hmmm (version 1.0-4)

hmmm.model.X: hmm model with covariates effect on parameters

Description

Function to define a hmm model whose parameters depend on covariates.

Usage

hmmm.model.X(marg, lev, names, Formula = NULL, strata = 1, 
fnames = NULL, cocacontr = NULL, ncocacontr = NULL, replace=TRUE)

Arguments

marg

A list of the marginal sets and their marginal interactions as described in Bartolucci et al. (2007). See details of hmmm.model

lev

Number of categories of the response variables

names

A character vector whose elements are the names of the response variables

Formula

List of model-formulas; one formula for every marginal interaction

strata

Number of categories of the covariates that describe the strata

fnames

Names of the covariates that describe the strata

cocacontr

A list of zero-one matrices to build "r" logits created by the function `recursive'

ncocacontr

Number of contrasts for every covariate, if NULL the maximum number is used

replace

If TRUE a new model object with design matrix X is produced, if FALSE the list of design matrices associated to each element specified in Formula is returned

Value

An object of the class hmmmmod; it describes a marginal model with effects of covariates on the interactions. This model can be estimated by `hmmm.mlfit'.

Details

The arguments names and fnames report the names of responses and covariates according to the order in which the variables are declared, see details of function `hmmm.model'.

When the marginal interactions of a hmm model are defined in terms of a linear predictor of covariates Cln(Mm)=Xbeta, the list of model formulas defines additive effects of covariates on the interactions. In a case with two response variables declared by names<-c("A","B") and two covariates, named C and D by fnames=c("C","D"), the additive effect of the covariates on marginal logits of A and B and log odds ratios (A.B) of the two responses is specified by the following Formula: Formula<-list(A=~A*(C+D), B=~B*(C+D), A.B=~A.B*(C+D)). Use "zero" to constrain to zero all the interactions of a given type. The saturated model is the default if Formula is not specified.

References

Colombi R, Giordano S, Cazzaro M (2014) hmmm: An R Package for hierarchical multinomial marginal models. Journal of Statistical Software, 59(11), 1-25, URL http://www.jstatsoft.org/v59/i11/.

Glonek GFV, McCullagh P (1995) Multivariate logistic models for contingency tables. Journal of the Royal Statistical Society, B, 57, 533-546.

Marchetti GM, Lupparelli M (2011) Chain graph models of multivariate regression type for categorical data. Bernoulli, 17, 827-844.

See Also

hmmm.model, create.XMAT, summary.hmmmmod, print.hmmmmod, marg.list, recursive, hmmm.mlfit

Examples

# NOT RUN {
data(accident)
y<-getnames(accident,st=9,sep=";")
# responses: 1 = Type, 2 = Time; covariates: 3 = Age, 4 = Hour

marginals<-marg.list(c("b-marg","marg-g","b-g"))
al<-list(
Type=~Type*(Age+Hour),
Time=~Time*(Age+Hour),
Type.Time=~Type.Time*(Age+Hour)
)
# model with additive effect of the covariates on logits and log-o.r. of the responses
model<-hmmm.model.X(marg=marginals,lev=c(3,4),names=c("Type","Time"),
Formula=al,strata=c(3,2),fnames=c("Age","Hour"))
mod<-hmmm.mlfit(y,model,y.eps=0.1)
# }