Fitting multinomial logistic regression models and loglinear models to data related to life assurance policies

Abstract

The data that is modelled in this thesis was obtained from HSBC Life Assurance Malta Ltd. It includes five insurance life products and several predictors. The five products are: Savings Plan, Personal Protector Plan, Children's Plan, Single Premium Plan and Private Retirement Plan. The predictors are: location, gender, marital status and age of the policyholder and term and total sum assured of the policy. This data is analysed through the Multinomial Logistic Regression and Loglinear Models. The Multinomial Logistic Regression Model has a generalised logit link of the form log (Pi/Pj)=nj where nj is the linear predictor. The error distribution for this model is multinomial. It models the given data and gives the probability of choosing a product at the given values of the covariates. Multinomial Logistic Regression Models are also used when the predictors are either factors or covariates or a combination of both. These models are applied when the response variable is a factor. The Loglinear Model has a log link of the form log(µi) = ni . The error distribution is poisson. This type of model deals solely with factors and it is used to find the expected frequencies of policyholders given their individual characteristics and policy attributes. The parsimonious Multinomial Logistic Regression Model and parsimonious Loglinear Model are formulated to obtain simple models that adequately explain the data. Also, the equivalence of the Multinomial Logistic Regression Model and Loglinear Model is demonstrated when the two models include only factors.