# Autologistic

A Julia package for computing with the autologistic (Ising) probability model and performing autologistic regression.

Autologistic regression is like an extension of logistic regression that allows the binary responses to be correlated. An undirected graph is used to encode the association structure among the responses.

The package follows the treatment of this model given in the paper Better Autologistic Regression. As described in that paper, different variants of "the" autologistic regression model are actually different probability models. One reason this package was created was to allow researchers to compare the performance of the different model variants. You can create different variants of the model easily and fit them using either maximum likelihood (for small-n cases) or maximum pseudolikelihood (for large-n cases).

At present only the most common "simple" form of the model--with a single parameter controlling the association strength everywhere in graph--is implemented. But the package is designed to be extensible. In future different ways of parametrizing the association could be added.

Much more detail is provided in the documentation.

```
# To get a feeling for the package facilities.
# The package uses LightGraphs.jl for graphs.
using Autologistic, LightGraphs
g = Graph(100, 400) #-Create a random graph (100 vertices, 400 edges)
X = [ones(100) rand(100,3)] #-A matrix of predictors.
Y = rand([0, 1], 100) #-A vector of binary responses.
model = ALRsimple(g, X, Y=Y) #-Create autologistic regression model
# Estimate parameters using pseudolikelihood. Do parametric bootstrap
# for error estimation. Draw bootstrap samples using perfect sampling.
fit = fit_pl!(model, nboot=2000, method=perfect_read_once)
# Draw samples from the fitted model and get the average to estimate
# the marginal probability distribution. Use a different perfect sampling
# algorithm.
marginal = sample(model, 1000, method=perfect_bounding_chain, average=true)
```