variables (predictors). Originating from Gauss's early 19th-century work and formalized by Draper and Smith (1966), it estimates linear equations predicting outcomes from multiple predictors while accounting for confounding relationships, making it indispensable in epidemiology, economics, psychology, and clinical research.

Draper, N. R., & Smith, H. (1966). Applied Regression Analysis. John Wiley & Sons.

Cohen, J., Cohen, P., West, S. G., & Aiken, L. S. (1992). Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences (2nd ed.). Lawrence Erlbaum.

Marquardt, D. W. (1980). You should standardize the independent variables in your regression models. Discussion of a paper by G. David Knottnerus. Journal of the American Statistical Association, 75(369), 87–91.

analysis-of-variance logistic-regression factor-analysis structural-equation-modeling


Multiplex Network Analysis

Multiplex Network Analysis (Multi-Layer Network Analysis with Shared Node Sets)

multiplex networks
multi-layer network analysis
multilayer network analysis
MNA

Multiplex network analysis studies systems where the same set of nodes is connected by multiple distinct types of relationships, each represented as a separate network layer. By analyzing layers simultaneously rather than in isolation, it reveals how different relation types interact, reinforce each other, or compensate for one another across the same actors or entities.

Relational / edge-list data across multiple relation types

Kivela, M., Arenas, A., Barthelemy, M., Gleeson, J. P., Moreno, Y., & Porter, M. A. (2014). Multilayer networks. Journal of Complex Networks, 2(3), 203–271.

Boccaletti, S., Bianconi, G., Criado, R., del Genio, C. I., Gomez-Gardenes, J., Romance, M., Sendina-Nadal, I., Wang, Z., & Zanin, M. (2014). The structure and dynamics of multilayer networks. Physics Reports, 544(1), 1–122.

social-network-analysis two-mode-network-analysis multilayer-social-network-analysis community-detection betweenness-centrality network-diffusion-analysis


multi-scale geographically weighted regression

A. Stewart Fotheringham, Wei Yang, and Wei Kang

Multiscale Geographically Weighted Regression (MGWR) is a local spatial regression framework that relaxes the single-bandwidth constraint of standard GWR by allowing each predictor to operate at its own spatial scale. Each coefficient surface is calibrated with its own bandwidth, enabling the model to distinguish drivers that vary slowly across space from those that vary sharply.

Georeferenced cross-sectional or panel data with continuous outcome

Fotheringham, A. S., Yang, W., & Kang, W. (2017). Multiscale geographically weighted regression (MGWR). Annals of the American Association of Geographers, 107(6), 1247-1265.

Oshan, T. M., Li, Z., Kang, W., Wolf, L. J., & Fotheringham, A. S. (2019). mgwr: A Python implementation of multiscale geographically weighted regression for investigating process spatial heterogeneity and scale. ISPRS International Journal of Geo-Information, 8(6), 269.

geographically-weighted-regression spatial-lag-model spatial-error-model local-spatial-regression spatial-durbin-model kriging


Multiscale Getis-Ord Gi*

Multiscale Getis-Ord Gi* Hot Spot Analysis

multi-distance Gi*
multiscale hot spot analysis
multi-bandwidth Getis-Ord
scale-varying Gi*

1995 (Gi* basis); multiscale application 2000s onward

Ord & Getis (1995); multiscale extension developed in applied spatial analysis practice

Multiscale Getis-Ord Gi* extends the classic local hot spot statistic by computing Gi* z-scores across a range of spatial distance bands or neighborhood sizes. This reveals whether clusters of high or low values are scale-dependent — appearing only at fine local scales, only at broad regional scales, or persistently across all scales — providing richer spatial intelligence than a single-bandwidth analysis.

Georeferenced point or polygon data with a continuous attribute

Ord, J. K., & Getis, A. (1995). Local spatial autocorrelation statistics: Distributional issues and an application. Geographical Analysis, 27(4), 286-306.

Fotheringham, A. S., Brunsdon, C., & Charlton, M. (2002). Geographically Weighted Regression: The Analysis of Spatially Varying Relationships. Wiley.


Multiscale Moran's I

Multiscale Moran's I Spatial Autocorrelation

multi-scale Moran's I
spatial correlogram Moran
Moran correlogram
multiscale spatial autocorrelation

1950 (base); multiscale variant 1980s-1990s

P. A. P. Moran (base statistic, 1950); multiscale extension developed through spatial ecology and geography literature

Multiscale Moran's I extends the classic global Moran's I statistic by computing spatial autocorrelation across a series of distance lags or spatial scales. The resulting spatial correlogram reveals at which geographic scales clusters or dispersions of a variable exist, offering richer insight than a single summary statistic.

Georeferenced continuous or count variables; spatial weights matrix at multiple lag distances

Moran, P. A. P. (1950). Notes on continuous stochastic phenomena. Biometrika, 37(1-2), 17-23.

