# How to interpret coefficients of a multivariate mixed model in lme4 without overall intercept?

I'm trying to fit a multivariate (i.e., multiple response) mixed model in R. Aside from the ASReml-r and SabreR packages (which require external software), it seems this is only possible in MCMCglmm. In the paper that accompanies the MCMCglmm package (pp.6), Jarrod Hadfield describes the process of fitting such a model as like reshaping multiple response variables into one long-format variable and then suppressing the overall intercept. My understanding is that suppressing the intercept changes the interpretation of the coefficient for each level of the response variable to be the mean for that level. Given the above, is it therefore possible to fit a multivariate mixed model using lme4? For example:

data(mtcars)
library(reshape2)
mtcars <- melt(mtcars, measure.vars = c("drat", "mpg", "hp"))
library(lme4)
m1 <- lmer(value ~ -1 + variable:gear + variable:carb + (1 | factor(carb)),
data = mtcars)
summary(m1)
#  Linear mixed model fit by REML
#  Formula: value ~ -1 + variable:gear + variable:carb + (1 | factor(carb))
#     Data: mtcars
#   AIC   BIC logLik deviance REMLdev
#   913 933.5 -448.5    920.2     897
#  Random effects:
#   Groups       Name        Variance Std.Dev.
#   factor(carb) (Intercept) 509.89   22.581
#   Residual                 796.21   28.217
#  Number of obs: 96, groups: factor(carb), 6
#
#  Fixed effects:
#                    Estimate Std. Error t value
#  variabledrat:gear  -7.6411     4.4054  -1.734
#  variablempg:gear   -1.2401     4.4054  -0.281
#  variablehp:gear     0.7485     4.4054   0.170
#  variabledrat:carb   5.9783     4.7333   1.263
#  variablempg:carb    3.3779     4.7333   0.714
#  variablehp:carb    43.6594     4.7333   9.224


How would one interpret the coefficients in this model? Would this method also work for generalized linear mixed models?

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