Panel-based Descriptive Research

repeated cross-sectional descriptive panel

Developed within survey methodology and social science panel traditions (Lazarsfeld, Kish, and others)

Panel-based descriptive research follows the same set of individuals, households, or organizations across multiple time points and uses that repeated-measures structure to describe how variables, distributions, and patterns change over time — without imposing an experimental manipulation or testing causal hypotheses. It is distinguished from cross-sectional descriptive research by its capacity to document intra-individual change, and from explanatory panel research by its goal of accurate description rather than causal modelling.

Repeated measurements on the same sample units (survey, administrative, or registry data)

Menard, S. (2002). Longitudinal Research (2nd ed.). Sage Publications.

Kish, L. (1965). Survey Sampling. Wiley.

panel-research longitudinal-research descriptive-research cross-sectional-research survey-research cohort-research


Panel-based ex post facto design

Panel-Based Ex Post Facto Research Design

panel ex post facto study
longitudinal causal-comparative design
retrospective panel design
panel causal-comparative study

1950s–1970s (synthesized from ex post facto tradition and panel survey research)

Developed from Kerlinger's ex post facto framework combined with panel survey methodology (Lazarsfeld, Kerlinger)

A panel-based ex post facto design tracks the same group of participants across multiple time points to examine how pre-existing differences in an independent variable — one the researcher did not manipulate — are associated with changes in an outcome over time. It merges the temporal depth of panel methodology with the causal-comparative logic of ex post facto research, enabling stronger causal inference than a single cross-sectional snapshot while remaining fully non-experimental.

Non-experimental longitudinal observational design

Quantitative repeated-measures data collected from the same panel at multiple time points

Kerlinger, F. N. (1986). Foundations of Behavioral Research (3rd ed.). Holt, Rinehart and Winston.

panel-study ex-post-facto-design causal-comparative-design longitudinal-design cohort-study cross-lagged-panel-model


Panel-Based Exploratory Quantitative Research

exploratory panel study
panel survey design
longitudinal exploratory survey
repeated-measures exploratory design

1940s–1960s (formalized in social sciences)

Rooted in panel survey methodology developed broadly in social science (Lazarsfeld, 1940s; Kish, 1965)

Panel-based exploratory quantitative research tracks the same sample of participants across multiple measurement points to discover patterns, relationships, and change processes that a single snapshot cannot reveal. Because the research goal is exploratory — uncovering structure rather than testing a predetermined hypothesis — the design is especially valuable in emerging topic areas where theory is underdeveloped and the relevant variables are not yet well understood.

Quantitative observational research design

Repeated quantitative measurements from the same respondents over time (survey, questionnaire, structured observation)

Lynn, P. (Ed.). (2009). Methodology of Longitudinal Surveys. John Wiley & Sons.

longitudinal-survey cross-sectional-survey cohort-study time-series-analysis repeated-measures-design exploratory-factor-analysis


Panel-based Model Testing Research

Panel-based Model Testing Research Design

panel SEM
longitudinal model testing
panel structural equation modeling
panel-based hypothesis testing

1970s–1980s (panel econometrics and SEM matured in parallel)

Developed across econometrics (Hsiao, Hausman) and psychometrics (Jöreskog, Bollen)

Panel-based model testing research combines the longitudinal power of panel survey designs with the confirmatory rigor of structural model testing — such as structural equation modeling (SEM), path analysis, or confirmatory factor analysis — applied to data collected from the same units (individuals, firms, countries) across multiple time points. This approach enables researchers to test theoretically specified causal and mediation structures while controlling for unobserved unit-level heterogeneity and examining how relationships unfold over time.

Quantitative longitudinal research design

Repeated-measures panel data (same units observed across multiple time points)

Bollen, K. A. (1989). Structural Equations with Latent Variables. Wiley.

Hsiao, C. (2014). Analysis of Panel Data (3rd ed.). Cambridge University Press.

structural-equation-modeling confirmatory-factor-analysis longitudinal-research cross-lagged-panel-model multilevel-modeling latent-growth-curve-modeling


Panel-based Observational Quantitative Research Design

panel observational study
longitudinal observational panel design
panel survey research
repeated-measures observational design

1960s–1980s (formalized in econometrics); widely adopted in social sciences by 1990s

Established through econometrics literature; foundational contributions by Cheng Hsiao, Zvi Griliches, and Marc Nerlove

Panel-based observational quantitative research follows the same individuals, organizations, or units across two or more time points without experimentally manipulating any condition. By combining the within-unit depth of longitudinal tracking with the numerical precision of quantitative measurement, it enables researchers to study change over time, detect lagged effects, and control for stable unobserved characteristics — all while maintaining the ethical simplicity of pure observation.

Quantitative observational longitudinal design

Repeated numeric measurements on the same units across multiple time points (panel/longitudinal data)

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

Wooldridge, J. M. (2010). Econometric Analysis of Cross Section and Panel Data (2nd ed.). MIT Press.

longitudinal-survey cohort-study fixed-effects-model random-effects-model cross-sectional-survey difference-in-differences


Panel-Based Quantitative Content Analysis

longitudinal content analysis
repeated-measures content analysis
panel content analysis
tracking content analysis

1950s–1980s (formalized in communication research)

Synthesized from Berelson's content analysis tradition and panel study methodology

Panel-based quantitative content analysis applies systematic, numeric coding of media or textual content to the same fixed panel of sources at multiple time points. By holding the source panel constant while measurements repeat over time, researchers can track genuine change in content patterns rather than confounding source variation with temporal change. It is widely used in communication, media studies, and political science to monitor how coverage, framing, or topic salience evolves.

Coded text, media content, documents (numeric frequency/categorical counts)

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

Riffe, D., Lacy, S., Watson, B. R., & Fico, F. (2019). Analyzing Media Messages: Using Quantitative Content Analysis in Research (4th ed.). Routledge.


Panel-based Relational Survey

longitudinal relational survey
panel relational study
repeated-measures correlational survey
panel correlational design

1940s onward (panel survey); relational survey as standard practice by mid-20th century

Rooted in panel survey traditions systematized by Paul Lazarsfeld (1940s) and relational survey methodology codified by Kerlinger, Babbie, and de Leeuw

A panel-based relational survey is a quantitative design that recruits the same group of respondents and surveys them at two or more time points to examine how variables relate to, predict, or co-vary with one another over time. By combining the relational goal of uncovering associations among variables with the panel structure of repeated measurement from a stable sample, the design enables researchers to track how relationships evolve, test directional hypotheses about predictors and outcomes, and distinguish within-person change from between-person differences.

Quantitative observational longitudinal survey design

Repeated quantitative survey measures from the same respondents across two or more time points

de Leeuw, E. D., Hox, J. J., & Dillman, D. A. (Eds.). (2008). International Handbook of Survey Methodology. Lawrence Erlbaum Associates / Taylor & Francis.

Babbie, E. (2021). The Practice of Social Research (15th ed.). Cengage Learning.

panel-research relational-survey longitudinal-correlational-research correlational-research longitudinal-research cross-lagged-panel-model


Panel-based survey research

panel survey
longitudinal survey panel
repeated survey design
panel data survey

Mid-20th century; formalized as a distinct design by the 1940s–1960s in sociological and economic research

Established through social science survey methodology; foundational reference: Kasprzyk et al. (1989)

Panel-based survey research is a quantitative longitudinal design in which the same set of respondents — the panel — is surveyed with structured questionnaires at two or more distinct time points. By tracking the same individuals over time, the design captures intra-individual change, documents how outcomes evolve, and enables stronger causal inference than a single cross-sectional survey can provide. It is widely used in social science, economics, public health, and education research.

Quantitative longitudinal observational design

Structured survey questionnaires administered to the same sample at multiple time points

Kasprzyk, D., Duncan, G., Kalton, G., & Singh, M. P. (Eds.). (1989). Panel Surveys. Wiley.

panel-research longitudinal-research survey-research cohort-research cross-sectional-survey-research longitudinal-survey-research


Panel-based trend research

panel trend study
longitudinal panel design
repeated-measures panel survey
panel survey trend analysis

Established through survey methodology and panel econometrics; foundational contributions by Paul Lazarsfeld (1940s) and later systematized by econometricians including Zvi Griliches and Yair Mundlak

Panel-based trend research tracks the same group of respondents — the panel — across multiple measurement waves over time, enabling researchers to separate genuine individual-level change from cohort differences and to model how variables evolve within persons. Unlike repeated cross-sectional designs, which sample new participants at each wave, a panel design retains the same units, giving it the power to detect within-person trajectories and causal ordering among variables.

Repeated quantitative measurements from the same respondents across multiple time points

cohort-study cross-lagged-panel-model repeated-measures-anova time-series-analysis longitudinal-survey growth-curve-modeling


Panel Cointegration Tests

Panel Cointegration Tests (Pedroni, Kao, Westerlund)

Panel Eşbütünleşme Testleri (Pedroni, Kao, Westerlund)

Panel cointegration tests check whether a set of integrated variables share a stable long-run equilibrium relationship across a panel of cross-sectional units. Pedroni (1999, 2004) provides heterogeneous-panel tests with seven statistics, Kao (1999) gives an ADF-based homogeneous-panel test, and Westerlund (2007) adds error-correction-based tests robust to structural breaks and cross-sectional dependence.

Residual-based and error-correction-based panel tests

long-run equilibrium relationship (yes/no)

Pedroni, P. (2004). Panel Cointegration: Asymptotic and Finite Sample Properties of Pooled Time Series Tests with an Application to the PPP Hypothesis. Econometric Theory, 20(3), 597–625.

Westerlund, J. (2007). Testing for Error Correction in Panel Data. Oxford Bulletin of Economics and Statistics, 69(6), 709–748.

panel-fixed-effects amg-estimator vecm ols-regression panel-unit-root-tests


Panel Data Analysis

Panel Data Analysis (Longitudinal Data Analysis)

pooled cross-sectional time-series analysis

Balestra & Nerlove (1966); Mundlak (1978); Hausman (1978)

Panel data analysis models data that track multiple units — countries, firms, individuals — over time, enabling researchers to control for unobserved unit-level heterogeneity that would otherwise bias cross-sectional or time-series estimates. The two core specifications are fixed effects and random effects, selected via the Hausman test.

Balanced or unbalanced panel (N units × T time periods)

Baltagi, B. H. (2021). Econometric Analysis of Panel Data (6th ed.). Springer.

Hausman, J. A. (1978). Specification tests in econometrics. Econometrica, 46(6), 1251–1271.

fixed-effects-model random-effects-model panel-hausman-test dynamic-panel-data-model arellano-bond-gmm-estimator panel-ols


Panel Data Causal Impact Analysis

panel structural time-series causal analysis

2015 (base method); panel extension mid-2010s

Brodersen et al. (2015); panel extension by Holtz et al. and subsequent literature

Panel data causal impact analysis extends the Bayesian structural time-series approach of Brodersen et al. (2015) to multi-unit panel settings, estimating the counterfactual for several treated units simultaneously using control units as a donor pool. It produces credible intervals for the causal effect at each post-intervention time point, aggregated across units and periods.

