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I am running a logistic regression model to evaluate how age and another measured variable (endo_thickness) associate with clinical pregnancy as an outcome.

Both associate at a univariate level with the OR for age <1 and OR for endo_thickness>1.

Age is also a strong associated a predictor of endo_thickness and they have a weak but significant correlation (r=-0.03, p<0.001).

It makes me wonder if age and endo_thickness may have an effect on each other so I performed a model with the interaction term which reverses the OR for endo_thickness now. I'm not sure how to interpret this now? The interaction hovers above 0.05, does this mean that it shouldn't be included in the analysis?

Without the interaction term enter image description here

With the interaction term enter image description here

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You could verify this using software such as the free GPower: when N > 15,000 and an effect yields a p-value as large as .051, you can be sure it is a negligible, trivial effect. Including this interaction increases pseudo-RSQ by a mere .0002 but non-trivially complicates your task of interpretation and reporting.

Some would argue that, once you've tested the interaction, it would distort your inferential statistics to eliminate it from your analysis. That is a purist's view; in this situation most analysts would drop the interaction term. If you do decide to keep it in, in order to properly interpret it you'll need to consider the distributions of the other 2 predictors. What are their typical values, standard deviations, min, and max? (Also, what species is under study here?) What's clear is that as endo_thickness increases by 1 (and non-insiders like me won't know how meaningful an increase that is), the odds ratio linking age with clinical pregnancy increases by a factor of 1.0039. You could reverse the order of those two predictors and the statement would still be true.

From the pseudo-RSQ difference of .0002, we know that predicted values will hardly differ between your two solutions. This is true even though, as you've noted, one of your predictors changes signs from model 1 to model 2. The sign reversal is a compensation for the introduction of the interaction term. Knowing what you know from model 2, you can't precisely describe the main effect of endo_thickness without accounting for the interaction. You can't precisely describe the effect for femaleage either, though it does seem essentially to retain its main effect from model 1.

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  • $\begingroup$ Thanks for your advice! $\endgroup$ – rakelren May 13 at 11:22

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