Some of my predictors I want to use in a mixed model are correlated. Many seem independent but several are not (i.e. paternal and maternal age, delayed motor and verbal development). I may simply combine these scores together i.e. sum them. Or should I run PCA and include the components before the knee? I'm not a fan of this solution as I would lose interpretability of the variables.
Questions: 1)What level of correlation would warrant me combining a variable with another one?
Question 2) Could I just make the corelated variables random effects? What would that look like in lmer?
Question 3) I may want to nest waist circumference inside height and weight. I've provided a snippet of some lmer formula I may use. Note that I have not listed the full model here, I will likely fit all the variables at once after removing non significant ones and use elastic net.
dat is a dataframe from containing all my variables (both predictors and regressors) as columns.
lmer( dat[,predictor]~interview_age+rel_relationship+ehi_y_ss_scoreb+scale(smri_vol_scs_intracranialv)+ (1|mri_info_deviceserialnumber)+ #this models random effect for site (1|mri_info_deviceserialnumber:rel_family_id)+ #this models random effect by nesting family within the site (1|Hieght*Weight:waistcircumference) +dat[,regressor],data=temp)