I have longitudinal data on Health (0/1) for a set of individuals, each
of which has a cohort ID (defined by birth year). Each individual is
assessed for health for a range of ages. Call the data frame
longitudinal.df, which looks like
ID Age Cohort Health
individual_ID_1 age cohort health_at_age
individual_ID_1 age+1 cohort health_at_age+1
individual_ID_2 age cohort health_at_age
individual_ID_2 age+1 cohort health_at_age+1
etc.
if we fit, say,
glmer(Health ~ Cohort:as.factor(Age) + (Cohort|ID), data =
longitudinal.df, family = binomial)
we get a set of age-specific slopes:
Cohort:as.factor(Age)64
Cohort:as.factor(Age)66
.
.
.
Cohort:as.factor(Age)92
Cohort:as.factor(Age)94
each estimates the slope on the logit scale of the regression between
health (y) and cohort (x) for a given age.
This model has a much lower AIC than the model without age-specific
slopes. This means that there is support for the claim that there is
heterogeneity across ages with respect to slope.
I have an external hypothesis that the trend of these age-specific
slopes over age is increasing (with younger ages having negative slopes
and older ages having positive slopes).
How do I correctly test for an increasing trend over ages of the
age-specific regression slope estimates derived from the glmer model fit?