Legendre, P., & Fortin, M.-J. (1989). Spatial pattern and ecological analysis. Vegetatio, 80(2), 107-138.


Multiscale Spatial Autocorrelation

Multiscale Spatial Autocorrelation Analysis

Multiscale spatial autocorrelation extends classical spatial autocorrelation analysis by computing and comparing autocorrelation statistics (such as Moran's I) across a range of spatial scales simultaneously. This reveals at which geographic distances or resolutions spatial clustering or dispersion is strongest, providing a richer picture than a single global measure.

Georeferenced continuous or count data with spatial coordinates

Borcard, D., & Legendre, P. (2002). All-scale spatial analysis of ecological data by means of principal coordinates of neighbour matrices. Ecological Modelling, 153(1-2), 51-68.

Csillag, F., & Kabos, S. (2002). Wavelets, boundaries, and the spatial analysis of landscape pattern. Ecoscience, 9(2), 177-190.


Multistage Sampling

multistage cluster sampling
multi-stage sampling
nested sampling
hierarchical sampling

1950s–1960s (formalized in Kish 1965 and Cochran 1977)

Multistage sampling is a probability-based design that selects a sample by working through two or more successive levels of a population hierarchy — for example, first selecting regions, then districts within those regions, then households within those districts. It makes large-scale surveys practical when a complete population list is unavailable or when the population is geographically dispersed, by concentrating fieldwork within a manageable number of sampled units at each stage.

Population lists or maps organized in hierarchical units (e.g., regions, districts, households)

Kish, L. (1965). Survey Sampling. John Wiley & Sons.

Cochran, W. G. (1977). Sampling Techniques (3rd ed.). John Wiley & Sons.


Multitask Learning

MTL
Joint Learning
Shared Representation Learning
Çok Görevli Öğrenme

Multitask Learning (MTL) is a machine learning paradigm in which a model is trained simultaneously on multiple related tasks, sharing representations across them to improve generalization. Introduced formally by Rich Caruana in 1997, MTL draws on the intuition that auxiliary tasks act as inductive bias, providing extra supervision signals that help the shared layers learn richer, more robust feature representations than single-task training would yield.

Caruana, R. (1997). Multitask learning. Machine Learning, 28(1), 41–75.


Multivariate Causal-Comparative Research Design

multivariate causal-comparative design
MANOVA causal-comparative study
multi-outcome ex post facto research
multivariate ex post facto design

Mid-20th century onward; multivariate extension systematized 1970s–1990s

Extension of causal-comparative tradition (cf. Chapin, 1947; Gay, Mills & Airasian)

Multivariate causal-comparative research is a quantitative, non-experimental design that investigates whether pre-existing group differences (defined by a naturally occurring categorical variable) are associated with differences across multiple outcome variables considered simultaneously. By extending the classic causal-comparative framework to several dependent variables at once, it reduces Type I error inflation and captures the correlated structure of outcomes that univariate comparisons would miss.

Quantitative non-experimental comparative design

Numerical scores on multiple dependent and/or independent variables

Fraenkel, J. R., Wallen, N. E., & Hyun, H. H. (2019). How to Design and Evaluate Research in Education (10th ed.). McGraw-Hill.

Gay, L. R., Mills, G. E., & Airasian, P. W. (2012). Educational Research: Competencies for Analysis and Applications (10th ed.). Pearson.


Multivariate Cohort Research

multivariate cohort study
cohort study with multivariate analysis
multivariable cohort design
multivariate longitudinal cohort

1950s–1970s (cohort methods); multivariate extensions prominent from 1970s onward

Epidemiology and biostatistics tradition; advanced by Rothman, Breslow, and colleagues

Multivariate cohort research follows a defined group of individuals forward in time, collecting data on multiple exposures, outcomes, and covariates simultaneously. By applying multivariate statistical models — such as Cox regression, mixed-effects models, or structural equation models — researchers can disentangle the independent contributions of several predictors to one or more outcomes while controlling for confounders. The design is widely used in epidemiology, public health, psychology, and social sciences.

Observational quantitative research design

Repeated-measures numeric data; time-to-event data; multiple continuous and categorical variables

Rothman, K. J., Greenland, S., & Lash, T. L. (2008). Modern Epidemiology (3rd ed.). Lippincott Williams & Wilkins.

