Mobile Diary Method

Mobile Diary Method for Experience and Behavior Tracking

mobile diary study
smartphone diary method
mobile ESM diary
ecological momentary diary

1987 (ESM roots); mobile form ~2007–2010

Csikszentmihalyi & Larson (ESM foundation); mobile adaptation through 2000s smartphone proliferation

The Mobile Diary Method is a longitudinal self-report technique in which participants record their thoughts, feelings, behaviors, or events using a smartphone app or mobile platform over a defined study period — ranging from days to months. Rooted in the classic diary method and the Experience Sampling Method, its mobile form enables real-time, in-context capture of experience, dramatically reducing retrospective recall bias compared to one-shot surveys or end-of-day questionnaires.

Longitudinal self-report data collection technique

Repeated self-report entries (text, ratings, media) captured via mobile device

Csikszentmihalyi, M., & Larson, R. (1987). Validity and reliability of the Experience-Sampling Method. Journal of Nervous and Mental Disease, 175(9), 526–536.

Bolger, N., Davis, A., & Rafaeli, E. (2003). Diary methods: Capturing life as it is lived. Annual Review of Psychology, 54(1), 579–616.

diary-method mobile-experience-sampling experience-sampling-method ecological-momentary-assessment longitudinal-diary-method online-diary-method


Mobile Experience Sampling Method

ESM
ecological momentary assessment
EMA
daily diary via mobile

The Mobile Experience Sampling Method (ESM) collects repeated, time-stamped self-reports from participants in their natural environment using a smartphone app. By signaling participants multiple times per day over days or weeks, researchers capture psychological states, behaviors, and contexts as they occur — eliminating retrospective bias and revealing within-person dynamics that single-session surveys cannot detect.

Intensive longitudinal data collection technique

Self-report ratings, brief surveys, geo/sensor data collected via smartphone

Shiffman, S., Stone, A. A., & Hufford, M. R. (2008). Ecological momentary assessment. Annual Review of Clinical Psychology, 4, 1–32.

diary-method mobile-experience-sampling experience-sampling-method longitudinal-diary-method ecological-momentary-intervention sensor-data-collection


Mobile Experience Sampling

ESM
Experience Sampling Method
Ecological Momentary Assessment
EMA

Mobile Experience Sampling (ESM) is an intensive longitudinal data-collection technique in which participants respond to brief, repeated questionnaires delivered to their smartphones at random or scheduled intervals throughout the day. By capturing thoughts, feelings, behaviors, and context at or near the moment they occur, ESM minimises retrospective recall bias and provides a high-resolution picture of psychological and behavioral fluctuations in everyday life.

Repeated momentary self-reports (quantitative and/or qualitative)

Stone, A. A., Shiffman, S., Atienza, A. A., & Nebeling, L. (Eds.). (2007). The Science of Real-Time Data Capture: Self-Reports in Health Research. Oxford University Press.

diary-method longitudinal-survey sensor-data-collection participant-observation ecological-momentary-intervention survey


Mobile Field Notes

digital field notes
smartphone field notes
mobile ethnographic notes
in-situ digital notes

2000s–2010s (digital turn in ethnography)

Emergent from digital ethnography practice; theorised notably by Sarah Pink and colleagues

Mobile Field Notes is a data collection technique in which researchers use smartphones, tablets, or wearable devices to record observations, reflections, photographs, audio, or video in real time during fieldwork. By capturing data at the moment and place of occurrence, the method reduces recall bias and enables richer, contextually anchored documentation compared with traditional pen-and-paper notes written retrospectively.

Text notes, photographs, audio/video clips, geo-tagged observations

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

Kusenbach, M. (2003). Street phenomenology: The go-along as ethnographic research tool. Ethnography, 4(3), 455–485.

field-notes participant-observation mobile-experience-sampling non-participant-observation research-diary ethnography


Mobile Health Engagement Scale

Mobile Health Engagement Scale (mHealth Engagement Scale)

mHealth Engagement
Mobile Health Engagement

Oliver Perski, Anna Blandford, Robert West, Susan Michie

The Mobile Health Engagement Scale measures the extent to which individuals engage with mobile health applications and digital behaviour change interventions. Developed through systematic review and meta-analysis by Perski and colleagues (2017), it captures both behavioural and psychological dimensions of engagement—frequency of use, depth of interaction, and subjective satisfaction—essential for understanding the effectiveness of mHealth interventions in real-world settings.

Perski, O., Blandford, A., West, R., & Michie, S. (2017). Conceptualising engagement with digital behaviour change interventions: a systematic review, meta-analysis and integrated framework. European Health Psychologist, 19(2), 519–552.


Mobile In-depth Interview

mobile IDI
smartphone in-depth interview
mobile qualitative interview
mIDI

Adapted from traditional in-depth interviewing; mobile application popularised in qualitative research from the 2010s onward

A mobile in-depth interview (mIDI) is a qualitative data collection technique in which a researcher conducts an extended, exploratory conversation with a participant using a smartphone or tablet, either synchronously (voice or video call) or asynchronously (voice-message or text exchange). The approach retains the probing, open-ended character of traditional in-depth interviewing while leveraging the ubiquity and convenience of mobile technology to reach participants in naturalistic, everyday settings.

Audio, video, or text data captured via mobile devices

Galletta, A. (2013). Mastering the Semi-Structured Interview and Beyond. New York University Press.

Dejonckheere, M., & Vaughn, L. M. (2019). Semistructured interviewing in primary care research: a balance of relationship and rigour. Family Medicine and Community Health, 7(2), e000057.

in-depth-interview semi-structured-interview online-in-depth-interview mobile-experience-sampling mobile-focus-group telephone-assisted-in-depth-interview


Mobile Research Diary

mobile diary study
smartphone diary
digital research diary
mobile diary method

2000s–present (mobile adaptation of diary methods established ~2003–2010)

Bolger, Davis & Rafaeli (diary methods); smartphone adaptation emerged early 2000s

A Mobile Research Diary is a data collection technique in which participants record thoughts, experiences, behaviours, or events in structured diary entries submitted via a smartphone or tablet app over a defined study period. By moving the diary onto a mobile device, researchers gain time-stamped, geolocation-optional data captured close to the moment of experience, reducing retrospective recall bias while maintaining the rich, naturalistic quality of traditional diary methods.

Qualitative / mixed-methods data collection technique

Time-stamped self-reported text, audio, photo, or video entries via mobile device

Ohly, S., Sonnentag, S., Niessen, C., & Zapf, D. (2010). Diary studies in organizational research: An introduction and some practical recommendations. Journal of Personnel Psychology, 9(2), 79–93.

diary-method research-diary mobile-experience-sampling mobile-experience-sampling-method experience-sampling-method ecological-momentary-assessment


Mobile Semi-structured Interview

Adapted from semi-structured interview tradition; mobile variant emerged with widespread smartphone adoption

A mobile semi-structured interview is a qualitative data collection technique in which a researcher conducts a guided yet flexible conversation with a participant using a smartphone or tablet — through voice calls, video calls, or messaging apps. It inherits the structured flexibility of the classic semi-structured interview while leveraging mobile technology to reach participants in naturalistic, convenient, or geographically dispersed settings.

Audio, video, or text-based qualitative data collected via mobile devices

Kvale, S. (1996). InterViews: An Introduction to Qualitative Research Interviewing. Sage Publications.

James, N., & Busher, H. (2016). Online interviewing. In D. Silverman (Ed.), Qualitative Research (4th ed., pp. 245–261). Sage Publications.


Mobile Sensor Data Collection

mobile sensing
smartphone sensor data collection
wearable sensor data collection
passive mobile data collection

Mid-2000s (smartphone-era formalization ~2006–2010)

Andrew Campbell, Tanzeem Choudhury, and colleagues (early smartphone sensing research); broader field of ubiquitous computing

Mobile sensor data collection uses the built-in sensors of smartphones, tablets, or wearable devices to capture behavioral, physiological, and environmental data in real-world settings. Sensors such as accelerometers, GPS, heart rate monitors, ambient light detectors, and microphones record data passively or on demand, enabling researchers to study human behavior with high temporal resolution outside the laboratory.

Passive and active quantitative data collection technique

Continuous or event-triggered numeric sensor streams (accelerometer, GPS, heart rate, ambient light, microphone, etc.)

Lane, N. D., Miluzzo, E., Lu, H., Peebles, D., Choudhury, T., & Campbell, A. T. (2010). A survey of mobile phone sensing. IEEE Communications Magazine, 48(9), 140–150.

Harari, G. M., Lane, N. D., Wang, R., Crosier, B. S., Campbell, A. T., & Gosling, S. D. (2016). Using smartphones to collect behavioral data in psychological science: Opportunities, practical considerations, and challenges. Perspectives on Psychological Science, 11(6), 838–854.

sensor-data-collection mobile-experience-sampling ecological-momentary-assessment wearable-data-collection api-based-data-collection longitudinal-sensor-data-collection


Mobile Structured Interview

Mobile Structured Interview (Computer-Assisted Mobile Interviewing)

CAMI
smartphone-assisted interview
tablet-based structured interview
mobile CAPI

2000s–2010s (widespread adoption ~2010–2015)

Emerged from CAPI and mobile computing research communities

A mobile structured interview is a standardised data collection technique in which an interviewer — or a self-administering respondent — answers a fixed, pre-determined set of questions using a smartphone or tablet application. Every respondent receives identical question wording and response options, ensuring comparability across cases while leveraging the reach, geolocation capabilities, and offline functionality of mobile devices.

Quantitative / mixed-mode data collection technique

Structured verbal or typed responses, closed-ended and scaled items

Couper, M. P., & Peterson, G. (2017). Why do web surveys take longer on smartphones? Social Science Computer Review, 35(3), 357–377.

Buskirk, T. D., & Andrus, C. (2012). Making mobile browser surveys smarter: Results from a randomized experiment comparing online surveys completed via computer or smartphone. Field Methods, 24(4), 388–404.

structured-interview online-structured-interview face-to-face-structured-interview mobile-survey mobile-experience-sampling telephone-assisted-structured-interview


Mobile Survey

smartphone survey
mobile web survey
mobile questionnaire
m-survey

Late 2000s–2010s (accelerated with smartphone adoption, ~2007–2015)

Emerged from web survey methodology researchers (Couper, Buskirk, Toepoel, and others)

A mobile survey is a self-report questionnaire designed and administered through smartphones or tablets, either via a mobile-optimized web browser or a dedicated app. As mobile devices became the dominant mode of internet access globally, surveys must be built for small screens, touch interaction, and variable connectivity. Mobile surveys are used across social science, public health, market research, and organizational studies when reaching respondents in their natural, everyday context is a priority.

Quantitative / mixed data collection technique

Self-report responses collected via smartphone or tablet

Toepoel, V., & Lugtig, P. (2014). What happens if you offer a mobile option to your web panel? Evidence from a probability-based panel of internet users. Social Science Computer Review, 32(4), 544–560.

