XploRe Help : gplmest

Keywords - Function groups - @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Library:	gplm
See also:	gplmopt gplminit gplmcore gplmstat glmest gplmbootstraptest

Quantlet:		gplmest
Description:		gplmest fits a generalized partially linear model E[y\|x,t] = G(x*b + m(t)). This routine offers a convenient interface for GPLM estimation. A preparation of data is performed (inclusive sorting).

Reference(s):

Speckman, JRSSB, 1988; Hastie/Tibshirani, 1989

Link:

Tutorial: GPLM in XploRe

Usage:	`myfit = gplmest(code,x,t,y,h{,opt})`
Input:
	`code`	text string, the short code for the model (e.g. "bilo" for logit or "noid" for ordinary PLM).
	`x`	n x p matrix, the discrete predictor variables.
	`t`	n x q matrix, the continuous predictor variables.
	`y`	n x 1 vector, the response variables.
	`h`	q x 1 vector, the bandwidth vector.
	`opt`	optional, a list with optional input. "gplmopt" can be used to set up this parameter. The order of the list elements is not important.
	`opt.b0`	p x 1 vector, the initial coefficients. If not given, all coefficients are put =0 initially.
	`opt.m0`	n x 1 vector, the initial values for the nonparametric part. If not given, a default is used.
	`opt.tg`	ng x 1 vector, a grid for continuous part. If tg is given, the nonparametric function will also be computed on this grid.
	`opt.m0g`	ng x 1 vector, the initial values for the nonparametric part on the grid. These values are ignored if direct update for nonparametric function is possible. Otherwise, if not given, it is approximated from m0.
	`opt.weights`	string, type of observation weights. Can be "frequency" for replication counts, or "prior" (default) for prior weights in weighted regression.
	`opt.wx`	scalar or n x 1 vector, frequency or prior weights. If not given, set to 1.
	`opt.wc`	n x 1 vector, weights for convergence criterion, w.r.t. m(t) only. If not given, opt.wt is used.
	`opt.wt`	n x 1 vector, weights for t (trimming factors). If not given, all set to 1.
	`opt.off`	scalar or n x 1 vector, offset. Can be used for constrained estimation. If not given, set to 0.
	`opt.meth`	integer, if -1, a backfitting is performed, if 1 a profile likelihood method is used, and 0 a simple profile likelihood is used. The default is 0.
	`opt.fscor`	integer, if exists and =1, a Fisher scoring is performed (instead of the default Newton-Raphson procedure). This parameter is ignored for canonical links.
	`opt.shf`	integer, if exists and =1, some output is produced which indicates how the iteration is going on.
	`opt.nosort`	integer, if exists and =1, the continuous variables t and the grid tg are assumed to be sorted by the 1st column. Sorting is required by the algorithm, hence you should switch if off only when the data are already sorted.
	`opt.miter`	integer, maximal number of iterations. The default is 10.
	`opt.cnv`	integer, convergence criterion. The default is 0.0001.
	`opt.pow`	scalar, power for power link. If not given, set to 0.
	`opt.nbk`	scalar, extra parameter k for negative binomial distribution. If not given, set to 1 (geometric distribution).
Output:
	`myfit.b`	p x 1 vector, estimated coefficients
	`myfit.bv`	p x p matrix, estimated covariance matrix for coeff.
	`myfit.m`	n x 1 vector, estimated nonparametric part
	`myfit.mg`	ng x 1 vector, estimated nonparametric part on grid
	`myfit.stat`	list with the following statistics:
	`myfit.stat.deviance`	deviance,
	`myfit.stat.pearson`	generalized pearson's chi^2,
	`myfit.stat.loglik`	log-likelihood,
	`myfit.stat.r2`	pseudo R^2,
	`myfit.stat.it`	scalar, number of iterations needed.

Note:

This routine uses in some cases the dynamically loaded shared library gplm.dll (Windows) or gplm.so (Unix).

Example:

library("gplm") ;========================== ; simulate data ;========================== n=100 b=1|2 p=rows(b) x=2.*uniform(n,p)-1 t=sort(2.*uniform(n)-1,1) m=cos(pi.*t) y=( 1./(1+exp(-x*b-m)).>uniform(n) ) ;========================== ; semiparametric fit ;========================== h=0.6 sf=gplmest("bilo",x,t,y,h) b~sf.b ;========================== ; plot ;========================== library("plot") true=setmask(sort(t~m),"line","thin") estm=setmask(sort(t~sf.m),"line","blue") plot(true,estm)

Result:

A generalized partially linear logit fit for E[y|x,t] is
computed. sf.b contains the coefficients for the linear
part. sf.m contains the estimated nonparametric part
evaluated at observations t. The example gives the
true b together with the GPLM estimate sf.b. Also, the
estimated function sf.m is displayed together with the
true fit m.

Author: M. Mueller, 20010228