Differences between sexes across months with repeated IDs I'm trying to figure out the best way to analyze the difference between sexes and across months for the means of a specific behavior (most individuals measured have repeated measures across the 5 years of the project which will contribute to the mean).  
I thought a glmm would be most appropriate with 
behavior ~ month + sex + sex*month + (1|Individual ID) 
The month is coded as a factor (but with each month represented as a number 1-12) and so is the sex. Behavior is numeric. I need to account for the repeated measures of individuals across years because my samples sizes within a given year weren't always high (working with endangered zoo species but across the data set I do have 101 individuals just not always represented in each year and each month). The data produce the following graph. Males are green and females are blue. It has the general shape I was expecting (males stereotype more during the breeding season and females reduce stereotypes). 
 
I was expecting a significant interaction of sex*month based on the graph but I'm not seeing significance and I'm wondering, since the data are clearly not linear, if a glmm is actually appropriate? Any suggestions on analyses that would be best for this type of data?  
 A: It could just be an issue of precision. Repeated measures data have intraclass correlation, meaning that a correct analysis will be, on average, less precise/efficient than would be the case if the data were completely independent. That could be one reason why the LOESS curves you show do not agree with the model results: LOESS treats those data as independent. I agree the graph suggests that one or more month term should interact with sex, as measured by a statistical significance test. 
Have you inspected a panel or spaghetti plot to see if there is heterogeneity in the mean response by sex? That is, is the tendency toward 0/1 in the earlier months driven by a few individuals who lie more than a few SDs beyond the average response? One possible impact is that the random intercept predicts a large unobserved latent response for them, so that their contribution to the analysis is downweighted significantly. 
Are you using a logistic link or a linear link for your GLMM? 
You might also consider using a GEE to assess the reliability of the mixed model results. These handle the correlation structure in a slightly different way. In some ways, they make better use of outlying observations by not-so-dramatically downweighting their contribution to the estimated average and standard error.
