confRegCCR: Parameter Vector in Confidence Region CCR

Description

Determines whether a parameter vector is in the confidence region CCR, according to the definitions in Espinosa and Hennig (2023) <https://doi.org/10.48550/arXiv.2107.04946>.

Usage

confRegCCR(
  CMLE = NULL,
  paramVals = NULL,
  paramIDs = NULL,
  SignifLevel = 0.05,
  df,
  matY,
  matX
)

Value

confRegions: Data frame with columns: CMLE_logLik=log-likelihood of the constrained model, param_logLik=log-likelihood of the model using paramVals, monotonicBeta0=logical value, TRUE if the set of parameters of paramVals indicated by paramIDs are monotonic, df=degrees of freedom used to calculate the critical value, StatCCR=value of the statistic used for CCR, CritValue=critical value, chi-squared with df and 1-SignifLevel, SignifLevel=significance level used to calculate the critical value, inCCR=logical value, TRUE if paramVals belongs to the confidence region CCR,

Arguments

CMLE: A vector with the constrained maximum likelihood estimates.
paramVals: A vector with the parameter values for which it is needed to assess whether it is part of the confidence region or not. The order of the parameters must be the same as the one of CMLE. As in Espinosa and Hennig (2023), the parameter vector contains the parameters of interest, beta_0r, and the remaining ones are the constrained MLEs given beta_0r.
paramIDs: A vector indicating the positions of the parameter values of beta_0r in paramVals, which are those of interest, usually the ones corresponding to some ordinal predictor. For instance, paramIDs=7:11 indicates that the 7th to the 11th parameter values in paramVals are the ones of interest and correspond to some ordinal predictor.
SignifLevel: A decimal number indicating the significant level. Usually, 0.05.
df: Degrees of freedom to be used.
matY: matY resulting from mdcp().
matX: matX resulting from mdcp().

References

Espinosa, J., and Hennig, C. "Inference for the proportional odds cumulative logit model with monotonicity constraints for ordinal predictors and ordinal response." Arxiv (2023). <https://doi.org/10.48550/arXiv.2107.04946>.

Examples

Run this code

resAux <- mdcp(QoL ~ EduLevel + Age + IncQuint + Gender + Health, data = crovData)
plotCMLE(resAux)
myVector <- resAux$estimates
myVectorID <- 10:12
myVector[myVectorID]

# non-monotonic beta_{0r}
myVector[myVectorID] <- seq(0.195,0.185,length.out=3)
confRegCCR(CMLE=resAux$estimates, paramVals=myVector, paramIDs=myVectorID,SignifLevel=0.05, df=3,
matY= resAux$matY, matX= resAux$matX)

# monotonic beta_{0r} and paramVals in CCR
myVector[myVectorID] <- seq(0.048,0.049,length.out=3)
confRegCCR(CMLE=resAux$estimates, paramVals=myVector, paramIDs=myVectorID,SignifLevel=0.05, df=3,
matY= resAux$matY, matX= resAux$matX)

# monotonic beta_{0r} and paramVals out of CCR
myVector[myVectorID] <- seq(0.047,0.048,length.out=3)
confRegCCR(CMLE=resAux$estimates, paramVals=myVector, paramIDs=myVectorID,SignifLevel=0.05, df=3,
matY= resAux$matY, matX= resAux$matX)