Statistics — Page 36
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
MaxDiff / Best-Worst Scaling
MaxDiff, also known as best-worst scaling (BWS), measures the relative importance or preference of a set of items by repeatedly asking respondents to identify the best (most important or most preferred) and worst (least) item within small s...
Maximum Likelihood Estimation
Maximum Likelihood Estimation (MLE) is a general-purpose parametric method for estimating the unknown parameters of a statistical model by finding the parameter values that make the observed data most probable. Formalized by R. A. Fisher in...
McDonald's Omega
McDonald's hierarchical omega (ωh) is a coefficient derived from a bifactor confirmatory factor model that quantifies what proportion of total-score variance is attributable to a single general factor rather than to group-specific factors o...
McDonald's Omega
McDonald's omega is a factor-analysis-based reliability coefficient introduced by Roderick P. McDonald (1999) that quantifies the internal consistency of a composite score without requiring the restrictive assumption that all items contribu...
McNemar's test
McNemar's test is a nonparametric hypothesis test that compares two paired (correlated) binary proportions, such as a yes/no measurement taken on the same subjects before and after an intervention. It was introduced by Quinn McNemar in 1947...
Mean-Variance Portfolio Optimization
Mean-variance portfolio optimization is the foundational model of modern portfolio theory, introduced by Harry Markowitz in 1952. It describes portfolios in an expected-return versus risk (variance) plane and traces the efficient frontier o...
Measurement Invariance
Measurement invariance testing is a sequence of nested confirmatory factor analysis (CFA) models that examines whether a psychological scale measures the same latent construct in the same way across distinct groups or time points. Systemati...
Mediation Analysis
Mediation analysis is a statistical procedure that tests whether the effect of an independent variable X on an outcome Y operates wholly or partly through a third variable M, called the mediator. Formalised by Baron and Kenny in 1986, it de...
Mendelian Randomization
Mendelian randomization is a method for estimating causal effects of exposures on outcomes using genetic variants as instrumental variables. Introduced by George Davey Smith in the 1990s, it exploits Mendel's law of segregation to remove co...
Merton Default Model
The Merton model (1974) is a structural approach to credit risk in which a firm defaults when its asset value falls below liabilities at maturity. Equity is viewed as a call option on firm value, and debt is an implicit short put position....
Meta-Regression
Meta-regression is a statistical technique that extends conventional meta-analysis by regressing study-level effect sizes on one or more study characteristics (moderators) to explain between-study heterogeneity. Formalized by Thompson and H...
Method of Moments Quantile Regression
Method of Moments Quantile Regression combines moment-based estimation (GMM) with quantile regression to estimate distribution parameters while handling endogeneity, panel structure, and dynamic relationships. Introduced by Koenker (2004) a...
Metropolis-Hastings Algorithm
The Metropolis-Hastings (MH) algorithm is a general-purpose Markov chain Monte Carlo (MCMC) method for drawing samples from any probability distribution whose density can be evaluated up to a normalising constant. Introduced by Metropolis,...
Metropolis-Hastings for model comparison
Metropolis-Hastings for model comparison uses the Metropolis-Hastings MCMC algorithm to explore both parameter and model space simultaneously, producing posterior probabilities for competing models and enabling Bayes factor estimation witho...
Metropolis-Hastings with Missing Data
Metropolis-Hastings with missing data treats unobserved values as latent variables and samples them jointly with model parameters inside a single MCMC chain. By augmenting the target distribution to include both parameters and missing value...
Metropolis-Hastings with measurement error
Metropolis-Hastings with measurement error is a Bayesian MCMC approach that jointly estimates model parameters and the true (unobserved) covariate values when predictors or outcomes are recorded with noise. By treating the latent true value...
Micro-phenomenology
Micro-phenomenology is a qualitative research method for exploring subjective experience through detailed, guided introspection. Developed by Claire Petitmengin, this method uses specialized interview techniques to help participants articul...
Migrant Integration Index
The migrant integration index developed by Harder, Hainmueller, Laitin and colleagues in 2018 is a short, validated survey instrument that measures how integrated an individual immigrant is across six distinct dimensions: psychological, eco...
Migration Models
Migration models are quantitative frameworks for explaining and forecasting population movement between geographic units. Lee's (1966) push-pull theory classifies factors at origin and destination into positive and negative forces, modulate...
Mini Nutritional Assessment Short-Form
The Mini Nutritional Assessment Short-Form (MNA-SF) is a rapid, six-item screening tool for identifying undernutrition and its risk in older adults. It was developed by Laurence Rubenstein, John Harker, Antoni Salva, Yves Guigoz, and Bruno...
Mixed ANOVA
Mixed ANOVA is a parametric factorial analysis of variance that simultaneously examines at least one between-subjects factor and at least one within-subjects (repeated-measures) factor. Rooted in R. A. Fisher's ANOVA framework formalised in...
Mixed Effects Model
A mixed effects model (or linear mixed model) extends ordinary regression by including both fixed effects — population-level parameters shared by all observations — and random effects that capture subject-, group-, or cluster-level variabil...
Mixed Logit
The Mixed Logit model, introduced formally by McFadden and Train (2000) and elaborated in Train (2009), is a flexible discrete choice framework that allows preference parameters to vary randomly across decision-makers. By integrating standa...
Mixture Cure Model
The mixture cure model, first proposed by Boag in 1949 for cancer survival data, is a parametric survival model that explicitly accounts for a fraction of subjects who will never experience the event of interest — the so-called cured or imm...