Bayesian structural time-series causal inference

Multi-unit panel time-series (balanced or unbalanced)

Brodersen, K. H., Gallusser, F., Koehler, J., Remy, N., & Scott, S. L. (2015). Inferring causal impact using Bayesian structural time-series models. Annals of Applied Statistics, 9(1), 247-274.

Abadie, A., Diamond, A., & Hainmueller, J. (2010). Synthetic control methods for comparative case studies: Estimating the effect of California's tobacco control program. Journal of the American Statistical Association, 105(490), 493-505.

causal-impact-analysis synthetic-control-method panel-data-synthetic-control-method difference-in-differences panel-data-difference-in-differences panel-data-interrupted-time-series


Panel Data Coarsened Exact Matching

Panel Data Coarsened Exact Matching Estimator

coarsened exact matching with panel data

Iacus, King & Porro (CEM, 2012); panel extension via Imai, Kim & Wang (2021)

Panel Data Coarsened Exact Matching applies the Coarsened Exact Matching (CEM) algorithm to repeated-measures panel data, matching treated and control units within the same coarsened covariate strata across multiple time periods. It balances pre-treatment characteristics before estimating a causal treatment effect, combining the transparency of exact matching with the richer identification available in longitudinal datasets.

Panel data (repeated observations on units across multiple time periods)

Iacus, S. M., King, G., & Porro, G. (2012). Causal Inference without Balance Checking: Coarsened Exact Matching. Political Analysis, 20(1), 1-24.

Imai, K., Kim, I. S., & Wang, E. H. (2021). Matching Methods for Causal Inference with Time-Series Cross-Sectional Data. American Journal of Political Science, 67(3), 587-605.

coarsened-exact-matching propensity-score-matching panel-data-propensity-score-matching panel-fixed-effects difference-in-differences matching-estimator


Panel Data Difference-in-Differences

Panel Data Difference-in-Differences Estimator

Two-Way Fixed Effects DiD
TWFE
Panel DiD
Panel Diff-in-Diff

Ashenfelter & Card (1985); codified by Angrist & Pischke (2009); serial correlation critique by Bertrand, Duflo & Mullainathan (2004)

Panel Data Difference-in-Differences extends the classic two-period DiD design to settings with multiple units observed across many time periods. By absorbing unit-level fixed effects and time fixed effects simultaneously, it isolates the causal effect of a treatment or policy change while controlling for both time-invariant unit heterogeneity and common time shocks affecting all units.

Panel data (multiple units, multiple time periods)

Angrist, J. D., & Pischke, J.-S. (2009). Mostly Harmless Econometrics: An Empiricist's Companion. Princeton University Press.

Bertrand, M., Duflo, E., & Mullainathan, S. (2004). How Much Should We Trust Differences-in-Differences Estimates? Quarterly Journal of Economics, 119(1), 249-275.

difference-in-differences panel-fixed-effects staggered-difference-in-differences event-study-design propensity-score-matching synthetic-control-method


Panel Data Entropy Balancing

EB-panel
panel entropy balancing
entropy reweighting in panel data
panel-EB

2012 (cross-section); panel adaptation mid-2010s onward

Hainmueller (2012); extended to panel settings by subsequent applied econometric work

Panel data entropy balancing extends Hainmueller's (2012) entropy balancing method to longitudinal settings. It computes unit-level weights for control observations so that their covariate moments exactly match those of the treatment group across panel periods, then plugs these weights into a weighted panel regression to estimate causal treatment effects without requiring a correctly specified propensity score model.

Covariate balancing / reweighting estimator

Panel data (longitudinal) with binary treatment

Hainmueller, J. (2012). Entropy Balancing for Causal Effects: A Multivariate Reweighting Method to Produce Balanced Samples in Observational Studies. Political Analysis, 20(1), 25-46.

Zhao, Q. (2019). Covariate balancing propensity score by tailored loss functions. Annals of Statistics, 47(2), 965-993.


Panel Fuzzy RDD
Panel FRD
Fuzzy RD with Panel Data
Panel Fuzzy RD

2001 (fuzzy RDD); panel extension circa 2011

Hahn, Todd & Van der Klaauw; extended to panel settings by Papay, Willett & Murnane and others

Panel Data Fuzzy Regression Discontinuity Design (Panel FRD) extends the fuzzy RDD framework to settings where multiple observations per unit are available over time. It exploits a probabilistic — rather than deterministic — threshold-crossing rule to identify a local average treatment effect (LATE) while controlling for unit-level and time-level fixed effects, sharpening identification in repeated-measures contexts.

Panel data (repeated observations per unit) with a continuous running variable and a probabilistic treatment rule

Hahn, J., Todd, P., & Van der Klaauw, W. (2001). Identification and Estimation of Treatment Effects with a Regression-Discontinuity Design. Review of Economic Studies, 68(1), 201-209.

Lee, D. S., & Lemieux, T. (2010). Regression Discontinuity Designs in Economics. Journal of Economic Literature, 48(2), 281-355.


Panel Data Instrumental Variables

Instrumental Variables Estimation in Panel Data Settings

Panel IV
Panel 2SLS
Within-IV
Fixed-Effects IV

Hausman (1978); Anderson & Hsiao (1982); Arellano & Bond (1991)

Panel data instrumental variables combines the bias-correcting power of instrumental variables (IV) with the within-unit variation exploited by panel data methods. It addresses endogeneity — omitted variables, reverse causation, or measurement error — in longitudinal settings where observations are repeated across units and time. Seminal contributions come from Hausman (1978) on specification testing and Arellano and Bond (1991) on GMM-based panel IV.

Longitudinal / panel data (multiple units observed over multiple periods)

Arellano, M., & Bond, S. (1991). Some tests of specification for panel data: Monte Carlo evidence and an application to employment equations. Review of Economic Studies, 58(2), 277-297.

Hausman, J. A. (1978). Specification tests in econometrics. Econometrica, 46(6), 1251-1271.

instrumental-variables difference-in-differences panel-fixed-effects two-stage-least-squares generalized-method-of-moments dynamic-panel-data


Panel Data Interrupted Time Series

Panel Data Interrupted Time Series Analysis

panel ITS
multi-unit ITS
panel ITSA
controlled interrupted time series

Shadish, Cook & Campbell (design framework); Bernal, Cummins & Gasparrini (epidemiological tutorial)

Panel Data Interrupted Time Series (panel ITS) is a quasi-experimental method that estimates the causal effect of an intervention using repeated observations from multiple units over time. By exploiting variation across both units and time periods, it provides stronger causal identification than single-unit ITS, detecting changes in the level and slope of the outcome trajectory immediately following a clearly dated intervention.

Longitudinal panel data with repeated observations across multiple units and time points

Lopez Bernal, J., Cummins, S., & Gasparrini, A. (2017). Interrupted time series regression for the evaluation of public health interventions: a tutorial. International Journal of Epidemiology, 46(1), 348-355.

Shadish, W. R., Cook, T. D., & Campbell, D. T. (2002). Experimental and Quasi-Experimental Designs for Generalized Causal Inference. Houghton Mifflin.

interrupted-time-series difference-in-differences panel-fixed-effects event-study-design panel-data-difference-in-differences synthetic-control-method


Panel Data Inverse Probability Weighting Estimator

panel IPW
longitudinal IPW
time-varying IPW
panel IPTW

Panel Data Inverse Probability Weighting (panel IPW) estimates the causal effect of a time-varying treatment by reweighting observed units to create a pseudo-population in which treatment is independent of measured confounders at each time point. It extends the cross-sectional IPW framework to longitudinal settings where treatment status and confounders both evolve across multiple periods.

Panel / longitudinal (repeated observations per unit)

Robins, J. M., Hernan, M. A., & Brumback, B. (2000). Marginal structural models and causal inference in epidemiology. Epidemiology, 11(5), 550-560.

Hernan, M. A., & Robins, J. M. (2020). Causal Inference: What If. Boca Raton: Chapman & Hall/CRC.

propensity-score-weighting marginal-structural-model panel-data-doubly-robust-estimation panel-data-propensity-score-matching inverse-probability-weighting panel-data-matching-estimator


Panel Data Marginal Structural Model

Panel Data Marginal Structural Model with Inverse Probability Weighting

MSM panel
longitudinal MSM
panel MSM
time-varying treatment MSM

James M. Robins, Miguel A. Hernan, Babette Brumback

A panel data marginal structural model (MSM) uses inverse probability of treatment weighting (IPTW) across multiple time periods to estimate the causal effect of a time-varying treatment, while appropriately adjusting for time-varying confounders that are themselves affected by prior treatment — a bias source that conventional regression cannot handle.

Causal model for time-varying treatments

Longitudinal / panel data with time-varying treatment and confounders

Hernan, M. A., & Robins, J. M. (2020). Causal Inference: What If. Chapman & Hall/CRC.


Panel Data Matching Estimator

Panel Data Matching Estimator for Average Treatment Effects

panel matching
matching-on-panel-data
longitudinal matching estimator
PDME

Heckman, Ichimura & Todd (1997); Imai, Kim & Wang (2021) for panel extension

The panel data matching estimator identifies causal treatment effects by pairing each treated unit with one or more control units that share similar covariate histories in the pre-treatment periods. By exploiting the longitudinal structure of panel data, it controls for both observed time-varying confounders and stable unit characteristics, estimating the average treatment effect on the treated (ATT) without requiring a parallel-trends assumption.

Balanced or unbalanced panel (repeated observations per unit over time)

Heckman, J. J., Ichimura, H., & Todd, P. E. (1997). Matching as an econometric evaluation estimator: Evidence from evaluating a job training programme. Review of Economic Studies, 64(4), 605-654.

Imai, K., Kim, I. S., & Wang, E. H. (2021). Matching methods for causal inference with time-series cross-sectional data. American Journal of Political Science, 67(3), 587-605.

matching-estimator propensity-score-matching difference-in-differences panel-data-difference-in-differences coarsened-exact-matching panel-fixed-effects


Panel Data Placebo Test

Panel Data Placebo Test for Causal Inference Validation

placebo regression test
falsification test
pseudo-treatment test
in-time placebo

Bertrand, Duflo & Mullainathan; Abadie, Diamond & Hainmueller

A panel data placebo test is a falsification procedure used to assess the credibility of causal estimates in quasi-experimental panel designs. By applying the same estimation strategy to a period, group, or outcome where no true effect should exist, researchers verify that the observed treatment effect is not merely an artifact of model specification, coincidental trends, or data patterns unrelated to the intervention.

Panel data (repeated observations over time)

Abadie, A., Diamond, A., & Hainmueller, J. (2010). Synthetic Control Methods for Comparative Case Studies: Estimating the Effect of California's Tobacco Control Program. Journal of the American Statistical Association, 105(490), 493-505.

difference-in-differences panel-data-difference-in-differences sensitivity-analysis-for-causality synthetic-control-method event-study-design regression-discontinuity-design


Panel Data Propensity Score Matching

Propensity Score Matching with Panel Data

PSM with panel data
longitudinal PSM
panel PSM
difference-in-differences PSM

Panel data propensity score matching combines the bias-reduction of PSM with the longitudinal structure of panel data, enabling causal estimation of treatment effects by matching treated and control units on observable pre-treatment characteristics and then differencing within matched pairs over time. Developed in the framework of Heckman, Ichimura, and Todd (1998), it is especially valuable when randomisation is infeasible and both selection on observables and time-varying confounding must be addressed simultaneously.

