spaMM (version 4.5.0)

mv: Virtual factor for multivariate responses

Description

Motivation: In a multivariate-response model fitted by fitmv, one may wish to fit a random-coefficient term appearing in s submodels, that is a random effect with realized values for each of these submodels and each group, with values possibly correlated among submodels within groups. Hence one might wish to specify it as a term of the form (<submodel>|group), where <submodel> would represent a factor for the s submodels. But the data are not expected to contain a factor for these submodels, so such a syntax would not work without substantial data reshaping. Instead, this effect can be stated as mv(...) where the ... are the indices of the submodels here the random effect appears. For example if submodels 2 and 3 include this random-coefficient term, the term can be specified as (mv(2,3)|group).

Composite random effects, as defined in spaMM-package and illustrated by a bivariate-response quantitative-genetic model (Examples in Gryphon), combine correlations among response variables of different submodels as specified by mv(), and correlations within each response variable(as specified by a relatedness matrix in the same example).

The mv(...) expression is treated as a factor for all purposes, meaning or example that (0+mv(2,3)|group) can also be used, leading (as for any factor) to an alternative parametrization of the same random-coefficient model (see Examples). The parametrization through (0+mv...) is generally recommended as its results are easier to interpret. The random-effect term is treated as a random-coefficient term for all purposes, meaning for example that fixed values can be specified for its parameters using the ranCoefs syntax (see Examples).

Usage

# mv(...)

Value

Not a function, hence no return value. In the summary of the fit, levels for the different submodels s within each group are labelled .mvs.

Arguments

...

Indices of all the submodels (possibly more than two) where the random effect involving this virtual factor appears.

See Also

Gryphon for example of composite random effects.

The X2X argument of fitmv for fixed effects shared across sub-models.

Examples

if (spaMM.getOption("example_maxtime")>1.1) {
## data preparation
data("wafers")
me <- fitme(y ~ 1+(1|batch), family=Gamma(log), data=wafers, fixed=list(lambda=0.2))

set.seed(123)
wafers$y1 <- simulate(me, type="marginal")
wafers$y2 <- simulate(me, type="marginal")

## fits
(fitmv1 <- fitmv(
  submodels=list(mod1=list(formula=y1~X1+(mv(1,2)|batch), family=Gamma(log)),
                 mod2=list(formula=y2~X1+(mv(1,2)|batch), family=Gamma(log))), 
  data=wafers))
# alternative '0+' parametrization of the same model:
(fitmv2 <- fitmv(
  submodels=list(mod1=list(formula=y1~X1+(0+mv(1,2)|batch), family=Gamma(log)),
                 mod2=list(formula=y2~X1+(0+mv(1,2)|batch), family=Gamma(log))), 
  data=wafers)) 
# relationship between the *correlated* effects of the two fits
ranef(fitmv2)[[1]][,2]-rowSums(ranef(fitmv1)[[1]]) # ~ 0

# fit with given correlation parameter: 
update(fitmv2, fixed=list(ranCoefs=list("1"=c(NA,-0.5,NA)))) 
}