How should I interpret a non-significant model effect but significant parameter estimate? I am running a negative binomial analysis with 2 main effects and 1 interaction. For the variable called "NR", the model effects table shows a non-significant value, but then in the parameter estimates table, the same variables show a significant result (see Tables below).
How should I interpret this? Should I take it as non-significant overall?


 A: I am assuming that you copied this from some statistical package. I hope someone finds it clearer, but here is my understanding:
The first table is a test on the significance of the whole categorical variable; i.e. it breaks it down to n-1 dummies, where n is the number of possible outcomes and it shows you the overall result indicating whether the inclusion of this variable, on top of the rest, significantly increases the fit of the model, vs leaving that variable out of the model, keeping all others in.
On the second table, you get the results of one regression with all variables included, where the nominal variables are broken down to n-1 dummies. In this case, all the significant statistics are on the individual estimated parameters of each possible outcome of each nominal variable.
Hence, if my understanding is correct, it could be possible for example to see the full nominal variable being significant in the first table, while several of its possible outcomes are not significant (depending on the base outcome too). However, in this case, based on the degrees of freedom on the first table and the break-down on the second, it seems to me that your categorical variable (Condition) is a single dummy (i.e. 2 outcomes). Hence, normally, you should not have this difference. However, I believe that this is possibly caused by multicolinearity, which is very high if you throw all these parameters in (not 100% sure if things change, if you change the base outcome of Condition).
In general, bear in mind that if some of your "independent" variables are very highly correlated, the significance statistics will be a mess. Based on the first table, you lose little in terms of goodness of fit, if you drop NR from your model and use only Condition and the interaction term. Try that and I suspect the standard errors of these 2 terms will go down a lot and all significance statistics way up.