Panel or longitudinal observational data

Heckman, J. J., Ichimura, H., & Todd, P. (1998). Matching as an Econometric Evaluation Estimator. Review of Economic Studies, 65(2), 261-294.

Caliendo, M., & Kopeinig, S. (2008). Some Practical Guidance for the Implementation of Propensity Score Matching. Journal of Economic Surveys, 22(1), 31-72.

propensity-score-matching difference-in-differences panel-data-difference-in-differences panel-fixed-effects matching-estimator entropy-balancing


Panel Data Propensity Score Weighting

Panel Data Propensity Score Weighting Estimator

panel PSW
panel IPW
longitudinal propensity score weighting
panel inverse probability weighting

Hirano, Imbens & Ridder; Robins, Hernan & Brumback

Panel Data Propensity Score Weighting (panel PSW) extends inverse probability weighting to longitudinal settings where the same units are observed across multiple time periods. It reweights observations by the inverse of each unit's time-varying probability of receiving treatment, creating a pseudo-population in which treatment is balanced on observed covariates at each period, and then estimates causal effects from repeated-measures data.

Panel data with repeated observations on the same units over time

Hirano, K., Imbens, G. W., & Ridder, G. (2003). Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score. Econometrica, 71(4), 1161-1189.

Robins, J. M., Hernan, M. A., & Brumback, B. (2000). Marginal Structural Models and Causal Inference in Epidemiology. Epidemiology, 11(5), 550-560.


Panel Data Regression Discontinuity Design

Panel RD
Panel RDD
Longitudinal Regression Discontinuity
Fixed-Effects RDD

1960 (original RDD); panel extension codified 2000s–2010s

Thistlethwaite & Campbell (1960); panel extension developed through Lee & Lemieux (2010) and related applied work

Panel data regression discontinuity design (Panel RDD) combines the sharp local identification of a regression discontinuity with the within-unit variation available in repeated-observation panel data. Units are observed across multiple periods, and treatment is assigned based on whether a running variable crosses a known threshold. By leveraging both the discontinuity and panel structure, researchers can control for unobserved unit-level heterogeneity while estimating a causal treatment effect near the threshold.

Panel data with a continuous running variable and a threshold assignment rule

Hahn, J., Todd, P., & Van der Klaauw, W. (2001). Identification and Estimation of Treatment Effects with a Regression-Discontinuity Design. Econometrica, 69(1), 201-209.

regression-discontinuity-design fuzzy-regression-discontinuity difference-in-differences panel-fixed-effects panel-data-difference-in-differences panel-data-interrupted-time-series


Panel Data Synthetic Control Method

SCM panel
panel synthetic control
synthetic control estimator
comparative case study

Alberto Abadie, Alexis Diamond & Jens Hainmueller

The panel data synthetic control method estimates the causal effect of an intervention on a single treated unit by constructing a data-driven weighted combination of untreated units — a synthetic control — that best reproduces the treated unit's pre-treatment outcome trajectory. The post-treatment gap between the treated unit and its synthetic counterpart is the estimated treatment effect.

Panel data (multiple units, multiple pre- and post-treatment periods)

Abadie, A. (2021). Using Synthetic Controls: Feasibility, Data Requirements, and Methodological Aspects. Journal of Economic Literature, 59(2), 391-425.

difference-in-differences synthetic-control-method panel-data-difference-in-differences panel-fixed-effects matching-estimator panel-data-event-study-design


Panel DCC-GARCH

Panel Dynamic Conditional Correlation GARCH Model

DCC-GARCH panel
panel dynamic conditional correlation
multivariate DCC-GARCH
Panel DCC

The Panel DCC-GARCH model extends Engle's (2002) Dynamic Conditional Correlation GARCH framework to panel data settings, jointly modelling time-varying volatility and cross-sectional correlations across multiple units (countries, firms, or assets) over time. It allows pairwise correlations to vary dynamically in response to market shocks while preserving parsimony via a two-step estimation.

Panel time series; multivariate financial or macroeconomic data

Engle, R. F. (2002). Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroscedasticity models. Journal of Business and Economic Statistics, 20(3), 339-350.

Engle, R. F., & Sheppard, K. (2001). Theoretical and empirical properties of dynamic conditional correlation multivariate GARCH. NBER Working Paper 8554. National Bureau of Economic Research.

dcc-garch-model panel-garch-model panel-egarch panel-tgarch vector-autoregression panel-var-model


Panel DF-GLS

Elliott, Rothenberg, and Stock (adapted to panels)

Panel DF-GLS extends the Elliott, Rothenberg, and Stock (1996) GLS unit-root test to panel data, combining cross-sectional and time-series information to test whether variables contain unit roots. Introduced by Hadri and colleagues (2005), it is more powerful than standard panel unit-root tests (IPS, LLC) due to its GLS detrending approach. This test is essential for establishing stationarity before fitting cointegration or dynamic panel models.

Elliott, G., Rothenberg, T. J., & Stock, J. H. (1996). Efficient tests for an autoregressive unit root. Econometric Reviews, 13(4), 469-497.

Hadri, K., & Larsson, R. (2005). Testing for stationarity in heterogeneous panel data. Econometric Reviews, 24(4), 403-456.


Panel Dynamic Panel Data Model

dynamic panel model
lagged dependent variable panel model
Arellano-Bond type dynamic panel
GMM dynamic panel

Arellano & Bond (1991); Blundell & Bond (1998)

The dynamic panel data model extends standard panel regression by including one or more lagged values of the outcome variable as regressors. Because past outcomes directly predict current outcomes, the model captures persistence and adjustment dynamics — but it also introduces a correlation between the lagged dependent variable and the individual fixed effect, rendering OLS and standard fixed-effects estimators inconsistent. GMM-based approaches developed by Arellano-Bond and Blundell-Bond resolve this problem.

Balanced or unbalanced panel data (cross-sections observed over multiple time periods)

Arellano, M., & Bond, S. (1991). Some tests of specification for panel data: Monte Carlo evidence and an application to employment equations. Review of Economic Studies, 58(2), 277–297.

Blundell, R., & Bond, S. (1998). Initial conditions and moment restrictions in dynamic panel data models. Journal of Econometrics, 87(1), 115–143.

arellano-bond-gmm-estimator panel-system-gmm panel-difference-gmm dynamic-panel-data-model panel-fixed-effects-model panel-random-effects-model


Panel EGARCH

Panel Exponential Generalized Autoregressive Conditional Heteroscedasticity Model

Panel EGARCH model
panel exponential GARCH
EGARCH for panel data
cross-sectional EGARCH

1991 (EGARCH); panel extensions widely used from 2000s

Daniel B. Nelson (EGARCH); panel extension by applied econometrics literature

Panel EGARCH extends Nelson's (1991) Exponential GARCH model to a panel setting, allowing conditional variance to evolve asymmetrically over time for each cross-sectional unit. The log specification ensures non-negative variance without parameter constraints, and the leverage term distinguishes whether negative shocks amplify volatility more than positive ones of equal magnitude.

Panel data with time-series volatility dynamics (financial returns, macro series)

Nelson, D. B. (1991). Conditional heteroskedasticity in asset returns: A new approach. Econometrica, 59(2), 347–370.

Tsay, R. S. (2010). Analysis of Financial Time Series (3rd ed.). Wiley.

panel-garch-model panel-arch-model panel-tgarch panel-dcc-garch egarch-model panel-var-model


Panel Engle-Granger Cointegration

panel cointegration test
panel EG cointegration
Pedroni cointegration test
residual-based panel cointegration

Pedroni (1999), extending Engle & Granger (1987)

The Panel Engle-Granger cointegration test extends the classic two-step Engle-Granger procedure to panel data, allowing researchers to detect long-run equilibrium relationships among integrated variables across multiple cross-sectional units simultaneously. Pedroni (1999) developed panel statistics that pool information across units while allowing heterogeneous short-run dynamics and individual-specific intercepts and trends.

Balanced or unbalanced panel data with integrated (I(1)) variables

Pedroni, P. (1999). Critical values for cointegration tests in heterogeneous panels with multiple regressors. Oxford Bulletin of Economics and Statistics, 61(S1), 653-670.

Engle, R. F., & Granger, C. W. J. (1987). Co-integration and error correction: Representation, estimation, and testing. Econometrica, 55(2), 251-276.

panel-johansen-cointegration engle-granger-cointegration-test johansen-cointegration-test panel-vecm panel-ardl-bounds-test panel-adf-unit-root-test


Panel Event Study in Education Research

Panel Data Event Study Design in Education Research

education event study
panel event-study design
education policy event study
school event study

1993 (general method); 2000s (education applications)

Jacobson, LaLonde & Sullivan (1993); widely adopted in education economics from 2000s onward

The panel event study is a causal-inference design that tracks outcomes for a panel of educational units — students, teachers, schools, or districts — across relative time periods around a well-defined event such as a policy change, school reform, or staffing transition. By estimating period-by-period treatment effects, it reveals not only whether an intervention mattered but also when effects appeared and how long they persisted, making it especially valued in education economics.

Balanced or unbalanced panel data with student, school, or district units observed across multiple periods

Jacobson, L. S., LaLonde, R. J., & Sullivan, D. G. (1993). Earnings Losses of Displaced Workers. American Economic Review, 83(4), 685-709.

Freyaldenhoven, S., Hansen, C., Pérez, J. P. M., & Shapiro, J. M. (2021). Visualization, Identification, and Estimation in the Linear Panel Event-Study Design. NBER Working Paper No. 29170.


Panel Event Study

event-study regression
dynamic DiD
relative-time regression
distributed-lag panel model

Formalized by Freyaldenhoven, Hansen, Perez-Orive & Shapiro (2021); widely applied in finance (Fama et al. 1969) and policy evaluation

A panel event study estimates the dynamic causal effect of a treatment or policy by regressing an outcome on a full set of relative-time indicators — one for each period before and after the event — while controlling for unit and time fixed effects. The resulting coefficient plot shows how the treated units diverged from untreated units at each point in calendar time relative to their treatment date, making both pre-treatment trend violations and post-treatment effect trajectories immediately visible.

Quasi-experimental / causal panel design

Balanced or unbalanced panel data with a clearly dated treatment event per unit

Freyaldenhoven, S., Hansen, C., Perez-Orive, J., & Shapiro, J. M. (2021). Visualization, Identification, and Estimation in the Linear Panel Event-Study Design. NBER Working Paper 29170. National Bureau of Economic Research.

Callaway, B., & Sant'Anna, P. H. C. (2021). Difference-in-Differences with Multiple Time Periods. Journal of Econometrics, 225(2), 200-230.

difference-in-differences event-study-design panel-fixed-effects staggered-difference-in-differences synthetic-control-method dynamic-difference-in-differences


Panel Fixed Effects Model

Panel Data Fixed Effects Regression Model

within estimator
FE model
within-group estimator
LSDV model

Mundlak (1978); classical treatment in Wooldridge (2010) and Baltagi (2021)

The panel fixed effects (FE) model controls for all time-invariant, unit-specific unobserved heterogeneity by absorbing it into individual intercepts. By sweeping out unit means through the within transformation, FE yields unbiased estimates of the effect of time-varying regressors even when omitted unit-level confounders are correlated with those regressors.

