Skip to main content Accessibility help
×
Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-10-31T14:08:29.877Z Has data issue: false hasContentIssue false

2 - Binary Regression: The Logit Model

Published online by Cambridge University Press:  05 June 2012

Gerhard Tutz
Affiliation:
Ludwig-Maximilians-Universität Munchen
Get access

Summary

Categorical regression has the same objectives as metric regression. It aims at an economic representation of the link between covariables considered as the independent variables and the response as the dependent variable. Moreover, one wants to evaluate the influence of the independent variables regarding their strength and the way they exert their influence. Predicting new observations can be based on adequate modeling of the response pattern.

Categorical regression modeling differs from classical normal regression in several ways. The most crucial difference is that the dependent variable y follows a quite different distribution. A categorical response variable can take only a limited number of values, in contrast to normally distributed variables, in which any value might be observed. In the simplest case of binary regression the response takes only two values, usually coded as y = 0 and y = 1. One consequence is that the scatterplots look different. Figure 2.1 shows data from the household panel described in Example 1.2. The outcomes “car in household” (y = 1) and “no car in household” (y = 0) are plotted against net income (in Euros). It is seen that for low income the responses y = 0 occur more often, whereas for higher income y = 1 is observed more often. However, the structural connection between the response and the covariate is hardly seen from this representation. Therefore, in Figure 2.1 the relative frequencies for owning a car are shown for households within intervals of length 50. The picture shows that a linear connection is certainly not the best choice.

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×