Buskirk, T. D., & Andres, C. (2012). Smart surveys for smart phones: Exploring various approaches for adopting survey research to the smartphone era. Survey Practice, 5(1).

online-survey mobile-experience-sampling survey face-to-face-survey api-based-data-collection longitudinal-survey


MobileNet

MobileNets
Depthwise Separable CNN
Efficient Mobile Vision Network
Mobil Evrişimli Sinir Ağı

MobileNet is a family of lightweight convolutional neural network architectures introduced by Howard et al. at Google in 2017. It is designed to run image classification, object detection, and other vision tasks directly on mobile devices and embedded systems with limited computational budgets. By replacing standard convolutions with depthwise separable convolutions and exposing two global hyperparameters, MobileNet dramatically reduces multiply-add operations and model size while retaining competitive accuracy.

Howard, A. G., et al. (2017). MobileNets: Efficient convolutional neural networks for mobile vision applications. arXiv preprint.


Montreal Cognitive Assessment

MoCA
MoCA Test
Montreal Cognitive Assessment Test

The Montreal Cognitive Assessment (MoCA) is a brief 10-minute cognitive screening test designed to detect mild cognitive impairment (MCI) in older adults. Developed by Nasreddine and colleagues in 2005 at McGill University, MoCA is more sensitive to cognitive impairment than the Mini-Cog or MMSE, particularly for detecting early Alzheimer's disease and non-Alzheimer dementias, making it widely used in primary care, neurology, and geriatric medicine.

Nasreddine, Z. S., Phillips, N. A., Bédirian, V., Charbonneau, S., Whitehead, V., Collin, I., ... & Chertkow, H. (2005). The Montreal Cognitive Assessment, MoCA: a brief screening tool for mild cognitive impairment. Journal of the American Geriatrics Society, 53(4), 695–699.

Vlachos, G. S., & Scarmeas, N. (2019). Objectives, design and main findings of the REMEDIO project: a longitudinal study on the role of Mediterranean diet on cognitive decline. Journal of Alzheimer's Disease, 70(Suppl 1), S5–S22.

moca-blind cdr-dementia-rating mmse-test addenbrooke-cognitive


Modal Analysis

Modal Analysis of Mechanical Structures and Vibration Modes

Eigenvalue analysis
Frequency response analysis
Natural frequencies

Modal analysis is a computational and experimental method for determining the natural frequencies and associated mode shapes of a mechanical structure. By decomposing structural vibration into its fundamental modes (natural oscillation patterns), engineers can predict resonance frequencies, assess dynamic response to external forces, and design structures to avoid problematic vibrations. Developed rigorously by Clough and Penzien in their foundational work on structural dynamics, modal analysis is essential for designing robust mechanical systems.

Computational method for structural dynamics

Clough, R. W., & Penzien, J. (1975). Dynamics of Structures. McGraw-Hill.

Inman, D. J. (2014). Engineering Vibration (4th ed.). Pearson Education.

Ewins, D. J. (1984). Modal Testing: Theory and Practice. Research Studies Press.

design-for-manufacturing-and-assembly tolerance-stack-up cnc-tool-path-generation additive-manufacturing-slicing


Model Calibration

Classifier Calibration
Probability Calibration
Score Calibration
Model Kalibrasyonu

Model calibration is a post-hoc technique that adjusts the probability outputs of a trained classifier so that predicted confidence scores match empirical outcome frequencies. A classifier is said to be perfectly calibrated if, among all predictions made with confidence p, exactly a fraction p of them are correct. Systematic miscalibration of modern deep neural networks was rigorously documented by Guo et al. (2017), who showed that networks trained with standard cross-entropy loss tend to be overconfident, and proposed temperature scaling as a simple, effective remedy.

Post-hoc probability correction technique

Input: Predicted scores or logits from a trained classifier

Output: Calibrated probability estimates aligned with empirical frequencies

Guo, C., Pleiss, G., Sun, Y., & Weinberger, K. Q. (2017). On calibration of modern neural networks. International Conference on Machine Learning, 1321–1330.


Model Confidence Set

MCS Procedure
Superior Set of Models
Model Selection Confidence Set
Model Güven Kümesi

The Model Confidence Set (MCS) is a sequential hypothesis-testing procedure introduced by Hansen, Lunde, and Nason (2011) that identifies the smallest collection of forecasting or predictive models statistically indistinguishable from the best-performing model at a given confidence level. Instead of selecting a single winner, MCS returns a set of superior models, making it especially valuable in econometric forecast comparisons where the true best model is unknown.

Sequential hypothesis testing procedure for model comparison

Output: Set of models statistically indistinguishable from the best

Hansen, P. R., Lunde, A., & Nason, J. M. (2011). The model confidence set. Econometrica, 79(2), 453–497.


MOHO-ST

occupational occupational participation and motivation

The Model of Human Occupation Screening Tool (MOHO-ST) is a brief, clinician-administered interview-based assessment grounded in the Model of Human Occupation (MOHO) theoretical framework. Developed by Parkinson, Forsyth, and Kielhofner (2006), the MOHO-ST screens for occupational participation and motivation across four key dimensions: volition (interests, values, personal causation), habituation (roles and routines), performance capacity, and environmental supports/barriers. The MOHO-ST is used in occupational therapy across mental health, physical rehabilitation, vocational rehabilitation, and community practice to quickly assess occupational functioning and identify areas for intervention.

Parkinson, S., Forsyth, K., & Kielhofner, G. (2006). Model of Human Occupation Screening Tool (MOHO-ST): Version 2.0. MOHO Clearinghouse, University of Illinois at Chicago.

Kielhofner, G. (2008). Model of Human Occupation: Theory and Application (4th ed.). Lippincott Williams & Wilkins.

occupational-self-assessment copm frenchay-activities-index upper-extremity-functional-scale


Model Predictive Control

Model Predictive Control (MPC) is an advanced control strategy that uses an explicit process model to predict future system behavior over a finite horizon and solves an optimization problem at each control step. First formalized by Richalet et al. in 1978, MPC has become the dominant approach in process control industries, from chemical plants to autonomous vehicles, because it naturally handles constraints and can optimize multiple objectives simultaneously.

Richalet, J., Rault, A., Testud, J., & Papon, J. (1978). Model predictive heuristic control. Automatica, 14(5), 413-428.

Garcia, C. E., Prett, D. M., & Morari, M. (1989). Model predictive control: Theory and practice. Automatica, 25(3), 335-348.

Mayne, D. Q., Rawlings, J. B., Rao, C. V., & Scokaert, P. O. (2000). Constrained model predictive control: Stability and optimality. Automatica, 36(6), 789-814.

linear-quadratic-regulator hamilton-jacobi-bellman-equation feedback-linearization adaptive-control extended-kalman-filter


Model Testing Research

model-based research
structural model testing
theory-testing research
MTR

1970s (Joreskog 1969–1973); widely adopted in social sciences by the 1980s–1990s

Karl G. Joreskog (SEM/LISREL framework); formalized through structural equation modeling tradition

Model testing research is a confirmatory quantitative design in which the researcher specifies a theoretical model — depicting hypothesized relationships among constructs — and then tests how well that model fits empirical data. Drawing primarily on structural equation modeling (SEM) and confirmatory factor analysis (CFA), it evaluates whether the data-implied covariance structure is consistent with the theoretically derived one, yielding fit indices that indicate model-data correspondence.

Confirmatory quantitative research design

Continuous or ordinal survey data; multivariate numerical measures

Kline, R. B. (2015). Principles and Practice of Structural Equation Modeling (4th ed.). Guilford Press.

Joreskog, K. G., & Sorbom, D. (1993). LISREL 8: Structural Equation Modeling with the SIMPLIS Command Language. Scientific Software International.

confirmatory-research hypothesis-testing-research correlational-research longitudinal-research causal-comparative-research explanatory-research


Moderated Mediation

conditional process analysis
moderated mediation model
first-stage moderated mediation
second-stage moderated mediation

Moderated mediation tests whether the indirect effect of an independent variable on an outcome — transmitted through a mediator — differs in strength depending on the level of a moderator variable. It answers the question: for whom, or under what conditions, does the mediated pathway operate most strongly?

Continuous, binary, or ordinal outcomes with a mediator and moderator

Hayes, A. F. (2018). Introduction to Mediation, Moderation, and Conditional Process Analysis: A Regression-Based Approach (2nd ed.). Guilford Press.

Preacher, K. J., Rucker, D. D., & Hayes, A. F. (2007). Addressing moderated mediation hypotheses: Theory, methods, and prescriptions. Multivariate Behavioral Research, 42(1), 185–227.

mediation-analysis moderation-analysis structural-equation-modeling path-analysis multilevel-mediation-analysis bootstrap-mediation-analysis


Moderation Analysis

Düzenleyici Değişken Analizi (Moderation / İnteraksiyon)

Aiken & West (1991); Hayes (PROCESS, 2018)

Moderation analysis tests whether the effect of a predictor X on an outcome Y changes with the level of a third variable W, the moderator. It is estimated within a regression framework through an interaction term X×W, popularised by Aiken & West (1991) and Hayes's PROCESS macro (2018).

Least squares on a moderated regression model

Hayes, A. F. (2018). Introduction to Mediation, Moderation, and Conditional Process Analysis (2nd ed.). Guilford Press.

Aiken, L. S. & West, S. G. (1991). Multiple Regression: Testing and Interpreting Interactions. Sage Publications.

ols-regression conditional-process-analysis causal-mediation logistic-regression panel-fixed-effects


Modern Racism Scale

The Modern Racism Scale (MRS) is a 7-item self-report measure developed by John B. McConahay in 1986 to assess subtle, contemporary forms of racial prejudice. Rather than measuring overt hostility, the MRS captures attitudes reflecting the belief that discrimination no longer exists and that racial minorities make illegitimate demands. The scale addresses limitations of earlier instruments by focusing on modern manifestations of racial bias.

McConahay, J. B. (1986). Modern racism, ambivalence, and the Modern Racism Scale. In J. F. Dovidio & S. L. Gaertner (Eds.), Prejudice, discrimination, and racism (pp. 91–125). Academic Press.

ambivalent-sexism-inventory social-dominance-orientation-scale right-wing-authoritarianism-scale cultural-values-scale


MODFLOW Groundwater Modeling

MODFLOW Modular Three-Dimensional Finite-Difference Groundwater Flow Model

1984 (original release); continuously updated through MODFLOW-6 (2017)

Michael G. McDonald and Arlen W. Harbaugh (U.S. Geological Survey)

MODFLOW is the U.S. Geological Survey's open-source, modular finite-difference model for simulating three-dimensional groundwater flow through porous media. First released in 1984 and continuously updated — most recently as MODFLOW-6 — it is the global standard for quantitative hydrogeological analysis, widely used in civil engineering, environmental consulting, water-resource management, and groundwater contamination studies.

Spatial grid data, hydraulic conductivity fields, boundary conditions, recharge rates, pumping records

Harbaugh, A. W. (2005). MODFLOW-2005, the U.S. Geological Survey modular ground-water model — the Ground-Water Flow Process. U.S. Geological Survey Techniques and Methods 6-A16.

Langevin, C. D., Hughes, J. D., Banta, E. R., Niswonger, R. G., Panday, S., & Provost, A. M. (2017). Documentation for the MODFLOW 6 Groundwater Flow Model. U.S. Geological Survey Techniques and Methods 6-A55.

finite-element-method numerical-groundwater-modeling darcy-flow contaminant-transport-modeling groundwater-recharge-estimation hydraulic-head-analysis


Modified Rankin Scale

Rankin scale original (Rankin, 1957); modified version by van Swieten et al.

