How to define link function in glmfit?

[grace]

Dear all,

I am employing glmfit to solve Generalized Linear Models, and the link
function I choose is Weibull, which is also known as Gompertz,

y=1-exp(-exp(a+b*log10(x))) ;

The guiding information I find in help reads "cell array of the form
{FL FD FI}, containing three function handles, created using @, that
define the link (FL), the derivative of the link (FD), and the inverse
link (FI)." And I try to write some code:


[b,dev,stats]=glmfit(X,Y,'normal','link',{@(y)(10^((log(-1og(1-y))-a)/
b)),@(y)(10.^((log(-1og(1-y))-a)/b)/(b*(-1og(1-y)*(1-y)))),@(y)(1-exp(-
exp(a+b*log10(y))))})


There are always errors. I am not familiar with function handles. And
I want to know if y should be a matrix, how to define the link
function in the right way?

Thanks a lot.

[Peter Perkins]

Grace, this is the expression you have passed into glmfit:

{ @(y) 10^((log(-1og(1-y))-a)/b), ...
@(y) 10.^((log(-1og(1-y))-a)/b)/(b*(-1og(1-y)*(1-y))), ...
@(y) 1-exp(-exp(a+b*log10(y))) }


Since you haven't provided the errors you get, we can only guess as to
what's happening. But there are a number of problems with this.

* You've used the character "1" (the number one) when you want "l" (the
letter ell)
* You've used matrix operators such as *, ^, and / when you want
elementwise operators such as .*, .^, and ./
* Your link function is parameterized by a and b, which you have not
defined.

You probably also want to make use of the log1p function and replace all
those log(1-y)'s with log1p(-y).

Hope this helps.

[Tom Lane]

In addition, this link function is usually used with 'binomial' instead of
'normal' -- did you really mean to use normal?

Also (assuming you did intend binomial), please verify this matches what you
want, but I think it would be equivalent and simpler to use

glmfit(log10(x),y,'binomial','link','comploglog')

That is, use the complementary log-log link on the log10 of your data,
instead of building the log10 transform into your function.

-- Tom

"Peter Perkins" <Peter.Remove...@mathworks.com> wrote in message
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