6.4 Options


opt = 12387 gplmopt (string1, value1, ...{, opt})
creates a list of options for GPLM estimation or appends options to an existing list

All options for the algorithm and optional parameters need to be collected in a list object. This allows just to set or to modify only those options which are necessary. All quantlets in the gplm quantlib (except for 12392 gplmcore ) allow options. It is possible to give the same list of options to different routines. For example,

  opt=gplmopt("miter",20,"name","MyDisplay")
will set the maximal number of iterations to 20 and the name of the output display to MyDisplay. Option lists used for the glm quantlib can be used as well.

With the above option settings, one can call first 12397 gplmest and then 12400 gplmout :

  l=gplmest("bilo",x,y,opt)
  glpmout("bilo",x,y,opt)
Both quantlets only consider those optional parameters which are intended for them. Hence 12403 gplmest will only care about miter whereas 12406 gplmout will only use the parameter name to present a display named MyDisplay.


6.4.1 Setting Options

As for the glm quantlib, it is recommended to use 12456 gplmopt to set the options. 12459 gplmopt is used in the same way as 12462 glmopt . Essentially, the possible options in the gplm quantlib are a superset of those in the glm quantlib. A list of options created with 12469 glmopt can hence be used or extended with 12472 gplmopt .


6.4.2 Grid and Starting Values

As shown in Subsection 6.3.1, it can be useful to estimate the nonparametric function $ m(\bullet)$ not only on the observations t, but also on a grid tg. The optional parameter is:

tg
grid values (on the same scale as t)
This parameter can also be used to compute predictions for $ m(\bullet)$ on other values than those given in t.

All presented algorithms for GPLM are iterative and require first an initialization step. Different strategies to initialize the iterative algorithm are possible:

The gplm quantlib uses the first method by default. If a different method is to be used, the necessary starting values can be given as optional input:
b0
initial values for the estimation of b.
m0
initial values for the estimation of m.
m0g
initial values for the estimation of mg.


6.4.3 Weights and Offsets

The estimation quantlet 12612 gplmest is able to handle special cases as weights and constraints on parameters (fix parameters). Setting weights and offsets is done in the same way as in the glm quantlib. Please consult the corresponding subsections of the

GLM tutorial.

Weights and offsets can always be given as a optional parameter. The corresponding components of the list of optional parameters are

weights
type of weights, either "frequency" for replication counts or "prior" for prior weights in weighted regression.
wx
weights, $ n \times 1 $ vector or scalar.
wt
trimming weights for estimation of the linear part, $ n \times 1 $ vector or scalar.
wc
weights to be used in the convergence criterion, $ n \times 1 $ vector or scalar.
wr
weights to be used in the modified LR test statistics, $ n \times 1 $ vector or scalar.
off
offset, $ n \times 1 $ vector or scalar.
None of these parameters should contains missing or infinity values. Defaults are weights="prior", wx=1, wt=1, wc=1, wr=1, and off=0.


6.4.4 Control Parameters

There is a number of control parameters which modify the used algorithm.

meth
method to be used for GPLM estimation: -1 for backfitting, 0 for generalized Speckman estimator and 1 for profile likelihood. The default value is meth=0 for the Speckman algorithm.
fscor
indicator for Fisher scoring (instead of Newton-Raphson optimization). fscor=1 means that the Fisher scoring is used. Default is fscor=0 for Newton-Raphson. This parameter is ignored for canonical link functions.
cnv
convergence criterion. The iteration stops when the relative change of the coefficients vector b, the estimated curve m and the deviance are less than cnv. Default is cnv=0.0001.
miter
maximal number of iterations.The iteration stops when this maximal number of iterations is reached. Default is miter=10.
nosort
nosort=0 forces not to sort the data by the first column of t (and tg, if the optional grid tg is given). Default is nosort=0, i.e., to sort.

The following parameter switches on/off information during the computation.

shf
shows how the iteration is going on, if shf=1 is set. Default is shf=0.


6.4.5 Model Parameters

These two parameters are only relevant for power link and negative binomial models, respectively:

pow
power for the power link function, default is pow=0 (logarithmic link).
nbk
parameter $ k$ for the negative binomial distribution, the default is nbk=1 (geometric distribution).


6.4.6 Specification Test

The modified LR test implemented in 12789 gplmbootstraptest (see Subsection 6.5.3) allows the following options:

wr
weights to be used in the modified LR test statistics, $ n \times 1 $ vector or scalar. The default value is wr=1.
tdesign
design matrix (in t) for the GLM hypothesis, $ n\times r$ matrix. The default design is matrix(n)~t.


6.4.7 Output Modification

The 12825 gplmout routine which shows the output display provides some special possibilities to modify the output:

nopic
suppresses the output display if nopic=1. Default is nopic=0.
xvars
string vector, $ p \times 1$, containing variable names for the columns of x.
name
single string, name for output and prefix for output displays from 12828 gplmout .
title
single string, title to be used in 12831 gplmout .