R help - Oct 2003 - Variance of a non-linear combination of the coefficient e stiamtes

< In Stata, I can just use "bs" function ...>
in STATA the bs command runs a bootstrap

If you want to use the bootstrap function (or you could linearize b*c/a :)
look under ?boot (you may need to load the package first).

Usage:

     boot(data, statistic, R, sim="ordinary", stype="i", 
          strata=rep(1,n), L=NULL, m=0, weights=NULL, 
          ran.gen=function(d, p) d, mle=NULL, ...)


I tried to provide an example - others can clean up the R code for me:
> test.df<-cbind(rnorm(25),rnorm(25),rnorm(25))
> test.model<-lm(test.df[,1]~test.df[,2]+test.df[,3])
> summary(test.model)
Call:
lm(formula = test.df[, 1] ~ test.df[, 2] + test.df[, 3])

Residuals:
    Min      1Q  Median      3Q     Max 
-1.3784 -0.6903 -0.2278  0.5879  2.7298 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)
(Intercept)  -0.03419    0.20907  -0.164    0.872
test.df[, 2] -0.29636    0.17705  -1.674    0.108
test.df[, 3]  0.16059    0.21060   0.763    0.454

Residual standard error: 1.018 on 22 degrees of freedom
Multiple R-Squared: 0.1439,     Adjusted R-squared: 0.06613 
F-statistic:  1.85 on 2 and 22 DF,  p-value: 0.1809 
>
test.model$coefficients[2]*test.model$coefficients[3]/test.model$coefficient
s[1]
test.df[, 2] 
    1.391884 
> umeno.stat<-function(xx,...){
+ xx.model<-lm(xx[...,1]~xx[...,2]+xx[...,3])
+
xx.model$coefficient[2]*xx.model$coefficient[3]/xx.model$coefficient[1]}
> umeno.stat(test.df,c(1:25))
xx[..., 2] 
  1.391884 
> boot(test.df,umeno.stat,100)
ORDINARY NONPARAMETRIC BOOTSTRAP


Call:
boot(data = test.df, statistic = umeno.stat, R = 100)


Bootstrap Statistics :
    original    bias    std. error
t1* 1.391884 0.2708119    16.32276
>
bob


-----Original Message-----
From: umeno [mailto:umeno@students.uiuc.edu] 
Sent: Thursday, October 30, 2003 1:19 PM
To: R-Help <r-help
Subject: [R] Variance of a non-linear combination of the coefficient
estiamtes

Hi,

I would like to know if anyone knows how to compute a variance of the 
non-linear combination of the coefficient estimates.

Say, I get a model of

y~c+ax+bz (1)
where x and z are the independent variables, c is the constant estimate, and
a 
and b are the coefficient estimates.

Then, I want to know the variance of

b*c/a (2).

How am I going to get it?

In Stata, I can just use "bs" function by defining the regression
model (1)
and the statistic of the interest(2).

Help!!!

Thank you
Soyoko

______________________________________
Ms. Soyoko Umeno
Graduate Research Assitant for the Illinois-Missouri Biotechnology Alliance
(IMBA) at http://www.imba.missouri.edu/
Ph.D. Student at the Department of Agricultural and Consumer Economics
at the University of Illinois at Urbana-Champaign
Office Phone: 217-333-3417 or 217-333-0364
Fax: 217-244-4817
Mailing Address: 1301 W. Gregory Dr. MC710, Urbana, IL 61801

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