Vittinghoff, E., Glidden, D. V., Shiboski, S. C., & McCulloch, C. E. (2012). Regression Methods in Biostatistics: Linear, Logistic, Survival, and Repeated Measures Models (2nd ed.). Springer.

cohort-research longitudinal-research multivariate-longitudinal-research panel-research causal-comparative-research survival-analysis


Multivariate Correlational Research

Multivariate Correlational Research Design

multivariate correlational design
multivariate relational research
multiple-variable correlational study
multivariate associational research

1920s–1930s (multivariate extensions); consolidated in applied social science by 1970s

Developed from Galton and Pearson's bivariate correlation work, extended to multivariate contexts by R.A. Fisher, Harold Hotelling, and others

Multivariate correlational research is a non-experimental quantitative design that examines the simultaneous associations among three or more variables. Rather than manipulating conditions, the researcher measures naturally occurring variables and uses techniques such as multiple regression, canonical correlation, or structural equation modeling to map the pattern and strength of their interrelationships. It is the dominant design when the goal is to understand how a set of predictors jointly relates to one or more outcome variables.

Non-experimental quantitative research design

Continuous, ordinal, or categorical measured variables (no manipulation)

Tabachnick, B. G., & Fidell, L. S. (2019). Using Multivariate Statistics (7th ed.). Pearson.

Cohen, J., Cohen, P., West, S. G., & Aiken, L. S. (2003). Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences (3rd ed.). Lawrence Erlbaum.

correlational-research multiple-regression structural-equation-modeling canonical-correlation multivariate-descriptive-research path-analysis


Multivariate Cross-Sectional Research

Multivariate Cross-Sectional Research Design

multivariate survey design
multi-variable cross-sectional study
MXSR
multivariate observational study

1960s–1970s (formalized with widespread multivariate methods)

Developed from the convergence of survey methodology (Kerlinger) and multivariate statistics (Tabachnick, Fidell)

Multivariate cross-sectional research collects data on multiple variables from a defined population at a single point in time and uses multivariate statistical techniques — such as multiple regression, MANOVA, factor analysis, or structural equation modeling — to examine simultaneous relationships among those variables. It combines the efficiency of a cross-sectional snapshot with the analytical power to handle complex, multi-variable research questions in a single study.

Structured survey/questionnaire data, multiple continuous or categorical variables

Kerlinger, F. N., & Lee, H. B. (2000). Foundations of Behavioral Research (4th ed.). Harcourt College Publishers.

cross-sectional-research multivariate-correlational-research multivariate-descriptive-research longitudinal-research survey-research correlational-research


Multivariate Explanatory Research

Multivariate Explanatory Research Design

multivariate explanatory design
explanatory multivariate research
multivariate causal-explanatory study
MER

Mid-to-late 20th century (consolidated ~1960s–1980s)

Rooted in the multivariate statistics tradition (R.A. Fisher, Harold Hotelling) combined with explanatory research design conventions codified by Kerlinger and others

Multivariate explanatory research is a quantitative design that simultaneously examines multiple independent variables to explain variance in one or more outcomes. Rather than describing what exists or simply correlating pairs of variables, it seeks causal or structural explanations by testing theoretically grounded models with techniques such as multiple regression, MANOVA, or structural equation modeling on survey, administrative, or observational numeric data.

Continuous, ordinal, or categorical numeric data across multiple variables

Hair, J. F., Black, W. C., Babin, B. J., & Anderson, R. E. (2019). Multivariate Data Analysis (8th ed.). Cengage Learning.

Creswell, J. W. (2014). Research Design: Qualitative, Quantitative, and Mixed Methods Approaches (4th ed.). Sage.

multivariate-correlational-research multivariate-confirmatory-research explanatory-research causal-comparative-research structural-equation-modeling multiple-regression


Multivariate Exploratory Quantitative Research Design

multivariate exploratory design
exploratory multivariate analysis
multivariate data exploration
MEQ research

1930s–1960s (foundational multivariate methods); codified in research design literature from the 1980s onward

Hair, Tabachnick, and colleagues (canonical synthesis); roots in Fisher, Hotelling, and Thurstone (early 20th century)

Multivariate exploratory quantitative research is a design in which researchers simultaneously examine multiple quantitative variables without imposing a predetermined structural model, using techniques such as exploratory factor analysis, cluster analysis, or principal component analysis to detect latent patterns, natural groupings, or underlying dimensions in the data. The goal is discovery and pattern recognition rather than hypothesis confirmation.

Continuous, ordinal, or categorical quantitative data; multiple variables measured simultaneously

exploratory-factor-analysis cluster-analysis principal-component-analysis exploratory-quantitative-research multivariate-correlational-research confirmatory-research


Multivariate Longitudinal Research

Multivariate Longitudinal Research Design

longitudinal multivariate design
MLR
multivariate panel study
multivariate repeated-measures design

1970s–1980s (formalized in behavioral sciences literature)

Nesselroade, Baltes, and the developmental/behavioral sciences tradition

Multivariate longitudinal research is a quantitative observational design that follows the same units — individuals, groups, or organizations — across two or more time points while measuring several outcome and predictor variables simultaneously. By combining the temporal dimension of longitudinal tracking with multivariate statistical analysis, it allows researchers to examine how a system of variables co-evolves, how early measures predict later outcomes across multiple domains, and whether relationships among variables are stable or change over time.