The Modified Rankin Scale is a simple 0-6 ordinal measure of global disability or dependency in patients with stroke and other neurological conditions. Originally developed by Rankin in 1957 and modified by van Swieten and colleagues in 1988, it remains the most widely used global disability outcome in stroke clinical trials and clinical practice. Its simplicity, brevity, and strong prognostic association make it the gold standard for acute stroke outcome measurement and is mandated as a primary endpoint in virtually all stroke therapeutic trials.

van Swieten, J. C., Koudstaal, P. J., Visser, M. C., Schouten, H. J., & van Gijn, J. (1988). Interobserver agreement for the assessment of handicap in stroke patients. Stroke, 19(5), 604-607.

stroke-specific-qol alsfrs-r msws-12 modified-rankin-scale


Modularity Analysis

Modularity Analysis (Newman-Girvan Community Detection Framework)

Q-modularity
community structure detection
network modularity optimization
graph partitioning by modularity

Modularity analysis is a network science method, formalized by Newman and Girvan in 2004, that detects community structure in graphs by measuring whether edges are more concentrated within groups than expected by chance. Its scalar quality index Q guides algorithms that partition nodes into cohesive clusters, making it the most widely adopted framework for community detection in social, biological, and technological networks.

Community detection / graph partitioning

Adjacency matrix or edge list (undirected or directed graphs)

Newman, M. E. J., & Girvan, M. (2004). Finding and evaluating community structure in networks. Physical Review E, 69(2), 026113.

Newman, M. E. J. (2006). Modularity and community structure in networks. Proceedings of the National Academy of Sciences, 103(23), 8577–8582.

social-network-analysis betweenness-centrality eigenvector-centrality exponential-random-graph-model network-diffusion-analysis two-mode-network-analysis


Modulus of Rupture and Elasticity

Modulus of Rupture and Elasticity Measurement

The Modulus of Rupture (MOR) and Modulus of Elasticity (MOE) are standardized measures of wood mechanical properties determined through static bending tests. MOR quantifies the maximum bending stress wood can withstand before failure; MOE measures stiffness (resistance to bending). These are fundamental properties used for wood grading, structural design, and assessment of wood quality and species suitability for applications requiring strength or stiffness.

ASTM D143-19. (2019). Standard test methods for small clear specimens of timber. ASTM International.

Green, D. W., Winandy, J. E., & Kretschmann, D. E. (2010). Mechanical properties of wood. General Technical Report FPL–GTR–190. Forest Products Laboratory.


MODWT

Maximal Overlap Discrete Wavelet Transform

MODWT
Stationary wavelet transform
Undecimated DWT

The maximal overlap discrete wavelet transform (MODWT) is a translation-invariant wavelet decomposition method that addresses a key limitation of the standard DWT: lack of shift invariance. Introduced by Percival and Walden (1995), MODWT applies the same wavelet filters at each scale without downsampling, producing an undecimated decomposition. Each detail and approximation coefficient array maintains the full length of the input signal, enabling both robust multi-scale analysis and translation-invariant feature extraction.

Percival, D. B., & Walden, A. T. (1995). Wavelet Methods for Time Series Analysis. Cambridge University Press.

Percival, D. B. (2000). Wavelet methods for time series analysis. Cambridge University Press.

Whitcher, B., Guttorp, P., & Percival, D. B. (2000). Wavelet analysis of covariance with application to atmospheric time series. Journal of Geophysical Research, 105(D11), 14941–14962.

discrete-wavelet-transform continuous-wavelet-transform stationary-wavelet-transform wavelet-coherence


Moirai

Moirai (Universal Time-Series Forecasting Transformer)

Evrensel Zaman Serisi Tahmin Transformatörü

Moirai is a foundation model for universal time-series forecasting introduced by Gerald Woo and colleagues at Salesforce Research in 2024 and presented at ICML. The core idea is to pre-train a single large Transformer on an exceptionally diverse corpus of time-series data (LOTSA) spanning many domains and frequencies, enabling zero-shot and few-shot forecasting on unseen datasets without task-specific retraining. Moirai employs patch-based tokenization, any-variate attention, and a mixture-of-distributions output head to handle variable frequencies, multiple variates, and probabilistic prediction in a unified architecture.

Foundation model for zero-shot time-series forecasting

Large-scale multi-domain time-series corpus (LOTSA)

Output: Probabilistic forecasts with multiple distributional heads

Woo, G., Liu, C., Kumar, A., Xiong, C., Savarese, S., & Sahoo, D. (2024). Unified training of universal time series forecasting transformers. ICML.


Molecular Docking

Molecular Docking and Binding Prediction

protein-ligand docking
binding prediction

Molecular docking predicts the preferred binding orientation and affinity of a ligand (small molecule) within a protein binding pocket. Pioneered by Kuntz and colleagues in 1982, this computational method searches conformational space to find energetically favorable ligand-protein complexes, enabling rapid screening of chemical libraries for drug discovery.

Kuntz, I. D., Blaney, J. M., Oatley, S. J., Langridge, R., & Ferrin, T. E. (1982). A geometric approach to macromolecule-ligand interactions. Journal of Molecular Biology, 161(2), 269-288.

Morris, G. M., Huey, R., Lindstrom, W., Sanner, M. F., Belew, R. K., Goodsell, D. S., & Olson, A. J. (2009). AutoDock4 and AutoDockTools: automated docking with selective receptor flexibility. Journal of Computational Chemistry, 30(16), 2785-2791.

Erickson, J. A., Jalaie, M., Robertson, D. H., Lewis, R. A., & Vieth, M. (2004). Lessons learned from the design and use of a focused library for discovery optimization. Journal of Chemical Information and Computer Sciences, 44(4), 1424-1436.

homology-modeling pharmacophore-modeling qsar ppi-network-topology


Molecular Dynamics

MD simulation
molecular dynamics simulation
atomistic simulation

Molecular Dynamics (MD) is a computational technique that simulates the motion of atoms and molecules by solving Newton's equations of motion under specified forces. Pioneered by Alder and Wainwright in 1957, MD integrates time-dependent atomic trajectories from initial positions, allowing prediction of material properties, phase transitions, and dynamic behavior. It bridges the gap between quantum mechanics (which determines interatomic forces) and macroscopic phenomena (accessible only through experiment), enabling study of timescales from femtoseconds to microseconds and length scales from angstroms to hundreds of nanometers.

Alder, B. J., & Wainwright, T. E. (1957). Phase transition for a hard sphere system. The Journal of Chemical Physics, 27(5), 1208-1209.

Frenkel, D., & Smit, B. (2002). Understanding Molecular Simulation: From Algorithms to Applications (2nd ed.). Academic Press.

Rapaport, D. C. (2004). The Art of Molecular Dynamics Simulation (2nd ed.). Cambridge University Press.


Molecular Symmetry Analysis

point group analysis
symmetry operations
group theory

Molecular symmetry analysis is the systematic application of group theory to understand the structure, bonding, spectroscopy, and reactivity of molecules. Developed comprehensively by F. Albert Cotton and others from the 1960s onward, this framework uses the mathematical properties of molecular symmetry to predict allowed electronic transitions, molecular orbital shapes, vibrational modes, and reaction pathways.

Cotton, F. A. (1990). Chemical Applications of Group Theory (3rd ed.). John Wiley & Sons.

Harris, D. C., & Bertolucci, M. D. (1992). Symmetry and Spectroscopy: An Introduction to Vibrational and Electronic Spectroscopy (2nd ed.). Dover Publications.


Moller-Plesset Perturbation Theory

Möller-Plesset perturbation theory is a post-Hartree-Fock method that systematically corrects the HF reference by treating electron correlation as a perturbation. Introduced in 1934, MP theory provides increasingly accurate energy estimates (MP2, MP3, MP4, ...) by expanding the correlation energy in orders of perturbation.

Möller, C., Plesset, M. S. (1934). Note on an approximation treatment for many-electron systems. Physical Review, 46, 618–622.

Head-Gordon, M., Gomperts, R., Pople, J. A. (1994). Kohn-Sham density-functional theory applied to excited states of closed-shell molecules. Chemical Physics Letters, 153, 503–506.

Szabo, A., Ostlund, N. S. (2012). Modern Quantum Chemistry. Dover Publications.


Monetary Unit Sampling

Monetary Unit Sampling for Substantive Testing in Auditing

Dollar Unit Sampling
MUS
Cumulative Monetary Amount Sampling

American Institute of Certified Public Accountants (AICPA) and audit theorists

Monetary Unit Sampling (MUS) is a statistical sampling method widely used in audit substantive testing that selects individual dollar amounts from an account population rather than individual transactions. This approach is particularly effective for testing the correctness of financial statement balances because large-dollar items are automatically included more frequently in the sample, making it efficient for detecting material misstatements.

Statistical sampling technique for substantive testing

American Institute of Certified Public Accountants (AICPA). (2015). Audit Sampling. AU-C Section 530. AICPA Professional Standards.

Leslie, D. A., Teitlebaum, A. D., & Anderson, R. J. (1982). Dollar unit sampling: A practical guide for auditors. Copp Clark Pitman.


Monin-Obukhov Similarity

Monin-Obukhov
Similarity theory
Monin-Obukhov length scale

Monin-Obukhov similarity theory is a fundamental framework in boundary layer meteorology that describes how wind speed, temperature, and humidity vary with height near the surface. Published in 1954, it shows that normalized vertical profiles depend on a single dimensionless parameter—the Monin-Obukhov stability parameter—which quantifies the balance between mechanical turbulence and buoyant convection.

Monin, A. S., & Obukhov, A. M. (1954). Basic laws of turbulent mixing in the ground layer of the atmosphere. Tr. Akad. Nauk SSSR, 24, 163-187.

Paulson, C. A. (1970). The mathematical representation of wind speed and temperature profiles in the unstable atmospheric surface layer. Journal of Applied Meteorology, 9(6), 857-861.


Monte Carlo Neutron & Particle Transport

Monte Carlo Neutron and Particle Transport Simulation

Monte Carlo simulation
stochastic transport
particle history method

Monte Carlo neutron and particle transport is a stochastic simulation method that tracks individual particle histories through matter, developed by Metropolis and Ulam in 1949 during the Manhattan Project. By sampling random numbers to determine collision locations, energy transfers, and scattering angles, it produces unbiased estimates of reaction rates, flux distributions, and detector responses without discretizing angle or energy variables.

Metropolis, N., & Ulam, S. (1949). The Monte Carlo Method. Journal of the American Statistical Association, 44(247), 335–341.

Lux, I., & Koblinger, L. (2004). Monte Carlo Particle Transport Methods: Neutron and Photon Calculations. CRC Press.

neutron-transport-calculation radiation-dose-assessment criticality-safety-analysis dosimetry-measurement radiation-shielding-design


Monte Carlo Process Variation

Monte Carlo Analysis of Semiconductor Process Variations

Monte Carlo simulation
Process variation analysis
PVT analysis

Monte Carlo Process Variation analysis quantifies the impact of manufacturing uncertainties on circuit performance using statistical sampling. As semiconductor technology scales, process variations (gate length, oxide thickness, dopant fluctuations) create significant uncertainties in delay, power, and leakage. Monte Carlo methods sample the random variation space, enabling statistical characterization of yield, timing margins, and reliability. Essential for modern technology nodes.

