按方法、领域与证据探索科学。

Moving Average Model

The Moving Average model of order q — written MA(q) — expresses the current value of a time series as a linear combination of the current and past random shocks (innovations). Unlike the AR model which uses lagged values of the series itself, the MA model uses lagged error terms, making it well-suited for capturing sho

psychometrics

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 fit, it determines whether comparisons of latent mean scores are justified.

psychometrics

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 establish that a scale measures its construct with equivalent precision across

psychometrics

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 explore dimensionality before imposing invariance constraints, and to diagnose grou

survey methodology

Multi-level Cluster Sampling

Multi-level cluster sampling is a probability sampling design for hierarchically structured populations — such as students nested within classrooms within schools within districts. Clusters are randomly selected at each level of the hierarchy before individual units are sampled within the final-level clusters. The desi

survey methodology

Multi-level Convenience Sampling

Multi-level convenience sampling is a non-probability approach in which units are selected by convenience at each of two or more nested levels of a hierarchy — for example, recruiting whatever schools agree to participate and then enrolling all available students within those schools. It is widely used in organizationa

survey methodology

Multi-level Stratified Sampling

Multi-level stratified sampling applies stratification at two or more hierarchical levels of a nested population structure — for example, first stratifying geographic regions, then stratifying schools within each region, then stratifying classrooms within each school. This layered control over the composition of the sa

survey methodology

Multi-level Typical Case Sampling

Multi-level typical case sampling is a purposive strategy that selects representative, average-profile units at each level of a hierarchical structure — for example, typical classrooms within typical schools, or typical employees within typical departments. It is used when the research goal is to describe or illustrate

survey methodology

Multi-level weighted sampling

Multi-level weighted sampling is a probability-based survey design that draws samples from hierarchically nested populations — such as students within classrooms within schools within districts — and assigns design weights at each level to account for unequal selection probabilities. The resulting weighted data enable

causal inference

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, or where researchers wish to evaluate cumulative and period-specific effects w

survival

Multi-State Model

The multi-state model is a generalised survival framework, formalised in the work of Andersen and Keiding and brought to wide biostatistical practice by Putter, Fiocco and Geskus (2007), that models individuals moving through multiple distinct health states — for example, healthy, ill and dead — over time. A separate h

epidemiology

Multicenter Competing Risks Analysis

Multicenter competing risks analysis is a time-to-event method applied across multiple clinical centers to estimate the probability of a specific event of interest when other mutually exclusive events — competing risks — can preclude its occurrence. By pooling data from diverse sites, it achieves the sample sizes neede

epidemiology

Multicenter Cox proportional hazards

Multicenter Cox proportional hazards regression extends the classic Cox PH model to studies conducted at two or more clinical sites or centers. It estimates the effect of predictors on time-to-event outcomes while explicitly accounting for clustering within centers, between-center heterogeneity, and potential differenc

epidemiology

Multicenter Kaplan-Meier analysis

Multicenter Kaplan-Meier analysis applies the Kaplan-Meier nonparametric estimator to time-to-event data collected from two or more clinical centers. By pooling or stratifying data across sites, it estimates survival functions and compares them between treatment groups while accounting for potential center effects, ena

statistics

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 is widely used to visualize the hidden structure of psychological, social, and be

bayesian

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 likelihood evaluation with simulations at each level of the hierarchy, accepting pa

bayesian

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 hyperparameters governing their variation, propagating full uncertainty through every leve

bayesian

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 predictions and parameter estimates across a set of candidate multilevel models, weig

bayesian

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 models at each level, with higher-level parameters governing the conditional pr

bayesian

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, hospitals), then drawing observations within each sampled cluster — so that bootst

psychometrics

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-group components, fitting a separate measurement model at each level, making it the

psychometrics

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 rated by panels from distinct cultural or professional groups. It ensures that scale

psychometrics

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 extends classical convergent validity from single-level measurement models into

psychometrics

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 patients in clinics. By accounting for hierarchical data structure, it separates genuin

psychometrics

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 validity checks into a multilevel confirmatory factor analysis framework, verifying

psychometrics

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 is essential whenever survey or test items are collected from respondents nested

psychometrics

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 score variance into components attributable to persons, facets, and their interactio

bayesian

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 conditional independence structure of the hierarchy to draw exact or near-exact

