R help - Jul 2005 - logistic regression asymptote problem

R-helpers,

I have a question about logistic regressions.

Consider a case where you have binary data that reaches an asymptote
that is not 1, maybe its 0.5.  Can I still use a logistic regression to
fit a curve to this data?  If so, how can I do this in R.  As far as I
can figure out, using a logit link function assumes that the asymptote
is at y = 1.

An example.  Consider the following data:

"tmp" <-
structure(list(x = c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 
14), yes = c(0, 0, 0, 2, 1, 14, 24, 15, 23, 18, 22, 20, 14, 17
), no = c(94, 101, 95, 80, 81, 63, 51, 56, 30, 38, 31, 18, 21, 
20)), .Names = c("x", "yes", "no"), row.names =
c("1", "2", "3",
"4", "5", "6", "7", "8",
"9", "10", "11", "12", "13",
"14"), class "data.frame")

where x is the independent variable, and yes and no are counts of
events.  plotting the data you can see that the data seem to reach an
asymptote at around y=0.5.  using glm to fit a logistic regression it is
easily seen that it does not fit well.

tmp.glm <- glm(cbind(yes,no) ~ x, data = tmp, family = binomial(link logit))
plot(tmp.glm$fitted, type = "l", ylim = c(0,1))
par(new=T)
plot(tmp$yes / (tmp$yes + tmp$no), ylim = c(0,1))

Any suggestions would be greatly appreciated.

Cheers,
Kevin

-- 
------------------------------------
------------------------------------
Kevin J Emerson
Center for Ecology and Evolutionary Biology
1210 University of Oregon
University of Oregon
Eugene, OR 97403
kemerson at darkwing.uoregon.edu

I saw a standard overdispersed binomial.  In particular, I saw NO 
evidence of saturation at 0.5 or anything below 1.  I did the following:


tmp$N <- tmp$yes+tmp$no

with(tmp, plot(x, yes))
with(tmp, plot(x, yes/N))

tmp.glm <- glm(cbind(yes,no) ~ x, data = tmp, family = binomial(link 
=logit))
tmp.glmq <- glm(cbind(yes,no) ~ x, data = tmp, family = 
quasibinomial(link =logit))
summary(tmp.glm)
summary(tmp.glmq)

plot(tmp.glm)
plot(tmp.glmq)

# Test the statistical significance of the "Dispersion" parameter
pchisq(summary(tmp.glmq)$dispersion*12, 12, lower=FALSE)

	  hope this helps.
	  spencer graves


Kevin J Emerson wrote:
> R-helpers,
> 
> I have a question about logistic regressions.
> 
> Consider a case where you have binary data that reaches an asymptote
> that is not 1, maybe its 0.5.  Can I still use a logistic regression to
> fit a curve to this data?  If so, how can I do this in R.  As far as I
> can figure out, using a logit link function assumes that the asymptote
> is at y = 1.
> 
> An example.  Consider the following data:
> 
> "tmp" <-
> structure(list(x = c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 
> 14), yes = c(0, 0, 0, 2, 1, 14, 24, 15, 23, 18, 22, 20, 14, 17
> ), no = c(94, 101, 95, 80, 81, 63, 51, 56, 30, 38, 31, 18, 21, 
> 20)), .Names = c("x", "yes", "no"), row.names
= c("1", "2", "3",
> "4", "5", "6", "7", "8",
"9", "10", "11", "12", "13",
"14"), class > "data.frame")
> 
> where x is the independent variable, and yes and no are counts of
> events.  plotting the data you can see that the data seem to reach an
> asymptote at around y=0.5.  using glm to fit a logistic regression it is
> easily seen that it does not fit well.
> 
> tmp.glm <- glm(cbind(yes,no) ~ x, data = tmp, family = binomial(link
> logit))
> plot(tmp.glm$fitted, type = "l", ylim = c(0,1))
> par(new=T)
> plot(tmp$yes / (tmp$yes + tmp$no), ylim = c(0,1))
> 
> Any suggestions would be greatly appreciated.
> 
> Cheers,
> Kevin
> 
-- 
Spencer Graves, PhD
Senior Development Engineer
PDF Solutions, Inc.
333 West San Carlos Street Suite 700
San Jose, CA 95110, USA

spencer.graves at pdf.com
www.pdf.com <http://www.pdf.com>
Tel:  408-938-4420
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