Question: Can you talk more about categorical and repeated Time? If I have 5 waves at ages 0, 1 year, 3 years, 5 years, and 9 years, would that be categorical or repeated? Does mixed account for different spacing in time?
Mixed models can account for different spacing in time and you’re right, it entirely depends on whether you treat Time as categorical or continuous.
First let me mention that not all designs can treat time as either categorical or continuous. The reason it could go either way in your example is because time is measured discretely, yet there are enough numerical values that you could fit a line to it.
In some designs, time really is measured continuously. For example, if the 5 ages were measured with different values for different subjects, like 14.5 months for one subject’s 1 year age and 11.2 months for another subject’s 1 year age, and if this level of detail mattered, you would have to treat time as continuous.
When you treat time as continuous in a mixed model, you’re fitting a line between time and the outcome Y for each subject. When you fit a line, it takes into account the spacing between each value of X.
In other designs, time is really measured in a qualitative way, like Before or After a treatment. In others, even if it is measured numerically, there are too few values to fit a meaningful line. In both examples, it only makes sense to treat time as categorical.
For example, I once helped a client who had time points of 6 and 8 years in her data. Just those two. There is no way to fit a line with only two values, nor would it make sense if you could.
So when you treat time as categorical, instead of fitting a line, you’re fitting a mean of Y for each category of time.
In this situation, the spacing of the time points doesn’t matter, so it’s fine here too. It’s not so much that the model is taking the spacing into account, it’s simply irrelevant. The model doesn’t care how far apart the X’s are or even if they have an order. It just fits a mean for each one, then tests if those means are different.
Hi! This was a really helpful post. If one were to model time as continuous as you mention is an option, would it be coded with date as a fixed effect and subject as a random effect? I.e., lmer(response~time+(1|Subject)
It would for a random intercept model. You could also include a random slope for time.