Quantitative observational research design

Continuous and categorical quantitative measures collected at multiple time points

Nesselroade, J. R., & Baltes, P. B. (Eds.). (1979). Longitudinal Research in the Study of Behavior and Development. Academic Press.

Bijleveld, C. C. J. H., van der Kamp, L. J. T., Mooijaart, A., van der Kloot, W. A., van der Leeden, R., & van der Burg, E. (1998). Longitudinal Data Analysis: Designs, Models and Methods. Sage.

longitudinal-research panel-research cohort-research cross-sectional-research multilevel-modeling structural-equation-modeling


Multivariate Model Testing Research

Multivariate Model Testing Research Design

multivariate model testing
multivariate structural testing
multivariate confirmatory modeling
MVMT research

1970s–1980s (multivariate model testing as a distinct approach)

Karl Jöreskog (SEM/LISREL framework); Barbara Tabachnick & Linda Fidell (multivariate methods synthesis)

Multivariate model testing research is a confirmatory quantitative design in which a theoretically derived model involving multiple variables and their interrelationships is formally tested against empirical data. Rather than exploring patterns inductively, the researcher specifies a model a priori — capturing hypothesized directional paths, latent constructs, or covariance structures — and then evaluates how well this model reproduces the observed data using techniques such as structural equation modeling, confirmatory factor analysis, or multivariate path analysis.

Quantitative confirmatory research design

Continuous, ordinal, or categorical multivariate data (multiple measured variables)

Kline, R. B. (2016). Principles and Practice of Structural Equation Modeling (4th ed.). Guilford Press.


Multivariate Panel Research

multivariate panel data analysis
panel data multivariate modeling
multi-outcome panel study
longitudinal multivariate panel design

1960s–1980s (econometrics); broader social-science uptake 1990s–2000s

Econometric tradition; formalized by Cheng Hsiao and Badi Baltagi

Multivariate panel research combines the repeated-measurement structure of panel data — the same subjects observed at multiple time points — with the simultaneous analysis of two or more outcome or predictor variables. By modeling joint trajectories across units and time, it controls for unobserved individual heterogeneity while capturing the interplay among variables, making it one of the most powerful non-experimental designs available for causal and predictive inference in the social, behavioral, and economic sciences.

Repeated measurements of multiple continuous, ordinal, or count variables across the same units over time

Hsiao, C. (2003). Analysis of Panel Data (2nd ed.). Cambridge University Press.

Baltagi, B. H. (2008). Econometric Analysis of Panel Data (4th ed.). Wiley.

panel-research longitudinal-research multivariate-longitudinal-research correlational-research structural-equation-modeling multilevel-modeling


Multivariate Pattern Analysis

MVPA
brain decoding
pattern classification

Multivariate Pattern Analysis (MVPA) is a machine learning approach to fMRI that decodes cognitive states, stimuli, or behavior from whole-brain spatial patterns of neural activity. Pioneered by Haxby and colleagues in 2001, MVPA treats fMRI as a classification problem: can a trained decoder predict what a person is perceiving or thinking based solely on their brain activity pattern?

Norman, K. A., Polyn, S. M., Detre, G. J., & Haxby, J. V. (2006). Beyond mind-reading: multi-voxel pattern analysis of fMRI data. Trends in Cognitive Sciences, 10(9), 424–430.

Haxby, J. V., Gobbini, M. I., Furey, M. L., et al. (2001). Distributed and overlapping representations of faces and objects in ventral temporal cortex. Science, 293(5539), 2425–2430.


Multivariate Quantitative Content Analysis

multivariate QCA
multivariate content analysis
MQCA
multivariate text analysis

Rooted in Holsti (1969) and Neuendorf (2002); multivariate extensions developed in communication and political science research from the 1970s onward

Multivariate quantitative content analysis (MQCA) is a systematic, replicable approach to measuring multiple attributes of communication content simultaneously and examining how those attributes relate to each other or to external variables. It extends standard content analysis by applying multivariate statistical techniques — such as factor analysis, cluster analysis, regression, or MANOVA — to coded content data, enabling researchers to uncover complex patterns across many variables at once.

Coded textual, visual, or audio content units with multiple measured variables

Neuendorf, K. A. (2002). The Content Analysis Guidebook. Sage Publications.

Holsti, O. R. (1969). Content Analysis for the Social Sciences and Humanities. Addison-Wesley.


Multivariate Regression

Çok Değişkenli Regresyon (MLR — Çoklu DV)

Johnson & Wichern (textbook treatment); classical multivariate least squares

Multivariate regression is a linear regression method that predicts several continuous dependent variables at the same time from a shared set of predictors. As developed in standard treatments such as Johnson and Wichern's Applied Multivariate Statistical Analysis (2007), each response equation can be fitted by ordinary least squares while the covariance structure of the residuals is used for joint testing across outcomes.

