When running time-lagged segment analyses in R the outcome variable is significantly predicted by the predictor variable at t-1 but not by the predictor variable at t, which seems not logical to me. Actually, the predictor variable at t-1 is only added to the model to be controlled for.

In more detail:

I am currently analysing data from an ecologically momentary assessment (EMA) study, delivering a huge amount of data entries for each subject. In the study we had two conditions (Variable StudyPhase).
I’m interested in the temporal dynamics of changes in all my dependent variables and therefore running so-called time-lagged segment analyses in R using the following code:

Outcome_t+1 ~ Outcome_t + Predictor_t * StudyPhase + Predictor_t-1 + (1 | VP_ID)

Like that I am controlling for the preliminary data entry of the outcome as well as the predictor variable, respectively, while still investigating possible time-lagged influences of the predictor to the outcome variable.

However, for every model, the Predictor_t-1 gets highly significant, whereas the Predictor_t variable often doesn’t reach significance. That confuses me as it seems not logical that the predictor significantly predicts the outcome over two assessment points but mostly not over one. Or is this significance due to the fact that I have both, the Predictor_t and the Predictor_t-1 as variables in my model? In that case I probably could “ignore” the Predictor_t-1 variable in the interpretation.

Thanks in advance for your help! 🙂