# design matrix for a hmm model Function to specify the matrix X of the linear predictor Cln(Mm)=Xbeta for a hmm model. ```r create.XMAT(model, Formula = NULL, strata = 1, fnames = NULL, cocacontr = NULL, ncocacontr = NULL, replace = TRUE) ``` ## Arguments - `model`: Object created by `hmmm.model' - `Formula`: List of model-formulas; one formula for every marginal interaction - `strata`: Number of categories of the factors that describe the strata - `fnames`: Names of the factors 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 factor, 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 ## Details 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. ## Returns A list of matrices or a hmm model with X as design matrix according to the input argument `replace`. The parameters beta in the predictor Cln(Mm)=Xbeta are the effects specified in `Formula` and correspond to the columns of X. ## References Lang JB (2004) Multinomial Poisson homogeneous models for contingency tables. The Annals of Statistics, 32, 340-383. Lang JB (2005) Homogeneous linear predictor models for contingency tables. Journal of the American Statistical Association, 100, 121-134. ## See Also `hmmm.model`, `hmmm.mlfit`, `summary.hmmmfit` ## Examples ```r data(accident) y<-getnames(accident,st=9,sep=";") # responses: 1 = Type, 2 = Time; covariates: 3 = Age, 4 = Hour marglist<-c("l-m","m-g","l-g") marginals<-marg.list(marglist,mflag="m") names<-c("Type","Time") modelsat<-hmmm.model(marg=marginals,lev=c(3,4), strata=6, names=names) # Create X to account for additive effect of Age and Hour on the logits of Type and Time # and constant association between Type and Time al<-list(Type=~Type*(Age+Hour), Time=~Time*(Age+Hour),Type.Time=~Type.Time) # list of matrices (replace=FALSE) listmat<-create.XMAT(modelsat,Formula=al,strata=c(3,2),fnames=c("Age","Hour"),replace=FALSE) # the model obtained by the modified X (replace=TRUE) model<-create.XMAT(modelsat,Formula=al,strata=c(3,2),fnames=c("Age","Hour")) fitmodel<-hmmm.mlfit(y,model,y.eps=0.00001,maxit=2000) print(fitmodel) ```

create.XMAT function