Balanced or unbalanced panel data (multiple units observed over multiple time periods)

Wooldridge, J. M. (2010). Econometric Analysis of Cross Section and Panel Data (2nd ed.). MIT Press.

Baltagi, B. H. (2021). Econometric Analysis of Panel Data (6th ed.). Springer.

random-effects-model panel-random-effects-model panel-hausman-test panel-ols difference-gmm fixed-effects-model


Panel Fixed Effects

fixed effects model
within estimator
panel fixed-effects regression
Panel Veri — Sabit Etkiler Modeli

Hsiao (textbook treatment); within transformation of panel data

The Panel Data Fixed Effects model estimates relationships from panel data (the same units observed over several time periods) while controlling for unit- and/or time-specific effects, supporting causal inference. It is developed as the within estimator in standard treatments such as Hsiao's Analysis of Panel Data (2014).

Hsiao, C. (2014). Analysis of Panel Data (3rd ed.). Cambridge University Press.

Wooldridge, J. M. (2019). Introductory Econometrics: A Modern Approach (7th ed.). Cengage Learning.

panel-random-effects ols-regression instrumental-variables difference-in-differences system-gmm


Panel GARCH model

Panel Generalized Autoregressive Conditional Heteroscedasticity Model

panel conditional heteroscedasticity model

1986 (GARCH); panel extension 1990s–2000s

Bollerslev (1986); extended to panel settings in subsequent literature

The Panel GARCH model extends Bollerslev's (1986) Generalized Autoregressive Conditional Heteroscedasticity framework to panel data, allowing conditional variance to evolve over time for each cross-sectional unit. It simultaneously captures unit-level heterogeneity and time-varying volatility clustering, making it the standard tool for modelling risk and uncertainty in multi-entity financial and macroeconomic panels.

Panel data (multiple cross-sectional units observed over time); returns or financial time series

Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31(3), 307–327.

Bauwens, L., Laurent, S., & Rombouts, J. V. K. (2006). Multivariate GARCH models: a survey. Journal of Applied Econometrics, 21(1), 79–109.

arch-model dcc-garch-model egarch-model tgarch-model panel-fixed-effects-model vector-autoregression


Panel Geary's C

Panel Data Geary's C Spatial Autocorrelation Statistic

Geary's C for panel data
spatial Geary C panel
panel spatial contiguity ratio
panel Geary contiguity statistic

R. C. Geary (1954); panel extension in spatial econometrics literature

Panel Geary's C extends the classic Geary contiguity ratio to panel datasets, measuring spatial autocorrelation across georeferenced units (regions, cities, countries) observed over multiple time periods. It detects whether neighboring units tend to have similar values, pooling or averaging evidence across the temporal dimension to yield more powerful inference than a single cross-section.

Panel data with georeferenced cross-sectional units

Geary, R. C. (1954). The contiguity ratio and statistical mapping. The Incorporated Statistician, 5(3), 115-145.

Elhorst, J. P. (2014). Spatial Econometrics: From Cross-Sectional Data to Spatial Panels. Springer.

panel-morans-i gearys-c morans-i local-gearys-c panel-spatial-lag-model panel-spatial-autocorrelation


geographically weighted panel regression

Fotheringham, Brunsdon & Charlton (foundational GWR); panel extension developed in spatial econometrics literature

Panel Geographically Weighted Regression (Panel GWR) extends the standard GWR framework to panel data, allowing regression coefficients to vary both across geographic locations and over time. It captures spatially non-stationary relationships in longitudinal or repeated-measures spatial datasets, combining local spatial estimation with panel-data controls for unit-specific heterogeneity.

Local spatial regression with panel structure

Georeferenced panel data (multiple observations per location over time)

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

Yu, H., Fotheringham, A. S., Li, Z., Oshan, T., Kang, W., & Wolf, L. J. (2020). Inference in Multiscale Geographically Weighted Regression. Geographical Analysis, 52(1), 87–106.


Panel GLS

Generalized Least Squares for panel data

Aitken (1935); extended to panel data by Baltagi and others

Panel GLS is a regression method for longitudinal data that explicitly models the non-spherical error structure — heteroscedasticity across units and serial correlation within units — to recover efficient coefficient estimates. Unlike OLS, it weights observations by the inverse of the error covariance matrix, yielding the Best Linear Unbiased Estimator when the error structure is correctly specified.

Balanced or unbalanced panel (cross-sectional units observed over time)

panel-ols panel-wls panel-fixed-effects-model panel-random-effects-model feasible-gls random-effects-model


Panel Granger Causality

panel causality test
Dumitrescu-Hurlin test
heterogeneous panel causality
panel Granger test

Holtz-Eakin, Newey & Rosen (1988); Dumitrescu & Hurlin (2012)

The Panel Granger Causality test examines whether past values of one variable help predict another variable across multiple cross-sectional units observed over time. It extends the classical Granger causality framework to panel data, accounting for cross-sectional heterogeneity and enabling more powerful inference by pooling information across units.

Panel data (balanced or unbalanced, stationary or pre-filtered)

Dumitrescu, E.-I., & Hurlin, C. (2012). Testing for Granger non-causality in heterogeneous panels. Economic Modelling, 29(4), 1450–1460.

Holtz-Eakin, D., Newey, W., & Rosen, H. S. (1988). Estimating vector autoregressions with panel data. Econometrica, 56(6), 1371–1395.

granger-causality-test toda-yamamoto-causality-test panel-var-model panel-vecm panel-ardl-bounds-test panel-johansen-cointegration


Panel Hausman Test

Hausman Specification Test for Panel Data

Hausman endogeneity test
Wu-Hausman test
fixed-vs-random effects test
Hausman chi-squared test

The Hausman specification test for panel data determines whether individual-specific effects are correlated with the regressors — a correlation that would make the random effects estimator inconsistent. A statistically significant result favours the fixed effects model; a non-significant result supports the more efficient random effects model.

Hausman, J. A. (1978). Specification tests in econometrics. Econometrica, 46(6), 1251–1271.

panel-fixed-effects-model panel-random-effects-model fixed-effects-model random-effects-model panel-data-analysis panel-ols


Panel Hot Spot Analysis

repeated cross-sectional hot spot analysis

1992 (Gi* statistic); 2004 (longitudinal/panel extension)

Weisburd et al. (longitudinal application); Getis & Ord (foundational Gi* statistic)

Panel Hot Spot Analysis applies hot spot detection — typically via the Getis-Ord Gi* statistic — repeatedly across multiple time periods on the same spatial units, enabling researchers to track where clusters of high or low values persist, emerge, or dissolve over time. It bridges cross-sectional spatial statistics with longitudinal panel methods.

Panel spatial data (repeated cross-sections of georeferenced areal or point data)

Weisburd, D., Bushway, S., Lum, C., & Yang, S.-M. (2004). Trajectories of crime at places: A longitudinal study of street segments in the city of Seattle. Criminology, 42(2), 283-321.

Getis, A., & Ord, J. K. (1992). The analysis of spatial association by use of distance statistics. Geographical Analysis, 24(3), 189-206.

hot-spot-analysis local-getis-ord-gi-star space-time-hot-spot-analysis panel-spatial-lag-model kernel-density-estimation local-indicators-of-spatial-association


Panel Johansen Cointegration

panel Johansen test
Larsson-Lyhagen-Lothgren test
LLL panel cointegration
panel trace test

Larsson, Lyhagen & Lothgren (building on Johansen 1988/1991)

The Panel Johansen cointegration test extends Johansen's maximum-likelihood framework to panel data, allowing researchers to test whether multiple non-stationary variables share long-run equilibrium relationships across cross-sectional units. It pools the likelihood-ratio statistics from individual Johansen tests and compares the standardised average against a standard normal distribution, yielding greater power than single-country approaches.

Balanced or unbalanced panel; I(1) time series for multiple cross-sections

Larsson, R., Lyhagen, J., & Lothgren, M. (2001). Likelihood-based cointegration tests in heterogeneous panels. Econometrics Journal, 4(1), 109–142.

Johansen, S. (1991). Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregressive models. Econometrica, 59(6), 1551–1580.

johansen-cointegration-test panel-engle-granger-cointegration panel-vecm panel-granger-causality vector-error-correction-model panel-ardl-bounds-test


Panel Kernel Density Estimation

Panel KDE
longitudinal kernel density estimation
repeated-measures KDE
panel nonparametric density estimation

1962 (KDE); panel extension: 1990s–2000s

Parzen (1962); Silverman (1986); extended to panel contexts in spatial econometrics literature

Panel Kernel Density Estimation (Panel KDE) extends the standard kernel density estimator to panel (longitudinal) data, estimating smooth density surfaces for spatial or attribute variables observed across multiple units and time periods. It reveals how the distribution of a phenomenon shifts, concentrates, or disperses over time and across groups, making it a natural tool for tracking spatial patterns in repeated-measures or panel datasets.

Continuous or count spatial data observed across multiple units and time periods (panel structure)

Parzen, E. (1962). On estimation of a probability density function and mode. Annals of Mathematical Statistics, 33(3), 1065-1076.

Silverman, B. W. (1986). Density Estimation for Statistics and Data Analysis. Chapman and Hall, London.

kernel-density-estimation panel-spatial-regression panel-hot-spot-analysis space-time-kernel-density-estimation local-kernel-density-estimation panel-spatial-autocorrelation


Panel KPSS test

KPSS panel stationarity test
panel stationarity test
Hadri LM test
panel KPSS

Hadri (2000), extending Kwiatkowski, Phillips, Schmidt, and Shin (1992)

The Panel KPSS test, introduced by Hadri (2000), tests the null hypothesis that all series in a panel are stationary against the alternative that some or all contain a unit root. It extends the univariate KPSS framework to panel data by aggregating individual LM statistics, providing higher power than unit-root tests when most series are in fact stationary.

Balanced or unbalanced panel data (time series cross-section)

Hadri, K. (2000). Testing for stationarity in heterogeneous panel data. Econometrics Journal, 3(2), 148-161.

Kwiatkowski, D., Phillips, P. C. B., Schmidt, P., & Shin, Y. (1992). Testing the null of stationarity against the alternative of a unit root. Journal of Econometrics, 54(1-3), 159-178.

panel-adf-unit-root-test panel-pp-unit-root-test panel-zivot-andrews-test augmented-dickey-fuller-unit-root-test phillips-perron-unit-root-test panel-data-analysis


Panel Kriging

longitudinal kriging
repeated-measures kriging
spatio-temporal panel kriging
panel geostatistical interpolation

Cressie & Wikle (spatio-temporal kriging framework)

Panel Kriging is a geostatistical interpolation method that combines kriging's spatial prediction framework with a panel (longitudinal) data structure. It estimates unknown values at unobserved locations and times by borrowing strength from repeated spatial observations across multiple time periods, accounting for both spatial dependence and temporal autocorrelation simultaneously.

