[R] Extrapolating values from a glm fit

[David Winsemius]

On Jan 26, 2011, at 10:52 PM, Ahnate Lim wrote:

> Dear R-help,
>
> I have fitted a glm logistic function to dichotomous forced choices
> responses varying according to time interval between two stimulus. x  
> values
> are time separation in miliseconds, and the y values are proportion
> responses for one of the stimulus. Now I am trying to extrapolate x  
> values
> for the y value (proportion) at .25, .5, and .75. I have tried several
> predict parameters, and they don't appear to be working. Is this  
> correct use
> and understanding of the predict function? It would be nice to know  
> the
> parameters for the glm best fit, but all I really need are the  
> extrapolated
> x values for those proportions. Thank you for your help. Here is the  
> code:
>
> x <-
> c(-283.9, -267.2, -250.5, -233.8, -217.1, -200.4, -183.7, -167,
> -150.3, -133.6, -116.9, -100.2, -83.5, -66.8, -50.1, -33.4, -16.7,
> 16.7, 33.4, 50.1, 66.8, 83.5, 100.2, 116.9, 133.6, 150.3, 167,
> 183.7, 200.4, 217.1, 233.8, 250.5, 267.2, 283.9)
>
> y <-
> c(0, 0.333333333333333, 0, 0, 0, 0, 0, 0, 0, 0.333333333333333,
> 0, 0.133333333333333, 0.238095238095238, 0.527777777777778,
> 0.566666666666667,
> 0.845238095238095, 0.55, 1, 0.888888888888889, 1, 1, 1, 1, 1,
> 1, 1, 1, 1, 1, 1, 1, 1, 1, 0.5)
>
> weight <-
> c(1, 3, 2, 5, 4, 4, 3, 5, 5, 4, 5, 11, 22, 11, 15, 16, 11, 7,
> 14, 10, 16, 19, 11, 5, 4, 5, 6, 9, 4, 2, 5, 5, 2, 2)
>
> mylogit <- glm(y~x,weights=weight, family = binomial)
>
> # now I try plotting the predicted value, and it looks like a good  
> fit,
> hopefully I can access what the glm is doing
>
> ypred <- predict(mylogit,newdata=as.data.frame(x),type="response")
> plot(x, ypred,type="l")
> points(x,y)
>
> # so I try to predict the x value when y (proportion) is at .5, but
> something is wrong..

Right. Predict goes in the other direction ... x predicts y.

Perhaps if you created a function of y w.r.t. x and then inverted it.

?approxfun  # and see the posting earlier this week "Inverse  
Prediction with splines" where it was demonstrated how to reverse the  
roles of x and y.
>
> predict(mylogit,newdata=as.data.frame(0.5))
>
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>
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David Winsemius, MD
West Hartford, CT