[R-sig-ME] Some very basic questions about modelling heteroscedasticity of within subjects variance in repeated measures obserational studies

[Chris Evans]

I'm a psychotherapist not a theoretical nor a professional statistician so apologies if some of these questions are embarrassingly stupid. I have done some searching for pertinent publications and answers but I'm no finding answers, perhaps I may be using entirely the wrong search terms/questions. 

I took a vow over a decade ago to stick with R for all my stats and don't intend to break it.  I'm slowly getting my head around mostly linear mixed models and mostly for changes on continuous measures in therapies mostly from naturalistic datasets from services, but just now also of some non-help-seeking general population samples. So far I've been using lmer from the lme4 package and lme and nlme from the nlme package. As I don't have the resource of colleagues with real skills in this area I've been trying to check my assumptions and analyses by modelling and seeing if analyses of models fit what I expect. Finding the simstudy package recently looks as if it will help with this and replace my otherwise clumsy models. 

My particular interest is in what I'm calling "heteroscedasticity of within subjects variance in repeated measures", I think it could also be called "allowing a random variance term within individuals" or something like that. I have good theoretical and some (quite old but robust looking pre-mixed models) empirical work that suggests that such a random effect may be present in most of my datasets. I know how to model random offsets (centred or not), random slopes and even piecewise random and nonlinear slopes (all of which are realistic in clinical datasets). However, I'm really unclear how I should model a random variance term, if I'm explaining myself clearly. I found some discussion off [ https://www.researchgate.net/post/Is_heteroscedasticity_considered_in_multilevel_random_effects_hierarchical_modeling | https://www.researchgate.net/post/Is_heteroscedasticity_considered_in_multilevel_random_effects_hierarchical_modeling ] but the only software implementations seemed to refer to MLWin and though I have great respect for MLWin and have used it in the past, I would really like to keep my vow to do everything in R. 

1) Can anyone point me to work within the mixed models tradition that looks as random within subjects variance?
2) Can anyone point me to work using R tools that explores this?

Many thanks in advance to all, and, while I'm here, huge thanks to the people who have written all these tools and so often give incredibly helpful and thoughtful Emails here from which I've learned much of what I do know about his area,

Chris

-- 
Chris Evans <chris using psyctc.org> Visiting Professor, University of Sheffield <chris.evans using sheffield.ac.uk>
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