Interpretation of Linear mixed models with interaction terms

[anjana rajendra]

Hi All,

Do we have to use margins command to get coefficients for group differences in linear mixed model with interaction terms? For eg: how to estimate if there is an association between baseline physical activity on the rate of change of cognitivescore over a period 9 years. I'm confused whether to use the coefficient derived from the below code or do we need margins code to answer my question? Please help me to understand the difference between interpretation of coefficients retrieved from the below code and the coefficients retrieved from the margins code in Stata. What would help me to get an overall effect of baseline physical activity on the cogitive outcome measured at different timepoints over 9 years.

My code [mi estimate: mixed cognitivescore baselinephysicalactivity Timeinyears c.Timeinyears#c.baselinephysicalactivity sex age || Patientid:]

Thank you so much!

[Clyde Schechter]

Use Daniel Klein's -mimrgns- command, available from SSC. -margins- itself, and -lincom- (another way of calculating marginal effects in ordinary circumstances) do not work after -mi estimate-.

[anjana rajendra]

Thank you so much Clyde. Yes, I have been using mimrgns command but the question here is whether we can interpret the coefficients obtained from the mi estimate itself. Are they relaible in linear mixed effect models with an interaction term (althought interaction is not signitficant in my model) or do we need to use mimrgn command to interpret the results? Thank you so much!

[Clyde Schechter]

The interpretation of the coefficients in a model estimated with multiple imputation is the same as in a model estimated without multiple imputation. The reason I am suggesting you use -mimrgns- here and ignore the coefficients is because, as I understand it, your interaction involves continuous variables.

In the simple case where we interact one dichotomous variable with another, the coefficient of the interaction term has an easy interpretation as a difference-in-differences estimate. So a glance at the coefficient and its associated statistics is often all that is needed to interpret the results. But with continuous variables, whether multiple imputation has been used or not, it is more complicated than not. The coefficient of the interaction term is a mixed second-order partial derivative. If you're mathematically inclined, you may find that sufficient for your understanding. But most people aren't that sophisticated, and you will have difficulty explaining it to others. So to make a continuous#continuous interaction comprehensible, we usually want to do things like calculate, and graph, the marginal effects of each of those variables at a range of values of the other. That's much easier for people to understand. Since the ordinary -margins- command will not use multiply imputed estimates, you have to use -mimrgns- to do that.