I have a multilevel model (with poisson distribution specified for the outcome which is a count variable). I have one main predictor at level one which has the slope specified as fixed rather than random (had no theoretical/a priori reason for specifying it as random). However, the reliability estimate for the intercept is 0.00. When I ran the model with the slope as random the reliability estimate for the intercept is 0.56. So despite not having a theory that explains why the slope would vary, should I use that model?
Additional details about the model: The other level 1 predictors are all demographic dichotomous variables (race, etc.) most of which are not significant. In the fully unconditional model, the reliability estimate for the intercept is 0.349.
Also, variance component for level 2 is 0.00001 for the model with the predictor specified as fixed, but is 3.90787 when the predictor is specified as random. According to the fully unconditional model only 2% of the variance is at level 2.