I am using lmer() (lme4 package) in r to test whether a hormonal factor (x) predicts score on a mental health scale (y). I am using linear mixed models rather than a standard GLM because the outcome score is provided by 2 raters (i.e. multiple response data). My baseline model consists of 3 fixed factors: age (continuous), sex (m/f) and rater (person 1/person 2) and I would like to include my primary variable of interest, x, in a subsequent model.
My question is: how should I include x as an ordinal variable when x is very differently distributed among males and females (see density plots below).
- (I am aware of the information-loss that goes along with discretising continuous variables but in this particular context, specific hormone values are less interesting to me than group rankings. I think creating hormone groups would simplify results & aid interpretation)
Let's say I split the hormonal variable x into quartiles...
Should I create quartiles on the entire sample (top plot)? Thus resulting in 0 females in the top quartile & few males in the bottom quartile (a problem when it comes to group interactions)?
Or can I create sex-specific quartiles (middle plot for females; bottom plot for males)? And can these sex-specifc rankings...
Female: FQ1, FQ2, FQ3, FQ4
Male: MQ1, MQ2, MQ3, MQ4
... be merged into one group variable with just 4 response options (Q1, Q2, Q3, Q4) & included as a predictor in our linear mixed model?
I imagine there is something wrong with doing it the latter way (sex-specific quartiles) but I don't know what exactly that is. Is it a comparable issue to including a continuous variable that has been standardised within each sex but entered as 1 variable?
The ultimate aim is to compare models without x (Model 0) and with x (Model 1) and in subsequent models, to add interaction terms such as the x:sex interaction.
(This data has previously been discussed with regards to its random effects on this thread: Mixed Model using lme4 in R for multiple response data )