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# st: Interaction of Invariant Predictor and Polynomial Function in Growth Curve Analysis

 From Anthony Fulginiti To statalist@hsphsun2.harvard.edu Subject st: Interaction of Invariant Predictor and Polynomial Function in Growth Curve Analysis Date Sun, 17 Mar 2013 12:47:18 -0700 (PDT)

```Hello Statalist,

I have run across several examples of 2 level growth curve models using xtmixed with a polynomial function of time at level 1 and invariant predictors at level 2.  For instance, in a problem trying to determine if boys and girls differ in their growth trajectories in some outcome as the age.  After they determine that there is a quadratic trajectory at Level 1, they then typically move forward to test if boys and girls differ in the linear (instantaneous rate of growth) or quadratic (curvature) slopes as well in intercepts.

In most examples, I notice that they show results where the linear and quadratic time terms and interaction of gender with time terms are significant (with code like below).

xtmixed age age2 gender genderByage genderByage2||id: age, covariance(un) variance mle

However, I started wondering what would happen if age and age2 remain significant but only the linear interaction (genderByage) is significant but the quadratic interaction (genderByage2) is not significant (or vise versa) in the output?

1) Is it appropriate to drop the non-significant interaction term (let's use an example where the curvature is found to be non-significant) from a final model or does it not make sense to do so given that the age and age2 would still be in model?

Example of code with dropped curvature (quadratic term) interaction:  xtmixed age age2 gender genderByage||id: age, covariance(un) variance mle

2) If you keep the non-signficant interaction in model, is it appropriate to interpret the significant interaction term?  (For instance, saying that boys and girls differ in instantaneous rate of chance but not in curvature)

I thought I could get some initial feedback from all of you to see if you have tried to interpret such output or have some notions of what may be the best approach.