Interaction in linear mixed model

[Gaëlle Meert]

Hello,

I ran a linear mixed model with a continuous predictor (within-
subject) and a categorical predictor (between-subject; 2 levels coded
0 vs. 1) as fixed effects. The random factors were the random
intercept and slope for participants. I would like to test the
interaction between the two fixed effects. When I entered the
interaction in the model, the coefficient of the continuous predictor
was inflated. I think that this inflation could be due to collinearity
between the main effects and the interaction. Moreover, p-values for
the test of fixed effects differed from p-values for the parameter
estimates.

How can I test the interaction? Can I test the difference between the
parameter estimates for each level of the categorical predictor by
using a t-test for independent b?

Thank you

Gaëlle

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[Swank, Paul R]

Type II tests and tests of parameter estimates can be different especially when categorical variables are concerned. Have you tried centering your continuous predictor?

Paul R. Swank, Ph.D
Professor and Director of Research
Children's Learning Institute
University of Texas Health Science Center
Houston, TX 77038


-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Gaëlle Meert
Sent: Tuesday, October 07, 2008 7:24 AM
To: [hidden email]
Subject: Interaction in linear mixed model

Hello,

I ran a linear mixed model with a continuous predictor (within-
subject) and a categorical predictor (between-subject; 2 levels coded
0 vs. 1) as fixed effects. The random factors were the random
intercept and slope for participants. I would like to test the
interaction between the two fixed effects. When I entered the
interaction in the model, the coefficient of the continuous predictor
was inflated. I think that this inflation could be due to collinearity
between the main effects and the interaction. Moreover, p-values for
the test of fixed effects differed from p-values for the parameter
estimates.

How can I test the interaction? Can I test the difference between the
parameter estimates for each level of the categorical predictor by
using a t-test for independent b?

Thank you

Gaëlle

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[MaxJasper]

If based on Wald test you cannot reject the null hypothesis that the
variability associated with interaction is 0 then you have to use more
reliable likelihood-ratio test by finding the difference of -2restricted
log-likelihood for the two models (with vs without interaction). The
difference has ChiSq distribution with df= df (model1) - df (model2). You
can reject hypo that interactions effect is 0 if sig level < 0.05 for
example or your preferred sig level.

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