Statistics — Page 28
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
Multilevel Metropolis-Hastings
Multilevel Metropolis-Hastings applies the Metropolis-Hastings MCMC algorithm to hierarchical (multilevel) Bayesian models, sampling jointly from group-level parameters and hyperparameters by proposing candidate values and accepting or reje...
Multilevel Monte Carlo Simulation
Multilevel Monte Carlo (MLMC) is a variance-reduction technique that estimates expectations by combining simulations run at multiple levels of numerical resolution. Coarse, cheap simulations capture most of the signal; fine, expensive simul...
Multilevel Neighborhood Effects
Multilevel models of neighborhood effects estimate how the places people live shape their health, over and above who those people are. Individuals are nested within neighborhoods, so their outcomes are not independent: residents of the same...
Multilevel Power Analysis
Multilevel power analysis is a sample-size planning procedure designed for hierarchical, clustered, or longitudinal study designs in which observations are nested within higher-level units such as students within schools or patients within...
Multilevel Rasch Model
The multilevel Rasch model extends the standard Rasch model to data with a nested structure — for example, students within classrooms within schools — by embedding person ability parameters inside a hierarchical linear model. It yields item...
Multilevel Reliability Analysis
Multilevel reliability analysis estimates the internal consistency of scale scores separately at the within-group (individual) and between-group (cluster) levels. It corrects the bias that arises when ordinary alpha or omega is applied to h...
Multilevel Scale Development
Multilevel scale development constructs and validates measurement instruments for data collected from individuals nested within higher-level units such as classrooms, organizations, or clinics. It partitions item variance into within-group...
Multilevel Test-Retest Reliability
Multilevel test-retest reliability estimates how consistently a measurement instrument produces the same scores across repeated administrations when observations are nested within higher-level units — such as patients within clinics or stud...
Multilevel Variational Inference
Multilevel variational inference (MLVI) is a scalable approximate Bayesian method that fits hierarchical (multilevel) models by optimizing a variational approximation to the posterior, rather than drawing MCMC samples. It exploits the group...
Multilevel nomological validity
Multilevel nomological validity evaluates whether a psychological construct and its network of theoretical relationships hold consistently across multiple levels of analysis — such as individual, team, and organization. It extends classical...
Multinomial Logistic Regression
Multinomial logistic regression extends binary logistic regression to outcomes with three or more unordered categories. It models the log-odds of each category relative to a chosen reference category as a linear function of the predictors,...
Multinomial Logit
Multinomial logistic regression is a maximum-likelihood method for a nominal (unordered) dependent variable with more than two categories. Building on McFadden's 1974 treatment of qualitative choice, it gives each category its own set of co...
Multiple Correspondence Analysis
Multiple Correspondence Analysis (MCA) is a multivariate ordination technique designed to explore and visualize associations among three or more categorical variables simultaneously. By mapping both observations and variable categories onto...
Multiple Factor Analysis
Multiple Factor Analysis (MFA) is a dimension reduction technique developed by Escofier and Pagès (1985) for analyzing multiple groups of variables measured on the same observations. MFA balances the influence of each variable group to prov...
Multiple Linear Regression
Multiple linear regression (MLR) is a parametric regression model that expresses a continuous outcome as a weighted linear combination of two or more predictor variables plus a random error term. The unknown weights (regression coefficients...
Multiregional Migration Projection
Multiregional migration projection extends the classic cohort-component method from a single closed population to a system of several regions that exchange migrants. Developed principally by Andrei Rogers in his 1975 Introduction to Multire...
Multiscale Geographically Weighted Regression
Multiscale Geographically Weighted Regression (MGWR) is a local spatial regression framework that relaxes the single-bandwidth constraint of standard GWR by allowing each predictor to operate at its own spatial scale. Each coefficient surfa...
Multiscale Getis-Ord Gi*
Multiscale Getis-Ord Gi* extends the classic local hot spot statistic by computing Gi* z-scores across a range of spatial distance bands or neighborhood sizes. This reveals whether clusters of high or low values are scale-dependent — appear...
Multiscale Moran's I
Multiscale Moran's I extends the classic global Moran's I statistic by computing spatial autocorrelation across a series of distance lags or spatial scales. The resulting spatial correlogram reveals at which geographic scales clusters or di...
Multiscale Spatial Autocorrelation
Multiscale spatial autocorrelation extends classical spatial autocorrelation analysis by computing and comparing autocorrelation statistics (such as Moran's I) across a range of spatial scales simultaneously. This reveals at which geographi...
Multistate Life Table
The multistate life table, also called the increment-decrement life table, generalizes the ordinary life table to populations that move among several living states — such as healthy and disabled, married and unmarried, or employed and unemp...
Multivariate Regression
Multivariate regression is a linear regression method that predicts several continuous dependent variables at the same time from a shared set of predictors. As developed in standard treatments such as Johnson and Wichern's Applied Multivari...
Mundlak-Chamberlain
The Mundlak-Chamberlain correlated random effects (CRE) estimator, introduced by Mundlak (1978) and extended by Chamberlain (1982), is a panel data technique that reconciles the fixed effects and random effects approaches by explicitly mode...
NARDL Model
The NARDL model, introduced by Shin, Yu and Greenwood-Nimmo in 2014, extends the ARDL framework to capture asymmetric long-run and short-run relationships, testing whether positive and negative changes in a regressor affect the dependent va...