MLE and Anonymous functions - why am I getting undefined arguments?

Apologies, I believe I just put this in the newsreader by mistake.

I'm trying to use maximum likelihood estimation with a logistic probability distribution to estimate the coefficients A, B and C of a model to fit my data.

I have:

P = @(x1, x2, x3, A, B, C) (exp(x1*A + x2*B + x3*C))/(1 + exp(x1*A + x2*B + x3*C));

phat = mle(Rvals, 'pdf', P, 'start', [0, 0, 0]);

My equation will take the form of R = Ax1 + Bx2 + Cx3 so R, x1, x2, and x3 are column vectors with my experimental data.

But I'm getting:

"??? Error using ==> mlecustom>checkFunErrs at 525
The following error occurred while trying to evaluate
the user-supplied pdf function
'@(x1,x2,x3,A,B,C)(exp(x1*A+x2*B+x3*C))/(1+exp(x1*A+x2*B+x3*C))':"

Input argument "B" is undefined.

P is an anonymous function, shouldn't it not care if B is defined? That's the whole point, I'm solving for it. And it's not complaining about A. Have I somehow defined my anonymous function wrong? Thanks in advance for your help.

Answer 1

[Walter Roberson]

http://www.mathworks.com/help/toolbox/stats/mle.html

Your pdf parameter must be a function handle to a function that takes a vector and a list of parameters for the distribution. Your 'start' parameter gives starting values for the parameters. You have 3 elements in your start vector, so to match your function handle must take a vector and then three parameters. Instead you are trying to work with 6 inputs, the first 3 of which seem to be known vectors from your workspace, and you are attempting to ignore the vector of data that will be passed in (that corresponds to Rvals)

The closest I can come to what you should do is

   P = @(data, A,B,C) (exp(x1*A + x2*B + x3*C))/(1 + exp(x1*A + x2*B + x3*C));

I have not yet been able to determine how the data vector should be used: perhaps it should be subtracted from the result of the division or something like that (thus giving an error term to work with.)

Question: are you sure you should be using the / operator instead of the ./ operator?

[B K]

Thanks for the response. I figured out about the same time as you that data needed to be a single vector. The crux of the issue is I am trying to get an estimate with three known quantities per datapoint instead of just one, as is seen in all of the documentation's examples. As you figured x1, x2, x3 are vectors representing each of my 3 values at each datapoint I have. I can't figure out how to handle it with more than one x though, even though I could have sworn I read somewhere it was allowed.