I have a strange situation with a linear mixed model I can't make any sense of.
I have an LMM specified with one categorical predictor (cat_pred; with the three levels A, B, C) and one dependent variable (DV) where I specified random intercepts for my participants (par). The model looks like the following:
lmer(DV ~ cat_pred + (1|par), data = mydata)
My cat_pred shows clear effects on the DV
Fixed effects: Estimate Std. Error df t value Pr(>|t|) (Intercept) 3.1250 0.1541 114.0570 20.278 < 2e-16 *** cat_predB -1.2500 0.2052 78.0000 -6.092 3.96e-08 *** cat_predC -1.4250 0.2052 78.0000 -6.945 1.00e-09 ***
I now add a continuous predictor (con_pred) and want to see if there is an interaction between my cat_pred and con_pred. So I add it to the model by specifying an interaction.
lmer(DV ~ cat_pred*con_pred + (1|par), data = mydata)
When I add it to the model, all my significant effects vanish.
Fixed effects: Estimate Std. Error df t value Pr(>|t|) (Intercept) 2.50835 0.46787 110.76817 5.361 4.56e-07 *** cat_predB -0.62591 0.62043 76.00000 -1.009 0.316 cat_predC -0.63014 0.62043 76.00000 -1.016 0.313 con_pred 0.01060 0.00759 110.76817 1.397 0.165 cat_predB:con_pred -0.01073 0.01006 76.00000 -1.066 0.290 cat_predC:con_pred -0.01366 0.01006 76.00000 -1.357 0.179
When I now run the model just with the con_pred I see, that it is not at all related to my DV.
Fixed effects: Estimate Std. Error df t value Pr(>|t|) (Intercept) 2.090e+00 3.207e-01 1.180e+02 6.517 1.85e-09 *** con_pred 2.470e-03 5.202e-03 1.180e+02 0.475 0.636
So this made me curious and I started to try out the effect of different other continuous predictors that have no association to my DV. Every time I add them to the model (it does not depend which one I use) my cat_pred loses it's significance. I even added random continuous variables just to check it.
Is this a power problem? My sample is rather small with N=40.
Thanks a lot for your input!!!