Interpreting covariate influence if interaction is not significant?

[Maresa]

Dear all, 

I have been setting up Multi-Species-Occupancy Models for 2 Species, using the occumulti() function. I have allowed interaction to vary with covariates. 

Some of my models showed non-significant p-values of the interaction-term, but the selected covariate still showed significant p-values... Also some of the plots gave a "significant-like" look, when plotting the interaction against the selected covariate. Nonetheless my intuition tells me, in cases when the intercept of the interaction is not significant, to not  interpret covariate effects. 

Am I right or am I maybe missing something important here?

Thanks in advance

Maresa

[Ken Kellner]

Hi Maresa,

The value of the interaction term is the combined values of the intercept + covariate effect. So I don't think it would be correct to look only at the value of the intercept, it also matters what's happening with the covariate. As you say at some values of the covariate, if the associated slope has a large (in an absolute sense) value, the total interaction term may be different from 0 at that value. Looking at the plots can help with this.

Consider the extreme situation where the interaction term is modeled as a function of a single categorical covariate with two levels (say, habitat types A and B). The intercept by itself will represent  the interaction term in habitat type A and the slope the additional effect of B. If the model estimates the value of the intercept at 0 and the effect of B at say 3 (with some small SE 0.2), it is clear that species are more likely to occur at the same sites in habitat B (total interaction term 3) but not in A (0). We wouldn't want to say there was no interaction in either habitat just because the intercept was 0.

Ken