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
)

Arguments

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,

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>.

See Also

confRegUCRandUCCR, mdcp, monoTestBonf, monoTestConfReg, plotCMLE, vlgm.

Examples

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)

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
)

Arguments

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,

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>.

See Also

confRegCCR, mdcp, monoTestBonf, monoTestConfReg, plotCMLE, vlgm.

Examples

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)

Real data example

Description

Uses real data

Usage

crovData

Format

Data frame with 9 variables

Monotonicity Direction Classification (MDC) procedure

Description

Fits a constrained regression model for an ordinal response with ordinal predictors and possibly others, Espinosa and Hennig (2019) <DOI:10.1007/s11222-018-9842-2>. The parameter estimates associated with an ordinal predictor are constrained to be monotonic. If a monotonicity direction (isotonic or antitonic) is not specified for an ordinal predictor (OP) by the user, then a constrained method to be indicated in the option method establishes it or the approach that tries all possible combinations of monotonicity directions an the chooses the one with maximum likelihood.

Usage

mdcp(
  formula,
  data = NULL,
  tryAllMonoDir = FALSE,
  monoDir = NULL,
  CLS1 = 0.95,
  TLBS2 = 0.85,
  TLNS2 = 0.999,
  StepSizeCLS2 = 1e-04,
  method = NULL,
  monoTestSignLevel = 0.05,
  reltol = 1e-05,
  mu = 1e-04,
  outer.eps = 1e-05
)

Arguments

Value

MDCproc: Data frame with the monotonicity direction classification (Isotonic, Antitonic, Both, or None) used for each ordinal predictor in each one of the steps of the MDC procedure (S1, S2 and S3), together with their individual confidence levels (CL). If monoDir is used, MDCproc shows the monotonicity directions in monoDir.

estimates: Vector of parameter estimates of the model.

log.lik: Value of the log-likelihood of the model.

allModels: Data frame with monotonicity directions, log-likelihood and parameter estimates of all models involved in the third step of the MDC procedure. If parameter monoDir is used, allModels shows these results from the model with monotonicity directions used in monoDir only. If parameter tryAllMonoDir is used, allModels shows these results from all the models according to all possible combinations of monotonicity directions.

constrOptimRes: List with the outcomes provided by the function constrOptim.

UMLE: Vector with the parameter estimates of the unconstrained version of the model.

UMLE_SE: Vector with the standard errors of the unconstrained version of the model.

q_cat_OrdPred: Vector with the number of ordinal categories for each ordinal predictor. Values are displayed in the same order as the ordinal predictors are incorporated in formula.

References

Espinosa, J., and Hennig, C. "A constrained regression model for an ordinal response with ordinal predictors." Statistics and Computing 29.5 (2019): 869-890. https://doi.org/10.1007/s11222-018-9842-2.

See Also

monoTestBonf, monoTestConfReg, confRegUCRandUCCR, confRegCCR, plotCMLE, constrOptim.

Examples

# Ordinal predictors: EduLevel, IncQuint and Health,
mdcpExample <- mdcp(QoL ~ EduLevel + Age + IncQuint + Gender + Health, data = crovData,
CLS1 = 0.95, TLBS2 = 0.90, TLNS2 = 0.99, StepSizeCLS2 = 0.0002)
mdcpExample$MDCproc
cbind("CMLE"=mdcpExample$estimates,"UMLE"=mdcpExample$UMLE)
mdcpExample$UMLE_SE
mdcpExample$log.lik
mdcpExample$allModels[1:6]

Monotonicity test

Description

Tests the null hypothesis of monotonicity over a set of parameters associated to an ordinal predictor, according to Espinosa and Hennig (2019) <DOI:10.1007/s11222-018-9842-2>.

Usage

monoTestBonf(simultAlpha = 0.05, OP_UMLE, OP_SE)

Arguments

Value

testRes: String value with outcomes either "Reject H_0" or "Not Reject H_0".

simultAlpha: Numerical value with the simultaneous significance level.

indivAlphaA: Numerical value with the individual significance level for each confidence interval.

simultPvalue: Numerical value with the p-value associated to the simultaneous significance level.

References

Espinosa, J., and Hennig, C. "A constrained regression model for an ordinal response with ordinal predictors." Statistics and Computing 29.5 (2019): 869-890. https://doi.org/10.1007/s11222-018-9842-2.

See Also

mdcp, monoTestConfReg, plotCMLE, vlgm.

Examples

monoTestBonf(simultAlpha=0.05, OP_UMLE = c(-0.352177095,-0.403928770,
-0.290875028,-0.769834449), OP_SE = c(0.246638339,0.247723681,0.267577633,0.300951441))

Monotonicity test using confidence regions

Description

Tests the null hypothesis of monotonicity over a set of parameters associated to an ordinal predictor. The log-likelihood ratio test is used after imposing ordinal constraints on the parameter estimates of a single ordinal predictor and comparing its results against the unconstrained MLEs.

Usage

monoTestConfReg(formula, data = NULL, monoDir = NULL, SignifLevel = 0.05)

Arguments

Value

resConfRegTest: Data frame with columns: OPName=Name of the ordinal predictor (OP), Num_Cat=Number of categories of the OP, UMLE_logLik=log-likelihood of the unconstrained model, CMLE_logLik=log-likelihood of the constrained model using mdcp assuming monotonicity for each OP, degreesOfFreedom=degrees of freedom used in the hypothesis test, Statistic=value of the statistic, CritValue=critical value resulting from the statistic, SignifLevel=significance level used in the test, P.Value=p-value, RejectMonotonicity=TRUE if the null hypothesis of monotonicity is rejected, FALSE otherwise.

See Also

mdcp, monoTestBonf, confRegUCRandUCCR, confRegCCR, plotCMLE, vlgm.

Examples

# Ordinal predictors: EduLevel, IncQuint and Health
  monoTestConfRegExample <- monoTestConfReg(QoL ~ EduLevel + Age + IncQuint + Gender +
  Health, data = crovData, monoDir=c(0,-1,-1), SignifLevel = 0.05)
  monoTestConfRegExample$resConfRegTest

Plot unconstrained and constrained proportional odds logit model

Description

Uses the results of function mdcp to produce a plot for the Maximum Likelihood Estimators of the parameters of both the unconstrained and constrained proportional odds logit models (UMLE and CMLE correspondingly). The UMLE includes confidence intervals. Parameter estimates of ordinal predictors are graphically linked with segments.

Usage

plotCMLE(
  mdcpResult = NULL,
  SignifLevel = 0.05,
  xposLegend = NULL,
  yposLegend = NULL,
  xcex.axis = 0.8,
  ycex.axis = 0.8,
  cexLegend = 1,
  methodName = "Not indicated"
)

Arguments

Value

Plot.

See Also

monoTestBonf, monoTestConfReg, monoTestBonf, constrOptim.

Examples

# Ordinal predictors: EduLevel, IncQuint, Health,
# Overcrowd, and NumChildren
mdcpExample <- mdcp(QoL ~ EduLevel + Age + IncQuint + Gender + Health, data = crovData,
CLS1 = 0.95, TLBS2 = 0.90, TLNS2 = 0.99, StepSizeCLS2 = 0.0002)
plotCMLE(mdcpResult=mdcpExample,SignifLevel=0.05,xposLegend=14, yposLegend=4.8,
cexLegend=0.8, method="MDCS3")