Equation-by-equation least squares with joint residual covariance

Johnson, R. A. & Wichern, D. W. (2007). Applied Multivariate Statistical Analysis (6th ed.). Pearson.

ols-regression mancova hotelling-t2 ridge-regression logistic-regression


Mundlak-Chamberlain

Mundlak-Chamberlain Correlated Random Effects

Correlated Random Effects
CRE Estimator
Mundlak Device
Korelasyonlu Rassal Etkiler

The Mundlak-Chamberlain correlated random effects (CRE) estimator, introduced by Mundlak (1978) and extended by Chamberlain (1982), is a panel data technique that reconciles the fixed effects and random effects approaches by explicitly modelling the correlation between unobserved individual heterogeneity and the observed regressors. By including within-group means of time-varying covariates as additional regressors in a random effects framework, CRE yields estimates numerically equivalent to the within (fixed effects) estimator while permitting identification of time-invariant variables.

Mundlak, Y. (1978). On the pooling of time series and cross section data. Econometrica, 46(1), 69–85.


Muscle Synergy Analysis

Motor synergy
Synergy extraction
Motor primitives

Muscle synergy analysis decomposes complex motor behavior into a small set of coactivated muscle groups (synergies or motor primitives). Pioneered by Marc Tresch and colleagues studying frog motor control, this approach reveals how the nervous system simplifies the control of many muscles by organizing them into task-relevant combinations.

Dimensionality reduction and pattern extraction

Tresch, M. C., Saltiel, P., Bizzi, E., & Bizzi, E. (1999). The construction of movement by the spinal cord. Nature Neuroscience, 2(2), 162-167.

Lee, D. D., & Seung, H. S. (2016). Learning the parts of objects by non-negative matrix factorization. Nature, 401(6755), 788-791.


Music Genre Classification

genre recognition
music categorization
style classification

Music genre classification is the task of automatically assigning genre labels (rock, jazz, classical, pop, etc.) to audio recordings. Introduced formally by Tzanetakis and Cook (2002), it is one of the earliest and most studied music information retrieval problems. It remains critical for music discovery, recommendation systems, digital library organization, and music streaming services. Modern systems achieve high accuracy on standard datasets using deep learning.

Tzanetakis, G., & Cook, P. (2002). Musical genre classification of audio signals. IEEE Transactions on Speech and Audio Processing, 10(5), 293-302.

Sturm, B. L. (2014). The state of the art ten years after A comparison of document content analysis approaches for genre classification of musical audio signals. Journal of the American Society for Information Science and Technology, 65(9), 1757-1766.

Costa, Y. M., Oliveira, L. S., & Silla Jr, C. N. (2014). An evaluation of convolutional neural networks for music classification using mel-frequency cepstral coefficients. In Proceedings of the International Joint Conference on Neural Networks.

beat-tracking music-similarity-measure music-segmentation timbre-analysis automatic-music-transcription


Music Segmentation

Music Segmentation and Structure Detection Algorithm

structural segmentation
music structure analysis
section boundary detection

Music segmentation is the task of dividing a musical recording into distinct structural sections (e.g., verse, chorus, bridge, pre-chorus, outro). Introduced by Goto (2001), it identifies major structural boundaries and labels sections according to musical form. Segmentation is essential for music understanding, audio editing, and composition analysis. It enables higher-level tasks like cover song identification and song structure-aware music generation.

Goto, M., & Hasegawa, Y. (2001). Automatic transcription of popular music audio. In Proceedings of the Fourth International Conference on Music Information Retrieval.

Levy, M., & Sandler, M. (2008). Structural segmentation of musical audio by constrained clustering. IEEE Transactions on Audio, Speech, and Language Processing, 16(2), 318-326.

McVicar, M., Santos-Rodríguez, R., Ni, Y., & De Bie, T. (2014). Automatic annotation of musical key and time signature from audio using Hidden Markov Models. In Proceedings of the International Society for Music Information Retrieval Conference.

beat-tracking music-genre-classification chord-recognition tempo-estimation melody-extraction


Music Similarity Measure

Music Similarity Distance and Measure Algorithm

music distance metric
timbral similarity
content-based similarity

Music similarity measures are computational methods for assessing how musically related two audio recordings are. Introduced by Logan (2001), similarity measures enable content-based music recommendation, playlist generation, and music discovery. Unlike fingerprinting, which identifies the same song, similarity measures gauge stylistic, timbral, and structural resemblance between different songs. Measures can be acoustic (comparing spectral features), high-level (genre, mood), or hybrid.

Logan, B., & Salomon, A. (2001). A music similarity function based on song structure. In Proceedings of the International Conference on Music Information Retrieval.

Mandel, M. I., & Ellis, D. P. (2005). Song-level features and support vector machines for music classification. In Proceedings of the International Society for Music Information Retrieval Conference.

