confRegUCRandUCCR: Parameter Vector in Confidence Regions UCR and/or UCCR

Description

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

Usage

confRegUCRandUCCR(
  UMLE = NULL,
  paramVals = NULL,
  paramIDs = NULL,
  SignifLevel = 0.05,
  df,
  matY,
  matX
)

Value

confRegions: Data frame with columns: UMLE_logLik=log-likelihood of the unconstrained 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, StatUCR=value of the statistic used for UCR, StatUCCR=value of the statistic used for UCCR, CritValue=critical value, chi-squared with df and 1-SignifLevel, SignifLevel=significance level used to calculate the critical value, inUCR=logical value, TRUE if paramVals belongs to the confidence region UCR, inUCCR=logical value, TRUE if paramVals belongs to the confidence region UCCR,

Arguments

UMLE: A vector with the unconstrained maximum likelihood estimates.
paramVals: A vector with the parameter values for which it is needed to assess whether it is part of one of the confidence regions or not. The order of the parameters must be the same as the one of UMLE. As in Espinosa and Hennig (2023), the parameter vector contains the parameters of interest, beta_0r, and the remaining ones are the unconstrained 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}, paramVals in UCR but not in UCCR
myVector[myVectorID] <- seq(0.195,0.185,length.out=3)
confRegUCRandUCCR(UMLE=resAux$UMLE, paramVals=myVector, paramIDs=myVectorID,SignifLevel=0.05, df=3,
matY= resAux$matY, matX= resAux$matX)

# monotonic beta_{0r}, paramVals in UCR and UCCR
myVector[myVectorID] <- seq(0.073,0.074,length.out=3)
confRegUCRandUCCR(UMLE=resAux$UMLE, paramVals=myVector, paramIDs=myVectorID,SignifLevel=0.05, df=3,
matY= resAux$matY, matX= resAux$matX)

# monotonic beta_{0r}, paramVals out of UCR and UCCR
myVector[myVectorID] <- seq(0.072,0.073,length.out=3)
confRegUCRandUCCR(UMLE=resAux$UMLE, paramVals=myVector, paramIDs=myVectorID,SignifLevel=0.05, df=3,
matY= resAux$matY, matX= resAux$matX)