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On a number of occassions, I have seen people remark that you should always interact your covariates with the with your slope when running multilevel models. That is, for example, you should not run the following code:

lme(fixed=y ~ treat + time + x1 + x2 + x3, random = ~time|ID, data=data)

Rather, you should always run the following:

lme(fixed=y ~ treat + time + x1 + x2 + x3 + treat:time + x1:time + x2:time + x3:time, random = ~time|ID, data=data)

However, I have never understood why? Can someone explain to me why this is the case? In addition, does this also apply to using generalized estimating equations for longitudinal data?

Any references for explanations would also be deeply appreciated?

statslearner13
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1 Answers1

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Since you have tagged [lme4-nlme], I am going to answer your question in the context of lme4::lmer. Without any links to references where you have might have read that fitting non-interactions terms as fixed effects is not correct, I would say that I have not come across any such references - rather I think you have misinterpreted the the syntax of lmer formula.

For example, in lme4::lmer, the formula y ~ x1 * x2 + (1 + time | ID) is exactly similar to y ~ x1 + x2 + x1:x2 + (1 + time | ID). See this question for example.

The two models you have specified are testing different hypotheses. The second model is exactly similar to fitting a model lme4::lmer(y ~ treat*time + x1*time + x2*time + x3*time + (1 + time | data), data=data).

If you meant to say that fitting a model with random slopes without having an interaction term in the formula is not correct, i.e., lme4:lme(y ~ treat + time ... + (1 + time | id) is not correct, then again, I don't think this is correct - please see GLMM worked examples - Tundra Carbon, where the author has fitted a linear mixed effects model with random slopes and random intercepts with only one fixed effect term.

medium-dimensional
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