Mike Hughes writes:
I have been looking a your blog entries from about 8 years ago in which you comment on the number of groups that is appropriate in multilevel regression. I have a research problem in which I have 6 groups and would like to use multilevel regression.
Here is the situation. I have racial attitudes data from samples of University of Alabama students drawn in 1963, 1966, 1969, 1972, 1982, and 1988. (I also have data from 2013, but I am not including them in this analysis).
I have run a number of analyses predicting social distance attitudes in which the level-2 group variable is year. The main predictor is endorsement of racial stereotypes. I am interested in whether the association between endorsement of racial stereotypes and social distance declines over time (it does), so I specify a random slope for racial stereotypes, and I look at the cross level interaction between the racial stereotypes coefficient and year, included in the fixed part of the equation as number of years since 1963 (1963=0, 1966=3, etc.). I use xtmixed in Stata14.
The models run, and the likelihood ratio test vs the linear model is significant. AIC and BIC indicate that the xtmixed model is better than the OLS model that I run in Stata. Also, the OLS model predicts values of the dependent variable that are beyond its range (1 to 5), but the xtmixed model does not.
So my question is, is it ok to present my multi-level model, with 6 groups, rather than the OLS model? If so, is there something I can cite to provide some backing for using the model with 6 groups?
My reply: I agree that it makes sense to include a linear predictor for time and also allow intercepts and slopes to vary by discrete survey (so that you have 6 values for each coefficient). And once you do this, there’s not problem using the model to extrapolate. Whether that’s a good idea, is another story.