I am attempting to run a linear mixed effects regression using the lme4qtl R package. This is a package very similar to lme4, but it allows you to specify a kinship matrix so that you can account specifically for family structure in the model.
The variable I want to predict is a measure of connectivity between two brain regions. The predictor is a measure of alcohol intake over the past 7 days, with additional covariates being gender, age in years, and years in education. I have just under 1200 participants. The model looks like this:
relmatLmer(Brain_Connection ~ Drinks_7days + Age_in_Yrs + Gender + Yrs_in_Education + (1|Family_ID) + (1|Subject), data = df, relmat = list(myID = kinship_matrix))
When I run this with the raw data I get convergence errors like this:
Model failed to converge: degenerate Hessian with 1 negative eigenvalues
To get around this I have tried many ways to transform the data. I have tried scaling the data, using log, inverse log, sqrt, or cube transforms. However with the exception of the scaling method (either for the drinking variable, or the brain connectivity one), these still give me convergence errors. After getting through this stage, when I then run residual diagnostics they are not normally distributed.
My question is - is there a more sensible way to figure out what may be happening other than transforming the variables in different ways and hoping for the best. Second, if the scaling method is the only one that doesn't lead to convergence errors, but the residuals are still not normal, does this mean that this model is simply incorrect or not appropriate? If so, how can I go about assessing a relationship between the variables?
The raw drinking data looks like this:
The raw connectivity data looks like this:
The residuals from the 'successful' scaled model look like this:
As you can probably tell I am quite new to this so please forgive me if this is a silly question.
Many thanks for your time.