I am comparing two nested fixed-effects models, which are shown as follows
yit= b0 + b1 xit + b2 (xit)2 +..., (1)
and
yit= b0 + b1 xit + b2 (xit)2 + b3 zitx1it + b4 zit(x1it)2 + b5 zit+... (2)
where zit is the moderation variable of interest and x has been mean-centered.
Question 1: my estimates of b3 and b4 in (2) are significant. However, the within R-squared value only increased marginally in Model (2), and the increase is not statistically significant. How should I interpret the outcome, as some references seem to suggest that a significant increase in R-squared is important in a moderation analysis?
Question 2: I observed that the b1 and b2 coefficients of Model (1) are quite different from those in Model (2). I thought this is not indicative of a problem since these are two different models. Yet I got comments from a colleague, who said that, given that the R-squared of these two models are not significantly different , this result shows that the significance of b3 and b4 in Model (2) are likely to be falsely driven by multicollinearity. But later I computed vif for Model (2), and the scores didn't suggest multicollinearity problems with the augmented variables in model (2). Values of the standard errors also look quite reasonable. Should I worry about multicollinearity in this case?
Thank you all in advance. Any comments and thoughts are appreciated.
yit= b0 + b1 xit + b2 (xit)2 +..., (1)
and
yit= b0 + b1 xit + b2 (xit)2 + b3 zitx1it + b4 zit(x1it)2 + b5 zit+... (2)
where zit is the moderation variable of interest and x has been mean-centered.
Question 1: my estimates of b3 and b4 in (2) are significant. However, the within R-squared value only increased marginally in Model (2), and the increase is not statistically significant. How should I interpret the outcome, as some references seem to suggest that a significant increase in R-squared is important in a moderation analysis?
Question 2: I observed that the b1 and b2 coefficients of Model (1) are quite different from those in Model (2). I thought this is not indicative of a problem since these are two different models. Yet I got comments from a colleague, who said that, given that the R-squared of these two models are not significantly different , this result shows that the significance of b3 and b4 in Model (2) are likely to be falsely driven by multicollinearity. But later I computed vif for Model (2), and the scores didn't suggest multicollinearity problems with the augmented variables in model (2). Values of the standard errors also look quite reasonable. Should I worry about multicollinearity in this case?
Thank you all in advance. Any comments and thoughts are appreciated.
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