[R] logistic regression asymptote problem

[Spencer Graves]

	  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
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