I conducted an experiment where people either endorsed or did not endorse a statement at the commencement of a one-week training session, at the end of the one-week training session, and at a follow-up interview one week later. I hypothesised that the odds of endorsing the statement would increase between pre-training, and post-training measurement, but would decrease between post-training and follow-up. Here is the graph of the proportions endorsing the statement at each time point (pre-training =
pre, post-training =
post, follow-up =
I turned the three-level time predictor into an ordered factor (
fu) in order to estimate linear and quadratic trends across the three time points and ran a repeated-measures logistic regression (i.e. a mixed effects model).
Here is the output of that analysis
Estimate Std.Err z-value p-value (Intercept) 2.9262 0.5042 5.8036 < 1e-04 timeOrd.L 0.8594 0.4039 2.1278 0.033354 timeOrd.Q -1.6452 0.7628 -2.1566 0.031034
After exponentiating the log-odds coefficients and confidence intervals these are the results.
or lowCI hiCI p linear trend 2.36 1.07 5.21 0.033 quadratic trend 0.19 0.04 0.86 0.031
So for the linear trend I gather the interpretation would be "the odds of endorsing the statement at each time point increase an estimated 2.36 times, compared to the previous time point."
However, I am struggling with how to interpret the quadratic trend. This post has some clues but that is for a model where the time predictor is continuous rather than a factor with three levels.