Panel (repeated spatial observations over time)

Cressie, N. A. C. (1993). Statistics for Spatial Data (revised ed.). Wiley.

Cressie, N., & Wikle, C. K. (2011). Statistics for Spatio-Temporal Data. Wiley.

ordinary-kriging space-time-kriging panel-spatial-regression geographically-weighted-regression spatial-autocorrelation kernel-density-estimation


Panel KSS

Kwiatkowski, Phillips, Schmidt, and Shin (panel version by Hadri)

The Panel KSS test reverses the null hypothesis of unit-root tests: it tests whether variables are stationary (stationarity is the null) versus nonstationary (unit root is the alternative). Introduced by Kwiatkowski et al. (1992) and extended to panels by Hadri (2000), this complementary approach provides robustness when combined with unit-root tests like Panel DF-GLS. Using both tests together reduces the risk of erroneous conclusions about variable persistence.

Kwiatkowski, D., Phillips, P. C., Schmidt, P., & Shin, Y. (1992). Testing the null hypothesis of stationarity against the alternative of a unit root. Journal of Econometrics, 54(1-3), 159-178.

Hadri, K. (2000). Testing for stationarity in heterogeneous panel data. Econometric Reviews, 19(4), 367-397.


Panel LISA
spatiotemporal LISA
panel local spatial autocorrelation
LISA panel extension

1995 (LISA); panel extension 2000s–2010s

Anselin (1995), panel extension developed through spatial econometrics literature

Panel Local Indicators of Spatial Association extends Anselin's LISA statistics — most commonly Local Moran's I — to panel datasets, identifying spatial clusters and outliers at each location across multiple time periods. By applying local autocorrelation measures repeatedly over time, researchers can detect whether spatial concentration patterns emerge, persist, or dissolve, giving a richer spatiotemporal picture than a single cross-section allows.

Panel data with spatial coordinates (georeferenced observations repeated over multiple time periods)

Anselin, L. (1995). Local indicators of spatial association — LISA. Geographical Analysis, 27(2), 93–115.

Millo, G., & Piras, G. (2012). splm: Spatial panel data models in R. Journal of Statistical Software, 47(1), 1–38.


Panel Multiscale Geographically Weighted Regression

panel spatially varying coefficient model

Fotheringham, Yang & Kang (MGWR base); panel extension developed in spatial econometrics literature

Panel MGWR extends Multiscale Geographically Weighted Regression to repeated-observations (panel) data, allowing each predictor to operate at its own spatial bandwidth while controlling for unit-specific or time-specific fixed effects. It is used when both spatial heterogeneity and temporal structure matter simultaneously.

Spatially varying coefficient panel regression

Georeferenced panel data (repeated cross-sectional or longitudinal with spatial coordinates)

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

Yu, H., Fotheringham, A. S., Li, Z., Oshan, T., Kang, W., & Wolf, L. J. (2020). Inference in Multiscale Geographically Weighted Regression. Geographical Analysis, 52(1), 87-106.


Panel NARDL

Panel Nonlinear Autoregressive Distributed Lag Model

Panel Nonlinear ARDL
panel asymmetric ARDL
panel NARDL bounds test
nonlinear panel cointegration model

Shin, Yu & Greenwood-Nimmo (2014), extended to panel settings by subsequent authors

Panel NARDL extends the time-series NARDL framework of Shin, Yu and Greenwood-Nimmo (2014) to a panel data setting, allowing researchers to detect asymmetric long-run and short-run relationships between variables across multiple cross-sections simultaneously. By decomposing the regressor into positive and negative partial sums, the model tests whether increases and decreases in an explanatory variable have different effects on the outcome.

Balanced or unbalanced panel (time-series cross-section)

Shin, Y., Yu, B., & Greenwood-Nimmo, M. (2014). Modelling asymmetric cointegration and dynamic multipliers in a nonlinear ARDL framework. In R. C. Sickles & W. C. Horrace (Eds.), Festschrift in Honor of Peter Schmidt (pp. 281–314). Springer.

Pesaran, M. H., Shin, Y., & Smith, R. J. (2001). Bounds testing approaches to the analysis of level relationships. Journal of Applied Econometrics, 16(3), 289–326.

ardl-bounds-test nardl panel-cointegration panel-vecm panel-fixed-effects panel-pmg-estimator


Panel Network-Based Spatial Analysis

Panel Data Network-Based Spatial Analysis

panel spatial network analysis
longitudinal network spatial analysis
panel network spatial econometrics
PNBSA

Developed from LeSage & Pace spatial econometrics and Elhorst panel spatial frameworks

Panel Network-Based Spatial Analysis extends standard spatial econometric models to repeated-measures (panel) data by representing spatial dependence through network connectivity rather than simple geographic proximity. It captures how units connected in a network influence each other's outcomes over time, while controlling for unit-level and time-level fixed effects.

Georeferenced panel data with network connectivity structure

LeSage, J. P., & Pace, R. K. (2009). Introduction to Spatial Econometrics. CRC Press / Taylor & Francis.

Elhorst, J. P. (2014). Spatial Econometrics: From Cross-Sectional Data to Spatial Panels. Springer.


Panel OLS

Panel Data Ordinary Least Squares Regression

pooled OLS
pooled ordinary least squares
panel least squares
POLS

Classical least squares applied to pooled panels; foundational treatment in Hsiao (2003) and Wooldridge (2010)

Panel OLS — also called Pooled OLS — applies the classical ordinary least squares estimator to panel data by stacking all cross-sectional units and time periods into a single sample. It estimates one common set of slope coefficients under the assumption that the intercept and slopes are homogeneous across units and time.

Balanced or unbalanced panel (cross-sectional units observed over multiple time periods)

Wooldridge, J. M. (2010). Econometric Analysis of Cross Section and Panel Data (2nd ed.). MIT Press.

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

fixed-effects-model random-effects-model panel-gls panel-wls panel-hausman-test ols-regression


Panel Ordinary Kriging

ordinary kriging for panel data
longitudinal ordinary kriging
repeated-measures spatial kriging
panel geostatistical interpolation

1963 (Ordinary Kriging origin); panel extensions formalized in 1990s–2000s

Extension of Ordinary Kriging (Matheron, 1963) to panel/longitudinal spatial settings

Panel Ordinary Kriging extends the classical geostatistical interpolation method — Ordinary Kriging — to panel (longitudinal) datasets where the same set of spatial locations is observed repeatedly over multiple time periods. It produces optimal linear unbiased predictions at unsampled locations for each time slice, accounting for spatial dependence while leveraging the temporal structure of the repeated observations.

Repeated georeferenced measurements across locations and time periods

Cressie, N. A. C. (1993). Statistics for Spatial Data (revised ed.). Wiley-Interscience.

Matheron, G. (1963). Principles of geostatistics. Economic Geology, 58(8), 1246-1266.

ordinary-kriging panel-spatial-regression panel-kriging universal-kriging co-kriging spatial-autocorrelation


Panel PP unit root test

Panel PP test
Phillips-Perron panel unit root
Im-Pesaran-Shin PP panel test
panel nonparametric unit root test

1988 (original PP); panel adaptation widely established by 2003

Phillips & Perron (1988); panel extension by Im, Pesaran & Shin (2003)

The Panel PP unit root test extends the nonparametric Phillips-Perron correction for serial correlation to a multi-individual panel setting. It tests the null hypothesis that all cross-sectional units contain a unit root, using a pooled or averaged PP-type statistic that is robust to heteroscedastic and serially correlated errors without requiring explicit lag selection.

Balanced or unbalanced panel (cross-sections × time periods)

Im, K. S., Pesaran, M. H., & Shin, Y. (2003). Testing for unit roots in heterogeneous panels. Journal of Econometrics, 115(1), 53-74.

Phillips, P. C. B., & Perron, P. (1988). Testing for a unit root in time series regression. Biometrika, 75(2), 335-346.

panel-adf-unit-root-test phillips-perron-unit-root-test panel-kpss-test augmented-dickey-fuller-unit-root-test panel-engle-granger-cointegration panel-ardl-bounds-test


Panel Quantile-on-Quantile Regression

Panel QQ regression
panel QQ approach
panel quantile-on-quantile approach
PQQ regression

2015 (QQ); panel applications from ~2018

Sim and Zhou (cross-section QQ); panel extension in applied energy/finance econometrics

Panel quantile-on-quantile (QQ) regression jointly maps any quantile of the outcome distribution onto any quantile of the predictor distribution across multiple cross-sectional units observed over time. It generalises Sim and Zhou's (2015) cross-sectional QQ framework to a panel setting, revealing a full dependence surface rather than a single average effect, while accounting for individual heterogeneity through fixed or random effects correction.

Sim, N., & Zhou, H. (2015). Oil prices, US stock return, and the dependence between their quantiles. Journal of Banking and Finance, 55, 1-8.

Koenker, R., & Bassett, G. (1978). Regression quantiles. Econometrica, 46(1), 33-50.

quantile-on-quantile-regression panel-fixed-effects-model panel-random-effects-model panel-ols panel-gls panel-granger-causality


Panel Random Effects Model

random effects estimator
RE model
GLS random effects
error components model

The panel random effects (RE) model treats individual-specific effects as random draws from a population distribution rather than fixed constants, enabling efficient estimation by generalised least squares and allowing inference about time-invariant regressors that are swept away in fixed effects estimation.

Balestra, P., & Nerlove, M. (1966). Pooling cross section and time series data in the estimation of a dynamic model: The demand for natural gas. Econometrica, 34(3), 585–612.

fixed-effects-model panel-hausman-test panel-ols panel-gls panel-data-analysis random-effects-model


Random Effects Model

random effects panel model
RE estimator
GLS random effects
Panel Veri — Rassal Etkiler Modeli

Baltagi (textbook treatment); classical random-effects panel estimator

The Random Effects model is a panel-data regression that treats unobserved individual heterogeneity as a random component drawn from a common distribution, rather than a separate parameter for each unit. It is a standard estimator in panel econometrics, developed in textbook treatments such as Baltagi's Econometric Analysis of Panel Data (2021).

Feasible generalised least squares (FGLS)

Baltagi, B. H. (2021). Econometric Analysis of Panel Data (6th ed.). Springer.

panel-fixed-effects ols-regression instrumental-variables difference-in-differences ridge-regression


Panel Research

panel study
panel survey
longitudinal panel
repeated-measures panel

1970s-1980s (econometric formalization); earlier social survey use from 1940s

Social science and econometric traditions; systematized by Cheng Hsiao and others from the 1970s-1980s

Panel research is a quantitative longitudinal design in which the same individuals, organizations, or other units are measured repeatedly across two or more time points. Unlike cross-sectional surveys that capture a single snapshot, a panel tracks change within units, enabling researchers to separate genuine within-unit change from between-unit differences and to model causal dynamics over time.

Repeated quantitative measurements on the same units over time (numeric, ordinal, categorical)

longitudinal-research cohort-research cross-sectional-research survey-research trend-research repeated-measures-design


Panel SARIMA model

Panel Seasonal Autoregressive Integrated Moving Average Model

Panel SARIMA
Seasonal ARIMA panel model
SARIMA panel estimation
grouped seasonal time series model

Box & Jenkins (SARIMA foundation); panel extension via mean-group and pooled estimators

The Panel SARIMA model applies the Seasonal Autoregressive Integrated Moving Average (SARIMA) framework to panel data, fitting individual or pooled seasonal time series models across multiple cross-sectional units. It captures both non-seasonal and seasonal autocorrelation, trends, and periodicity, making it suitable for datasets where multiple entities share a common seasonal structure over time.

