I tested a set of models assessing lagged effects using DSEM. I find that my fixed effects in the unstandardized output is non-significant (but approaching significance), whereas the the standardized estimates (specifically, the Within-Level Standardized Estimates Averaged Over Clusters) is flagged as significant. When I run the same models in MLM, the fixed effects are significant and parallel the standardized output in DSEM. Why am I seeing these differences, and should I trust the unstandardized or the standardized output in DSEM? Thanks!
I would recommend looking at the significance of the cluster specific effects (i.e. the random effect) instead of the fixed effect.
The "Within-Level Standardized Estimates Averaged Over Clusters" standard error does not have the same meaning as the model estimate standard error. That is because it is conditional on the sample. That SE can be used to determine if the average effect for the individuals in the sample is >0. The model estimate is regarding the average effect for the population where the sample comes from.
MLM also underestimates SE due to not accounting for the dependence of the variables due to proximity of times of observations.
Thank you so much, that was really helpful. I had another question. I noticed that sometimes, the estimates for fixed effects/cluster-specific effects are significant in both MLM and DSEM, but they appear to flip in direction. In MLM, the estimate is negative, but in DSEM, the estimate is positive. Do you know why this happens?
This might also be an indication that the model needs AR(2) modeling rather than AR(1) or that you should use the lagged command also for the covariate and add the lagged covariate as a predictor as well.
Thank you for your response. The readings were really helpful too. I just want to clarify your response to my first question. When you said look at the significance of 'cluster-specific effects,' you meant the random effects in the unstandardized output, right? Or did you mean that we should look at the significance of the "Within-Level Standardized Estimates Averaged Over Clusters?"