# Considering residuals as new dependent variables after applying a linear mixed effect model to a set of data

I have a dataset including for each subject :

• 22 DV (linears, range [0-1]. These DV are intercorrelated). These measures are volume of different brain regions.
• 1 main effect to test (disease status; 0,1 or 2)
• 2 confounding IV (Age of the subject (linear), sex(binary 1 or 2) ; which have a known impact on my measures)
• 1 "site effect", as both subjects and measures are from different sites (1, 2 or 3)

My aim is to evaluate the effect of disease status on each of my 22 measures, after controlling for age, sex and site effects.

I have planned to use MANCOVA but I have to deal with non homogenous regression slopes. To overcome this problem, I have been told that I should use a linear mixed effect model, 1 model for each DV :

Measure1 ~ AGE:fixed + SEX:fixed + DISEASE_STATUS:fixed + (SITE:random)


The problem is that I would like to test whether there is a global main effect of the disease on my 22 measures, and in a second part of the analysis check which measure is significantly affected by the disease status.

Questions:

1. Do you think that I can run my analysis this way : first apply a model for each measure measure ~ AGE:fixed + SEX:fixed + (SITE:random) and then perform my analysis on the residuals of this first model (ie, a multivariate ANOVA) to check if there is a disease effect on residuals, and thus on DVs ?

2. If analysis of residuals are not appropriate, do you know if there a way to use some kind of "multivariate linear mixed effect model" ?

The reason why I do not want to apply one model to explain each DV is the multiple comparison issue, as I would dramatically inflate my alpha level.

Thank you in advance for your advices, and thank you for all the previously published answers that are very useful to non-statisticians researchers !

Edit

Thank you for your reply. I think I'll follow your advice and I'll use an FDR correction. My first question has been focused on a more general problem concerning the use of residuals as DV. Does the community have an opinion about this strategy?

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Are there any natural constraints in your DVs? For example would there be something like $DV1 + DV2>DV7$. Taking these into account may be useful for your analysis. – probabilityislogic Oct 6 '12 at 10:42

## 1 Answer

It looks like a multiple testing issue. Multiple adjustment seems to be the right approach to me. I don't see how a fancy method will get around it. Of course there are sometimes clever designs to use that can overcome the problem but not without some price being paid. Hierarchical stepdown testing is one thing that comes to mind. Also what makes you think that you have to pay too high a price. If it is because the Bonferroni bound is too high, there may be less conservative bounds that can apply. Maybe FWER control is not necessary and you can settle for FDR control. Resampling approaches to p-value adjustments will also be less conservative than Bonferroni.

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