Effect Modification in Linear Mixed Models

[Tschuls Mnk]

Dear all,

i have a question concerning the effect modification in a linear mixed model..
i am examining the influence of air pollution on blood pressure and on the change of blood pressure over time.
My model/the command for the analysis that i am using is the following:

mixed blutdruck_sys no2 age2 no2_age2 || id: age2

where blutdruck_sys is the variable for systolic blood pressure, no2 is the variable for air pollution, age2 is the variable for the age (centered at age 39)
and no2_age2 is the product of no2 and age2.

To examine whether there is an effect modification by sex i used the following command:

mixed blutdruck_sys c.no2#efm_geschlecht age2 c.no2_age2#efm_geschlecht geschlecht || id: age2

where the variables are the same as above and geschlecht is the variable for sex.
The output is the following:

Is it right to say that for women the estimated effect for the influence of no2 on blood pressure is 0.048 and for men it is 0.074?
How can i see if the difference in these estimated effects in women and men is significant?

Thank you in advance!

[Clyde Schechter]

First, your model is mis-specified. By failing to use factor variable notation for the no2#age interaction in your model, you have fooled Stata, but more importantly, fooled yourself into not realizing that your second model includes a three way interaction. In order to properly estimate that model, there needs to be an efm_geschlecht#age2 term in the model.

Even had you not made that error, your interpretation of the results is not correct. But, really when you fix the modeling, you are faced with interpreting a three way interaction, which is extremely confusing and difficult to do by sight. So fix the model using factor-variable notation consistently and then use the -margins- command to get the marginal effects you want. The model should look like:

mixed blutdruck_sys c.no2##efm_geschlecht##c.age2  || id: age2

After that, there is no such thing as the estimated effect for women (nor for men) of the influence of NO2 on blood pressure. There is a different effect for each value of age. So you need to decide whether you want to average that across all ages (which I do not recommend, personally, but many people like), or pick a specific age or ages that are of interest and get the effects estimated at those ages.

The -margins- command is very powerful and can calculate all of these things for you. It is also somewhat difficult to learn. While the manual section is comprehensive and has many worked examples, I think it is easier to start with Richard Williams' excellent article from the Stata journal: http://www.stata-journal.com/sjpdf.h...iclenum=st0260.