Probabilistic modeling of semiconductor manufacturing variability

Fishman, G. S. (1996). Monte Carlo: Concepts, Algorithms, and Applications. Springer-Verlag.

Nassif, S. R. (2003). Modeling and analysis of manufacturing variations. In Proc. CICC (pp. 223-228). IEEE.

Agarwal, A., Blaauw, D., Zolotov, V., & Sundareswaran, S. (2005). Statistical timing analysis with dual-Vth devices. IEEE Transactions on VLSI Systems, 13(3), 319-328.


Monte Carlo Simulation with Missing Data Handling

stochastic simulation with incomplete data

Monte Carlo simulation with missing data combines stochastic simulation — drawing random values from probability distributions — with principled missing-data strategies such as multiple imputation. Instead of discarding incomplete records or substituting a single fill-in value, the method generates many simulated complete datasets, runs the target analysis on each, and pools the results to yield estimates that honestly reflect both sampling uncertainty and uncertainty due to missingness.

Any data with missing values (continuous, categorical, mixed)

Little, R. J. A. & Rubin, D. B. (2002). Statistical Analysis with Missing Data (2nd ed.). Wiley.

van Buuren, S. (2018). Flexible Imputation of Missing Data (2nd ed.). CRC Press / Chapman & Hall.

multiple-imputation bayesian-inference-with-missing-data mcmc-with-missing-data sequential-monte-carlo gibbs-sampling-with-missing-data bootstrap-simulation-with-missing-data


MONTE-CARLO-SIMULATION

MONTE-CARLO-SIMULATION (Monte Carlo Simulation — Stochastic uncertainty propagation through MCDM model) is a ranking multi-criteria decision-making (MCDM) method introduced by Metropolis, N., Ulam, S. in 1949. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Robustness wrapper — Monte Carlo uncertainty propagation

Metropolis, N., Ulam, S. (1949). The Monte Carlo method. Journal of the American Statistical Association


Montgomery-Åsberg Depression Rating Scale (MADRS)

Montgomery-Asberg Depression Rating Scale

The Montgomery-Åsberg Depression Rating Scale is a 10-item clinician-rated assessment designed by Stuart Montgomery and Marie Åsberg in 1979 to measure depression severity and track treatment response. Published in the British Journal of Psychiatry, the MADRS was developed as an alternative to longer instruments like the Hamilton Depression Rating Scale, emphasizing items most sensitive to treatment change. It has become a primary outcome measure in antidepressant trials and is widely used in both research and clinical practice across psychiatry, primary care, and medical specialty settings.

Montgomery, S. A., & Åsberg, M. (1979). A new depression scale designed to be sensitive to change. British Journal of Psychiatry, 134, 382–389.

Snaith, R. P. (1993). The concepts of mild depression. British Journal of Psychiatry, 150(3), 387–393.

Faries, D. E., Pontén, M., Gregor, K. L., & Montgomery, S. A. (2000). Responsiveness of the Montgomery-Åsberg Depression Rating Scale. International Clinical Psychopharmacology, 15(6), 340–347.

phq-9 bdi-ii hamilton-depression-rating-scale quick-inventory-depressive clinical-global-impressions-scale


Mood's Median Test

median test
Brown-Mood median test
Mood Medyan Testi

Mood's median test is a nonparametric procedure that compares the medians of k independent groups by counting how many observations in each group fall above and below the pooled (grand) median, then applying a chi-square test to the resulting 2×k contingency table. It traces to A. M. Mood's 1954 work on nonparametric two-sample tests.

Chi-square on a 2×k above/below-median contingency table

Mood, A. M. (1954). On the Asymptotic Efficiency of Certain Nonparametric Two-Sample Tests. Annals of Mathematical Statistics, 25(3), 514-522.

Hollander, M., Wolfe, D. A., & Chicken, E. (2014). Nonparametric Statistical Methods (3rd ed.). Wiley.

kruskal-wallis-test mann-whitney-u-test conover-iman-test kolmogorov-smirnov-2sample levene-brown-forsythe


MOORA

MOORA (Multi-Objective Optimisation by Ratio Analysis) is a ranking multi-criteria decision-making (MCDM) method introduced by Brauers, W. K. M., Zavadskas, E. K. in 2006. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Ratio system + reference point (vector normalisation)

Brauers, W. K. M., Zavadskas, E. K. (2006). The MOORA method and its application to privatization in a transition economy. Control and Cybernetics

multimoora ahp anp bwm bwm-bayesian ccsd cilos cimas


MOOSRA

MOOSRA (Multi-Objective Optimization on the basis of Simple Ratio Analysis) is a ranking multi-criteria decision-making (MCDM) method introduced by Sarkar, A. Panja, S. C. Das, D. Sarkar, B. in 2015. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Ratio of benefit to cost weighted normalized scores

Sarkar, A., Panja, S. C., Das, D., Sarkar, B. (2015). Developing an efficient decision support system for non-traditional machining process selection. Journal of Intelligent Manufacturing


Moral Injury Events Scale

Nash, Marino Carper, Mills, Au, Goldsmith, & Litz

The MIES is a 9-item self-report measure assessing exposure to morally injurious events in military personnel. Developed by Nash and colleagues in 2013, it captures three dimensions: perpetration (committing acts that violate personal values), betrayal (witnessing leaders/unit members violate moral standards), and observed moral violations. The MIES measures moral injury burden distinct from PTSD and is increasingly used in veteran mental health screening and treatment.

Nash, W. P., Marino Carper, T. L., Mills, M. A., Au, T. A., Goldsmith, A. A., & Litz, B. T. (2013). Psychometric evaluation of the Moral Injury Events Scale. Clinical Psychology & Psychotherapy, 20(3), 249-263.

Litz, B. T., Stein, N. B., Delaney, E., Lebowitz, L., Nash, W. P., Silva, C., & Maguen, S. (2009). Moral injury and moral repair in war veterans: A preliminary model and intervention strategy. Clinical Psychology Review, 29(8), 695-706.

pcl-military combat-exposure-scale post-deployment-reintegration peritraumatic-distress-inventory


Moran's I

global Moran's I
spatial autocorrelation test
Moran's I Uzamsal Otokorelasyon Testi

Moran's I is a global statistic, introduced by Patrick Moran in 1950, that measures whether and how a continuous variable is spatially autocorrelated across mapped units. A positive value signals clustering of similar values, a negative value signals a dispersed (checkerboard) pattern, and it is most often used as a diagnostic before moving to spatial regression.

Global spatial autocorrelation statistic

Permutation / analytical inference on a weighted cross-product

Moran, P.A.P. (1950). Notes on Continuous Stochastic Phenomena. Biometrika, 37(1/2), 17–23.

Cliff, A.D. & Ord, J.K. (1981). Spatial Processes: Models and Applications. Pion.

lisa-analysis spatial-lag-model spatial-error-model spatial-durbin-model pearson-correlation


Moran's Index of Spatial Autocorrelation

Moran's I statistic
global Moran's I
spatial autocorrelation index
Moran index

Moran's I is the standard global statistic for detecting spatial autocorrelation: whether nearby locations tend to share similar values. The index ranges from approximately −1 (perfect dispersion) through 0 (spatial randomness) to +1 (perfect clustering), allowing researchers to test whether a geographic pattern differs from complete spatial randomness with a single, interpretable number.

Georeferenced continuous or count data with a spatial weights matrix

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

Cliff, A. D., & Ord, J. K. (1981). Spatial Processes: Models and Applications. Pion.

spatial-autocorrelation gearys-c local-indicators-of-spatial-association local-morans-i local-getis-ord-gi-star geographically-weighted-regression


Morisky Medication Adherence Scale

Morisky Medication Adherence Scale (MMAS)

MMAS
Morisky Scale
Medication Adherence Scale

The Morisky Medication Adherence Scale is a brief, validated tool developed by Donald Morisky in 1986 to measure patients' adherence to prescribed medications. Originally created to assess hypertension medication compliance, it has since become a standard screening instrument across chronic disease management, primary care, and pharmaceutical research. The scale is valued for its brevity, ease of administration, and predictive validity for clinical outcomes.

Morisky, D. E., Green, L. W., & Levine, D. M. (1986). Concurrent and predictive validity of a self-reported measure of medication adherence. Med Care, 24(1), 67-74.


Morphological Analysis

stemming
lemmatization
Morfolojik Analiz ve Kök Bulma

Morphological analysis splits words into their stems and affixes so that different surface forms of the same word can be treated as one. It covers two complementary approaches — rule-based stemming, such as the Porter (1980) and Snowball algorithms, and dictionary-aware lemmatization — and is a critical text-normalisation step for agglutinative languages such as Turkish and Arabic.

Stemming (Porter, Snowball) / lemmatization

Output: Word stems or dictionary lemmas

Porter, M.F. (1980). An Algorithm for Suffix Stripping. Program, 14(3), 130-137.

Schmid, H. (1994). Probabilistic Part-of-Speech Tagging Using Decision Trees. Proceedings of the International Conference on New Methods in Language Processing (NEMLAP).

sentiment-analysis tf-idf language-identification text-segmentation


Morse Fall Scale

Morse Fall Scale for Fall Risk Assessment

The Morse Fall Scale (MFS) is a brief, reliable tool for assessing the risk of falling in hospitalized patients. Developed by Janice M. Morse through research identifying characteristics of fall-prone patients, the MFS evaluates six specific risk factors: history of falling, secondary diagnoses, ambulatory aids, intravenous therapy, gait, and mental status. The scale's simplicity, short administration time, and strong predictive validity have made it one of the most widely adopted fall risk assessment instruments in acute care settings.

Morse, J. M., Tylko, S. J., & Dixon, H. A. (1987). Characteristics of the fall-prone patient. The Gerontologist, 27(4), 516-522.

Morse, J. M. (1997). Preventing patient falls: establishing a fall intervention program. New York: Springer Publishing Company.

patient-fall-risk-assessment care-dependency-scale nursing-sensitive-indicators early-warning-score


MOS Social Support Survey

MOS-SS
Medical Outcomes Study Support Scale

Functional and social support assessment

Cathy D. Sherbourne and Alice L. Stewart

The Medical Outcomes Study Social Support Survey (MOS-SS) is a 19-item self-report measure of social support developed by Sherbourne and Stewart in 1991. It assesses functional aspects of social relationships—emotional, informational, tangible, and social companionship support—relevant to health outcomes in diverse populations.

Sherbourne, C. D., & Stewart, A. L. (1991). The MOS Social Support Survey. Social Science & Medicine, 32(6), 705–714.

Stewart, A. L., Hays, R. D., & Ware, J. E. (1988). The MOS Short-Form General Health Survey: reliability and validity in a patient population. Medical Care, 26(7), 724–735.

Cohen, S. (1992). Stress, social support, and disorder. In S. H. Friedman (Ed.), Hostility, coping, and health (pp. 109–128). American Psychological Association.

sf-36 whoqol-bref haq-disability-index promis duke-health-profile


Mosaic Plagiarism

Mosaic Plagiarism: Blending Copied Phrases With Original Text Without Attribution

patch-writing
patchwork plagiarism
incremental plagiarism

Academic integrity framework (modern definition)

Mosaic plagiarism, also called patch-writing, occurs when an author mixes copied phrases and sentences from a source with original text, rearranges material from multiple sources, or interweaves paraphrased and verbatim passages without proper citation or quotation marks. It is difficult to detect because the copied portions are interspersed with original writing, creating a surface appearance of original work.

