Cens.SMN.PCR: Estimation and diagnostics for partially linear censored...
In PartCensReg: Estimation and Diagnostics for Partially Linear Censored Regression Models Based on Heavy-Tailed Distributions

Description Usage Arguments Details Value Warning Note Author(s) References See Also Examples

View source: R/Cens.SMN.PCR.R

Return the MPL estimates obtained through of ECME algorithm for partially linear regression models with censored data under scale-mixture of normal (SMN) distributions (some members are the normal, Student-t, slash and contaminated normal distribution). The types of censoring considered are left and right. Graphics for diagnostic analysis such as case-deletion and local influence techniques are provided to show its robust aspect against outlying and influential observations.

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Cens.SMN.PCR(x, y, c, cens = "left", tt, nu = NULL, error = 10^-6, iter.max = 200,
type = "Normal", alpha.FIX = TRUE, nu.FIX = TRUE, alpha.in = 10^-3, k = 1,
Diagnostic = TRUE, a = 2)

`x`	Matrix or vector of covariates.
`y`	Vector of responses.
`c`	Vector of censoring indicators. For each observation: 1 if censored and 0 if non-censored.
`cens`	'left' for left censoring and 'right' for rigth censoring.
`tt`	Vector of values of a continuous covariate for the nonparametric component of the model.
`nu`	Initial value of the parameter of the SMN family. In the case of the Student-t and slash is a scalar, in the contaminated normal is a vector bidimensional.
`error`	The convergence maximum error. By default = 10^-6.
`iter.max`	The maximum number of iterations of the ECME algorithm. By default = 200.
`type`	Represents the type of distribution to be used in fitting: 'Normal' for normal, 'T' for Student-t, 'Slash' for slash and 'NormalC' for contaminated normal distribution respectively. By default ='Normal'
`alpha.FIX`	`TRUE` or `FALSE`. Indicate if smoothing parameter will be estimated. By default = `TRUE`.
`nu.FIX`	`TRUE` or `FALSE`. Indicate if ν will be estimated. By default = `TRUE`.
`alpha.in`	Initial value of smoothing parameter.
`k`	For the local influence in explanatory variable perturbation, indicates the k-th explanatory variable (assumed continuous) of the design matrix X to be perturbed.
`Diagnostic`	`TRUE` or `FALSE`. Indicates if diagnostic graph should be built for the fitted model (index plot in local influence). By default = `TRUE`.
`a`	The value for a considered in the benchmark value for the index plot in local influence: M(0)_{l} > \bar{M(0)}+aSM(0)*.

We consider a partial linear model which belongs to the class of semiparametric regression models with vector of response Y=(Y_{1},...,Y_{n}) and with errors ε_{i} which are independent and identically distributed according to a SMN distribution. To be more precise,

Y_{i} = x_i^{T}β +n_i^{T}f + ε_{i},

for i=1,...,n, where f = (f(t_1^{0}),...,f(t_r^{n})^{T} is an r x 1 vector with t_1^{0},...,t_r^{n} being the distinct and ordered values of t_i; n_i is a r x 1 vector of incidence whose s-th element equals the indicator function I(t_i=t_s^{0}) for s=1,...,r.

`beta`	ECME estimates for the parametric component.
`sigma2`	ECME estimates for the scale parameter.
`Alpha`	If `alpha.FIX` = `FALSE`, it returns the estimated value of the smoothing parameter, else returns the initial value assigned in `alpha.in`.
`AIC`	AIC criteria for model selection.
`ff`	ECME estimates for the nonparametric component.
`yest`	Predicted values of the model.
`loglik`	Value of the log-likelihood under the fitted model.
`iter`	Number of iterations of the ECME algorithm.
`nu`	If `nu.FIX` = `FALSE`, it returns the estimated value of ν parameter, else returns the initial value assigned in `nu`.
`MI`	Observed information matrix.
`D`	A list of objects for diagnostic analysis that contains: the Hessian matrix (`Hessian`), values for generalized Cook's distance (`GD1`) and the values of the conformal normal curvature for the following perturbation schemes: Case-weight (`Curvature_W`), scale (`Curvature_S`), explanatory variable (`Curvature_E`) and response variable (`Curvature_R`).

For the contaminated normal case, if nu parameters were close to the bounds, i.e., close to 0 or 1, computational problems could arrise.

When alpha.FIX = FALSE the algorithm may take a long time to converge. The package estimates the value ν in each iteration taking as an estimate the argument that maximizes the actual marginal log-likelihood function, already evaluated in the estimates of β and σ^{2}. The diagnostic analysis is performed considering the estimated final value of θ obtained in the last iteration of the ECME algorithm.

Marcela Nunez Lemus, Christian E. Galarza, Larissa Avila Matos and Victor H. Lachos.

Ferreira, C. S., & Paula, G. A. (2017). Estimation and diagnostic for skew-normal partially linear models. Journal of Applied Statistics, 44(16), 3033-3053.

Ibacache-Pulgar, G., Paula, G. A., & Cysneiros, F. J. A. (2013). Semiparametric additive models under symmetric distributions. Test, 22(1), 103-121.

Ibacache-Pulgar, G., & Paula, G. A. (2011). Local influence for Student-t partially linear models. Computational Statistics & Data Analysis, 55(3), 1462-1478.

CensReg.SMN

dtawage = get(data(PSID1976,package = "AER"))
y  = dtawage$wage
cc = c(rep(0,428),rep(1,325))
tt = dtawage$exper
x  = cbind(dtawage$education,dtawage$age, dtawage$hhours, dtawage$hwage, dtawage$tax,
dtawage$youngkids, dtawage$oldkids)

#Normal case by default with only 10 iterations
PCR.default1 = Cens.SMN.PCR(x=x, y=y, c=cc, cens="left",tt =tt,iter.max = 10,Diagnostic = FALSE)

## Not run: 
#This may take few minutes
#Normal case by default with full (200) iterations
PCR.default2 = Cens.SMN.PCR(x=x, y=y, c=cc, cens="left",tt =tt)

#contaminated normal case
PCR.CN = Cens.SMN.PCR(x=x, y=y, c=cc, cens="left",tt =tt,type="NormalC",
nu = c(0.1,0.1),iter.max = 100)

## End(Not run)