Examining ordinal categorical data related to the gaming industry using multilevel modelling

Abstract

Multilevel models, also known as hierarchical linear models, extend generalized linear regression models by relaxing the assumption of independence among the responses. Multilevel models are explicitly designed to analyze clustered data structures where observations at the micro level are nested in macro level structures, which in turn may be nested in clusters of higher order. Moreover, multilevel models can accommodate both fixed and random variables, where the equations defining the hierarchical linear models contain an error term at each level of nesting. This makes it possible to study the variation at different levels of the hierarchy. When parameters are estimated, multilevel models take into account the hierarchical nested structure of the data such that the intra-class correlation describe the proportion of the total variance due to within cluster variance. This dissertation mainly focuses on two and three level models together with the numerical approximations techniques used in order to obtain the parameter estimates. The ordinary Gaussian quadrature and the adaptive Gaussian quadrature are the numerical techniques used to approximate the marginal likelihood, which is then maximized by using the modified Newton-Raphson algorithm. Mixed effects multilevel models have several research applications since hierarchical structured data arises in many research fields. In this dissertation, the dataset is related to a betting application, where the gains made by the betting company on each customer have an ordinal categorical scale. This dependent variable is related to a number of explanatory variables including the age of the player, betting amount, betting count, deposit amount, withdrawal amount, bonus cost, acquisition source and product played among other explanatory variables. The appropriateness of multilevel models arises from the fact that customers are nested in countries yielding a two level structure, where customers are the level-1 units and countries are the level-2 units. An alternative approach is to consider the repeated measures of several explanatory variables to be nested in customers, which in tum are nested in different countries, yielding a three level structure