Roig, M. (2015). Avoiding plagiarism, self-plagiarism, and other questionable writing practices: A guide to ethical writing. U.S. Department of Health and Human Services Office of Research Integrity.

Harris, R. A. (2004). Using sources effectively: Strengthening your writing. Pyrczak Publishing.

Steneck, N. H. (2007). Introduction to the responsible conduct of research. U.S. Department of Health and Human Services Office of Research Integrity.

verbatim-plagiarism paraphrasing-plagiarism similarity-vs-plagiarism turnitin-ithenticate


Motivational Interviewing

Motivational Interviewing (MI) is a client-centered counseling approach designed to elicit and strengthen intrinsic motivation for behavioral change. Developed by William R. Miller and Stephen Rollnick in 1991, MI has been extensively applied to substance use disorders, health behavior change, mental health treatment engagement, and numerous other areas where ambivalence about change is a primary obstacle.

Miller, W. R., & Rollnick, S. (2002). Motivational interviewing: Preparing people for change (2nd ed.). Guilford Press.

Miller, W. R., & Rollnick, S. (2009). Ten things that motivational interviewing is not. Behavioural and Cognitive Psychotherapy, 37(2), 129–140.


MAS

The Motor Assessment Scale (MAS) is a clinician-rated, performance-based measure of motor function specifically developed for stroke survivors. Created by Carr, Shepherd, and colleagues (1985) at the University of Sydney, the MAS evaluates 8 fundamental motor tasks reflecting functional mobility and motor control relevant to post-stroke recovery. The MAS has become a standard outcome measure in stroke rehabilitation research and clinical practice, widely used to assess and track motor recovery following acute and chronic stroke.

Carr, J. H., Shepherd, R. B., Nordholm, L., & Lynne, D. (1985). Investigation of a new motor assessment scale for stroke patients. Physical Therapy, 65(2), 175-180.

Carr, J. H., & Shepherd, R. B. (2010). Neurological rehabilitation: Optimizing motor performance (2nd ed.). Churchill Livingstone Elsevier.

wolf-motor-function-test nine-hole-peg-test upper-extremity-functional-scale motor-assessment-scale


Motor Drive Efficiency Analysis

Motor Drive Efficiency Analysis and Loss Assessment

motor efficiency assessment
drive system losses
motor performance evaluation

Rotating machinery and motor system efficiency

Motor drive efficiency analysis quantifies energy losses in electrical motors and variable frequency drive (VFD) systems, which together comprise the largest industrial electrical load. Methods assess copper losses in windings, core (iron) losses, mechanical losses, and converter losses to identify efficiency improvements and estimate annual energy and cost savings.

IEEE Std 841-2023: IEEE Guide for the Selection and Use of AC Electric Motors with Adjustable Speed Drives.

U.S. Department of Energy (2019). Motor System Efficiency: Industrial Assessment Center Data.

Deephansuwan, P., & Areerak, K. L. (2018). Review on three phase induction motor efficiency improvement. Applied Mechanics and Materials, 893, 249-257.

power-quality-assessment harmonic-distortion-analysis power-flow-analysis protection-relay-coordination


Moving Average Model

MA model
MA(q) process
moving-average process
Box-Jenkins MA

The Moving Average model of order q — written MA(q) — expresses the current value of a time series as a linear combination of the current and past random shocks (innovations). Unlike the AR model which uses lagged values of the series itself, the MA model uses lagged error terms, making it well-suited for capturing short-lived disturbances that dissipate over q periods.

Univariate time series (continuous, equally spaced observations)

Box, G. E. P., Jenkins, G. M., & Reinsel, G. C. (1976). Time Series Analysis: Forecasting and Control (revised ed.). Holden-Day.

Hamilton, J. D. (1994). Time Series Analysis. Princeton University Press.

autoregressive-model arma-model arima-model sarima-model vector-autoregression exponential-smoothing


MPF-DOMBI-WA

MPF-DOMBI-WA (m-Polar Fuzzy Dombi Weighted Averaging / Geometric MCDM (Akram, Yaqoob, Ali & Chammam 2020 / Akram & Adeel 2023 Ch. 8) — single-DM m-PF MCDM ranking via Dombi t-conorm/t-norm-based aggregation operators (mFDWA primary, mFDWG companion) followed by m-PF score-based descending ordering) is a aggregationoperator multi-criteria decision-making (MCDM) method introduced by Akram, M., Yaqoob, N., Ali, G., Chammam, W. in 2020. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Dombi-norm aggregation operator MCDM — Dombi sum/product on m-PF numbers (Eq. 4), weighted averaging (mFDWA, Eq. 6) and weighted geometric (mFDWG, Def. 9) operators, m-PF score function S(ζ)=(1/m)Σ p_i◦ζ (Eq. 1) ranking

Akram, M., Yaqoob, N., Ali, G., Chammam, W. (2020). Extensions of Dombi Aggregation Operators for Decision Making under m-Polar Fuzzy Information. Journal of Mathematics (Hindawi)


MPF-ELECTRE-I

MPF-ELECTRE-I (m-Polar Fuzzy extension of ELECTRE-I (Akram, Waseem & Liu 2019)) is a outranking multi-criteria decision-making (MCDM) method introduced by Akram, M., Waseem, N., Liu, P. in 2019. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Outranking — m-PF concordance/discordance with aggregate dominance graph

Akram, M., Waseem, N., Liu, P. (2019). Novel approach in decision making with m-polar fuzzy ELECTRE-I. International Journal of Fuzzy Systems

ahp anp bwm bwm-bayesian ccsd cilos cimas critic


MPF-ELECTRE-II

MPF-ELECTRE-II (m-Polar Fuzzy extension of ELECTRE-II for multi-criteria group decision making (Akram & Adeel 2023)) is a outranking multi-criteria decision-making (MCDM) method introduced by Akram, M., Adeel, A. in 2023. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Outranking — m-PF strong/weak relations with five concordance & discordance thresholds and forward/reverse/average iterative ranking

Akram, M., Adeel, A. (2023). MCDM Methods with Multi-polar Fuzzy Information — Chapter 4, §4.4 The m-Polar Fuzzy ELECTRE II Method. Studies in Fuzziness and Soft Computing, vol. 430, Springer Nature


MPF-ELECTRE-III

MPF-ELECTRE-III (m-Polar Fuzzy extension of ELECTRE-III with pseudo-criterion thresholds, Shannon-entropy objective weights and Li–Wang net credibility ranking (Akram & Adeel 2023)) is a outranking multi-criteria decision-making (MCDM) method introduced by Akram, M., Adeel, A. in 2023. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Pseudo-criterion outranking — q/p/ν thresholds, Shannon-entropy objective weights, partial concordance/discordance and Li–Wang credibility-based net ranking

Akram, M., Adeel, A. (2023). MCDM Methods with Multi-polar Fuzzy Information — Chapter 5, §5.2 An m-Polar Fuzzy ELECTRE III Method. Studies in Fuzziness and Soft Computing, vol. 430, Springer Nature


MPF-ELECTRE-IV

MPF-ELECTRE-IV (m-Polar Fuzzy extension of ELECTRE-IV with weight-free pseudo-criterion outranking, five dominance classes (quasi/canonical/pseudo/sub/veto), Vallée–Zielniewicz credibility levels and Belton–Stewart ascending+descending distillation (Akram & Adeel 2023)) is a outranking multi-criteria decision-making (MCDM) method introduced by Akram, M., Adeel, A. in 2023. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Weight-free pseudo-criterion outranking — q/p/ν thresholds, dominance-class counts (NP, NQ, NI, NE), Vallée–Zielniewicz ζ ∈ {1, 0.8, 0.6, 0.4, 0.2, 0} credibility, two-way distillation pre-orders intersected to a final pre-order

Akram, M., Adeel, A. (2023). MCDM Methods with Multi-polar Fuzzy Information — Chapter 6, §6.2 An m-Polar Fuzzy ELECTRE IV Method. Studies in Fuzziness and Soft Computing, vol. 430, Springer Nature


MPF-HF-TOPSIS

MPF-HF-TOPSIS (m-Polar Hesitant Fuzzy TOPSIS (Akram, Adeel & Alcantud 2019, Symmetry 11(6):795) — multi-criteria group decision-making by extending TOPSIS to the m-polar hesitant fuzzy (mHF) set framework; pole-wise mHPIS/mHNIS extraction, mHF Euclidean distance and closeness coefficient ranking) is a ranking multi-criteria decision-making (MCDM) method introduced by Akram, M., Adeel, A., Alcantud, J. C. R. in 2019. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Distance-based ranking — m-polar hesitant fuzzy TOPSIS — pole-wise max/min ideals on a weighted mHF decision matrix (Eqs. 1–2), mHF Euclidean distance (Eqs. 3–4), closeness coefficient E_j' (Eq. 5)

Akram, M., Adeel, A., Alcantud, J. C. R. (2019). Multi-Criteria Group Decision-Making Using an m-Polar Hesitant Fuzzy TOPSIS Approach. Symmetry (MDPI)


MPF-PROMETHEE

MPF-PROMETHEE (m-Polar Fuzzy extension of PROMETHEE I/II with AHP-derived crisp weights, six Brans–Vincke generalized criteria preference functions, and positive/negative/net outranking flows (Akram, Shumaiza & Alcantud 2020 / Akram & Adeel 2023 Ch. 7)) is a outranking multi-criteria decision-making (MCDM) method introduced by Akram, M., Shumaiza, Alcantud, J. C. R. in 2020. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Outranking-flow PROMETHEE — six generalized criteria preference functions (I–VI), AHP-assisted scalar weights, positive/negative/net outranking flows, PROMETHEE I partial pre-order + PROMETHEE II complete order

Akram, M., Shumaiza, Alcantud, J. C. R. (2020). An m-Polar Fuzzy PROMETHEE Approach for AHP-Assisted Group Decision-Making. Mathematical and Computational Applications (MDPI)


MPF-TOPSIS-LING

MPF-TOPSIS-LING (m-Polar Fuzzy Linguistic TOPSIS for MCGDM (Adeel, Akram & Koam 2019, Symmetry 11(6):735) — multi-criteria group decision-making via m-polar fuzzy linguistic variables (mFLV), expert-aggregated m-PF linguistic decision matrix, aggregated linguistic-term-set weights, m-PF linguistic positive/negative ideal solutions (mPIS / mNIS), m-PF linguistic Euclidean distances, relative closeness coefficient E'_j descending ranking) is a ranking multi-criteria decision-making (MCDM) method introduced by Adeel, A., Akram, M., Koam, A. N. A. in 2019. It turns a decision matrix of alternative

Distance-based group-decision MCDM under m-polar fuzzy linguistic information — aggregated m-PF linguistic decision matrix d'^i_jk = (1/r) Σ_l d^l,i_jk, weighted matrix e^i_jk = w'_k d^i_jk, m-PF linguistic Euclidean distances (Eqs. 3–4) to mPIS / mNIS (Eqs. 1–2), closeness coefficient E'_j (Eq. 5) descending ranking

Adeel, A., Akram, M., Koam, A. N. A. (2019). Group Decision-Making Based on m-Polar Fuzzy Linguistic TOPSIS Method. Symmetry (MDPI)


MPLS

Multiprotocol Label Switching (MPLS) is a forwarding paradigm that prepends a short label to packets, enabling routers to make forwarding decisions based on the label rather than IP destination address. Introduced by IETF (2001), MPLS was designed to enable traffic engineering, VPN creation, and fast rerouting in IP networks. While MPLS complexity is high, it remains foundational in service provider backbones for traffic engineering and Quality of Service (QoS) provisioning.

