Log Multinomial Regresyon Modeline Hosmer Lemeshow Uyum İyiliği Testi Uyarlanması

Abstract

Logistic regression is used to model the relationship between categorical response variables and covariates. In case of more than one covariate variable, the odds ratio is estimated by logistic regression. Log multinomial regression model offers relative risk estimation, unlike logistic regression models. In general, it is a significant step to evaluate the model fitting after regression analysis. In addition to various statistics, goodness of fit tests is also used to evaluate the fit of the regression model to the data. It is known that statistics used in determining and evaluating the goodness of fit of the linear regression models are less useful in generalized linear models and logistic regression analysis. A better way to assess the fit of a binary or multinomial logistic regression model is the goodness of fit test proposed by Hosmer and Lemeshow. There is no method for evaluating the fit in the log multinomial regression model to the data. Therefore, there is a need to measure how well the log multinomial regression model fits the observed data. In this thesis, it is illustrated the applicability of the Hosmer-Lemeshow goodness of fit test in the evaluation of the log multinomial regression model’s goodness of fit is analyzed under various scenarios. In these scenarios, different structures of response variable and covariates are compared with the help of simulation study at various sample sizes. In the simulation study, a total of 70 different combinations are used, considering categorical response variables with more than two categories, continuous or categorical covariates and different sample sizes. Each scenario is repeated 1000 times and evaluations were carried out by obtaining the type I and type II error frequencies, which are the results of the goodness of fit test, in each repetition. According to the results it is determined that adapted goodness of fit test performed well in testing the goodness of fit in the log multinomial regression model. In this thesis, the Hosmer-Lemeshow test is proposed as a goodness of fit test to be used in the log multinomial regression model and is brought to the statistical literature.