GLDreg (version 1.1.2)

GLDreg-package: This package fits standard and quantile and accerlerated Failure Time regression models using RS and FMKL/FKML generalised lambda distributions via maximum likelihood estimation and L moment matching.

Description

Owing to the rich shapes of GLDs, GLD standard/quantile regression is a competitive flexible model compared to standard/quantile regression. The proposed method has some major advantages: 1) it provides a reference line which is very robust to outliers with the attractive property of zero mean residuals and 2) it gives a unified, elegant quantile regression model from the reference line with smooth regression coefficients across different quantiles. The goodness of fit of the proposed model can be assessed via QQ plots and Kolmogorov-Smirnov tests and Data Driven Smooth Test, to ensure the appropriateness of the statistical inference under consideration. Statistical distributions of coefficients of the GLD regression line are obtained using simulation, and interval estimates are obtained directly from simulated data.

Author

Steve Su <[e-mail]>

Details

Package:	GLDreg
Type:	Package
Version:	1.1.1
Date:	2024-01-23
License:	CC BY-NC-SA 4.0

The primary fitting function for GLD regression model is GLD.lm.full. The output of GLD.lm.full can then be passed to summaryGraphics.gld.lm to display coefficients of GLD regression model graphically. Once a GLD reference model is obtained, quantile regression is obtained using GLD.quantreg.

The corresponding fitting algorithms for survival data are GLD.lm.full.surv which can then be passed to summaryGraphics.gld.surv.lm to display coefficients of GLD regression model graphically.

References

Su, S. (2015) "Flexible Parametric Quantile Regression Model" Statistics & Computing 25 (3). 635-650. doi:10.1007/s11222-014-9457-1

Su S. (2021) "Flexible parametric accelerated failure time model" J Biopharm Stat. 2021 Sep 31(5):650-667. doi:10.1080/10543406.2021.1934854

See Also

GLDEX

Examples

## Dummy example

## Create dataset

set.seed(10)

x<-rnorm(200,3,2)
y<-3*x+rnorm(200)

dat<-data.frame(y,x)

## Fit a FKML GLD regression

example<-GLD.lm(y~x,data=dat,fun=fun.RMFMKL.ml.m,param="fkml")

## Fit FKML GLD regression with 3 simulations

fit<-GLD.lm.full(y~x,data=dat,fun=fun.RMFMKL.ml.m,param="fkml",n.simu=3)

## Find median regression, use empirical method

med.fit<-GLD.quantreg(0.5,fit,slope="fixed",emp=TRUE)

if (FALSE) {

## Extract the Engel dataset 

library(quantreg)
data(engel)

## Fit GLD Regression along with simulations

engel.fit.all<-GLD.lm.full(foodexp~income,data=engel,
param="fmkl",fun=fun.RMFMKL.ml.m)

## Plot coefficient summary

summaryGraphics.gld.lm(engel.fit.all)

## Fit quantile regression from 0.1 to 0.9, with equal spacings between 
## quantiles

result<-GLD.quantreg(seq(0.1,.9,length=9),engel.fit.all,intercept="fixed")

## Plot quantile regression lines

fun.plot.q(x=engel$income,y=engel$foodexp,fit=engel.fit.all[[1]],result,
xlab="income",ylab="Food Expense")

## Sometimes the maximum likelihood estimation may fail, for example when 
## minimum/maximum support of GLD is exactly at the minimum/maximum value of the 
## dataset, if this the case, try to use the L-moment matching method.

engel.fit.all<-GLD.lm.full(foodexp~income,data=engel,
param="fmkl",fun=fun.RMFMKL.lm)

## Fit Accelerated Failure Time model to actg data:

actg.rs<-GLD.lm.full.surv(log(time)~factor(txgrp)+hemophil+cd4+priorzdv+age,
censoring=actg[which(actg$txgrp!=3 & actg$txgrp!=4),]$censor, 
data=actg[which(actg$txgrp!=3 & actg$txgrp!=4),],
param="rs",fun=fun.RPRS.ml.m,summary.plot=F,n.simu=1000)

summaryGraphics.gld.surv.lm(actg.rs,label=c("(Intercept)",
"IDV versus no IDV","Hemophiliac","Baseline CD4",
"Months of prior \n ZDV use","Age"),exp="TRUE")

}