I know there’s an extensive literature on this topic and also an ongoing discussion (e.g., http://www.stat.columbia.edu/~gelman/research/published/AOS259.pdf). However, I’m confused of whter I should model time as a random or fixed effects in a mixed model in my specific case.
Assume an RCT with two groups (intervention vs. control), 5 measurement points (Baseline, 3 weeks, 6 weeks, 3 months, 6 months), and I’m interested in testing the hypothesis of an effect of the intervention group. The dependent variable is a continuous score.
When visualizing my data, it is clear that the scores vary at baseline (intercept) and at time (slope), so e.g, some people start with significantly lower values of the score and show significantly other slopes (improving in score values with time) than others (whose score highly worsens with ongoing time). Plotting the data, I would assume that I should use a random intercept random slope model with time having a random effect.
However, depending on the 5 definitions Andrew Gelman (Gelman, 2004, Analysis of variance—why it is more important than ever) provides, I would agree or disagree to use time as a random effect in my model when testing the group effect:
E.g., taking statement #1 provided in the source above:
“Fixed effects are constant across individuals, and random effects vary. For example, in a growth study, a model with random intercepts ai and fixed slope b corresponds to parallel lines for different individuals i, or the model yit=ai+bt. Kreft and De Leeuw (1998) thus distinguish between fixed and random coefficients.”
I would model my time as random effect.
Taking statement #3
“Effects are fixed if they are interesting in themselves or random if there is interest in the underlying population. Searle, Casella, and McCulloch (1992, Section 1.4) explore this distinction in depth”
I would model time as fixed effect, especially given that it only has 5 levels.
Apart from that, in each case I would model my subjects as random effect (having a random intercept model). Could you shed some light on my specific issue?
Thanks a lot in advance.