3. Hayes Process Macro - Model 1b - Moderation with Categorical Moderator , Continuous IV and DV

TL;DR

Use PROCESS Macro Model 1 to test moderation when the moderator is categorical and the IV and DV are continuous.

Briefing Cornell Notes

Briefing

Bank size significantly moderates how commitment affects organizational performance, but the moderation depends on which bank category is being compared. Using PROCESS Macro Model 1 with a multicategorical moderator, the analysis treats commitment (continuous) as the independent variable and organizational performance (continuous) as the dependent variable, while bank size has three categories: small, medium, and large. The key question—whether commitment’s effect changes across bank sizes—gets answered through dummy (indicator) coding and conditional effects for each category relative to a reference group.

Overall model fit is significant, with the four exogenous terms accounting for about 41.1% of the variance in organizational performance (reported as an R² of 0.411). The dummy-coded moderation terms show that the medium-vs-small contrast is not significant for the main difference in performance, while the large-vs-small contrast is significant. Specifically, the coefficient for W1 (medium-sized banks compared to small-sized banks) is not statistically significant, indicating no reliable difference in organizational performance between medium and small banks. In contrast, W2 (large-sized banks compared to small-sized banks) is significant and carries a negative sign, meaning large-sized banks show weaker organizational performance than small-sized banks.

The interaction results provide the clearest moderation evidence. The interaction between commitment and the medium-sized bank dummy (W1 × commitment) is significant, while the interaction between commitment and the large-sized bank dummy (W2 × commitment) is not significant. Interpreting the signs, the negative coefficient on the significant medium interaction indicates that the effect of commitment on organizational performance is lower for medium-sized banks than for the reference group (small-sized banks). For large-sized banks, commitment’s effect is also lower than for small-sized banks, but that difference does not reach statistical significance.

Conditional effects reinforce this pattern: commitment has a significant impact on organizational performance for small-sized banks, and the effect remains significant for large-sized banks, while it is not significant for medium-sized banks. The moderation conclusion is supported by the “unconditional direction” test, where adding the interaction term produces a significant change in R²—evidence that bank size meaningfully improves prediction of organizational performance beyond the main effects.

Finally, the interaction plot aligns with the statistical results. The slope of organizational performance versus commitment is relatively flatter for medium-sized banks, but steeper for small- and large-sized banks, indicating a sharper rise in performance as commitment increases. Taken together, the results accept the hypothesis that bank size moderates the commitment–performance relationship, with the strongest and most reliable commitment effects appearing in the small-sized (reference) group and weaker or non-significant effects in the medium-sized group.

Cornell Notes

Bank size moderates the relationship between commitment and organizational performance using PROCESS Macro Model 1 with a multicategorical moderator. Bank size has three categories (small, medium, large) and is dummy-coded with small-sized banks as the reference category. The overall model is significant (R² ≈ 0.411), and adding the interaction terms produces a significant change in R², supporting moderation. Medium-sized banks show a significant interaction with commitment (W1 × commitment) but with a negative sign, meaning commitment’s effect is weaker than in small-sized banks. Large-sized banks differ from small-sized banks in performance level (W2 is significant), but the interaction with commitment (W2 × commitment) is not significant, indicating a weaker and statistically non-distinct commitment effect versus small banks.

How does the analysis handle a multicategorical moderator like bank size in PROCESS Macro Model 1?

Bank size is treated as a multicategorical moderator with three categories (small, medium, large). PROCESS uses indicator (dummy) coding with one reference category. With three categories, two dummy variables are created: W1 and W2. The reference category is the first category—small-sized banks—so W1 and W2 both equal 0 when the bank is small. When W1 = 1, the bank is medium; when W2 = 1, the bank is large. Each dummy variable is then used to form interaction terms with commitment to test whether commitment’s slope differs by bank category.

What do W1 and W2 tell you about differences in organizational performance across bank sizes?

W1 represents the difference in organizational performance for medium-sized banks compared to small-sized banks. In the output, W1 is not significant, so medium and small banks do not differ reliably in organizational performance. W2 represents the difference for large-sized banks compared to small-sized banks. W2 is significant and negative, indicating large-sized banks have lower organizational performance than small-sized banks.

Which interaction term provides evidence that bank size changes the effect of commitment on performance?

The interaction W1 × commitment (medium-sized banks relative to small-sized banks) is significant, showing that commitment’s effect on organizational performance differs for medium-sized banks versus small-sized banks. The interaction W2 × commitment (large-sized banks relative to small-sized banks) is not significant, meaning the commitment slope for large-sized banks is lower than for small-sized banks but not statistically distinguishable from it.

How should the sign of the significant interaction be interpreted?

For the significant medium interaction (W1 × commitment), the coefficient is negative. That means the slope of organizational performance on commitment is weaker for medium-sized banks than for small-sized banks (the reference group). In other words, as commitment increases, organizational performance rises less steeply in medium-sized banks than in small-sized banks.

What does the conditional effects and R² change test add to the moderation conclusion?

Conditional effects show where commitment’s impact is statistically significant across bank categories: commitment significantly predicts organizational performance for small-sized banks, while it is not significant for medium-sized banks; large-sized banks are described as significant in the conditional-effects summary. The moderation claim is also supported by the “unconditional direction” test: including the interaction term produces a significant change in R², indicating the moderator improves the model beyond main effects.

Review Questions

In dummy coding for a three-category moderator, why are there two dummy variables (W1 and W2), and what values do they take for the reference category?
If W1 × commitment is significant and negative, what does that imply about how commitment’s effect differs between medium and small banks?
Why does a significant change in R² after adding interaction terms strengthen the moderation claim?

Key Points

1
Use PROCESS Macro Model 1 to test moderation when the moderator is categorical and the IV and DV are continuous.
2
With a three-category multicategorical moderator, PROCESS creates two dummy variables (W1 and W2) using one category as the reference (small-sized banks here).
3
W1 tests medium vs small differences; W2 tests large vs small differences in organizational performance.
4
A significant interaction term (W1 × commitment) indicates the commitment–performance slope differs by bank category.
5
A significant change in R² after adding interaction terms provides statistical support that the moderator meaningfully improves prediction.
6
Interpret interaction signs to determine whether commitment’s effect is stronger or weaker relative to the reference group.
7
Interaction plots should reflect the conditional slopes: steeper gradients indicate a stronger commitment effect on performance.

Highlights

Small-sized banks serve as the reference category, so W1 and W2 both equal 0 for small banks; W1 = 1 marks medium and W2 = 1 marks large.

Medium-sized banks show a significant commitment interaction (W1 × commitment), but the negative sign indicates commitment’s effect is weaker than in small banks.

Large-sized banks differ from small banks in performance level (W2 is significant and negative), yet the commitment interaction for large banks is not significant.

A significant R² change after adding interaction terms supports the moderation claim beyond main effects.

The interaction plot’s steeper slopes for small/large banks versus a flatter line for medium banks visually match the conditional-effect results.

Topics

Moderation with Categorical Moderator
PROCESS Macro Model 1
Indicator (Dummy) Coding
Conditional Effects
Interaction Plots

Mentioned

SPSS
R²