- Binomial regression
statistics, binomial regression is a technique in which the response (often referred to as "Y") is the result of a series of Bernoulli trials, or a series of one of two possible disjoint outcomes (traditionally denoted "success" or 1, and "failure" or 0). The results are assumed to be binomially distributed and are often fit as a generalized linear modelwhose predicted values μ are the probabilities that any individual event will result in a success. The likelihoodof the predictions is then given by
where 1A is the
indicator functionwhich takes on the value one when the event "A" occurs, and zero otherwise. This likelihood is usually maximized over the μs.
Models used in binomial regression can often be extended to multinomial data.
There are many methods of generating the values of μ in systematic ways that allow for interpretation of the model; they are discussed below.
Models based on a probability distribution
Many models can be fit into the form
where "g" is the
cumulative distribution functionof some probability distribution. This form can be arrived at by using the formula
where is taken from the probability distribution in question with mean zero and dispersion or variance of one.
Here the model is based on a
probitmodel the probability distribution in question is the normal distribution.
Linear probability model
Here the probability distribution in question is the
uniform distributionand the resulting model is referred to as the linear probability model.
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