R help - May 2006 - probit analysis

Dear all,

I have a very simple set of data and I would like to analyze them
with probit analysis. 

dose event trial
0.0 3  15
1.1 4  15
1.3 4  15
2.0 3  15
2.2 5  15
2.8 4  15
3.7 5  15
3.9 9  15
4.4 8  15
4.8 11 15
5.9 12 15
6.8 13 15

The dose should be transformed with log10().

I use glm(y ~ log10(dose), family=binomial(link=probit)) to
do probit analysis, however, I have to exclude the first 
observation. In an experimental design, the first observation 
may be as a control group. I think it should not be simple 
excluded from the datasets when constructing a model.

I refered to SAS online doc for probit procedure, it use the first 
observation to estimate the natural (threshold) response rate (C). 
And the final model will be:

p = Pr(Y = 0) = C + (1 - C)F(x'\beta)  

However, I don't know how to considered the control effect 
when using glm().

Any suggestions will be really appreciated.

Best Regards,

Jinsong Zhao

The model becomes nonlinear when you add the natural response rate. In
R, that means that you switch from using the glm function to using the
nls function. As long as you're willing to use logistic regression
instead of Probit analysis, nls has a 'self starting' option (SSLogis)
for a three parameter logistic model. The third parameter will be your
natural response rate. Unless you are looking at the tails of the
distribution, the Probit and logistic models will agree closely. If you
are highly motivated to use Probit analysis, you can use SSLogis to
figure out how to do that.

 

With regard to the SAS Probit procedure, it's been a few years since I
last used it but I wasn't happy when I did. The natural response rates I
got from that procedure were often unrealistic. As always, it's a good
idea to plot your data. 

 

Chuck

------------------------------

 

Message: 55

Date: Sat, 6 May 2006 15:08:33 +0800

From: "Jinsong Zhao" <jszhao@mail.hzau.edu.cn>

Subject: 

To: "r-help" <r-help@stat.math.ethz.ch>

Message-ID: <346899462.32251@eyou.net>

Content-Type: text/plain;     charset="gb2312"

 

Dear all,

 

I have a very simple set of data and I would like to analyze them

with probit analysis. 

...

 

I use glm(y ~ log10(dose), family=binomial(link=probit)) to

do probit analysis, however, I have to exclude the first 

observation. In an experimental design, the first observation 

may be as a control group. I think it should not be simple 

excluded from the datasets when constructing a model.

 

I refered to SAS online doc for probit procedure, it use the first 

observation to estimate the natural (threshold) response rate (C). 

And the final model will be:

 

p = Pr(Y = 0) = C + (1 - C)F(x'\beta)  

 

However, I don't know how to considered the control effect 

when using glm().

 

Any suggestions will be really appreciated.

 

Best Regards,

 

Jinsong Zhao

 

 


	[[alternative HTML version deleted]]

On Sat, 6 May 2006, White, Charles E WRAIR-Wash DC wrote:
> The model becomes nonlinear when you add the natural response rate. In
> R, that means that you switch from using the glm function to using the
> nls function.
Not in the usual sense of `linear': it is still just as linear in the 
explanatory variables as a glm is.
>  As long as you're willing to use logistic regression
> instead of Probit analysis, nls has a 'self starting' option
(SSLogis)
> for a three parameter logistic model. The third parameter will be your
> natural response rate. Unless you are looking at the tails of the
> distribution, the Probit and logistic models will agree closely. If you
> are highly motivated to use Probit analysis, you can use SSLogis to
> figure out how to do that.
Quick comment: logistic regression via nls is by least-squares, not the 
meaning of the term for glm(family=binomial(logit)).  If you want the 
latter, it is easy to adapt the code on MASS4 p.445 to a probit+const link 
function (and even to estimate the constant).

[...]

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

Hi Jinsong,

you can use the package  drc  on CRAN to fit logit and Weibull models
(but not the probit model) with natural mortality/response and/or
natural immunity to binomial data (maximum likelihood estimation).

To get an idea try:

library(drc)
?earthworms


Christian