Premium
A Goodness‐of‐Fit Test for Multinomial Logistic Regression
Author(s) -
Goeman Jelle J.,
le Cessie Saskia
Publication year - 2006
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.1541-0420.2006.00581.x
Subject(s) - goodness of fit , covariate , multinomial logistic regression , test statistic , statistics , logistic regression , mathematics , pearson's chi squared test , outcome (game theory) , null hypothesis , metric (unit) , test (biology) , econometrics , statistical hypothesis testing , paleontology , operations management , mathematical economics , economics , biology
Summary This article presents a score test to check the fit of a logistic regression model with two or more outcome categories. The null hypothesis that the model fits well is tested against the alternative that residuals of samples close to each other in covariate space tend to deviate from the model in the same direction. We propose a test statistic that is a sum of squared smoothed residuals, and show that it can be interpreted as a score test in a random effects model. By specifying the distance metric in covariate space, users can choose the alternative against which the test is directed, making it either an omnibus goodness‐of‐fit test or a test for lack of fit of specific model variables or outcome categories.