Balanced or unbalanced panel with seasonal time series per unit

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

Pesaran, M. H., & Smith, R. (1995). Estimating long-run relationships from dynamic heterogeneous panels. Journal of Econometrics, 68(1), 79-113.

sarima-model panel-arima-model panel-arma-model panel-var-model arima-model panel-data-analysis


Panel Simple Linear Regression

panel SLR
longitudinal simple regression
two-way panel simple regression
fixed-effects simple linear regression

Hsiao (1986); Baltagi (seminal textbook treatments)

Panel simple linear regression models a continuous outcome as a linear function of a single predictor using data that track the same entities (individuals, firms, countries) across multiple time periods. It separates within-entity variation from between-entity variation, enabling control for unobserved time-invariant characteristics that would confound a plain cross-sectional regression.

Continuous outcome, one continuous predictor, repeated observations on entities over time

panel-multiple-linear-regression ols-regression panel-fixed-effects panel-random-effects mixed-effects-model hierarchical-linear-model


Panel Smooth Transition Regression

Panel Smooth Transition Regression Model

Panel Smooth Transition Regression (PSTR) models nonlinear panel relationships where coefficients transition smoothly (rather than abruptly) between regimes as a transition variable crosses thresholds. Introduced by Gonzalez et al. (2005), it extends univariate smooth-transition autoregression (STAR) models to panels, capturing gradual shifts in economic behavior. This approach is realistic when adjustment costs cause smooth (not sudden) regime changes.

Gonzalez, A., Terasvirta, T., & van Dijk, D. (2005). Panel smooth transition regression models. Research Paper, Melbourne Institute of Applied Economic and Social Research.

Terasvirta, T. (1994). Specification, estimation, and evaluation of smooth transition autoregressive models. Journal of the American Statistical Association, 89(425), 208-218.


Panel Spatial Autocorrelation

Panel Data Spatial Autocorrelation Analysis

spatial autocorrelation in panel data
panel spatial dependence
spatio-temporal autocorrelation
cross-sectional dependence in panels

Panel Spatial Autocorrelation measures whether observations that are geographically close also tend to have similar values across repeated time periods. It extends classic cross-sectional spatial autocorrelation statistics such as Moran's I to panel data, enabling researchers to detect spatial dependence consistently over time and to diagnose whether a panel regression model requires a spatial component.

Panel data with geographic coordinates or spatial weights

Anselin, L. (2013). Spatial Econometrics: Methods and Models. Springer Netherlands. (Originally published 1988.)

Elhorst, J. P. (2014). Spatial Econometrics: From Cross-Sectional Data to Spatial Panels. Springer Berlin Heidelberg.

morans-i local-spatial-autocorrelation spatial-autocorrelation panel-spatial-lag-model panel-spatial-error-model geographically-weighted-regression


Panel Spatial Durbin Model

SDM panel
spatial Durbin panel model
panel SDM
PSDM

LeSage & Pace (2009); panel extension by Elhorst (2010)

The Panel Spatial Durbin Model (PSDM) extends the cross-sectional Spatial Durbin Model to panel data, capturing both spatial lag dependence in the outcome and spatial spillovers from neighbouring units' explanatory variables across multiple time periods. It simultaneously accounts for unobserved unit-specific and time-specific heterogeneity, making it one of the most comprehensive spatial panel specifications available.

Georeferenced panel (cross-section × time)

Elhorst, J. P. (2014). Spatial Econometrics: From Cross-Sectional Data to Spatial Panels. Springer.

LeSage, J. P., & Pace, R. K. (2009). Introduction to Spatial Econometrics. CRC Press/Taylor & Francis.

spatial-durbin-model panel-spatial-lag-model panel-spatial-error-model spatial-lag-model geographically-weighted-regression panel-spatial-regression


Panel Spatial Error Model

panel spatial autocorrelation error model

Anselin (1988); extended to panels by Elhorst (2003, 2014)

The Panel Spatial Error Model (panel SEM) extends the classical spatial error model to panel data, allowing spatial dependence to enter through the error term across cross-sectional units over multiple time periods. It accounts for spatially correlated omitted variables without imposing a substantive spatial spillover in the outcome itself.

Panel data with georeferenced cross-sectional units (areal or point data)

Anselin, L. (1988). Spatial Econometrics: Methods and Models. Kluwer Academic Publishers.

spatial-error-model panel-spatial-lag-model panel-spatial-durbin-model spatial-lag-model spatial-panel-model geographically-weighted-regression


Panel Spatial Regression

spatial panel model
panel spatial econometrics
spatial panel data regression
PSR

Anselin, Elhorst, and colleagues in spatial econometrics

Panel Spatial Regression extends standard panel data models by explicitly accounting for spatial dependence among cross-sectional units observed over time. It combines the temporal control of panel fixed or random effects with a spatial weights matrix that encodes geographic or network proximity, yielding unbiased and efficient estimates when observations are spatially correlated across units.

Georeferenced panel data (multiple units observed over time)

Anselin, L., Le Gallo, J., & Jayet, H. (2008). Spatial Panel Econometrics. In: The Econometrics of Panel Data (pp. 625-660). Springer, Berlin, Heidelberg.


Panel SVAR model

Panel Structural Vector Autoregression Model

Panel SVAR
PSVAR
Structural Panel VAR
Panel Structural VAR

2004 (panel extension); 1986 (SVAR origins)

Canova & Ciccarelli; Bernanke (SVAR identification)

The Panel SVAR model extends the Structural VAR framework to panel data, jointly modelling multiple endogenous time-series variables across several cross-sectional units (e.g., countries or firms). Structural restrictions — short-run, long-run, or sign restrictions — are imposed on the contemporaneous relationships among variables to identify economically meaningful causal shocks and trace their propagation across units and time.

Multivariate time-series model with structural identification

Balanced or unbalanced panel data; multiple variables observed across units and time

Canova, F., & Ciccarelli, M. (2004). Forecasting and turning point predictions in a Bayesian panel VAR model. Journal of Econometrics, 120(2), 327-359.

Kilian, L., & Lutkepohl, H. (2017). Structural Vector Autoregressive Analysis. Cambridge University Press.

structural-var panel-var-model panel-vecm vector-autoregression panel-fixed-effects-model vector-error-correction-model


Panel System GMM

Panel System Generalized Method of Moments Estimator

System GMM
Blundell-Bond estimator
SYS-GMM
two-step System GMM

Blundell & Bond (1998); Arellano & Bover (1995)

Panel System GMM is a two-equation GMM estimator for dynamic panel data that stacks the differenced equation (using lagged levels as instruments) with the levels equation (using lagged differences as instruments). Developed by Blundell and Bond (1998) on the foundation of Arellano and Bover (1995), it is the preferred tool when the lagged dependent variable is highly persistent or individual effects are large.

Panel data (multiple units observed over multiple time periods)

Blundell, R., & Bond, S. (1998). Initial conditions and moment restrictions in dynamic panel data models. Journal of Econometrics, 87(1), 115–143.

Arellano, M., & Bover, O. (1995). Another look at the instrumental variable estimation of error-components models. Journal of Econometrics, 68(1), 29–51.

arellano-bond-gmm-estimator difference-gmm panel-dynamic-panel-data-model panel-fixed-effects-model panel-random-effects-model panel-arellano-bond-gmm


Panel TGARCH

Panel Threshold Generalized Autoregressive Conditional Heteroscedasticity

Panel GJR-GARCH
Panel Asymmetric GARCH
Panel Threshold GARCH
TGARCH panel model

1993–1994 (panel extension: 2000s onward)

Glosten, Jagannathan & Runkle (1993); Zakoian (1994); extended to panel settings by subsequent applied finance literature

Panel TGARCH extends the Threshold GARCH (GJR-GARCH) model to panel data, allowing each cross-sectional unit to exhibit asymmetric volatility responses — where negative shocks generate larger variance increases than positive shocks of the same magnitude — while exploiting the cross-sectional dimension to obtain more efficient parameter estimates.

Balanced or unbalanced panel (multiple cross-sections, time series)

Glosten, L. R., Jagannathan, R., & Runkle, D. E. (1993). On the relation between the expected value and the volatility of the nominal excess return on stocks. Journal of Finance, 48(5), 1779–1801.

Zakoian, J.-M. (1994). Threshold heteroskedastic models. Journal of Economic Dynamics and Control, 18(5), 931–955.

panel-garch panel-egarch gjr-garch panel-arch panel-fixed-effects dcc-garch


Panel Toda-Yamamoto Causality

Panel Toda-Yamamoto Granger Non-Causality Test

Panel TY causality test
Toda-Yamamoto panel causality
panel modified Wald causality test
panel MWALD causality

Toda & Yamamoto (1995); extended to panel settings by Konya (2006) and others

The Panel Toda-Yamamoto (PTY) causality test extends the Toda-Yamamoto modified Wald approach to panel data, allowing researchers to test Granger non-causality across multiple cross-sectional units without requiring pre-testing for cointegration or imposing a common causality direction on all units.

Causality test (non-causality hypothesis)

Toda, H. Y., & Yamamoto, T. (1995). Statistical inference in vector autoregressions with possibly integrated processes. Journal of Econometrics, 66(1-2), 225-250.

Konya, L. (2006). Exports and growth: Granger causality analysis on OECD countries with a panel data approach. Economic Modelling, 23(6), 978-992.

panel-granger-causality toda-yamamoto-causality-test panel-var-model panel-vecm panel-johansen-cointegration granger-causality-test


Panel Universal Kriging

UK panel interpolation
panel UK
universal kriging for panel data
longitudinal universal kriging

1963 (base method); panel extension: 1990s–2000s

Matheron, G.; extended to panel settings by geostatistical literature

Panel Universal Kriging extends Universal Kriging to data structures with repeated spatial observations over time (panel or longitudinal format). It simultaneously estimates a deterministic trend surface — incorporating covariates that vary across both space and time — and a stochastic spatially correlated residual, pooling information across all time periods to improve prediction accuracy and parameter stability.

Repeated cross-sectional or panel spatial data with a continuous spatial field

Matheron, G. (1963). Principles of geostatistics. Economic Geology, 58(8), 1246–1266.

Cressie, N. A. C. (1993). Statistics for Spatial Data (Revised ed.). Wiley-Interscience.

universal-kriging ordinary-kriging panel-ordinary-kriging panel-co-kriging panel-spatial-regression space-time-kriging


Panel VAR

PVAR
panel vector autoregression
Panel VAR (PVAR)

Panel VAR extends the vector autoregression model to panel data, modelling the dynamic interactions among several variables while controlling for cross-unit heterogeneity through fixed effects. It was introduced by Holtz-Eakin, Newey and Rosen in 1988 and produces impulse-response functions and variance decompositions at the panel level.

