Hello. I need help interpreting the estimate coefficients of main effects and interaction terms of a mixed effects logistic regression with lme4::glmer(). In my data, I have two genders (male, female), two socioeconomic classes (lo, hi) and age in years as a continuous variable. I understand that when you have an interaction term, the interpretation of the main effects is different from when you don't have any interaction terms in the model. For example, if I had an interaction term between gender * socioecon, the estimate coefficient for gender=male would refer to the difference between males and females within only the reference level of the socioeconomic variable (hi, because it's alphabetically first).
My question is:
How can I interpret the estimate coefficients in a three-way interaction: gender * socioecon * age? For example, in my model, I get:
(The three-way interaction term itself was not selected as significant.) Do these results mean that females use the non-reference level of the dependent less than males when socioecon=hi? Does age affect the estimate coefficient of the main effects? And does "gender=female:socioecon=lo 5.936" mean that females use the non-reference level of the dependent variable more than males when socioecon=lo or socioecon=hi?
While I'd rather not have a three-way interaction term, I think my data need it. Thanks.
Fixed effects: Estimate Std. Error z value Pr(>|z|) (Intercept) 1.5833 0.9038 1.752 0.079801 . genderfemale -1.2275 0.7223 -1.699 0.089267 . socieconlo -2.4095 0.6737 -3.576 0.000348 *** scale(age) -1.1487 0.3317 -3.463 0.000535 *** scale(log(bigram_freq + 1)) 0.5872 0.1881 3.121 0.001802 ** scale(mi) 0.2966 0.1253 2.368 0.017899 * fol_phon_bin2nonHiV 0.2743 0.2654 1.034 0.301271 pre_phon_bin2nonHiV -0.8618 0.7411 -1.163 0.244866 genderfemale:socieconlo 5.9360 1.1968 4.960 7.05e-07 ***
genderfemale:scale(age) -0.4166 0.6677 -0.624 0.532654 socieconlo:scale(age) 1.7758 0.7652 2.321 0.020299 *