Package 'crov'

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

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().

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

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().

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

formula	A formula to be fitted with ordinal response, one or more ordinal predictors, and possibly one or more other predictors. For ordinal response and ordinal predictors use ordered factors.
data	A data.frame, list or environment (or object coercible by as.data.frame to a data.frame), containing the variables in formula. Neither a matrix nor an array will be accepted.
tryAllMonoDir	A logical value that indicates whether one model should be fitted for each one of the possible combinations of monotonicity directions of the ordinal predictors' effects. Use TRUE if no constrained method is used in method.
monoDir	Vector with monotonicity directions for the ordinal predictors to be used as constraints. Possible values for monoDir are 1, 0 and -1. Use 1 for "isotonic" and -1 for "antitonic". If the monotonicity direction of the prameters of an ordinal predictor has to be estimated, then use 0, which also allows to drop the monotonicity assumption when method is not "MDCS3". The order of the elements in monoDir must be the same as the order of the ordinal predictors in the object formula, i.e., the j-th element of monoDir must correspond to the monotonicity direction of the j-th ordinal predictor in formula. For example, monoDir=c(0,-1,-1,1,0) indicates that the monotonicity direction of the effects of the first OP will be estimated; the monotonicity direction of the effects of the second and third OPs are antitonic; the monotonicity direction of the effects of the fourth OP isotonic; and the monotonicity direction of the effects of the fifth OP will also be estimated. If tryAllMonoDir and monoDir are not used (default option), the monotonicity direction classification prodecure is executed on all of the ordinal predictors to find the monotonicity directions associated to the model with the maximum log-likelihood.
CLS1	Numerical value for the confidence level to be used in the first step of the MDC procedure. This parameter is active if tryAllMonoDir is not used.
TLBS2	Numerical value for the tolerance level to be used in the second step of the MDC procedure over those ordinal predictors classified as "Both" in the first step. This parameter is active if tryAllMonoDir and monoDir are not used.
TLNS2	Numerical value for the tolerance level to be used in the second step of the MDC procedure over those ordinal predictors classified as "None" in the first step. This parameter is active if tryAllMonoDir and monoDir are not used.
StepSizeCLS2	Numerical value for the magnitude in which the confidence levels will be increased or decreased during the second step of the MDC procedure. This parameter is active if tryAllMonoDir and monoDir are not used.
method	The type of constrained method to be used among "MDCS1", "MDCS2", "MDCS3", "CMLEbonferroni", "CMLEconfReg", and "CMLEfiltered". Default value is "MDCS3". "MDCS1" uses the first step of the MDC procedure described in Espinosa, J. and Christian H. (2019) to drop the monotonicity constraints on those ordinal predictors (OPs) classified as "both" or "none". "MDCS2" uses the second step of the MDC procedure described in Espinosa, J. and Christian H. (2019) to drop the monotonicity constraints on those OPs classified as "both" or "none". "MDCS3" performs the three steps of the MDC procedure described in Espinosa, J. and Christian H. (2019) and does not drop monotonicity constraints on the OPs, being the most restrictive method. "CMLEbonferroni" tests the null hypothesis of monotonic effects for an OP as described in Espinosa, J. and Christian H. (2019) and drops the monotonicity constraints on those OPs for which the monotonicity test rejects the null hypothesis. "CMLEconfReg" tests the null hypothesis of monotonic effects for an OP based on the analysis of confidence regions and drops the monotonicity constraints on those OPs for which the monotonicity test rejects the null hypothesis. "CMLEfiltered" uses the first step of the MDC procedure described in Espinosa, J. and Christian H. (2019) to drop the monotonicity constraints on those ordinal predictors (OPs) classified as "none".
monoTestSignLevel	Significance level used when method is "CMLEbonferroni" or "CMLEconfReg". Default value 0.05.
reltol	Passed to constrOptim().
mu	Passed to constrOptim().
outer.eps	Passed to constrOptim().

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

simultAlpha	Numerical value for the simultaneous significance level.
OP_UMLE	Vector with the unconstrained parameter estimates of an ordinal predictor's categories represented by dummy variables in an unconstrained model for ordinal response (see vlgm).
OP_SE	Vector with the standard error of the parameters of an ordinal predictor's categories represented by dummy variables in an unconstrained model for ordinal response (see vlgm).

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

formula	A formula to be fitted with ordinal response, one or more ordinal predictors, and possibly one or more other predictors. For ordinal response and ordinal predictors use ordered factors.
data	A data.frame, list or environment (or object coercible by as.data.frame to a data.frame), containing the variables in formula. Neither a matrix nor an array will be accepted.
monoDir	Vector with monotonicity directions for the ordinal predictors to be used as constraints. Possible values for monoDir are 1, 0 and -1. Use 1 for "isotonic", -1 for "antitonic", and 0 o test monotonicity of the prameters of an ordinal predictor. The order of the elements in monoDir must be the same as the order of the ordinal predictors in the object formula, i.e., the j-th element of monoDir must correspond to the monotonicity direction of the j-th ordinal predictor in formula. If monoDir is not used (default option), the monotonicity of all ordinal predictors' effects are tested.
SignifLevel	Numerical value for the significance level.

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

mdcpResult	An object of class list storing the results of function mdcp, which fits both the unconstrained and constrained proportional odds logit models.
SignifLevel	Significance level to be used when constructing the confidence intervals for each parameter of the unconstrained proportional odds logit model. Default value 0.05.
xposLegend	Position of legend on the x-axis. If xposLegend or yposLegend are not used, then the legend is located using topleft option.
yposLegend	Position of legend on the y-axis. If xposLegend or yposLegend are not used, then the legend is located using topleft option.
xcex.axis	Size of cex.axis for the x-axis. Default value is 0.8.
ycex.axis	Size of cex.axis for the y-axis. Default value is 0.8.
cexLegend	Size of legend text to be assigned to cex. Default value is 1.
methodName	Method name to be used in the main title of the plot.

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")

---