Some aspects of fitting multinomial models in a GLM framework
type: CreativeWork
description: This thesis discusses how an iteratively re - weighted least squares algorithm can be used to fit a multinomial regression model, with logit link function or own link functions, with any number of explanatory variables. The responses of each individual can be aggregated and the data can then be represented in a contingency table as are given in examples used in this study. A satisfying aspect of the iteratively re-weighted least squares (IRLS) algorithm gives for fitting a multinomial regression model is that the calculations only require a program which can handle ordinary least squares and hence can be handled by a range of standard statistical software. The approach in this thesis applies an interesting and simple form of the Cholesky decomposition to a matrix that consists of diagonal sub - matrices to find the iterative weight matrix W ij. This method requires no matrix algebra facilities as all the calculations are carried out in an array format. This makes it amenable to implementation in most statistical software, including GLIM and shows how to fit a multinomial logit model without recourse to the Poisson trick approach of Francis et al. (1992). The method given here also allows us to find the ‘hat - matrix’ as is needed in the calculation of leverages and Cook’s distances. These statistics in general can be used for diagnostic purposes or to detect the influential observations but in multinomial models the ‘hat - matrix’ may have a very little or no use at all for detecting any inappropriate observation. Our approach is in contrast to any potential naive use of the Poisson trick approach of Francis et al. (1992) model that would then produce inappropriate leverages and Cook’s distances. We check that our approach gives exactly the same scaled deviance with correct degrees of freedom, parameter estimates and standard errors as are obtained from the Poisson trick approach with some minor rounding errors. Our approach has the freedom to consider any number of…
abstract: This thesis discusses how an iteratively re - weighted least squares algorithm can be used to fit a multinomial regression model, with logit link function or own link functions, with any number of explanatory variables. The responses of each individual can be aggregated and the data can then be represented in a contingency table as are given in examples used in this study. A satisfying aspect of the iteratively re-weighted least squares (IRLS) algorithm gives for fitting a multinomial regression model is that the calculations only require a program which can handle ordinary least squares and hence can be handled by a range of standard statistical software. The approach in this thesis applies an interesting and simple form of the Cholesky decomposition to a matrix that consists of diagonal sub - matrices to find the iterative weight matrix W ij. This method requires no matrix algebra facilities as all the calculations are carried out in an array format. This makes it amenable to implementation in most statistical software, including GLIM and shows how to fit a multinomial logit model without recourse to the Poisson trick approach of Francis et al. (1992). The method given here also allows us to find the ‘hat - matrix’ as is needed in the calculation of leverages and Cook’s distances. These statistics in general can be used for diagnostic purposes or to detect the influential observations but in multinomial models the ‘hat - matrix’ may have a very little or no use at all for detecting any inappropriate observation. Our approach is in contrast to any potential naive use of the Poisson trick approach of Francis et al. (1992) model that would then produce inappropriate leverages and Cook’s distances. We check that our approach gives exactly the same scaled deviance with correct degrees of freedom, parameter estimates and standard errors as are obtained from the Poisson trick approach with some minor rounding errors. Our approach has the freedom to consider any number of…
author: Ali, Muhammad Younis
keywords: 510 Mathematics
date published: 2010-06
date modified: 2026-07-24T02:54:44Z
provider: London Metropolitan University
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: London Metropolitan University