Mixed models vs traditional regression

[Paul Harvey]

I am very new to using mixed models and I would like to hear peoples thoughts.

i have a dataset where a certain outcome was measured several times across a population as were all covariates

the particular covariate of interest has about 10000 people in group A and 100 in group B at baseline , although a certain but very small number of group A end up being in group B some point down the track.

We want to look at the relationship between the covariate of interest and the outcome, but we don’t really care about time per se - it was collected multiple times to enrich/enlarge the dataset, but we don’t care the effect that time had on the outcome.

In your opinion, given the very small numbers who changed from group A to group B, would it be better to amalgamate all the data together from various time points together and treat as a traditional logistic regression model? Or is it still better to use a mixed method approach; even though a small number of people switched from group a to b?

Thankyou!

[Erik Ruzek]

Whether to use mixed models for this analysis or not is a tough question. Do you have repeated measures of the same individuals? Yes, and you therefore need to account for it if you analyze the entirety of the data. You are not forced to use mixed models, however. You could instead use so-called fixed effects models that deal with the repeated-measures by de-meaning (subtracting the appropriate individual mean from the time-varying outcome and covariates). See Stata's xtreg documentation.

The amalgamation approach, if I am appropriately inferring what you mean by that word, would be the equivalent of a between person effect, which can also be estimated using xtreg with the be option. A lot of people don't like this approach because you throw out the within-person variation, which is often interesting and can be powerfully utilized to estimate within-person effects of covariates of interest on the outcome. Sometimes these within-person effects are referred to as effects in which the person serves as their own control.

What concerns me is the severe sample size imbalance in your covariate of interest. It is one thing if you are looking at a 65-35 split, but you are looking at an almost 99.5-0.05 split in the sample size between the two groups. I'm not sure you will be able to detect differences in the groups on the outcome with that level of sample size imbalance.

[Erik Ruzek]

Please note that in my original response, I mentioned xtreg, which is the panel data analysis command for continuous outcomes, Since your outcome is dichotomous (you mention logistic regression), you cannot use xtreg and instead would need to use xtlogit, which has options for both random effects (re) and fixed effects (fe) but not between effects.