# Multivariate analyses using mixed models vs. other approaches

Multivariate analyses (i.e. several dependant variables) can be performed using mixed effects models. In brief, columns representing the dependent variables are stacked on top of one another into a single column called “values” and another variable called “name” is created which indicates each original dependent variable. The data now in long format can then be analysed using a “univariate” mixed model with “values” being the dependent variable, “name” interacting with covariates of interest, and random effects such as subject id to account for multiple observations from the same subject. An example is shown here.

I would like to know if other approaches to account for non independence can be used on long format data as described above? Specifically I was thinking of 1) a working independence model followed by clustered standard errors; (2) generalized least squares; and (3) generalized estimating equations.

One very simple workaround with this would be a piecewise structural equation model (SEM) using mixed models as paths in the SEM. More on this method can be found in the paper on this subject here. An example is given on the piecewiseSEM creator's book section here:

library(nlme)
library(lme4)

shipley_psem <- psem(

lme(DD ~ lat, random = ~ 1 | site / tree, na.action = na.omit,
data = shipley),

lme(Date ~ DD, random = ~ 1 | site / tree, na.action = na.omit,
data = shipley),

lme(Growth ~ Date, random = ~ 1 | site / tree, na.action = na.omit,
data = shipley),

glmer(Live ~ Growth + (1 | site) + (1 | tree),
family = binomial(link = "logit"), data = shipley)

)

summary(shipley_psem, .progressBar = FALSE)


You can see that within the psem function, this estimates:

• Three mixed model regression paths with a Gaussian response.
• One GLMM with a binomial response.
• Four DVs estimated among these four paths.
• This is interesting thank you. However, I would be grateful for some discussion on the validity of clustered standard errors, GLS and GEEs in this context too. Commented Jul 31 at 19:31