Rosen, E. C., Viswanathan, A., & Callon, R. (2001). Multiprotocol Label Switching Architecture. RFC 3031.

Awduche, D. O., Malcolm, J., Agogbua, J., et al. (2002). Requirements for Traffic Engineering over MPLS. RFC 2702.

bgp ospf diffserv software-defined-networking


MPSI

MPSI (Modified PSI method for objective weighting (Modified Preference Selection Index weighting)) is a weight objective multi-criteria decision-making (MCDM) method introduced by Maniya, K., Bhatt, M. G. in 2010. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Modified PSI variance-based objective weighting (weight extraction from PSI preference variation)

Maniya, K., Bhatt, M. G. (2010). A selection of material using a novel type decision-making method: Preference selection index method. Materials & Design

ahpsort aploco aras aroman artasi cobra cocoso codas


MRC Dyspnoea

The MRC Dyspnoea Scale is a simple 5-grade ordinal classification of dyspnea severity based on the exertional threshold at which breathlessness limits activity. Developed by the UK Medical Research Council (MRC) in 1959, it remains one of the most widely used dyspnea assessments globally due to its brevity, ease of administration, and strong prognostic correlation in chronic obstructive pulmonary disease and other chronic respiratory diseases. The scale is used in clinical practice, epidemiological surveys, and longitudinal disease monitoring to grade symptom severity and guide treatment intensity.

Van Swieten, J. C., Koudstaal, P. J., Visser, M. C., Schouten, H. J., & van Gijn, J. (1988). Interobserver agreement for the assessment of handicap in stroke patients. Stroke, 19(5), 604-607.

Bestall, J. C., Paul, E. A., Garrod, R., Garnham, R., Jones, P. W., & Wedzicha, J. A. (1999). Usefulness of the Medical Research Council (MRC) dyspnoea scale as a measure of disability in patients with chronic obstructive pulmonary disease. Thorax, 54(7), 581-586.


MSFC

Multiple sclerosis functional assessment

Gary Cutter, Richard Rudick, and NMSS Consortium

The Multiple Sclerosis Functional Composite (MSFC) is an objective, performance-based assessment of MS-related disability capturing three key functional domains: lower extremity mobility, upper extremity coordination, and cognitive/processing speed. Developed in 1999 by the National MS Society and adopted widely in clinical trials, the MSFC provides quantifiable endpoints complementing the Expanded Disability Status Scale (EDSS). The three-component design addresses EDSS limitations by including cognition and standardizing measurement via timed tasks.

Cutter, G. R., Baier, M. L., Rudick, R. A., et al. (1999). Development of a multiple sclerosis functional composite as a clinical trial outcome measure. Multiple Sclerosis, 5(4), 244-250.

edss-multiple-sclerosis updrs rivermead-mobility-index msfc


The MSQOL-54 is a disease-specific quality-of-life instrument designed to assess the physical and mental burden of multiple sclerosis on patients' daily functioning and well-being. Developed by Vickrey and colleagues in 1995, it combines the widely-used SF-36 generic health questionnaire with 18 MS-specific items to provide comprehensive measurement of QoL in MS populations. This scale is a cornerstone tool in MS clinical research and patient monitoring.

Vickrey, B. G., Hays, R. D., Genovese, B. J., Myers, L. W., & Ellison, G. W. (1995). Outcomes in Multiple Sclerosis: The Multiple Sclerosis Quality of Life-54 Scale. Health Psychology, 14(1), 34-42.


Jeremy C. Hobart, University of Plymouth

The MSWS-12 is a brief, patient-reported outcome measure specifically designed to assess the impact of multiple sclerosis on walking ability and limitation. Developed by Hobart and colleagues in 2003, this 12-item scale captures both the physical difficulty and functional consequences of MS-related gait impairment. It is highly responsive to change and widely used in MS clinical trials and practice as a primary outcome measure for assessing intervention effects on mobility.

Hobart, J. C., Riazi, A., Lamping, D. L., Fitzpatrick, R., & Thompson, A. J. (2003). Measuring the impact of MS on walking ability: The 12-Item MS Walking Scale (MSWS-12). Neurology, 60(1), 31-36.


MTT/MTS Assay

MTT/MTS Cell Viability and Proliferation Assay

The MTT assay, introduced by Tatsuro Mosmann in 1983, is a colorimetric method for quantifying cell viability and proliferation by measuring mitochondrial metabolic activity. The method detects the conversion of the water-soluble tetrazolium salt MTT (3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide) by active mitochondria, producing an insoluble purple formazan precipitate proportional to the number of viable cells. The related MTS assay, which does not require solubilization, offers improved kinetics and is now widely adopted in both academic research and pharmaceutical development.

Mosmann, T. (1983). Rapid colorimetric assay for cellular growth and survival: application to proliferation and cytotoxicity assays. Journal of Immunological Methods, 65(1-2), 55-63.

Slade, P. G. (1999). MTS tetrazolium compound (abstract). Methods in Cell Biology, 63, 65-72.

Riss, T. L., Moravec, R. A., Niles, A. L., et al. (2004). Cell viability assays. In Assay Guidance Manual. Eli Lilly & Company and the National Center for Advancing Translational Sciences.

live-dead-assay hemolysis-assay scratch-wound-assay electrospinning


Mueller-Stokes Calculus

Mueller-Stokes Calculus for Polarization

Mueller matrix method
Stokes parameters
Mueller calculus

Mueller-Stokes calculus is a mathematical framework for describing and analyzing the polarization properties of light, including partially polarized and unpolarized light. Grounded in George Gabriel Stokes' 1852 work on polarization parameters and extended by Hans Mueller in 1948, this formalism uses the four-component Stokes vector and the 4×4 Mueller matrix to track how optical systems transform polarization states.

Stokes, G. G. (1852). On the composition and resolution of streams of polarized light from different sources. Transactions of the Cambridge Philosophical Society, 9, 399-416.

Mueller, H. (1948). The foundations of optics. Journal of the Optical Society of America, 38(8), 661-644.

Goldstein, D. H. (2003). Polarized Light (2nd ed.). Marcel Dekker.


Multi-arm experiment

multi-arm trial
multiple-arm experiment
multi-group experiment
many-arm design

1990s–2000s (clinical formalization); multi-arm concept implicit in ANOVA-era factorial designs

Developed within clinical trials methodology; formalized by Parmar, Royston and colleagues (UK MRC CTU, early 2000s)

A multi-arm experiment simultaneously compares three or more treatment or intervention conditions — each called an arm — against a shared control or against one another. By testing multiple alternatives in a single study, it yields more information per participant than running separate two-group experiments sequentially, while controlling the overall Type I error rate through pre-specified comparison strategies.

Continuous, binary, or time-to-event outcome data across three or more treatment arms

Royston, P., Parmar, M. K. B., & Qian, W. (2003). Novel designs for multi-arm clinical trials with survival outcomes with an application in ovarian cancer. Statistics in Medicine, 22(14), 2239–2256.

factorial-experiment adaptive-experiment randomized-controlled-trial crossover-randomized-controlled-trial ab-test cluster-randomized-controlled-trial


Multi-Document Summarization

Çok Belgeli Özetleme (Multi-Document Summarization)

Multi-document summarization (MDS) is a natural-language-processing task that condenses a cluster of related documents into a single comprehensive, coherent, and non-redundant summary. Formally described by Erkan and Radev (2004) through the LexRank algorithm, MDS is used in news cluster analysis, systematic literature reviews, and research synthesis to give readers a unified view of information spread across multiple sources.

Extractive (graph-based, e.g., LexRank) / Abstractive (seq2seq, transformer-based)

Output: Comprehensive, coherent, non-redundant summary covering the document set

Redundancy management, cross-document coreference, information fusion

Erkan, G. & Radev, D.R. (2004). LexRank: Graph-Based Lexical Centrality as Salience in Text Summarization. Journal of Artificial Intelligence Research, 22, 457-479.

Liu, P.J. et al. (2018). Generating Wikipedia by Summarizing Long Sequences. International Conference on Learning Representations (ICLR).

sentiment-analysis text-classification topic-modeling tf-idf bert-embeddings extractive-summarization abstractive-summarization


Multi-Group Confirmatory Factor Analysis

MG-CFA
multi-group CFA
measurement invariance testing
multi-sample CFA

Multi-group confirmatory factor analysis tests whether a measurement model holds equivalently across two or more groups — such as cultures, genders, or time points. By imposing increasingly stringent equality constraints and comparing model fit, it determines whether comparisons of latent mean scores are justified.

Continuous or ordinal indicators from two or more groups

Vandenberg, R. J. & Lance, C. E. (2000). A review and synthesis of the measurement invariance literature: Suggestions, practices, and recommendations for organizational research. Organizational Research Methods, 3(1), 4–70.

Millsap, R. E. (2011). Statistical Approaches to Measurement Equivalence. Routledge.

confirmatory-factor-analysis measurement-invariance exploratory-factor-analysis structural-equation-modeling differential-item-functioning multi-group-exploratory-factor-analysis


Multi-group content validity

multi-group CVI
cross-group content validity
subgroup content validity index
multi-panel content validity

Lynn (1986); extended by Polit & Beck (2006)

Multi-group content validity extends the standard content validity index (CVI) procedure by computing and comparing item- and scale-level validity indices across two or more distinct expert panels or subgroups. It ensures that a scale's items are judged as relevant and representative not only overall but also within each subgroup of interest, supporting cross-group generalizability of the instrument.

Validity assessment / expert judgment aggregation

Ordinal ratings from multiple expert panels or subgroups

Polit, D. F. & Beck, C. T. (2006). The content validity index: Are you sure you know what's being reported? Critique and recommendations. Research in Nursing & Health, 29(5), 489–497.

Lynn, M. R. (1986). Determination and quantification of content validity. Nursing Research, 35(6), 382–385.

content-validity-index confirmatory-factor-analysis measurement-invariance delphi-method inter-rater-reliability scale-development


Multi-group convergent validity

Multi-group Convergent Validity Assessment

cross-group convergent validity
multi-sample convergent validity
MGCFA convergent validity
AVE across groups

Fornell & Larcker (convergent validity criteria); Vandenberg & Lance (multi-group extension)

Multi-group convergent validity examines whether items purported to measure the same latent construct relate strongly to that construct consistently across distinct subgroups such as demographic categories, cultures, or experimental conditions. It extends single-sample convergent validity checks into a comparative multi-group confirmatory factor analysis framework.

Ordinal or continuous scale items; multi-group CFA output

Fornell, C. & Larcker, D. F. (1981). Evaluating structural equation models with unobservable variables and measurement error. Journal of Marketing Research, 18(1), 39–50.


