# [R] 4-parameter logistic model

Thomas W Blackwell tblackw at umich.edu
Sun Feb 23 21:13:08 CET 2003

```Christian  -

I acknowledge Prof. Bates' answer and his superior knowledge.
But for the first equation you have typed below, theta1 is
clearly the asymptote as x goes to minus infinity, and theta2
is the asymptote as x goes to plus infinity.

The equation you have typed and the excerpt you have quoted
from the book clearly disagree.  I don't know anything about
the function  SSfpl(), inparticular whether it agrees with
the book or not.

-  tom blackwell  -  u michigan medical school  -  ann arbor  -

On Fri, 21 Feb 2003, Christian Mora wrote:

> Dear R users
>
> I'm a new user of R and I have a basic question about the 4-parameter
> logistic model. According to the information from Pinheiro & Bates the model
> is:
>
> y(x)=theta1+(theta2-theta1)/(1+exp((theta3-x)/theta4)) ==
> y(x)=A+(B-A)/(1+exp((xmid-input)/scal))
>
> from the graph in page 518 of the book of the same authors (mixed models in
> S) theta 1 corresponds to the horizontal asymptote as x goes to infinity and
> theta2 the horizontal asymptote as x goes to -infinity. When I use the
> function SSfpl(input,A,B,xmid,scal), I'm not sure why the value of A is the
> lower of the two asymptotes if according to the original function A should
> be equal to theta1 (upper asymptote).. or maybe I'm wrong.
>
> I'll appreciate any comment on this.
>
> Best Regards
>
> CM
>
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>

```