Implemented generalized linear model function `glmfit`

[ruchikasonagote]

Description

• The glmfit function fits a generalized linear model to the given data using the specified link function and distribution of the response variable.
• The model is fitted using IRLS method.
• The function take inputs X -> predictor data, y -> response, distribution, link and returns a vector beta of coefficient estimates for glm.
• For now, it only supports the poisson distribution.

Issue

(https://github.com/gnu-octave/statistics/issues/49) Implementing multinomial regression and generalized linear models functions

TestCase

X = (1:20)';
beta_true = [1; 0.1];
mu_true = exp(beta_true(1) + beta_true(2) * X);
y = exp(mu_true);
distribution = 'poisson';
link = 'log';
beta = glmfit(X, y, distribution, link);
disp(beta);

ScreenShot of output

beta_true is similar to beta

[pr0m1th3as]

Thanks for the PR. It looks promising!

A few things to take care of:

1. Restrict the texinfo docstring to 80 characters per line.
2. Add a dot at the end error messages (Octave core doesn't do this, but Statistics do)
3. Line comments should start with capitalized letter
4. Add BISTs for testing input validation.
5. Prefer warning ("glmfit: message.") instead of disp ('warning: ....')
6. It it best to select the link functions and save them as a function handle before getting into your main loop. It is much faster this way.
7. You could exploit fminsearch to compute beta.
8. Use b instead of beta for returning argument to be more consistent with MATLAB.
9. Keep in mind coding style

[pr0m1th3as]

10. Use 2 spaces instead of 4 spaces for tab
11. Parse the link argument as pair name-value style, to maintain MATLAB compatibility

[ruchikasonagote]

Sure, I will work on it.

[pr0m1th3as]

See the changes I 've made. Add input validation tests at the bottom using %!error syntax. Check other functions in statistics to get the idea

[pr0m1th3as]

I have merged this PR because I am about to make a new release. See the new issue about glmfit and let's continue there