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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) 

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Questions: 1)What level of correlation would warrant me combining a variable with another one?

I don't usually worry about correlated predictors unless the correlations are, say, >0.9

Question 2) Could I just make the corelated variables random effects? What would that look like in lmer?

No, this is not a justification for fitting random effects. For fitting random intercepts this only makes sense for variables that are factors, and represent some kind of grouping.

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.

Height, weight and waist circumference are explanatory variables / fixed effects. It does not make any sense to have one nested inside another. Even if there is actual nesting - levels of one factor being present in one and only one level of another - when they are fixed effects / explanatory variables this doesn't make sense, which brings me to the random part of your model:

(1|Hieght*Weight:waistcircumference)

if Height and Weight and waistcircumference are numeric variables, then this makes no sense at all. The grouping factors for random intercepts must be categorical factors. Even if they were categorised into say "small/medium/tall" this would be ordinal and still would not make sense. The only way that might make sense "to the software" is if you caode them just small/tall ie binary, but then you would open up a whole other can of worms. There is no reason to include height or weight as part of a grouping factor for random intercepts.

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    $\begingroup$ Thank you very much. $\endgroup$ May 31, 2021 at 15:58

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