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 gplmnoid gplmnoidbiased glmnoid

Macro: gplmnoidtest
Description: Test (using as. normality) linear vs. partially linear -- by default gplmnoidtest tests the "truly" linear model E[y|x,t] = x*b + t*g + c versus the partially linear model E[y|x,t] = x*b + m(t). Optional, an alternative design matrix can be specified for t or parametric estimates for b and m can be given directly.

Reference(s):

Link:
Usage: myfit = gplmnoidtest(x,t,y,h{,opt})
Input:
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 bandwith
opt optional, a list with optional input. The macro "gplmopt" can be used to set up this parameter. The order of the list elements is not important. Parameters which are not given are replaced by defaults (see below).
opt.wx scalar or n x 1 vector, prior weights. If not given, set to 1.
opt.wt n x 1 vector, weights for t (trimming factors). If not given, all set to 1.
opt.tdesign n x r matrix, design for linear fit. If not given a "truly" linear function will be tested by using the design matrix(n)~t. The parameter opt.tdesign will not be considered if opt.b0 and opt.m0 are given.
opt.b0 p x 1 vector, coefficients for parametric fit. If not given, it will be estimated by glmnoid. The parameter opt.b0 will not be used if opt.m0 is not given.
opt.m0 n x 1 vector, parametric fit for m(t). If not not given, it will be estimated by glmnoid. The parameter opt.m0 will not be used if opt.b0 is not given.
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.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.noinit integer, if exists and =1, the estimation of the partial linear model is not initialized by the parametric fit.
opt.miter integer, maximal number of iterations. The default is 10.
opt.cnv integer, convergence criterion. The default is 0.0001.
opt.wtc n x 1 vector, weights for convergence criterion, w.r.t. m(t) only. If not given, opt.wt is used.
opt.off scalar or n x 1 vector, offset in predictor.
Output:
myfit.b k x 1 vector, estimated coefficients.
myfit.bv k x k matrix, estimated covariance matrix for b.
myfit.m n x 1 vector, estimated nonparametric part.
myfit.mg ng x 1 vector, estimated nonparametric part on grid, if opt.tg was given.
myfit.rr scalar, quasi-likelihood test statistic, see Haerdle/Mammen/Mueller (1996).
myfit.alpha scalar, significance level for rejection of the parametric hypothesis.
myfit.glmfit list with output b, bv and stat from glm fit. See macro glmnoid for details. This is empty if opt.b0 and opt.m0 were given.
myfit.stat list with the following statistics:
myfit.stat.deviance deviance,
myfit.stat.pearson generalized pearson's chi^2,
myfit.stat.r2 pseudo R^2,
myfit.stat.dispersion dispersion parameter estimate
myfit.stat.it integer, number of iterations needed in semiparametric fit

Example:
library("glm") 
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=0.5*cos(pi.*t)+0.5*t
y=x*b+m+normal(n)./2
;=============================
;  semiparametric fit & test
;=============================
h=0.6
sf=gplmnoidtest(x,t,y,h)
b~sf.glmfit.b[1:2]~sf.b
sf.alpha
pic=createdisplay(1,1)
show(pic,1,1,t~m,t~sf.m)
Result:
A generalized partially linear logit fit for E[y|x,t] is 
computed and tested against the parametric logit. 
sf.b contains the coefficients for the linear 
part, sf.glmfit.b the linear glmfit. sf.m is the estimated 
nonparametric function evaluated at observations t. The example 
gives the true b together with the LS estimate  and the GPLM 
estimate sf.b. Also the estimated function sf.m is  
displayed together with the true and the linear fit. 
sf.alpha contains significance level for rejection of the
linear model.

Library: gplm
See also: gplmopt gplmnoid gplmnoidbiased glmnoid

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

Author: Marlene Mueller, 970523
(C) MD*TECH Method and Data Technologies, 28.6.1999