Nonsignificant main effect, nonsignificant interaction and significant interaction I performed a binomial logit glm in R and I got the following results, which I am not sure how to interpret.
I used the following code:
model <- glm(DV~x*y + x*z + CV + CV + CV + CV + CV + CV + CV,
             data = data,
             family = binomial(link = logit))





Variables
Model 1
Model 2
Model 3




x
0.150**
0.120
0.118


y
.250***
.250***
.250***


z
-.400***
-.400***
-.400***


x*y
.100**

.050


x*z

.200***
.220***




The confidence levels are as follows:
* - 0.1, ** - 0.05, *** 0.01
the DV is a dichotomous variable
Now, I am thinking that the Hypothesis of an effect of x on the DV is only partially supported, right?
The same is for the interaction effect of x*y on the DV, right?
For x*z the Hypothesis of an interaction effect is confirmed, right?
My interpretation would be, that x influences the DV only if z is large or not in the model. I am honestly pretty lost here because I dont know what these results mean. Could you please help me?
Additionally, I made a robustness check with another measure for z and the results stay the same apart from the effect of x becoming significant. What does this mean for my analysis?
 A: First, if you thought based on your understanding of the subject matter that the interaction terms would be important, then the first 2 models are essentially irrelevant--particularly in logistic regression. Omitting any outcome-associated predictor from a logistic regression can lead to omitted variable bias in the coefficient estimates for included predictors. If you think interactions are important and you have enough data to evaluate them, you should include them. Focus on Model 3.
Second, lower-level coefficients of predictors involved in interactions do not mean what they might seem at first. In Model 3, the coefficient for x represents its association with outcome when both y and z have values of 0. Whether that coefficient for x is different from 0 or not doesn't matter on its own.
If, say, y is a continuous predictor, then the coefficient for x will change depending on whether or not you centered y. If, say, z is a binary predictor, then the coefficient for x will change if you switch the reference level for z.
Those manipulations of y and z don't change the fundamental model or any predictions from the model--they just change the coefficient values reported for the other predictors with which they interact. This page shows a simple worked-through example.
So the apparent "significance" of the coefficient reported for x doesn't directly represent the statistical or practical significance of x in your model. Evaluating the significance of x needs to take into account all of the terms that involve it, including its interactions.