System GMM on forward orthogonal (Helmert) deviations

Holtz-Eakin, D., Newey, W. & Rosen, H. S. (1988). Estimating Vector Autoregressions with Panel Data. Econometrica, 56(6), 1371-1395.

Abrigo, M. R. M. & Love, I. (2016). Estimation of Panel Vector Autoregression in Stata. Stata Journal, 16(3), 778-804.

panel-fixed-effects var-model vecm dynamic-panel-gmm ols-regression


Panel VARX

Panel Vector Autoregression with Exogenous Variables

Panel VARX extends vector autoregression to heterogeneous panels with exogenous variables, enabling simultaneous modeling of multiple endogenous variables alongside observed external factors across many units. Introduced by Holtz-Eakin et al. (1988) and advanced by Canova and Ciccarelli (2013), it captures dynamic relationships within units while allowing parameters to vary across units. This framework is essential for macroeconomic panels and understanding cross-unit heterogeneity in responses to common shocks.

Canova, F., & Ciccarelli, M. (2013). Panel vector autoregressive models: A survey. Advances in Econometrics, 32, 205-246.

Holtz-Eakin, D., Newey, W., & Rosen, H. S. (1988). Estimating vector autoregressions with panel data. Econometrica, 56(6), 1371-1395.


Panel VECM

Panel VECM
panel vector error correction model
PVECM
panel cointegrating VAR

Engle & Granger (1987) for VECM; Holtz-Eakin, Newey & Rosen (1988) for panel VAR extension

Panel VECM combines vector error correction modelling with panel data, simultaneously capturing the long-run cointegrating equilibrium among multiple I(1) variables and their short-run adjustment dynamics across multiple cross-sectional units. It is the standard framework when panel variables share at least one common stochastic trend.

Balanced or unbalanced panel; I(1) time series across multiple cross-sectional units

Engle, R. F., & Granger, C. W. J. (1987). Co-integration and error correction: Representation, estimation, and testing. Econometrica, 55(2), 251–276.

Holtz-Eakin, D., Newey, W., & Rosen, H. S. (1988). Estimating vector autoregressions with panel data. Econometrica, 56(6), 1371–1395.

vector-error-correction-model panel-var-model panel-johansen-cointegration panel-engle-granger-cointegration panel-granger-causality panel-arellano-bond-gmm


Panel Zivot-Andrews test

Panel Zivot-Andrews Structural Break Unit Root Test

panel ZA test
panel structural break unit root test
Zivot-Andrews panel unit root test
panel endogenous break unit root test

Zivot & Andrews (1992); extended to panel settings by subsequent literature

The Panel Zivot-Andrews test extends the single-series Zivot-Andrews (1992) structural break unit root test to panel data, allowing each cross-sectional unit to have its own endogenously determined break date. It tests the null of a unit root against the alternative of stationarity with a one-time structural break, accounting for regime shifts that bias standard panel unit root tests toward false non-rejection.

Unit root test with endogenous structural break

Balanced or unbalanced panel time series (continuous numeric)

Zivot, E., & Andrews, D. W. K. (1992). Further evidence on the great crash, the oil-price shock, and the unit-root hypothesis. Journal of Business & Economic Statistics, 10(3), 251–270.

Pedroni, P. (1999). Critical values for cointegration tests in heterogeneous panels with multiple regressors. Oxford Bulletin of Economics and Statistics, 61(S1), 653–670.

zivot-andrews-structural-break-test panel-adf-unit-root-test panel-pp-unit-root-test panel-kpss-test augmented-dickey-fuller-unit-root-test panel-engle-granger-cointegration


Panic Disorder Severity Scale

Katherine M. Shear, Timothy A. Brown, David H. Barlow, and collaborators

The Panic Disorder Severity Scale (PDSS) is a brief 7-item clinician-administered scale designed to measure the severity of panic disorder symptoms, including panic attack frequency, distress, anxiety anticipation, agoraphobic avoidance, and interoceptive fear. Developed by Shear, Brown, Barlow, and collaborators in 1997, the PDSS has become the standard assessment tool for panic disorder severity in clinical trials, research, and routine practice.

Shear, M. K., Brown, T. A., Barlow, D. H., Money, R., Sholomskas, D. E., Woods, S. W., ... & Papp, L. A. (1997). Multicenter collaborative panic disorder severity scale. Depression and Anxiety, 5(4), 189-196.


PANIC

PANIC: Panel Analysis of Non-stationarity in Idiosyncratic and Common Components

PANIC (Panel Analysis of Non-stationarity in Idiosyncratic and Common Components) is a second-generation panel unit root test introduced by Bai and Ng (2004). It decomposes each panel series into common factors and idiosyncratic components, then tests for unit roots in each part separately, making it robust to cross-sectional dependence — a critical limitation of first-generation tests such as IPS or LLC.

Common factors + idiosyncratic components

Bai, J., & Ng, S. (2004). A PANIC attack on unit roots and cointegration. Econometrica, 72(4), 1127–1177.


Positive and Negative Syndrome Scale

Positive and Negative Syndrome Scale (PANSS)

The PANSS is a 30-item clinician-administered scale designed to measure the presence and severity of positive symptoms (delusions, hallucinations, disorganization), negative symptoms (affective flattening, alogia, avolition), and general psychopathology in schizophrenia and related psychotic disorders. Developed by Kay, Fiszbein, and Opler in 1987, the PANSS has become the standard rating scale in schizophrenia research, antipsychotic medication trials, and clinical monitoring. It provides comprehensive assessment across three symptom domains and yields a total score reflecting overall disease severity.

Kay, S. R., Fiszbein, A., & Opler, L. A. (1987). The positive and negative syndrome scale (PANSS) for schizophrenia. Schizophrenia Bulletin, 13(2), 261–276.

Opler, L. A., Kay, S. R., Rosado, V., & Lindenmayer, J. P. (1992). Structured Clinical Interview for the Positive and Negative Syndrome Scale. North Tonawanda, NY: Multi-Health Systems.

Crippa, J. A., Zuardi, A. W., Garolano, N. L., Impastato, B., Borduqui, T., Guimarães, F. S., ... & Dursun, S. M. (2009). Effects of cannabidiol (CBD) on regional cerebral blood flow. Neuropsychobiology, 58(1), 1–7.


PAQLQ

Pediatric Asthma Quality of Life Questionnaire

The PAQLQ is a 23-item self-report instrument developed by Juniper et al. in 1996 to measure quality of life in children aged 7–17 years with asthma. It assesses how asthma and its treatment affect daily functioning, emotions, and activity levels. The instrument has become the gold standard for evaluating asthma-specific health-related quality of life in pediatric populations.

Child self-report; parent version available

Juniper, E. F., Guyatt, G. H., Feeny, D. H., Ferrie, P. J., Griffith, L. E., & Townsend, M. (1996). Measuring quality of life in children with asthma. Quality of Life Research, 5(1), 35-46.

Juniper, E. F., Guyatt, G. H., Feeny, D. H., Griffith, L. E., & Ferrie, P. J. (2003). Minimum skills required for interviewers administering therapeutic guidelines. Journal of Asthma, 40(5), 573-581.

pedsql-diabetes qolce pedsql-cardiac pedsql-cancer


Parametric Bootstrap

parametrik bootstrap
model-based bootstrap
parametric resampling

The parametric bootstrap is a resampling method that estimates standard errors and confidence intervals by drawing repeated samples from a parametric model that has been fitted to the data. Developed in the bootstrap literature of Efron and Tibshirani (1993) and Davison and Hinkley (1997), it replaces analytic derivations for non-normal distributions and complex statistics.

Simulation from a fitted parametric model

Efron, B. & Tibshirani, R. J. (1993). An Introduction to the Bootstrap. CRC Press.

Davison, A. C. & Hinkley, D. V. (1997). Bootstrap Methods and Their Application. Cambridge University Press.

bootstrap-inference bca-bootstrap wild-bootstrap bayesian-bootstrap permutation-test


Paraphrase Detection

Parafroz Tespiti (Paraphrase Detection)
paraphrase identification
semantic equivalence detection

Paraphrase detection is a natural-language-processing task that decides whether two sentences expressed in different wordings carry the same meaning. The task and its benchmark resources were established by Dolan and Brockett (2005), and it underpins plagiarism detection, question matching, and data deduplication.

Semantic similarity / embedding-based / dependency-feature

Output: Paraphrase / not-paraphrase label per sentence pair

Dolan, W. B. & Brockett, C. (2005). Automatically Constructing a Corpus of Sentential Paraphrases. Proceedings of the Third International Workshop on Paraphrasing (IWP).

Wan, S., Dras, M., Dale, R. & Paris, C. (2006). Using Dependency-Based Features to Take the Para-farce Out of Paraphrase. Proceedings of the Australasian Language Technology Workshop (ALTA).

textual-entailment sentiment-analysis bert-embeddings text-classification


Paraphrasing Plagiarism

Paraphrasing Plagiarism: Inadequate Rewording Without Citation

insufficient paraphrase
close paraphrase
lazy paraphrasing

Academic integrity framework (modern definition)

Paraphrasing plagiarism occurs when an author rewrites another's ideas in different words but does not cite the source. Unlike verbatim plagiarism (copying word-for-word), paraphrasing plagiarism involves changing vocabulary and sentence structure while retaining the original argument, logic, or conceptual content without attribution. It is harder to detect than direct copying but is still a clear violation of academic integrity.

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.

Hirsch, L. R. (2013). Recognizing plagiarism: A guide for academic professionals. Teaching Professor Blog.

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 mosaic-plagiarism similarity-vs-plagiarism idea-plagiarism


Parasitological Examination

Systematic Parasitological Examination in Veterinary Diagnostics

parasite screening
fecal examination
parasitism diagnosis

Parasitological examination is a systematic laboratory diagnostic process for detecting and identifying parasites and parasitic infections in animals. Foundational to veterinary medicine since the 1800s and formalized through modern standard operating procedures, it relies on morphological identification of eggs, larvae, oocysts, or adult parasites in feces, blood, tissue, or other body specimens to establish parasitic diagnoses and guide therapeutic and preventive decisions.

Bowman, D. D. (2009). Georgis' Parasitology for Veterinarians (9th ed.). St. Louis, MO: Elsevier Saunders.

Foreyt, W. J. (2001). Veterinary Parasitology: Reference Manual (5th ed.). Ames, IA: Iowa State University Press.

Soulsby, E. J. L. (1982). Helminths, Arthropods, and Protozoa of Domesticated Animals (7th ed.). London: Bailliere Tindall.


Parent-Child Relationship Inventory

The Parent-Child Relationship Inventory (PCRI) is a 78-item (or 35-item short form) parent self-report measure of parenting attitudes, behaviors, and relationship quality with their child ages 3–15 years. Developed by Abraham Gerard in 1994, the PCRI assesses six dimensions of parenting: Parental Support, Satisfaction with Parenting, Involvement, Communication, Limit Setting, and Autonomy Granting. It is used in clinical, developmental, and research settings to evaluate parenting strengths and challenges, guide parenting interventions, and measure outcomes of family-based treatments.

Gerard, A. B. (1994). Parent-Child Relationship Inventory (PCRI): Technical Manual. Western Psychological Services.

