GLD.lm: This function fits a GLD regression linear model

In GLDreg: Fit GLD Regression/Quantile/AFT Model to Data

This function fits a GLD regression linear model

Description

Similar to lm, this function fits a linear model using RS/FKML GLDs and assess the goodness of fit of GLD with respect to the data via qq plot and Kolmogorov-Smirnoff (KS) test. Note that the use of KS test when parameters of a distribution are estimated from data is generally frowned upon. This is because one often gets inflated p-value with increased type II error due to the fact that the KS test requires independence between test sample and parameters of distribution. Therefore, the the resample KS test over 1000 simulation runs from GLDEX package is probably a more reasonable measure. It is probably reasonable to consider the resample KS test may in fact decrease the p-values, as testing is done on resampled data from fitted distribution so there is a certain degree of inaccuracy there. The provision of these results is to give some indication of optimistic and pessimistic goodness of fit measure, as currently, there is an absence of a specialised GLD goodness of fit test. A generic Data Driven Smooth Test from ddst library in R is also incorporated to assess goodness of fit.

When in doubt, QQ plot should always be considered ahead of these results.

Usage

GLD.lm(formula, data, param, maxit = 20000, fun, method = "Nelder-Mead", 
diagnostics = TRUE, range = c(0.01, 0.99), init = NULL, alpha = 0.05)

Arguments

formula	A symbolic expression of the model to be fitted, similar to the formula argument in lm, see formula for more information
data	Dataset containing variables of the model
param	Can be "rs", "fmkl" or "fkml"
maxit	Maximum number of iterations for numerical optimisation
fun	If param="fmkl" or "fkml", this can be one of fun.RMFMKL.ml.m, fun.RMFMKL.ml, for maximum likelihood estimation (*.ml.m is a faster implementation of *.ml) and fun.RMFMKL.lm for L moment matching. If param="rs", this can be one of fun.RPRS.ml.m, fun.RPRS.ml, for maximum likelihood estimation (*.ml.m is a faster implementation of *.ml) and fun.RPRS.lm for L moment matching.
method	Defaults to "Nelder-Mead" algorithm, can also be "SANN" but this is a lot slower and may not as good
diagnostics	Defaults to TRUE, which computes Kolmogorov-Smirnoff test and do QQ plot
range	The is the quantile range to plot the QQ plot, defaults to 0.01 and 0.99 to avoid potential problems with extreme values of GLD which might be -Inf or Inf.
init	Choose a different set of initial values to start the optimisation process. This can either be full set of parameters including GLD parameter estimates, or it can just be the coefficient estimates of the regression model.
alpha	Significant level of KS test.

Value

Message	Short description of estimation method used and whether the result converged
Bias Correction	Bias correction used to ensure the line has zero mean residuals
Estimated parameters	A set of estimate coefficients from GLD regression
Fitted	Predicted response value from model
Residual	Residual of model
formula	Formula used in the model
param	Specify whether RS/FKML/FMKL GLD was used
y	The response variable
x	The explanatory variable(s)
fun	GLD fitting function used in the computation process, outputted for internal programming use

Author(s)

Steve Su

References

Su (2015) "Flexible Parametric Quantile Regression Model" Statistics & Computing May 2015, Volume 25, Issue 3, pp 635-650

See Also

GLD.lm.full, GLD.quantreg

Examples

## Dummy example

library(GLDEX)

## 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")

## Not run: 

## Extract the Engel dataset 
library(quantreg)
data(engel)

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

## Extract the mammals dataset 
library(MASS)

mammals.fit<-GLD.lm(log(brain)~log(body),data=mammals,param="rs",
fun=fun.RPRS.lm)

## Using quantile regression coefficients as starting values
library(quantreg)

mammals.fit1<-GLD.lm(log(brain)~log(body),data=mammals,param="rs",
fun=fun.RPRS.lm,init=rq(log(brain)~log(body),data=mammals)$coeff)

# As an exercise, use the result from mammals.fit1 as initial values

GLD.lm(log(brain)~log(body),data=mammals,param="rs",
fun=fun.RPRS.lm,init=mammals.fit1[[3]])

## End(Not run)

GLDreg documentation built on May 13, 2022, 9:06 a.m.