Multiple Regression

Multiple linear regression is a statistical method that allows us to summarize and study relationships between two or more continuous (quantitative) variables.

Extension of the basic multiple regression model

• Moderation models that contain interactions explain additional, non-additive contributions and represent cases in which the main effect is not constant but varies between levels of a moderating variable.

• Mediation models are relevant for causal attribution of an effect of x on y while disentangling the pathway of x on m on y. The impact of x on y is reduced when adding m to the model. Also, mediation holds if ß1*ß2 ≠ 0. Conditions: y ~ m, m ~ x, y ~ x + m

• Hierarchical regression can be an advantage to quantify the explained variance by a model, after a prior simpler model. Covariates may be entered first as control model, and predicto of interest last to see additional benefit. Tests between models help assess significant contribution of given predictor.

• Multilevel regression accounts for nested data, allowing random effects on specific levels. Random effects may be on the intercept or the slope, and represent the control for a categorical (dummy coded) variable or the interaction of a predictor with this moderator. See Mixed effects linear models.