Multi-group Cronbach's alpha

Multi-group Cronbach's Alpha Reliability Analysis

group-stratified alpha
cross-group alpha comparison
subgroup internal consistency
MG-alpha

1951 (alpha); multi-group application from 1980s onward

Lee J. Cronbach (alpha); multi-group extension in cross-cultural and measurement invariance research

Multi-group Cronbach's alpha estimates and compares the internal consistency reliability of a scale separately within each of two or more defined subgroups. It is used in cross-cultural, demographic, and comparative psychometric research to establish that a scale measures its construct with equivalent precision across groups before making cross-group comparisons.

Reliability / internal consistency comparison

Ordinal or interval item responses across two or more defined groups

Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16(3), 297–334.

van de Schoot, R., Lugtig, P., & Hox, J. (2012). A checklist for testing measurement invariance. European Journal of Developmental Psychology, 9(4), 486–492.


Multi-group Differential Item Functioning

differential item functioning across groups

Shealy & Stout (SIBTEST framework); Lord (IRT-based DIF)

Multi-group differential item functioning examines whether test or scale items function equivalently across three or more distinct groups — such as gender, ethnicity, or country — after matching respondents on the underlying trait being measured. Items that behave differently across groups threaten fair measurement and valid score comparisons.

Dichotomous or polytomous item responses across three or more groups

Millsap, R. E. (2012). Statistical Approaches to Measurement Invariance. Routledge.

Magis, D., Beland, S., Tuerlinckx, F., & De Boeck, P. (2010). A general framework and an R package for the detection of dichotomous differential item functioning. Behavior Research Methods, 42(3), 847-862.


Multi-group discriminant validity

Multi-group Discriminant Validity Assessment

cross-group discriminant validity
multi-sample discriminant validity
MGDV
discriminant validity across groups

1981 (foundational criterion); multi-group extension 1990s–2000s

Fornell & Larcker (for the AVE-based criterion); extended to multi-group settings by the SEM invariance literature

Multi-group discriminant validity assessment tests whether constructs measured by a scale are empirically distinct not just in one sample but consistently across two or more groups (e.g., cultures, genders, age cohorts). It extends standard discriminant validity criteria — such as the AVE rule and the HTMT ratio — into a multi-group confirmatory factor analysis framework to verify that conceptual distinctness is replicable across subpopulations.

Ordinal or continuous indicators from two or more groups


Multi-group EFA

multi-sample exploratory factor analysis

exploratory factor analysis with multiple groups

Multi-group exploratory factor analysis estimates the latent factor structure of a set of items separately within each of two or more groups and then examines whether the discovered structures are consistent across groups. It is used to explore dimensionality before imposing invariance constraints, and to diagnose group-specific factor patterns that would invalidate cross-group comparisons.

Latent variable / multi-group dimension reduction

Continuous or ordinal item responses across two or more groups

Muthén, B. & Christoffersson, A. (1981). Simultaneous factor analysis of dichotomous variables in several groups. Psychometrika, 46(4), 407–419.

Browne, M. W. (2001). An overview of analytic rotation in exploratory factor analysis. Multivariate Behavioral Research, 36(1), 111–150.


Multi-group Generalizability Theory

MG G-theory
multi-group G-theory
generalizability theory across groups
cross-group G-study

Lee J. Cronbach and colleagues (Cronbach, Gleser, Nanda, Rajaratnam), extended to multi-group contexts by Brennan and others

Multi-group generalizability theory (MG G-theory) extends classical generalizability theory to estimate and compare variance components — attributable to persons, items, raters, occasions, and their interactions — simultaneously across two or more defined groups. It reveals whether a measurement procedure is equally reliable and generalizable for every group studied, supporting fair and equitable score interpretation.

Variance component / reliability generalization

Continuous or polytomous ratings/scores nested in facets (raters, occasions, items) across groups

Brennan, R. L. (2001). Generalizability Theory. Springer.

Shavelson, R. J. & Webb, N. M. (1989). Generalizability theory: 1973–1988. British Journal of Mathematical and Statistical Psychology, 42(1), 3–27.


Multi-group item analysis

MGIA
group-comparative item analysis
subgroup item analysis
cross-group item analysis

Classical test theory tradition; systematised by Crocker & Algina (1986)

Multi-group item analysis computes classical item statistics — difficulty, discrimination, and corrected item-total correlations — separately for each subgroup in a sample and then compares those statistics across groups. It is a standard diagnostic step in scale development and test fairness evaluation, revealing items that behave differently for men versus women, across age cohorts, or across cultural groups before more formal DIF testing.

Dichotomous or polytomous item responses across two or more known groups

Crocker, L. & Algina, J. (1986). Introduction to Classical and Modern Test Theory. Holt, Rinehart and Winston.

Embretson, S. E. & Reise, S. P. (2000). Item Response Theory for Psychologists. Lawrence Erlbaum Associates.


Multi-group item response theory

MG-IRT
multiple-group IRT
multi-group latent trait model
IRT across groups

Multiple contributors; formalized by Birnbaum (1968) for IRT; multi-group extensions developed through 1980s–1990s

Multi-group item response theory fits IRT models simultaneously across two or more defined groups — such as males and females, or different cultural samples — to determine whether item parameters are invariant across those groups. It is the primary IRT-based framework for testing measurement equivalence and detecting differential item functioning (DIF) at the model level.

Dichotomous or polytomous item responses across defined groups

Kim, S.-H. & Cohen, A. S. (1998). Detection of differential item functioning under the graded response model with the likelihood ratio test. Applied Psychological Measurement, 22(4), 345–355.


Multi-group McDonald's omega

Multi-group McDonald's Omega Reliability Analysis

multi-group omega
omega across groups
group-comparative omega
MG-omega

1999 (multi-group extension: 2000s–2010s)

Multi-group McDonald's omega estimates and compares the reliability of a scale across two or more distinct groups. Rooted in confirmatory factor analysis, it uses the factor loadings and unique variances from each group's measurement model to compute omega, then tests whether reliability is statistically equivalent across groups.

Reliability coefficient (multi-group extension)

Ordinal or continuous item scores across two or more groups

McDonald, R. P. (1999). Test Theory: A Unified Treatment. Lawrence Erlbaum Associates.

Hayes, A. F. & Coutts, J. J. (2020). Use omega rather than Cronbach's alpha for estimating reliability. But … Communication Methods and Measures, 14(1), 1–24.


Multi-group measurement invariance

Multi-group Measurement Invariance Testing

measurement invariance
factorial invariance
cross-group invariance
MI testing

Jöreskog, K. G. (1971); Meredith, W. (1993)

Multi-group measurement invariance testing examines whether a latent construct is measured in the same way across two or more distinct groups — such as cultures, genders, or age cohorts. It is a prerequisite for meaningful group comparisons of latent means or relationships, ensuring that observed score differences reflect true differences rather than measurement artifacts.

Ordinal or continuous item responses across two or more groups

Vandenberg, R. J. & Lance, C. E. (2000). A review and synthesis of the measurement invariance literature: Suggestions, practices, and recommendations for organizational research. Organizational Research Methods, 3(1), 4–70.

Putnick, D. L. & Bornstein, M. H. (2016). Measurement invariance conventions and reporting: The state of the art and future directions for psychological research. Developmental Review, 41, 71–90.


Multi-group Rasch model

MG-Rasch
Rasch measurement invariance
multi-group 1PL IRT
cross-group Rasch analysis

1960 (Rasch); 1980s–1990s (multi-group extensions)

Georg Rasch (single-group); extended to multi-group applications by Fischer, Molenaar, and others

The multi-group Rasch model fits the one-parameter logistic item response model simultaneously across two or more distinct groups, testing whether item difficulty parameters are invariant across groups. It is the primary psychometric tool for establishing that a scale measures the same latent trait with the same metric in each group, a prerequisite for meaningful score comparisons.

Item response model / measurement invariance test

Dichotomous or polytomous item responses from two or more identified groups

Fischer, G. H. & Molenaar, I. W. (Eds.) (1995). Rasch Models: Foundations, Recent Developments, and Applications. Springer.

Andrich, D. (1988). Rasch Models for Measurement. Sage Publications.


Multi-group Reliability Analysis

reliability comparison across groups
group-specific reliability estimation
multi-sample reliability analysis
cross-group internal consistency

Classical test theory traditions; synthesized in modern practice by Vandenberg & Lance (2000) and Sijtsma (2009)

Multi-group reliability analysis estimates internal consistency or stability coefficients separately within each group and then formally compares them to determine whether a scale functions with equal precision across populations. It is a foundational step in cross-group measurement research, typically carried out alongside or prior to measurement invariance testing.

Ordinal or interval item responses from two or more distinct groups

Sijtsma, K. (2009). On the use, the misuse, and the very limited usefulness of Cronbach's alpha. Psychometrika, 74(1), 107–120.


Multi-group scale development

MGSD
cross-group scale development
multi-sample scale development
comparative scale construction

1971 (multi-group CFA); 2000 (applied synthesis for scale development)

Jöreskog, K. G. (multi-group SEM framework); systematised for scale development by Vandenberg & Lance (2000)

Multi-group scale development constructs and validates a measurement scale simultaneously across two or more distinct populations or groups. The approach integrates standard item generation and factor-analytic procedures with a systematic hierarchy of measurement invariance tests to ensure that the resulting scale measures the same construct in the same way in every target group.

Scale development / measurement model testing

Ordinal or continuous item-level responses from two or more groups

Vandenberg, R. J., & Lance, C. E. (2000). A review and synthesis of the measurement invariance literature: Suggestions, practices, and recommendations for organizational research. Organizational Research Methods, 3(1), 4–70.

Millsap, R. E. (2011). Statistical Approaches to Measurement Invariance. Routledge.


Multi-group test-retest reliability

Multi-group Test-Retest Reliability Analysis

multi-group temporal stability
cross-group test-retest reliability
group-comparative retest reliability
multi-sample temporal consistency

Systematic multi-group extensions developed alongside measurement invariance frameworks (Vandenberg & Lance, 2000); intraclass correlation foundation in Shrout & Fleiss (1979)

Multi-group test-retest reliability evaluates whether a measure produces stable scores across time separately for two or more defined groups — such as different genders, age cohorts, or clinical populations — and determines whether the degree of that temporal stability is equivalent across those groups.

Repeated-measures scores from two or more defined groups

Shrout, P. E. & Fleiss, J. L. (1979). Intraclass correlations: Uses in assessing rater reliability. Psychological Bulletin, 86(2), 420–428.


Multi-layer Perceptron

Multi-layer Perceptron (Feedforward Neural Network with Backpropagation)

MLP
feedforward neural network
fully connected neural network
artificial neural network
dense neural network

The Multi-layer Perceptron (MLP) is a feedforward neural network architecture trained by backpropagation, formalised by Rumelhart, Hinton, and Williams in their landmark 1986 Nature paper. Composed of an input layer, one or more hidden layers of neurons with nonlinear activation functions, and an output layer, the MLP can approximate any continuous function to arbitrary accuracy and serves as the conceptual bridge between classical machine learning and modern deep learning.

Feedforward neural network (supervised learning)

Classification, regression, function approximation

Rumelhart, D. E., Hinton, G. E., & Williams, R. J. (1986). Learning representations by back-propagating errors. Nature, 323, 533–536.

