Statistics — Page 27
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
Multi-group Cronbach's alpha
Multi-group Cronbach's alpha estimates and compares the internal consistency reliability of a scale separately within each of two or more defined subgroups. It is used in cross-cultural, demographic, and comparative psychometric research to...
Multi-group EFA
Multi-group exploratory factor analysis estimates the latent factor structure of a set of items separately within each of two or more groups and then examines whether the discovered structures are consistent across groups. It is used to exp...
Multi-group confirmatory factor analysis
Multi-group confirmatory factor analysis tests whether a measurement model holds equivalently across two or more groups — such as cultures, genders, or time points. By imposing increasingly stringent equality constraints and comparing model...
Multi-period Causal Impact Analysis
Multi-period Causal Impact Analysis extends the Bayesian structural time-series framework of Brodersen et al. (2015) to settings where an intervention occurs across multiple distinct periods, is applied at staggered times to different units...
Multidimensional Scaling
Multidimensional scaling maps objects described only by pairwise similarities or dissimilarities into a low-dimensional geometric space so that distances in that space reflect the original proximity structure as faithfully as possible. It i...
Multidimensional Unfolding
Multidimensional unfolding places both individuals and the stimuli they evaluate — candidates, parties, bills — in a single joint low-dimensional space, so that each person's preferences are explained by their proximity to the stimuli. In p...
Multilevel Approximate Bayesian Computation
Multilevel Approximate Bayesian Computation (multilevel ABC) extends simulation-based Bayesian inference to hierarchically structured data. When the likelihood is intractable and observations are nested within groups, it replaces direct lik...
Multilevel Bayesian Inference
Multilevel Bayesian inference combines Bayesian probability with hierarchical data structures, treating group-level parameters as drawn from a common population distribution. It simultaneously estimates unit-level effects and the hyperparam...
Multilevel Bayesian Model Averaging
Multilevel Bayesian model averaging (ML-BMA) extends classical Bayesian model averaging to grouped or hierarchically structured data. Rather than committing to a single multilevel model specification, it computes a weighted average of predi...
Multilevel Bayesian Network
A multilevel Bayesian network extends the standard Bayesian network to data with hierarchical or grouped structure — students within schools, patients within hospitals, observations within subjects — by placing separate but linked graphical...
Multilevel Bootstrap Simulation
Multilevel bootstrap simulation is a resampling technique designed for clustered or hierarchically structured data. It preserves the nested data structure by resampling at each level independently — first drawing clusters (e.g., schools, ho...
Multilevel CFA
Multilevel confirmatory factor analysis tests a pre-specified factor structure while simultaneously accounting for the non-independence of observations caused by clustered data. It decomposes item variance into within-group and between-grou...
Multilevel Content Validity
Multilevel content validity extends the classical content validity framework to settings where items, raters, or respondents are nested within hierarchical structures — such as students within schools, patients within clinics, or items rate...
Multilevel Convergent Validity
Multilevel convergent validity evaluates whether items or scales intended to measure the same construct show coherent, strong associations at each level of a nested data structure — within individuals, within groups, and between groups. It...
Multilevel Differential Item Functioning
Multilevel DIF analysis detects whether individual test or survey items function differently across groups when respondents are clustered within higher-level units — such as students nested in schools, employees in organizations, or patient...
Multilevel Discriminant Validity
Multilevel discriminant validity evaluates whether theoretically distinct constructs are empirically separable when data are nested within higher-level units such as teams, schools, or organizations. It extends single-level discriminant val...
Multilevel EFA
Multilevel exploratory factor analysis uncovers latent factor structures simultaneously at two or more levels of a data hierarchy — for example, both within individuals and between groups — without imposing a fixed structure in advance. It...
Multilevel Generalizability Theory
Multilevel generalizability theory extends classical G-theory to measurement designs where observations are nested within higher-level units — for example, items nested within raters, or students nested within classrooms. It decomposes scor...
Multilevel Gibbs Sampling
Multilevel Gibbs sampling applies the Gibbs MCMC algorithm to hierarchical (multilevel) Bayesian models, cycling through the conditional distributions of group-level parameters and population-level hyperparameters in turn. This exploits the...
Multilevel Hamiltonian Monte Carlo
Multilevel Hamiltonian Monte Carlo (Multilevel HMC) combines the variance-reduction strategy of multilevel Monte Carlo with the efficient gradient-driven exploration of Hamiltonian Monte Carlo. By running coupled HMC chains at increasing le...
Multilevel MCMC
Multilevel MCMC applies Markov chain Monte Carlo sampling to hierarchical (multilevel) Bayesian models. It draws samples from the joint posterior of both group-level and population-level parameters simultaneously, propagating uncertainty ac...
Multilevel McDonald's omega
Multilevel McDonald's omega estimates reliability at two distinct levels — within groups and between groups — for scales administered to individuals nested in clusters such as classrooms, teams, or organizations. It accounts for the non-ind...
Multilevel Measurement Invariance
Multilevel measurement invariance testing evaluates whether a latent construct is measured equivalently both within clusters (e.g., individuals within teams) and between clusters (e.g., team-level aggregates). It extends standard measuremen...
Multilevel Mediation Analysis
Multilevel mediation analysis is a parametric structural method that estimates indirect (mediated) effects within hierarchically nested data, such as students within schools or employees within organisations. Formalised for lower-level medi...