spaMM (version 4.7.0)

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 where 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). *No* “argument name” should be attached to the indices, as any named element will be treated distinctly (cf. lhs argument), or ignored.

The mv syntax can be used further to declare composite random effects. As defined in composite-ranef and illustrated by a bivariate-response quantitative-genetic model (Examples in Gryphon), these effects 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(..., xpr)

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. *No* “argument name” should be attached to the indices.

xpr

(experimental) a character string which, when evaluated as an expression in the environment specified by the internal copy of the data, evaluates to a vector (one element per row of the data). as.numeric() is then applied to the vector, so that the resulting weights are numeric values by which the rows of the design matrix for the random effects will be pre-multiplied.

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)))) 
}