Binomial Data with 0's in glmfit

I am using glmfit to perform logistic regression on a set of data. If I run the code

b = glmfit(X,[y n],'binomial','link','logit')

where y contains a few 0 values, how does Matlab handle the 0's? Are they set to very small values? Is it necessary or beneficial to use the empirical log-odds

log((y+0.5)/(n-y+0.5)

to determine y_new and n_new (where y_new does not contain 0's)?

Thank you.

Answer 1

[the cyclist]

In a logistic regression, the response variable (y) is typically a binary variable (and can represented as 0's and 1's).

Why do you think 0's would be a problem?

[Anna]

Thank you for the quick reply. I may misunderstand what is going on with logistic regression. I believe that if we want to estimate the probability of an event, we may compute p=events/trials. If we then compute log(p/(1-p)), we run into trouble. Does glmfit compute anything like this?

I am curious about the following lines in glmfit:

function mu = startingVals(distr,y,N)
% Find a starting value for the mean, avoiding boundary values
switch distr
case 'poisson'
    mu = y + 0.25;
case 'binomial'
    mu = (N .* y + 0.5) ./ (N + 1);

Is the 0.5 in the numerator of the term in case 'binomial' to buffer against 0?

Thank you, Anna

[the cyclist]

In the logistic model, you would only say the probability is equal to 1 as X approaches infinity.

It's true that if for some particular value of X, you happen to see all "successes" (say, 15 out of 15 successes when X = 300), then the code is going to make a starting estimate of the probability (at that value of X) to be just a bit smaller than 1, while it tries to find the best fit across all values of X.

I think the only time you will have a problem fitting is if you see only successes at all values of X. But, then you don't really need a model, do you? :-)