Serra, X., Gómez, E., Herrera, P., & Gómez, P. (2008). Chroma binary similarity and local alignment for cover song identification. IEEE Transactions on Audio, Speech, and Language Processing, 16(5), 1029-1037.

music-genre-classification audio-fingerprinting timbre-analysis beat-tracking chord-recognition


Music Therapy Assessment Tool

The MTAT is a comprehensive assessment instrument for measuring client outcomes and music therapist competency in music therapy. Developed by Hanson and colleagues, it operationalizes music therapy impact across emotional, social, behavioral, and physiological domains, suitable for diverse populations including psychiatric, pediatric, geriatric, and neurological populations.

Multi-method: client self-report, clinician observation, behavioral coding

Thaut, M. H. (2005). Rhythm, music, and the brain: Scientific foundations and clinical applications. New York: Routledge.

Hanson, B., Clark, M., & Plante, W. (2008). A music therapy assessment tool for psychiatric patients. Journal of Music Therapy, 45(3), 341–359.

World Federation of Music Therapy. (2011). Music therapy assessment and outcome measures. Nordoff-Robbins Foundation.

therapeutic-touch-assessment holistic-caring-inventory spiritual-care-competence-scale attitudes-cam-scale


Muskingum Routing

Flood routing
Stream flow attenuation
Hydrologic routing

The Muskingum method is a hydrologic flood routing technique that predicts how a flood wave attenuates (reduces in peak) and spreads as it travels down a river reach. Developed by McCarthy in 1938 for the US Army Corps of Engineers, the method is simple enough for hand calculations while capturing the essential physics of flood propagation.

Hydrologic method for flood attenuation in rivers

McCarthy, G. T. (1938). The Unit Hydrograph and Flood Routing. US Army Corps of Engineers Document 608.

Cunge, J. A. (1969). On the subject of a flood propagation computation method (Muskingum method). Journal of Hydraulic Research, 7(2), 205-230.

Chow, V. T., Maidment, D. R., & Mays, L. W. (1988). Applied Hydrology. McGraw-Hill.


MUST Malnutrition Universal Screening Tool

The Malnutrition Universal Screening Tool (MUST), developed by Elia and endorsed by BAPEN (British Association for Parenteral and Enteral Nutrition), is a rapid 3-component screening tool for identifying adults at risk of malnutrition in hospital and community settings. It is based on BMI, unintentional weight loss, and acute disease severity.

Elia, M. (2003). Screening for malnutrition: a multidisciplinary responsibility. Development and use of the Malnutrition Universal Screening Tool (MUST) for adults. BAPEN (British Association for Parenteral and Enteral Nutrition).

Stratton, R. J., Hackston, A., Longmore, D., et al. (2004). Malnutrition in hospital outpatients and inpatients: prevalence, concurrent validity and ease of use of the Malnutrition Universal Screening Tool (MUST) for adults. British Journal of Nutrition, 92(5), 799-808.


Mutation Testing

mutation analysis
mutant testing
fault injection

Richard DeMillo, Richard Lipton, and Frederick Sayward

Mutation Testing is a fault-injection technique developed by DeMillo, Lipton, and Sayward in 1978 that evaluates test suite effectiveness by introducing small, deliberate bugs (mutations) into source code and checking if tests catch them. A test suite that kills (detects) all mutants is stronger than one that achieves high code coverage without killing mutants.

DeMillo, R. A., Lipton, R. J., & Sayward, F. G. (1978). Hints on test data selection: Help for the practicing programmer. IEEE Computer, 11(4), 34–41.

Just, R., Jalali, D., Inozemtseva, L., Ernst, M. D., & Holmes, R. (2014). Are mutants killed by tests? How test suite composition affects the effectiveness of mutation testing. Proceedings of the 22nd ACM SIGSOFT International Symposium on Foundations of Software Engineering.

Jia, Y., & Harman, M. (2010). An analysis and survey of the development of mutation testing. IEEE Transactions on Software Engineering, 37(5), 649–678.

test-coverage fault-injection software-testing regression-testing


N-ARAS

N-ARAS (Neutrosophic ARAS) is a ranking multi-criteria decision-making (MCDM) method introduced by Adalı, Esra Aytaç Öztaş, Tayfun Özçil, Abdullah Öztaş, Gülin Zeynep Tuş, Ayşegül in 2023. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Single-valued neutrosophic extension of ARAS

Adalı, Esra Aytaç, Öztaş, Tayfun, Özçil, Abdullah, Öztaş, Gülin Zeynep, Tuş, Ayşegül (2023). A New Multi-Criteria Decision-Making Method Under Neutrosophic Environment: ARAS Method With Single-Valued Neutrosophic Numbers. International Journal of Information Technology & Decision Making


N-AROMAN

N-AROMAN (Neutrosophic extension of AROMAN) is a ranking multi-criteria decision-making (MCDM) method introduced by Bošković et al. in 2023. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Neutrosophic outranking/ranking — Single-Valued Neutrosophic Set (SVNS: T, I, F; T,I,F ∈ [0,1], T+I+F ≤ 3)

Bošković et al. (2023). Neutrosophic Alternative Ranking Order Method Accounting for two-step Normalization. IEEE Access

ahp anp bwm bwm-bayesian ccsd cilos cimas critic


N-BEATSx

N-BEATSx is an extension of the N-BEATS neural time series forecasting model that incorporates exogenous (external) variables through a cross-learner architecture. Published in 2023, N-BEATSx improves upon N-BEATS by enabling the model to leverage additional features beyond the historical time series values.

