I have a model with a dependent variable (Y), an independent variable (X), and three moderator variables (M1, M2, M3).

Using a Zero Inflated Negative Binomial (appropriate in my case), I have run different models, to explain the dependent variable Y: Model 1 includes: X + Three Moderators; Model 2: X + Three Moderators + XM1; Model 3: X + Three Moderators + XM2; Model 4: X + Three Moderators + XM3; Model 5 (full model): X + Three Moderators + XM1+XM2+XM3

The table I show reflects the results of the beta coefficients I have obtained, and whether they are significant or not.

I have the following questions in relation to the interpretation of results:

a) Could anyone tell me how to interpret M1, M2, and M3 effects on the relation between X and Y? I am confused since their positive or negative sign and significance level change, depending on the model.

b)Is the full model the most important one to explain Y, as it includes the effect of all moderators and interaction terms? If so, does it mean that M3 has no significant effect on the relation X-->Y, despite the results of model 4 suggest the opposite?

c) Should I plot the simple slopes for model 2, 3, and 4 (where moderators have significant effects?). Or also for model 5? Not sure how to do the last one.

d) Finally, are these results too weak? Or are they meaningful in a ZINB model?

(a) you have to keep in mind that if you consider interaction terms (like X*M_i), the main effects of X and M_i are not anlyonger easy and "legal" to interpret directly, since their meaning changes if you habe an interaction term. Without interaction term, you can interpret them directly. With interction term, their meaning is "the effect of M_i under the constraint that X=0" and the other way round.

(b) Usually you use the AIC value of a model tu judge if it is the "best" model. Because the amount of predictors have to be balanced with respect to the amount of variance explained. You can't do this just by the amount of significant regression coefficients. So you should calculate the AIC values for each model and should favour the model with the lowest AIC value

(c) Are X, Y and the M_i variables continuous or categorical? What exactly do you want to plot?

(d) weak regarding what? You have significant regression coefficients, thus, you have something to interpret. I guess you have a log-link function, which would e.g. mean that per unit of X the outcome changes by a factor of exp(0.1) = 1.1. You have to judge if this effect is high or low in the context of your variables. What I miss in your outcome: should't be there also a regression coefficients regarding the "zero-inflated" part of your model, i.e., the Bionmial part of the model?

Thanks a lot for your detailed response! This is very helpful!

You are right; I forgot to present the constant terms and also the coefficients regarding the inflated part of the model (is it necessary to report them as well?). In the model, all the variables are continuous.

In relation to plotting the interactions, I refer to those plots that can be used to show how X affects Y at different levels of the moderating variables; low or high for example - (Jeremy Dawson provides helpful tools in his website:http://www.jeremydawson.co.uk/slopes.htm). Just looking at the coefficients, as you said, it is difficult to interpret (especially when the moderating effects are significant).

I simply don't know if I should plot the interaction of model 4 (initially significant that, however, is not significant in the full model). How do I theoretically interpret this?

Another question: apart from computing AIC values, can I use likelihood ratio test as well to check the same?