CensReg.SMN {SMNCensReg}

Fit Univariate Right, Left or Interval Censored Linear Regression Model Under Scale Mixtures of Normal Distributions

Description

Return EM algorithm output for right, left or interval censored regression model under SMN distributions (Normal, Student-t, Pearson VII, Slash or Contaminated Normal), built the corresponding envelope graph and compute some criteria for model selection, such as AIC, BIC and EDC.

Usage

CensReg.SMN(cc,x,y,LS=NULL,nu=3,delta=NULL,cens="left",dist="T",
show.envelope="FALSE", error=0.0001,iter.max=300)

Arguments

cc

Vector of censoring indicators. For each observation: 0 if non-censored, 1 if censored.

x

Matrix or vector of covariates.

y

Vector of responses in case of right/left censoring. Vector of lower limits if censoring is intervalar.

LS

Vector of upper limits if interval censoring. Must not be provided in case of left/right censoring.

nu

Initial value of the parameter of the scale variable of the SMN family. Must not be provided in case of Normal distribution. Must be a bidimensional vector in case of contaminated normal distribution (NormalC).

delta

Second parameter of Pearson VII, fixed. Must not be provided in case of Normal, Student-t or slash distribution.

cens

"left" for left censoring, "right" for right censoring, "interval" for interval censoring.

dist

Distribution to be used in fitting: "Normal" for Normal model, "T" for Student-t model, "PearsonVII" for Pearson VII model, "Slash" for slash model and "NormalC" for contaminated Normal model.

show.envelope

TRUE or FALSE. Indicates if envelope graph should be built for the fitted model (based on transformed Martingale residuals). Default is FALSE.

error

The convergence maximum error.

iter.max

The maximum number of iterations of the EM algorithm. Default=300.

Details

For the contaminated Normal distribution, each component of the bidimensional vector "nu" must lie on (0,1). For the Pearson VII distribution, delta is fixed as the provided value and is not estimated. The parameters beta and sigma2 are initialized with the minimum square estimators of the regression x vs y. If you want to fit a regression model for non-censored data, just set "cc" as a vector of zeros and "cens" as either "right" or "left".

Value

beta

EM estimates for the regression coefficients.

sigma2

EM estimates for the scale parameters.

logver

Returned the value of the log-likelihood under the fitted model.

count

Number of interations until convergence.

AIC

AIC criteria for model selection.

BIC

BIC criteria for model selection.

EDC

EDC criteria for model selection.

SE

Standard error estimates.

Author(s)

Aldo M. Garay [e-mail], Monique Bettio Massuia [e-mail] and Victor Hugo Lachos [e-mail]

References

Aldo M. Garay, Victor H. Lachos, Heleno Bolfarine, Celso R. Cabral. "Linear Censored Regression Models with Scale Mixture of Normal Distributions". Statistical Papers.(2017) 58:247–278.

Examples

 ##see examples in \code{\link{wage.rates}}