bayesian

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 levels of model fidelity or discretisation, it achieves accurate posterior estimat

psychometrics

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-independence induced by grouping and avoids the bias that single-level omega produc

bayesian

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 across levels and enabling inference in clustered or nested data structures where

psychometrics

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 measurement invariance procedures to nested data structures commonly encountered in organi

statistics

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 mediation in multilevel models by Kenny, Korchmaros and Bolger (2003), it simultaneo

bayesian

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 rejecting them via a ratio that respects the full joint posterior across all levels

research design

Multilevel Mixed Methods Design

Multilevel mixed methods design is a research approach that collects and integrates both quantitative and qualitative data at two or more distinct levels of a social or organizational hierarchy — for example, individuals nested within classrooms, classrooms within schools, or patients within healthcare teams. By pairin

research statistics

Multilevel Modeling

Multilevel modeling (also called hierarchical linear modeling, mixed-effects modeling) is a statistical framework for analyzing data organized in nested or clustered structures—students within schools, patients within hospitals, repeated measures within individuals. Developed by Bryk and Raudenbush (1992), it accounts

bayesian

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 simulations correct only the remaining small difference — dramatically reducing total

psychometrics

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 construct validation to nested data structures, ensuring that a measure means t

statistics

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 clinics. Formalized in the multilevel modeling literature by Snijders and Bosker

psychometrics

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 difficulty estimates on a logit scale while simultaneously partitioning person-

psychometrics

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 hierarchically nested data, such as employees within organizations or students wi

psychometrics

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 and between-group components, ensuring that reliability and factor structure are

psychometrics

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 students within classrooms. It partitions total score variance across levels using i

bayesian

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 grouped structure of multilevel data — individuals nested within groups, groups neste

statistics

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, and estimates all parameters simultaneously via maximum likelihood. It is the st

econometrics

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 coefficients relative to a reference category.

research statistics

Multiple Comparisons Problem

When conducting multiple statistical tests, the probability of obtaining at least one false positive by chance increases with the number of tests. The multiple comparisons problem (also called the multiplicity problem) occurs because if you conduct 100 hypothesis tests at α = 0.05, you expect ~5 false positives by chan

statistics

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 a shared low-dimensional space, MCA reveals hidden structure in nominal or ordi

psychometrics

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 provide a unified view of how observations relate across multiple perspectives.

statistics

Multiple Imputation

Multiple Imputation (MI), formally introduced by Donald B. Rubin in 1987, is a principled statistical procedure for handling missing data. Rather than replacing each missing value once, MI fills the gaps m times — each time drawing plausible values from the posterior predictive distribution of the missing data — produc

statistics

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) are estimated by ordinary least squares (OLS), which minimises the sum of squa

research statistics

Multiple Regression Analysis

Multiple regression analysis is a statistical method for modeling the relationship between a continuous dependent variable and two or more independent variables (predictors). Originating from Gauss's early 19th-century work and formalized by Draper and Smith (1966), it estimates linear equations predicting outcomes fro

spatial analysis

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 surface is calibrated with its own bandwidth, enabling the model to distinguish drive

spatial analysis

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 — appearing only at fine local scales, only at broad regional scales, or persistently ac

spatial analysis

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 dispersions of a variable exist, offering richer insight than a single summary sta

spatial analysis

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 geographic distances or resolutions spatial clustering or dispersion is strongest, provid

research design

Multivariate Causal-Comparative Research

Multivariate causal-comparative research is a quantitative, non-experimental design that investigates whether pre-existing group differences (defined by a naturally occurring categorical variable) are associated with differences across multiple outcome variables considered simultaneously. By extending the classic causa

research design

Multivariate Correlational Research

Multivariate correlational research is a non-experimental quantitative design that examines the simultaneous associations among three or more variables. Rather than manipulating conditions, the researcher measures naturally occurring variables and uses techniques such as multiple regression, canonical correlation, or s

econometrics

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 modelling the correlation between unobserved individual heterogeneity and the observ

numerical methods

Mutation Testing

Mutation Testing is a fault-injection technique developed by DeMillo, Lipton, and Sayward in 1978 that evaluates test suite effectiveness by introducing small, deliberate bugs (mutations) into source code and checking if tests catch them. A test suite that kills (detects) all mutants is stronger than one that achieves