Statistics — Page 39
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
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 Item Response Theory
Multilevel item response theory (MLIRT) joins two powerful frameworks: an IRT measurement model that turns item responses into a latent ability, and a multilevel structural model that explains how that ability varies across nested groups su...
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...
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...