effectsmodel

Effects model is a broad term in statistics for a class of models that explain variation in a response variable by incorporating parameters for the influence of units, groups, or experimental conditions. It is commonly used in analyses that include categorical predictors, hierarchical structures, or repeated measurements, and it often appears within the broader framework of analysis of variance, regression with categorical factors, and linear mixed models. The core idea is to explicitly model the effect sizes associated with different conditions or levels, rather than treating those influences implicitly.

In fixed-effects versions of an effects model, the levels of a factor are treated as fixed quantities and their effects are estimated directly from the data. This leads to parameter estimates that describe the observed groups and makes inferences appropriate for the specific groups studied. Fixed-effects models are straightforward to interpret but can have limited generalizability beyond the observed levels.

In random-effects versions, the levels of a factor are assumed to be drawn from a common distribution, introducing random effects and a variance component. This approach allows generalization to new, unobserved levels and often improves efficiency when there are many levels with limited observations per level. Estimation is typically performed using maximum likelihood or restricted maximum likelihood (REML).

In meta-analysis, an effects model frequently refers to a random-effects framework that accounts for between-study heterogeneity. Across disciplines, the terminology may vary, but the central idea remains the same: modeling the influence of hierarchical or grouped structures to better understand the contributions of different conditions while adequately accounting for variability.