This preview shows page 1. Sign up to view the full content.
Unformatted text preview: inear
functions in , while at the same time ensuring that they sum to one and remain in [0,1].Logistic regression models are usually fit by maximum likelihood, using the conditional
likelihood ,using
. Since
completely specifies the conditional distribution, the multinomial distribution is appropriate. This model is widely used in
biostatistical applications for two classes. For instance: people survive or die, have a disease or not, have a risk factor or not. logis tic function
A logistic function (http://en.wikipedia.org/wiki/Logistic_function) or logistic curve is the most common sigmoid curve. 1. 2. wikicour senote.com/w/index.php?title= Stat841&pr intable= yes 27/74 10/09/2013 Stat841  Wiki Cour se Notes 3.
4.
5. The logistic curve shows early exponential growth for negative t, which slows to linear growth of slope 1/4 near t = 0, then approaches y = 1 with an exponentially
decaying gap. Intuition behind Logis tic Regres s ion
Recall that, for classification purposes, the linear regression model presented in the above section is not correct because it does not force
sum to 1. Consider the following log odds (http://en.wikipedia.org/wiki/Logit) model (for two classes): to be between 0 and 1 and Calculating
leads us to the logistic regression model, which as opposed to the linear regression model, allows the modelling of the posterior
probabilities of the classes through linear methods and at the same time ensures that they sum to one and are between 0 and 1. It is a type of Generalized Linear Model
(GLM) (http://en.wikipedia.org/wiki/Generalized_linear_model) . The Logis tic Regres s ion Model
The logistic regression model for the two class case is defined as
Clas s 1 Then we have that
Clas s 0
P(Y = 1  X = x) Fitting a Logis tic Regres s ion
Logistic regression tries to fit a distribution. The fitting of logistic regression models is usually accomplished by maximum likelihood
(http://en.wikipedia.org/wiki/Maximum_likelihood) , using Pr(YX). The maximum likelihood of maxi...
View
Full
Document
This document was uploaded on 03/07/2014.
 Winter '13

Click to edit the document details