Hierarchical and Simultaneous Multiple Regression

Vocabulary practice flashcards reviewing hierarchical and simultaneous multiple regression concepts, effect sizes, and model interpretation.

Hierarchical Multiple Regression

A multiple regression analysis procedure where the researcher enters predictor variables one at a time or in blocks into the regression equation in a predetermined order based on theory or prior knowledge.

Simultaneous Multiple Regression

A regression procedure where all predictor variables are forced into the regression equation at the same time to estimate direct effects and evaluate relative variable importance.

Change in R-squared ($\Delta R^2$)

The amount of additional variance in the dependent variable explained by entering a new variable or block of variables into a hierarchical regression model.

Shared Variance Attribution in Hierarchical MR

In a Venn diagram representation, the overlapping variance between predictors (area 3) is attributed entirely to whichever predictor variable ($X_1$ or $X_2$) is entered first into the model.

Cohen's $f^2$ (Overall)

A measure of overall regression effect size defined by the formula $f^2 = \frac{R^2}{1 - R^2}$, with guidelines where small = $.02$, medium = $.15$, and large = $.35$.

Cohen's $f^2$ (Increase in $R^2$)

A measure of effect size for the addition of variables to a model, defined by the formula $f^2 = \frac{R_{y12}^2 - R_{y1}^2}{1 - R^2}$.

Total Effects

The combined direct and indirect effects of a predictor on an outcome variable in an implied model, estimated by regression coefficients as each variable is entered step-by-step in hierarchical regression.

Direct Effects

The unmediated effect of a predictor variable on an outcome variable, directly estimated by simultaneous multiple regression coefficients.

Semipartial Correlation

A correlation (also known as part correlation) representing the unique contribution of an independent variable to the dependent variable; its square equals the change in $R^2$ when entering that variable last.

F-statistic for Increase in $R^2$

An F-test formula used to evaluate the statistical significance of adding a new block of predictor variables: $F = \frac{(R_{12}^2 - R_1^2) / (k_{12} - k_1)}{(1 - R_{12}^2) / (N - k_{12} - 1)}$.

Rules of Thumb for $R$ and $R^2$

Conventional effect size guidelines where $R$ values of $.10$, $.30$, and $.50$ (or $R^2$ values of $.01$, $.09$, and $.25$) represent small, medium, and large effect sizes, respectively.

Simultaneous vs. Hierarchical Regression Comparison

A methodology comparison where simultaneous regression forces all variables in at once to estimate direct effects and overall $R^2$, whereas hierarchical regression enters variables sequentially to assess total effects, curve components, interactions, and $\Delta R^2$.