Interpretation of three-way interaction

[ekbrown77]

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:

gender=female -1.2275

socioecon=lo -2.4095

age -1.1487

gender=female:socioecon=lo 5.936

gender=female:age -0.4166

socioecon=lo:age 1.7758

(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.

[Stefan Th. Gries]

Just to clarify: if "The three-way interaction term itself was not
selected as significant", then why do you still say " I think my data
need it"?

(Plus, we likely need the complete summary output (at least the
fixed-effects part).)

[ekbrown77]

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 *  

[Stefan Th. Gries]

Now, generally speaking,
- your summary output suggests that the effect of GENDER is not
identical across the two levels of SES;
- your summary output suggests that the effect of AGE is not identical
across the two levels of SES.
- your summary output suggests that the effect of AGE is not different
in the two levels of GENDER, (which means it could(/should?) be
deleted);
- your mail said the 3-way interaction is not significant (so it's
good that it's not included here).

I think if you do

plot(allEffects(model.final), type="response", ylim=c(0,1), grid=TRUE)

you will see all that's going on right away.

[ekbrown77]

Thank you much!