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 gplmbilotest gplmbilobootstraptest gplmbilobiased glmbilo

Macro: gplmbilo
Description: GPLM (logit) -- gplmbilo fits a generalized partially linear model where y|x,t is binomial distributed and E[y|x,t] and x*b + m(t) are linked via the logistic function (canonical link).

Reference(s):

Link:
Usage: myfit = gplmbilo(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. y[i] may have (integer) values between 0 and opt.wx[i] or opt.wx (if opt.wx is scalar).
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, usually the binomial index vector. If not given, set to 1.
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, log((1+2y)./(3-2y)) is used.
opt.wt n x 1 vector, weights for t (trimming factors). If not given, all set to 1.
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 values for the nonparametric part on the grid. If not given, it is approximated from m0.
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.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 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:

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=gplmbilo(x,t,y,h)
b~sf.b
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. 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. 

Library: gplm
See also: gplmopt gplmbilotest gplmbilobootstraptest gplmbilobiased glmbilo

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, 970702
(C) MD*TECH Method and Data Technologies, 28.6.1999