hmmm.chibar {hmmm}

chi-bar statistic test for hmm models

Description

Function to calculate weights and pvalues of a chi-bar-square distributed statistic for testing hypotheses of inequality constraints on parameters of hmm models. The models in input are objects inheriting from class hmmmfit or mphfit.

Usage

hmmm.chibar(nullfit, disfit, satfit, repli = 6000, 
kudo = FALSE, TESTAB = FALSE, 
alpha = c(0.02,0.03,0), pesi = NULL)

Arguments

nullfit

The estimated model with inequalities turned into equalities

disfit

The estimated model with inequalities

satfit

The estimated model without inequalities

repli

Number of simulations

kudo

If TRUE, the chi-bar weights are not simulated but computed by the Kudo's method

TESTAB

If TRUE, the LR tuned testing procedure is performed (see Details)

alpha

Three significance levels c(alpha1, alpha2, alpha12) of the LR tuned testing procedure

pesi

The chi-bar weights if they are known

Details

All the 3 argument models must be obtained by ‘hmmm.mlfit’ or by ‘mphineq.fit’. The method "Simulation 2" described in Silvapulle and Sen, 2005, pg. 79 is used if kudo = FALSE, otherwise the Kudo's exact method is used as described by El Barmi and Dykstra (1999). The Kudo's method can be reasonably used with less than 10-15 inequalities. If TESTA is the LR statistics for nullfit against the disfit model while TESTB is the LR statistics for disfit against the satfit model then the LR tuned testing procedure (Colombi and Forcina, 2013) runs as follows: accept nullfit if TESTB < y2 and TESTA < y1, where Pr(TESTB > y2) = alpha2-alpha12 and Pr(TESTA < y1, TESTB < y2) = 1-alpha1-alpha2, reject nullfit in favour of disfit if TESTA > y1 and TESTB < y12, where Pr(TESTA > y1, TESTB < y12) = alpha1, otherwise reject nullfit for satfit.

Value

A list with the statistics test of type A and B (Silvapulle and Sen, 2005, pg. 61) and their pvalues. If TESTAB = TRUE details on the LR tuned testing procedure (Colombi and Forcina, 2013) are reported.

References

Colombi R. Forcina A. (2013) Testing order restrictions in contingency tables. Submitted.

El Barmi H, Dykstra R (1999) Likelihood ratio test against a set of inequality constraints. Journal of Nonparametric Statistics, 11, 233-261.

Silvapulle MJ, Sen PK (2005) Constrained statistical inference, Wiley, New Jersey.

See Also

summary.hmmmchibar, print.hmmmchibar

Examples

data(polbirth)
# 1 = Politics; 2 = Birthcontrol
y<-getnames(polbirth,st=12,sep=";")                     
names<-c("Pol","Birth")
marglist<-c("l-m","m-l","l-l")
marginals<-marg.list(marglist,mflag="m")
ineq<-list(marg=c(1,2),int=list(c(1,2)),types=c("l","l"))

# definition of the model with inequalities on interactions in ineq
model<-hmmm.model(marg=marginals,dismarg=list(ineq),lev=c(7,4),names=names)

# saturated model
msat<-hmmm.mlfit(y,model)

# model with non-negative local log-odds ratios: "Likelihood ratio monotone dependence model"
mlr<-hmmm.mlfit(y,model,noineq=FALSE)

# model with null local log-odds ratios: "Stochastic independence model"
model0<-hmmm.model(marg=marginals,lev=c(7,4),sel=c(10:27),names=names)
mnull<-hmmm.mlfit(y,model0)

# HYPOTHESES TESTED:
#     testA --> H0=(mnull model) vs H1=(mlr model)
#     testB --> H0=(mlr model) vs H1=(msat model)

P<-hmmm.chibar(nullfit=mnull,disfit=mlr,satfit=msat)
summary(P)