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what kind of analysis should be used when there are several correlated dependent variables?

4 messages · Liliana Martinez, David Atkins

David Atkins
# 
Liliana--

One route would be to fit a multivariate mixed-effects model, in which 
the multiple outcomes are jointly treated as a DV.  Neither lme() nor 
lmer() have a way of explicitly specifying a multivariate model (ie, 
MCMCglmm can "cbind" multiple outcomes together), but it is possible to 
fit at least some basic multivariate models with some data manipulation.

The main "trick" here is to reshape your data by stacking all DVs into a 
single DV column and creating a factor that identifies which values in 
the DV correspond to your 4 separate DVs.

I recently used lme() to do this with a study of daily positive mood, 
negative mood, and fatigue in women with breast cancer (each woman had 
30 days of data).

Here was the code to reshape the data (where "id" identifies the 
individual, and "day" identifies -- shockingly -- day):

tmp.long.df <- reshape(my.df,
                       idvar=c("id","day"),
                       varying = c("posemo","negemo","fatigue"),
                       v.names = "dv",
                       times = 1:3,
                       direction="long")
names(tmp.long.df)[8] <- "dv.f" # rename times
tmp.long.df$dv.f <- factor(tmp.long.df$dv.f, 1:3, 
c("posemo","negemo","fatigue"))

So, your separate columns of DVs are specified on "varying", and the new 
data.frame has a column called "times" that identifies which DV is which 
in your new "dv" column.  I change times (which just happened to be the 
8th column in my data, you'll likely need to change that) to "dv.f" and 
then change that to factor with levels identifying separate DVs.

Then, here is an example of a call to lme() that I used:

mult.lme3.2 <- lme(dv ~ -1 + dv.f/(supp.sat.c*(emot.iss.c + phys.iss.c + 
comm.iss.c)),
				 data = mult.df, na.action = na.omit, control = list(msVerbose = TRUE),
				 random = list(id = ~ -1 + dv.f),
				 weights = varIdent(form = ~ 1 | dv.f),
				 correlation = corAR1(form = ~ 1 | id/dv.f))

So, a couple comments:

-- With this set-up, getting rid of the intercept makes the models a bit 
easier to interpret (for me) as you get separate intercepts for each DV.

-- Similarly, the "dv.f/..." fits the covariates nested within each DV, 
which again makes things a bit easier to interpret.

-- The random statement fits separate random-intercepts by DV that are 
correlated.

-- The weights statement allows different residual error terms by DV.

-- For our data, we fit an AR1 correlation model because of 30 days of data.

Hope that helps; I think David Afshartous has some postings about 
multivariate models in lme which you can probably find in the archive 
(if memory serves).

[And, I am again impressed at how flexible the mixed-effects tools are 
in R -- kudos to Jose and Doug for the great software.]

cheers, Dave
David Atkins
#
Liliana Martinez wrote:
Honestly, I would recommend trying to do some background reading and 
seek consultation from someone local.  The model that I suggested (and 
you fit) is quite complex.

The Pinheiro and Bates book is the "bible" for lme and will discuss 
model syntax, including weights and correlation.

The following article discusses multivariate models, and I am sure there 
are others:

MacCallum, R. C., Kim, C., Malarkey, W. B., & Kiecolt-Glaser, J. K. 
(1997). Studying multivariate change using
multilevel models and latent curve models. Multivariate Behavioral 
Research, 32, 215-253.

[Also, assuming that the data reshaping and model were specified 
correctly, there appears to be *no* correlation between DVs.  Though, 
there are huge differences across variances; I do not know your data, 
but this strikes me as odd]

All the best, Dave