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

### Usage

1 2 |

### Arguments

`formula` |
A symbolic expression of the model to be fitted, similar to the formula
argument in |

`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 If param="rs", this can be one of |

`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

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 | ```
## 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)
``` |