# 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,

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?

• Please edit the question to show the actual model formulas and coefficient estimates for y and z where relevant. It’s hard to understand what is going on without that information.
– EdM
May 27, 2022 at 14:17
• Thank you! Added the missing information May 27, 2022 at 14:25
• Can you please clarify what you are looking for? I.e. are you just interested in correlations of your variables or are you looking for causality? Also, if you conduct hypothesis tests you need to specify the required confidence level. Can you provide the confidence levels for the stars displayed in the table? May 27, 2022 at 18:19
• Thank you for the suggestions. I added the confidence levels. I am looking for causality. What i am most interested about is what it means that the main effect and the first interaction term become nonsignificant after introduction of the second interaction. Does it mean that when z is large, the effect of x is gone? May 27, 2022 at 18:34

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.

• Thank you very much for your answer, I really appreciate it. I get that there is danger of omitted variable bias if i interpret the results of Model 1 or 2. However, someone told me that you should also consider the results of the "partial models" (1 and 2) when you interpret interaction effects and test the hypotheses. For clarification, i standardized the variables before performing the regression. Let's say the effects in the table are the hypothesized effects. Does that mean, that H1 (effect x -> DV) and H2 (x*y -> DV) are not supported and H3 (x*z -> DV) is? May 27, 2022 at 19:32
• @Snappie you can't properly evaluate your x -> DV hypothesis without specifying values of y and z or doing a combined test (e.g., a Wald test) of all the coefficients involving x. The magnitude of the x -> DV effect depends on y and z. The x:y interaction might not be "statistically significant," but keeping it in the model is likely to improve predictions. Also, be very careful in trying to infer causality from a model like this.
– EdM
May 27, 2022 at 19:46