Gerard, A. B. (2005). Parent-Child Relationship Inventory: Validity studies. Journal of Clinical Child & Adolescent Psychology, 34(1), 21–35.


PIIS

PIIS
Parent-Infant Interaction Coding System

The PIIS is an observational coding system designed to assess the quality and reciprocity of parent-infant interaction during naturally occurring or semi-structured contexts. Developed by Summers et al. (2001) in the context of early intervention research, it captures dimensions of parental sensitivity, responsiveness, and infant engagement. The PIIS is primarily used in research examining attachment quality, intervention effectiveness, and developmental trajectories in infants at risk for developmental delay or social-emotional difficulties.

Summers, J. A., Behr, S. K., & Turnbull, A. P. (2001). Conceptualizing and Measuring Family and Professional Collaboration in Early Intervention. Topics in Early Childhood Special Education, 21(1), 46-58.

Bakermans-Kranenburg, M. J., van Ijzendoorn, M. H., & Juffer, F. (2005). Disorganized Infant Attachment and Preventive Interventions: A Review and Meta-Analysis. Infant Mental Health Journal, 26(3), 191-216.


Parenting Stress Index

PSI
Parenting Stress Index – Full Length
PSI-SF

The Parenting Stress Index is the most widely used multidimensional assessment of parenting stress in mothers and fathers of children from infancy through age 10. Developed by Richard Abidin in 1983, it measures three major stress domains: parental distress (feeling overwhelmed, loss of control, role restriction), parent–child dysfunctional interaction (negative reciprocal patterns), and difficult child characteristics (behavioral and developmental challenges). The PSI has become essential in early intervention programs, family support services, and clinical evaluation of parenting difficulties.

Abidin, R. R. (1983). Parenting Stress Index: Administration, scoring, and interpretation manual. Charlottesville, VA: Pediatric Psychology Press.

Abidin, R. R. (1995). Parenting Stress Index professional manual (3rd ed.). Lutz, FL: Psychological Assessment Resources.

Loyd, B. H., & Abidin, R. R. (2011). Revision of the Parenting Stress Index. Journal of Pediatric Psychology, 30(4), 325-335.


NMSS

Non-Motor Symptoms Scale for Parkinson's Disease

Parkinson's Non-Motor Scale
NMSQ
NMS Scale

K. Ray Chaudhuri, National Hospital for Neurology and Neurosurgery, London

The NMSS is a comprehensive 30-item scale designed to assess the prevalence and impact of non-motor symptoms (NMS) in Parkinson's disease. Developed by Chaudhuri and colleagues in 2007, it addresses the reality that non-motor features—sleep disorders, mood disturbances, autonomic dysfunction, cognitive impairment, and pain—often cause greater disability and suffering than motor symptoms in many PD patients. The scale is essential for comprehensive PD assessment and is increasingly recognized as a critical outcome measure reflecting true patient burden.

Self-report questionnaire and clinician interview

Chaudhuri, K. R., Martinez-Martin, P., Brown, R. G., Sethi, K., Stocchi, F., Odin, P., Ondo, W., Whone, A., Rye, D., Bhattacharya, K., Naidu, Y., Schapira, A. H., Brozova, H., Nutt, J., Macphee, G., Carroll, C., Hilten, J. V., Verschuuren, J., & Bonuccelli, U. (2007). The metric properties of a novel non-motor symptoms scale for Parkinson's disease: Results from an international pilot study. Movement Disorders, 22(13), 1901-1911.

msqol-54 modified-rankin-scale huntington-qol migraine-disability-assessment


Partial Correlation

partial r
controlled correlation
Kısmi Korelasyon (Partial Correlation)

Partial correlation measures the linear relationship between two continuous variables after removing the shared influence of one or more control variables. The technique was formalised by R. A. Fisher in 1924 and is the standard approach whenever a researcher suspects that a third variable inflates or suppresses the observed association between two variables of interest.

Parametric correlation with covariate control

Student t (for significance test of partial r)

n - 2 - k  (k = number of control variables)

Fisher, R.A. (1924). The Distribution of the Partial Correlation Coefficient. Metron, 3, 329–332.

Kim, S. (2015). ppcor: An R Package for a Fast Calculation to Semi-Partial Correlation Coefficients. Communications for Statistical Applications and Methods, 22(6), 665–674.

pearson-correlation spearman-correlation multiple-regression linear-regression canonical-correlation


PCM / GPCM

Kısmi Kredi Modeli (PCM / GPCM)
Generalized Partial Credit Model
GPCM
PCM

Geoff N. Masters (PCM, 1982); Eiji Muraki (GPCM, 1992)

The Partial Credit Model is an extension of the Rasch measurement framework designed for ordered polytomous items — items whose responses fall into more than two ordered categories, such as partial-credit tasks in performance assessment or open-ended scoring rubrics. Proposed by Geoff Masters in 1982 and later generalised by Eiji Muraki in 1992, the model estimates a separate threshold (step) parameter for each adjacent-category transition within every item, allowing fine-grained calibration of how much each additional credit level contributes to locating a person on the latent trait.

Ordered polytomous items (e.g. partial-credit scores, Likert-type)

Masters, G. N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47(2), 149–174.

Muraki, E. (1992). A generalized partial credit model: Application of an EM algorithm. Applied Psychological Measurement, 16(2), 159–176.

rasch-model graded-response-model item-response-theory exploratory-factor-analysis dif-analysis


Partial Least Squares

PLS regression
projection to latent structures
PLSR
kısmi en küçük kareler

Herman Wold; popularized by Svante Wold in chemometrics

Partial least squares regression predicts a response from many, often highly collinear predictors by projecting them onto a small set of latent components — but, unlike principal components regression, it chooses those components to maximize their covariance with the response, not just the variance of the predictors. This supervised dimension reduction makes PLS a workhorse in chemometrics, spectroscopy, and other wide-data settings where predictors vastly outnumber observations.

Latent directions maximizing covariance with the response

Output: Regression on a few supervised components

Wold, S., Sjöström, M., & Eriksson, L. (2001). PLS-regression: a basic tool of chemometrics. Chemometrics and Intelligent Laboratory Systems, 58(2), 109–130.

Geladi, P., & Kowalski, B. R. (1986). Partial least-squares regression: a tutorial. Analytica Chimica Acta, 185, 1–17.

principal-components-regression principal-component-analysis multiple-linear-regression ridge-regression


Participant Debriefing Procedures

Post-Study Disclosure and Ethical Debriefing Protocols for Research Participants

debriefing
post-study debriefing
debrief session
participant disclosure

American Psychological Association; International research ethics community

Participant debriefing is a post-study conversation or disclosure providing information to participants after research participation concludes. Debriefing serves multiple ethical purposes: (1) explaining the research aims and design, (2) revealing any deception (if applicable), (3) addressing misconceptions, (4) offering support if the research caused discomfort, (5) providing information about study findings, and (6) ensuring participants understand their rights (e.g., right to withdraw data). Debriefing is especially important in research involving deception (participants must learn the truth), sensitive topics (participants may experience distress), or invasive procedures (participants deserve explanation). The American Psychological Association's Ethical Code, ESOMAR guidelines, and international research ethics frameworks emphasize debriefing as a core protective procedure.

American Psychological Association. (2017). Ethical Principles of Psychologists and Code of Conduct. Section 8.08 - Debriefing.

ESOMAR. (2016). ESOMAR Guideline: Conducting Qualitative Research Ethically. Data Collection Ethics.

The National Commission for the Protection of Human Subjects of Biomedical and Behavioral Research. (1979). The Belmont Report: Ethical Principles and Guidelines for the Protection of Human Subjects of Research.

Williamson, V., & Williams, M. (2011). Using Narratives to Assess Ethical Issues in Longitudinal Research. Qualitative Research in Sport, Exercise and Health, 3(1), 92-106.

deception-in-research ethics-committee-application vulnerable-populations-research participant-debrief risk-benefit-assessment


Participant Observation

Participant Observation in Ethnographic Research

ethnographic observation
participatory observation
overt observation
immersive observation

Participant observation is a qualitative research method in which the researcher embeds themselves within a community, organization, or social setting for an extended period, engaging in the activities and relationships of the group while systematically observing and documenting behavior, interactions, and cultural meaning. Pioneered by Malinowski in the 1920s and developed in anthropology, the method has been adopted across sociology, education, health sciences, and organizational research. The researcher functions as both insider (participating in group activities) and outsider (maintaining analytical distance), generating thick description—rich accounts of context, behavior, and meaning that reveal how people actually live and interact.

Geertz, C. (1973). The Interpretation of Cultures. Basic Books.

Emerson, R. M., Fretz, R. I., & Shaw, L. L. (1995). Writing Ethnographic Fieldnotes. University of Chicago Press.

Hammersley, M., & Atkinson, P. (1995). Ethnography: Principles in Practice (2nd ed.). Routledge.

Spradley, J. P. (1980). Participant Observation. Holt, Rinehart and Winston.

in-depth-interview-method document-analysis reflexivity-in-research qualitative-rigor-criteria


The Participation Measure for Post-Acute Care (PM-PAC) is a brief, clinician-administered tool designed to measure functional participation and independence in hospitalized rehabilitation patients across self-care, mobility, cognition, and social domains. Developed by Wang, Hart, Stratford, and Mioduski, PM-PAC is widely used in inpatient rehabilitation facilities (IRF) and skilled nursing facilities (SNF) to track progress, predict discharge outcomes, and inform therapy intensity planning.

Wang, Y. C., Hart, D. L., Stratford, P. W., & Mioduski, J. E. (2012). Baseline dependency, not diagnosis, drives therapy intensity and discharge outcome after inpatient rehabilitation. Journal of Stroke and Cerebrovascular Diseases, 21(6), 431–437.

Gandy, S., Wang, Y. C., Schauder, K., Hart, D. L., Mioduski, J. E., & Meek, M. (2014). Utility of the Participation Measure for Post-Acute Care (PM-PAC) in predicting rehabilitation outcomes. Archives of Physical Medicine and Rehabilitation, 95(12), 2387–2392.

community-integration-questionnaire assessment-life-habits impact-participation-autonomy participation-scale reintegration-to-normal-living


Participation Scale

P-Scale
Participation Scale (van Brakel)

The Participation Scale (P-Scale) is a brief, 8-item measure designed to assess restrictions in participation across social and occupational roles in people with chronic conditions or disabilities. Developed by van Brakel and colleagues, the P-Scale is widely used in low- and middle-income country (LMIC) settings and in global health research where conciseness and cross-cultural applicability are essential. It offers a quick, validated snapshot of how much a condition limits a person's engagement in work, self-care, communication, and social participation.

van Brakel, W. H., Officer, A., & Nicol, M. (2020). Handbook of Disability and Health Equity: Toward Achieving the Sustainable Development Goals. Frontiers Media. Chapter: Participation.

Turan, J. M., & van Brakel, W. H. (2007). Reliability and validity of a participatory rural appraisal tool for assessing participation and inclusion in leprosy elimination programmes. Disability & Rehabilitation, 29(13), 993–1003.

community-integration-questionnaire impact-participation-autonomy craig-handicap-assessment assessment-life-habits whodas-2