Challu, C., Olivares, K. Q., Oreshkin, B., Garza, F., Mergenthaler-Canseco, M., & Dubrawski, A. (2023). N-BEATSx: Neural Basis Expansion Analysis for Interpretable Time Series Forecasting. In ICLR 2023 Workshop on Multimodal Learning for Science (p. 4).

timegpt mamba vision-mamba spatial-temporal-gcn


N-Body Simulation

gravitational N-body problem
many-body simulation

N-body simulation is a computational method for modeling the dynamics of a system of particles under mutual gravitational forces. Originating from Newton's laws of motion and gravitation, it solves the fundamental equations of celestial mechanics. This technique is essential for understanding planetary orbits, star cluster evolution, and cosmological structure formation.

Poincaré, H. (1892). Les méthodes nouvelles de la mécanique céleste. Gauthier-Villars.

Newton, I. (1687). Philosophiæ Naturalis Principia Mathematica. Royal Society.

Aarseth, S. J. (1985). Direct methods for N-body simulations. In Multiple Time Scales (pp. 377-418). Springer.

orbit-determination gravity-assist hohmann-transfer light-curve-analysis cosmological-perturbation-theory


N-COCOSO

N-COCOSO (Neutrosophic CoCoSo) is a ranking multi-criteria decision-making (MCDM) method introduced by Nabeeh, N. A. Sallam, K. M. in 2024. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Single-valued neutrosophic extension of CoCoSo

Nabeeh, N. A., Sallam, K. M. (2024). A Combined Compromise Solution (CoCoSo) of MCDM Problems for Selection of Medical Best Bearing Ring. Neutrosophic Optimization and Intelligent Systems


N-CODAS

N-CODAS (Neutrosophic extension of CODAS) is a ranking multi-criteria decision-making (MCDM) method introduced by Pamučar, D., Badi, I., Sanja, K., Obradović, R. — NOTE: paper uses LNN (Linguistic NS), not SVNN. SVNN CODAS originator unknown. in 2018. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

(). N-CODAS — SVN extension; "Yüksel 2020" anchor UNCONFIRMED per LVR.


N-COPRAS

N-COPRAS (COPRAS-IN — COPRAS with Interval Neutrosophic Numbers (INN)) is a ranking multi-criteria decision-making (MCDM) method introduced by Şahin, R. in 2019. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Interval Neutrosophic ranking — INN: <[T_L,T_U],[I_L,I_U],[F_L,F_U]> with 0 ≤ T_U+I_U+F_U ≤ 3

Şahin, R. (2019). COPRAS Method with Neutrosophic Sets. Fuzzy Multi-criteria Decision-Making Using Neutrosophic Sets, Studies in Fuzziness and Soft Computing, vol 369, Springer, Cham


N-DNMA

N-DNMA (Neutrosophic DNMA) is a ranking multi-criteria decision-making (MCDM) method. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Single-valued neutrosophic extension of DNMA

(). N-DNMA — Internal Extension (no SVN-DNMA paper in literature). Complex & Intelligent Systems


N-EDAS

N-EDAS (Neutrosophic extension of EDAS) is a ranking multi-criteria decision-making (MCDM) method introduced by Stanujkić, D., Karabašević, D., Popović, G., Pamučar, D., Stević, Ž., Zavadskas, E. K., Smarandache, F. in 2021. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Stanujkić, D., Karabašević, D., Popović, G., Pamučar, D., Stević, Ž., Zavadskas, E. K., Smarandache, F. (2021). A single-valued neutrosophic extension of the EDAS method. Axioms


N-GRA

N-GRA (Neutrosophic extension of GRA) is a ranking multi-criteria decision-making (MCDM) method introduced by Biswas, P., Pramanik, S., Giri, B. C. in 2014. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Biswas, P., Pramanik, S., Giri, B. C. (2014). Entropy based grey relational analysis method for multi-attribute decision-making under single valued neutrosophic assessments. Neutrosophic Sets and Systems


N-MABAC

N-MABAC (Neutrosophic MABAC) is a ranking multi-criteria decision-making (MCDM) method introduced by Peng, Xindong Dai, Jingguo in 2018. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Single-valued neutrosophic extension of MABAC