Goodfellow, I., Bengio, Y., & Courville, A. (2016). Deep Learning (Ch. 6–7). MIT Press.

Bishop, C. M. (2006). Pattern Recognition and Machine Learning (Ch. 5). Springer.

logistic-regression random-forest xgboost convolutional-neural-network recurrent-neural-network support-vector-machine


Multi-level Cluster Sampling

hierarchical cluster sampling
nested cluster sampling
multi-stage cluster sampling
clustered multilevel sampling

1950s-1970s (cluster sampling); multilevel extension formalized 1980s-1990s

W. G. Cochran (cluster sampling foundations); extended into multilevel contexts by survey methodologists

Multi-level cluster sampling is a probability sampling design for hierarchically structured populations — such as students nested within classrooms within schools within districts. Clusters are randomly selected at each level of the hierarchy before individual units are sampled within the final-level clusters. The design mirrors the natural nesting of real-world populations and enables efficient large-scale data collection while supporting multilevel statistical analysis.

Quantitative; nested/hierarchical population data

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

Snijders, T. A. B., & Bosker, R. J. (2012). Multilevel Analysis: An Introduction to Basic and Advanced Multilevel Modeling (2nd ed.). Sage.

cluster-sampling multistage-sampling stratified-sampling proportional-cluster-sampling systematic-sampling simple-random-sampling


Multi-level Convenience Sampling

hierarchical convenience sampling
nested convenience sampling
multilevel accessibility sampling
multi-tier convenience sampling

1980s–1990s (concurrent with multilevel modeling development)

Emerged from multilevel/hierarchical research traditions

Multi-level convenience sampling is a non-probability approach in which units are selected by convenience at each of two or more nested levels of a hierarchy — for example, recruiting whatever schools agree to participate and then enrolling all available students within those schools. It is widely used in organizational, educational, and health research where the researcher has limited control over access but must respect the nested structure of the population.

Any data collected at two or more nested organizational or social levels

Hox, J. J. (2010). Multilevel Analysis: Techniques and Applications (2nd ed.). Routledge.

Etikan, I., Musa, S. A., & Alkassim, R. S. (2016). Comparison of convenience sampling and purposive sampling. American Journal of Theoretical and Applied Statistics, 5(1), 1-4.

convenience-sampling multistage-sampling cluster-sampling purposive-sampling multi-level-cluster-sampling multi-level-stratified-sampling


Multi-level Maximum Variation Sampling

hierarchical maximum variation sampling
nested maximum diversity sampling
multi-tier purposive variation sampling
MLMVS

Synthesized from Patton's maximum variation sampling (1990) and multi-level survey design traditions

Multi-level maximum variation sampling is a purposive strategy that deliberately selects cases at two or more nested organizational levels — such as schools within districts, or patients within clinics — while maximizing heterogeneity on key dimensions at each level. The aim is to capture the full range of variation within a hierarchically structured population so that patterns common across diverse contexts can be identified and context-specific differences can be documented with credibility.

Purposive qualitative/mixed-methods sampling design

Qualitative interviews, observations, or mixed-methods data at two or more nested organizational levels

Patton, M. Q. (2002). Qualitative Research and Evaluation Methods (3rd ed.). Sage. [Chapter 5: Maximum variation sampling and purposeful sampling strategies]

Bryman, A. (2016). Social Research Methods (5th ed.). Oxford University Press. [Multi-level and purposive sampling in mixed and qualitative designs]

maximum-variation-sampling purposive-sampling multistage-sampling stratified-sampling theoretical-sampling multi-level-purposive-sampling


Multi-level Purposive Sampling

hierarchical purposive sampling
nested purposive sampling
multi-tier purposive sampling
multi-site purposive sampling

Derived from Patton's purposive sampling framework; formalized in multi-site qualitative and mixed-methods research

Multi-level purposive sampling applies purposive selection criteria at two or more nested levels of a research hierarchy — for instance, first selecting sites or organizations, then selecting participants within each site. This layered approach allows researchers to align the theoretical logic of purposive sampling with the real-world structure of complex, hierarchical populations, making it especially valuable in multi-site qualitative studies and mixed-methods research.

Qualitative or mixed-methods data from hierarchically nested units

Patton, M. Q. (2002). Qualitative Research and Evaluation Methods (3rd ed.). Sage.

Miles, M. B., Huberman, A. M., & Saldana, J. (2014). Qualitative Data Analysis: A Methods Sourcebook (3rd ed.). Sage.

purposive-sampling multistage-sampling maximum-variation-sampling theoretical-sampling cluster-sampling stratified-sampling


Multi-level Stratified Sampling

hierarchical stratified sampling
nested stratified sampling
multilevel stratified design
stratified multilevel sampling

Formalized by Leslie Kish and William G. Cochran in the mid-20th century survey sampling literature

Multi-level stratified sampling applies stratification at two or more hierarchical levels of a nested population structure — for example, first stratifying geographic regions, then stratifying schools within each region, then stratifying classrooms within each school. This layered control over the composition of the sample at every level reduces variance and supports analysis at each level of the hierarchy, making it a powerful design for large-scale educational, epidemiological, and organizational surveys.

Hierarchically structured populations (e.g., students within schools, employees within firms)

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

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

stratified-sampling multistage-sampling cluster-sampling proportional-stratified-sampling systematic-sampling multi-level-cluster-sampling


Multi-level Typical Case Sampling

multilevel typical case selection
hierarchical typical case sampling
nested typical case sampling

Draws on Patton (typical case sampling) and multilevel research traditions (Hox, Raudenbush)

Multi-level typical case sampling is a purposive strategy that selects representative, average-profile units at each level of a hierarchical structure — for example, typical classrooms within typical schools, or typical employees within typical departments. It is used when the research goal is to describe or illustrate the ordinary functioning of a nested phenomenon rather than to capture its extremes or full variation.

Nested/hierarchical data (e.g., students within schools, employees within organizations)

Patton, M. Q. (2002). Qualitative Research and Evaluation Methods (3rd ed.). Sage Publications.

typical-case-sampling purposive-sampling multi-level-purposive-sampling multistage-sampling maximum-variation-sampling multi-level-cluster-sampling


Multi-level weighted sampling

hierarchical weighted sampling
nested weighted sampling
multilevel probability weighting
weighted hierarchical sampling

1960s–1980s (developed alongside large-scale survey programs)

Leslie Kish (probability sampling theory); complex survey methodologists

Multi-level weighted sampling is a probability-based survey design that draws samples from hierarchically nested populations — such as students within classrooms within schools within districts — and assigns design weights at each level to account for unequal selection probabilities. The resulting weighted data enable unbiased population-level inference despite the complex, non-proportional structure of the sampling frame. It is the backbone of major international assessments such as PISA and TIMSS.

Hierarchically structured populations (e.g., students within schools within districts)

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

Skinner, C. J., Holt, D., & Smith, T. M. F. (Eds.). (1989). Analysis of Complex Surveys. John Wiley & Sons. Chichester.

multistage-sampling stratified-sampling cluster-sampling weighted-sampling proportional-stratified-sampling systematic-sampling


Multi-objective agent-based modeling

MO-ABM
Multi-objective ABM
Pareto-based agent-based modeling
Multi-objective agent simulation

Multi-Objective Agent-Based Modeling (MO-ABM) couples agent-based simulation with multi-objective optimization to simultaneously optimize several conflicting performance criteria across complex adaptive systems. Autonomous agents interact according to behavioral rules while an optimizer searches for parameter configurations that achieve Pareto-optimal trade-offs among competing system-level goals.

Agent behavioral rules, performance objectives, environment parameters

Deb, K. (2001). Multi-Objective Optimization Using Evolutionary Algorithms. John Wiley & Sons, Chichester.

Tesfatsion, L., Judd, K. L. (Eds.) (2006). Handbook of Computational Economics, Volume 2: Agent-Based Computational Economics. North-Holland, Amsterdam.

agent-based-modeling multi-objective-optimization nsga-ii multi-objective-genetic-algorithm stochastic-agent-based-modeling multi-objective-system-dynamics


Multi-objective ant colony optimization

MOACO
Multi-Objective ACO
Pareto Ant Colony Optimization
Multi-objective ACO

Gambardella, Taillard & Agazzi; Dorigo & Stützle

Multi-Objective Ant Colony Optimization (MOACO) is a swarm-intelligence metaheuristic that extends the classic Ant Colony Optimization framework to simultaneously optimize two or more conflicting objectives. Artificial ants construct candidate solutions guided by pheromone trails and heuristic information, progressively building an archive of Pareto-optimal solutions rather than converging to a single best answer.

Combinatorial / continuous solution spaces with multiple conflicting objectives

Gambardella, L. M., Taillard, E., & Agazzi, G. (1999). MACS-VRPTW: A multiple ant colony system for vehicle routing problems with time windows. In D. Corne, M. Dorigo, & F. Glover (Eds.), New Ideas in Optimization (pp. 63–76). McGraw-Hill.

Dorigo, M., & Stützle, T. (2004). Ant Colony Optimization. MIT Press.


Multi-objective cellular automata

Multi-Objective Cellular Automata — Simulation-based spatial optimization with multiple competing objectives

MOCA
Multi-objective CA
Multi-criteria cellular automata
MO-CA

Various (Liu et al., White & Engelen, Clarke et al.)

Multi-Objective Cellular Automata (MOCA) couples the bottom-up spatial dynamics of cellular automata with multi-objective optimization to simultaneously pursue competing goals — such as maximizing urban compactness while minimizing ecosystem loss. Each grid cell updates its state based on transition rules that are calibrated or steered to satisfy a Pareto-optimal trade-off among two or more objectives, making the method widely used in land-use change simulation, urban growth modeling, and spatial planning under conflicting demands.

Spatial / raster grid, categorical or continuous state values

Liu, X., Liang, X., Li, X., Xu, X., Ou, J., Chen, Y., Li, S., Wang, S., Pei, F. (2017). A future land use simulation model (FLUS) for simulating multiple land use scenarios by coupling human and natural effects. Landscape and Urban Planning, 168, 94-116.

Jantz, C. A., Goetz, S. J., Shelley, M. K. (2004). Using the SLEUTH urban growth model to simulate the impacts of future policy scenarios on urban land use in the Baltimore-Washington metropolitan area. Environment and Planning B: Planning and Design, 31(2), 251-271.

cellular-automata multi-objective-optimization agent-based-modeling nsga-ii multi-objective-genetic-algorithm system-dynamics


MO-DES
Multi-objective DES
Pareto-based discrete-event simulation
DES with multi-objective optimization

Various (DES: Tocher 1963; multi-objective integration: 1990s–2000s OR literature)

Multi-Objective Discrete-Event Simulation (MO-DES) couples a discrete-event simulation engine with multi-objective optimization to explore trade-offs among two or more conflicting performance measures — such as throughput, cost, and waiting time — across stochastic, time-ordered process models. It is widely applied in manufacturing, logistics, healthcare, and service system design.

Event logs, process parameters, performance metrics

Kleijnen, J. P. C., & Gaury, E. (2003). Short-term robustness of production management systems: A case study. European Journal of Operational Research, 148(2), 452–465.

discrete-event-simulation multi-objective-optimization nsga-ii monte-carlo-simulation stochastic-discrete-event-simulation multi-objective-system-dynamics