Principal Component Analysis (PCA) summarizes a set of correlated variables into a smaller number of uncorrelated components. In SPSS, this is especially useful when a regression model contains several indicators that measure overlapping dimensions and may otherwise create multicollinearity.
1. Check whether PCA is appropriate
Begin with the correlation matrix. Variables should share meaningful correlations, but they should not be nearly identical. The Kaiser–Meyer–Olkin (KMO) statistic evaluates sampling adequacy: values above 0.60 are generally acceptable, while higher values indicate a clearer common structure. A significant Bartlett's test of sphericity supports the conclusion that the correlation matrix is suitable for component extraction.
2. Decide how many components to retain
SPSS reports eigenvalues and the percentage of variance explained by each component. The eigenvalue-greater-than-one rule provides a starting point, but the scree plot and substantive meaning should also guide the decision. A useful solution balances parsimony with sufficient cumulative explained variance.
3. Interpret the rotated component matrix
Component loadings show how strongly each original variable is associated with a component. After rotation, identify the variables with the largest absolute loadings on each component and assign a label that reflects their shared concept. The sign indicates the direction of the relationship; the magnitude indicates its strength. Cross-loading variables require caution because they may represent more than one underlying dimension.
4. Use component scores in regression
Saved component scores can serve as predictors in a linear regression. Because PCA components are uncorrelated, they reduce the multicollinearity created by overlapping original variables. In the SPSS coefficients table, a positive coefficient means that higher values of the component are associated with a higher predicted outcome, holding other components constant. A negative coefficient indicates the opposite relationship.
5. Interpret model fit and statistical evidence
The R-squared value gives the proportion of outcome variation explained by the retained components, while adjusted R-squared is preferable when comparing models with different numbers of predictors. The ANOVA F-test evaluates the model as a whole. For each component, examine its coefficient, confidence interval, and p-value, while distinguishing statistical significance from practical or economic importance.
6. Validate before reporting
Review residual plots for linearity and constant variance, inspect residual normality when inference depends on it, and check for influential observations. Although component scores address collinearity among the included components, they do not correct omitted-variable bias, poor measurement, nonlinearity, or an incorrectly specified regression model.
Interpretation principle
A component coefficient describes the effect of a latent combination of variables—not the isolated effect of any single original variable. Interpret the regression together with the rotated loadings and the conceptual label assigned to each component.