I'm trying to fit a multivariate (i.e., multiple response) mixed model in
R. Aside from the
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?