XploRe Help : hhtest

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:	metrics
See also:	hhmult glmest sker

Quantlet:		hhtest
Description:		hhtest calculates the H-H statistic to test the specification of the link function of a generalized linear model (such as the logit or probit model), assuming the index is correctly specified.

Reference(s):

Horowitz and Haerdle (1994), "Testing a parametric model against a semiparametric alternative", Econometric Theory,10, 821-848

Usage:	`{t,p} = hhtest(vhat,y,yhat,h,{c,{m}})`
Input:
	`vhat`	n x 1 matrix with the projected index
	`y`	n x 1 matrix
	`yhat`	n x 1 matrix with the parametric estimate of E(Y\|X)
	`h`	scalar (positive) -- the bandwidth for kernel regression with Quartic kernel
	`c`	scalar 0 =< c < 1 (optional) -- proportion of the sample to be cut in each extreme. Default is 0.05.
	`m`	n x 1 or the scalar 1. m should be given only for binary responses. If the data is binomial m is the vector with the binomial coeficients. If the data is bernouli, m=1. m is necessary to calculate the vari- ance of y. If y is not binary the variance will be given by a nonparametric regression of (y-fhat)^2 on vhat.
Output:
	`t`	scalar -- the statistic value
	`p`	scalar -- the p-value of t

Example:

library("metrics") x = read("kyphosis.dat") y = x[,4] x = x[,1:3] x = matrix(rows(x))~x h = 2 myfit=glmest("bilo",x,y) eta=x*myfit.b mu=1./(1+exp(-eta)) {t,p} = hhtest(eta,y,mu,h,0.05,1) t~p

Result:

test statistic, t, and p-value, p.

Author: A. Werwatz, 19960326