Peng, Xindong, Dai, Jingguo (2018). Approaches to single-valued neutrosophic MADM based on MABAC, TOPSIS and new similarity measure with score function. Neural Computing and Applications


N-MARCOS

N-MARCOS (Neutrosophic MARCOS) is a ranking multi-criteria decision-making (MCDM) method introduced by Pamučar, D. Ecer, F. in 2021. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

SVN extension of MARCOS with neutrosophic ideal/anti-ideal and utility functions

Pamučar, D., Ecer, F. (2021). Sustainable supplier selection in healthcare industries using a new MCDM method: Measurement of Alternatives and Ranking according to Compromise Solution (MARCOS). Computers & Industrial Engineering


N-MOORA

N-MOORA (Neutrosophic extension of MOORA) is a ranking multi-criteria decision-making (MCDM) method introduced by Gamal, A., Ismail, M., Smarandache, F. in 2018. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

(). N-MOORA — INTERNAL EXTENSION (no SVN-MOORA seminal in literature).


N-MULTIMOORA

N-MULTIMOORA (Neutrosophic extension of MULTIMOORA) is a ranking multi-criteria decision-making (MCDM) method introduced by Stanujkic, D., Zavadskas, E. K., Smarandache, F., Brauers, W. K. M., Karabasevic, D. in 2017. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Stanujkic, D., Zavadskas, E. K., Smarandache, F., Brauers, W. K. M., Karabasevic, D. (2017). A neutrosophic extension of the MULTIMOORA method. Informatica


N-of-1 Trial

Single-Patient N-of-1 Randomized Controlled Trial

single-patient RCT
n=1 trial
individual RCT
crossover n-of-1

Kravitz, Duan, Vohra, and single-patient methodology pioneers

An N-of-1 trial is a single-patient randomized controlled trial in which a patient alternates between treatment A and treatment B (or active drug and placebo) in repeated, randomized cross-over periods. Developed systematically in the 1990s–2010s by Kravitz, Duan, and Vohra, N-of-1 trials enable personalized medicine by determining which treatment works best for that specific individual, avoiding the assumption that population-average effects apply to all patients. They are ideal for chronic conditions with variable outcomes and heterogeneous treatment response.

Gabler, N. B., Duan, N., Vohra, S., & Kravitz, R. L. (2011). N-of-1 trials in the medical literature: a systematic review. Medical Care, 49(8), 761–768.

Kravitz, R. L., Duan, N., & Eslick, I. (2010). Evidence-based medicine, heterogeneity of treatment effects, and the trouble with averages. The Milbank Quarterly, 88(4), 503–520.

Vohra, S., Shamseer, L., Sampson, M., Barrowman, N., Yap, B., Uleryk, E., ... & Moher, D. (2015). CONSORT extension for reporting N-of-1 trials (CENT) 2015: explanation and elaboration. BMJ Open, 5(7), e007838.

randomized-controlled-trial crossover-trial-design pragmatic-clinical-trial personalized-medicine real-world-evidence


N-PROMETHEE

N-PROMETHEE (Neutrosophic extension of PROMETHEE) is a outranking multi-criteria decision-making (MCDM) method introduced by Abdel-Basset, M., Mohamed, M., Smarandache, F. in 2018. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Xu, D., Wei, X., Ding, H., Bin, H. (2020). A New Method Based on PROMETHEE and TODIM for Multi-Attribute Decision-Making with Single-Valued Neutrosophic Sets. Mathematics


N-PSI

N-PSI (Neutrosophic PSI) is a ranking multi-criteria decision-making (MCDM) method. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Single-valued neutrosophic extension of PSI

(). N-PSI — Internal Extension (no SVN-PSI paper in literature). Mathematics


N-RAFSI

N-RAFSI (Neutrosophic extension of RAFSI) is a ranking multi-criteria decision-making (MCDM) method introduced by UNCONFIRMED — Irvanizam & Zahara 2024 uses SVTraNN (trapezoidal), not SVNN. No SVN-RAFSI paper found. in undated — internal extension, no dedicated SVN-RAFSI paper. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

(). N-RAFSI — Internal Extension (no SVN-RAFSI paper in literature).


N-RAWEC

N-RAWEC (Neutrosophic extension of RAWEC) is a ranking multi-criteria decision-making (MCDM) method introduced by Mohamed, Mai; Salam, Amira; Ye, Jun (2024) — SVTrN variant. Crisp RAWEC: Puška et al. 2024. No SVNN RAWEC paper confirmed. in 2024. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Single-Valued Triangular Neutrosophic RAWEC — SVTrN ((l,m,u); T,I,F)

Mohamed, Mai, Salam, Amira, Ye, Jun (2024). Selection of Sustainable Material for the Construction of Drone Aerodynamic Wing using Neutrosophic RAWEC. Systems Assessment and Engineering Management