hmmm.model.X: hmm model with covariates effect on parameters
In hmmm: Hierarchical Multinomial Marginal Models

Description Usage Arguments Details Value References See Also Examples

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

1 2	hmmm.model.X(marg, lev, names, Formula = NULL, strata = 1, fnames = NULL, cocacontr = NULL, ncocacontr = NULL, replace=TRUE)

`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

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.

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’.

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.

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

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)