I have data from a simple intervention design (n=500), where participants were measured across a number of (continuous) outcome variables at pre- and post-intervention (there was no control - not my choice). I have used
lmer (from the
lme4 package) to specify a mixed-effects model (one for each outcome of interest) that captures the change from pre to post (treating pre-intervention
varAPRE as a predictor of post-intervention score
varAPOST) whilst partialling out the contribution/variance of a number of random effects (e.g., school of the participant
Each model looks something like this:
model = lmer(varAPOST ~ varAPRE + (1|School), REML = FALSE )
The issue i'm having is that the coefficient for the fixed effect
varAPREseems to always be positive regardless of the direction of change from pre to post intervention.
For example, the two-tired CI plot (see below) shows varA to decrease from pre to post (as hypothesised) - the mean change is -2.79. However, the model summary for the fixed effect is as follows:
Fixed effects: Estimate Std. Error df t value Pr(>|t|) (Intercept) 22.97028 1.99319 345.70193 11.52 <2e-16 *** varAPRE 0.49146 0.03598 463.48463 13.66 <2e-16 ***
Likewise, if I run a similar model for a different outcome variable, one where I expect an increase from pre to post (e.g.,
varB), see plot below.
model2 = lmer(varBPOST ~ varBPRE + (1|School), REML = FALSE )
I get the same coefficient direction in the output:
Fixed effects: Estimate Std. Error df t value Pr(>|t|) (Intercept) 27.54412 1.80938 280.17582 15.22 <2e-16 *** varBPRE 0.47579 0.03613 468.95373 13.17 <2e-16 ***
I am completely confused by this. It doesn't make any difference if I switch the order of pre and post in the model (one to the outcome, one to the predictor) or whether the pre-intervention score is centered or not. Everything in the model output looks correct, with the exception of the direction! Any help/clarity would be much appreciated.
Here are two plots varAPRE/varAPOST and varBPRE/varBPOST (coloured by school) which help to make sense of the coefficients in each model highlighted above: