A Flexible Link Function for Discrete-Time Duration Models

This paper proposes a discrete-time hazard regression approach based on the relation between hazard rate models and excess over threshold models, which are frequently encountered in extreme value modelling. The proposed duration model employs a flexible link function and incorporates the grouped-duration analogue of the well-known Cox proportional hazards model and the proportional odds model as special cases. The theoretical setup of the model is motivated, and simulation results are reported to suggest that it performs well. The simulation results and an empirical analysis of US import durations also show that the choice of link function in discrete hazard models has important implications for the estimation results, and that severe biases in the results can be avoided when using a flexible link function as proposed in this study

Random Effect Models in the Statistical Analysis of Human Fecundability Data: Application to artificial insemination with sperm from donor.

The main aim of this dissertation is to explore methodological approaches to correlated binary data and to assess their suitability for the analysis of data on human fertility. The dataset concerns a study of Artificial Insemination by Donor (AID). AID represents an unusual research opportunity to study both male and female fecundability simultaneously. In each attempt to conceive, artificial insemination is carried out in consecutive ovulatory cycles until conception or change of treatment. The probability of conception may differ between women, so that the data are discrete time survival data with censoring and between-subject heterogeneity. There is also potential heterogeneity between donors. Non-systematic allocation of the donor to recipient ensures that the same woman receives semen from several donors, This added heterogeneity as well as other cycle dependent covariates have to be taken into account. The analysis must also take account of covariates, most of them time-varying. Our dataset have a crossed hierarchical structure due to the presence of both, female and male factors. The rather complicated "design" calls for unit specific regression models. These models are presented as well as their lack of tractability except in some rather specific cases. The motivation for choosing Gaussian random effects in unit specific regression models is discussed. We demonstrate the use of an approximate inference method (Penalized Quasi Likelihood). This method is shown to be a useful and practical way of carrying out preliminary data analysis. Finally a Bayesian procedure (Gibbs sampling) provides validation and more accurate results despite the intensive computation it needs. The main substantive finding of the analysis is the unexpectedly pronounced heterogeneity of donor fecundability, even after inclusion of conventional measures of sperm quality into the model. These measures were shown to be predictive at the donor level but not at the level of individual donation

Advanced survival modelling for consumer credit risk assessment: addressing recurrent events, multiple outcomes and frailty

A thesis submitted in partial fulfillment of the requirements for the degree of Doctor in Information Management, specialization in Statistics and EconometricsThis thesis worked on the application of advanced survival models in consumer credit risk assessment, particularly to address issues of recurrent delinquency (or default) and recovery (cure) events as well as multiple risk events and frailty. Each chapter (2 to 5) addressed a separate problem and several key conclusions were reached. Chapter 2 addressed the neglected area of modelling recovery from delinquency to normal performance on retail consumer loans taking into account the recurrent nature of delinquency and also including time-dependent macroeconomic variables. Using data from a lending company in Zimbabwe, we provided a comprehensive analysis of the recovery patterns using the extended Cox model. The findings vividly showed that behavioural variables were the most important in understanding recovery patterns of obligors. This confirms and underscores the importance of using behavioural models to understand the recovery patterns of obligors in order to prevent credit loss. The findings also strongly revealed that the falling real gross domestic product, representing a deteriorating economic situation significantly explained the diminishing rate of recovery from delinquency to normal performance among consumers. The study pointed to the urgent need for policy measures aimed at promoting economic growth for the stabilisation of consumer welfare and the financial system at large.Chapter 3 extends the work in chapter 2 and notes that, even though multiple failure-time data are ubiquitous in finance and economics especially in the credit risk domain, it is unfortunate that naive statistical techniques which ignore the subsequent events are commonly used to analyse such data. Applying standard statistical methods without addressing the recurrence of the events produces biased and inefficient estimates, thus offering erroneous predictions. We explore various ways of modelling and forecasting recurrent delinquency and recovery events on consumer loans. Using consumer loans data from a severely distressed economic environment, we illustrate and empirically compare extended Cox models for ordered recurrent recovery events. We highlight that accounting for multiple events proffers detailed information, thus providing a nuanced understanding of the recovery prognosis of delinquents. For ordered indistinguishable recurrent recovery events, we recommend using the Andersen and Gill (1982) model since it fits these assumptions and performs well on predicting recovery.Chapter 4 extends chapters 2 and 3 and highlight that rigorous credit risk analysis is not only of significance to lenders and banks but is also of paramount importance for sound regulatory and economic policy making. Increasing loan impairment or delinquency, defaults and mortgage foreclosures signals a sick economy and generates considerable financial stability concerns. For lenders and banks, the accurate estimation of credit risk parameters remains essential for pricing, profit testing, capital provisioning as well as for managing delinquents. Traditional credit scoring models such as the logit regression only provide estimates of the lifetime probability of default for a loan but cannot identify the existence of cures and or other movements. These methods lack the ability to characterise the progression of borrowers over time and cannot utilise all the available data to understand the recurrence of risk events and possible occurrence of multiple loan outcomes. In this paper, we propose a system-wide multi-state framework to jointly model state occupations and the transitions between normal performance (current), delinquency, prepayment, repurchase, short sale and foreclosure on mortgage loans. The probability of loans transitioning to and from the various states is estimated in a discrete-time multi-state Markov model with seven allowable states and sixteen possible transitions. Additionally, we investigate the relationship between the probability of loans transitioning to and from various loan outcomes and loan-level covariates. We empirically test the performance of the model using the US single-family mortgage loans originated during the first quarter of 2009 and were followed on their monthly repayment performance until the third quarter of 2016. Our results show that the main factors affecting the transition into various loan outcomes are affordability as measured by debt-to-income ratio, equity as marked by loan-to-value ratio, interest rates and the property type. In chapter 5, we note that there has been increasing availability of consumer credit in Zimbabwe, yet the credit information sharing systems are not as advanced. Using frailty survival models on credit bureau data from Zimbabwe, the study investigates the possible underestimation of credit losses under the assumption of independence of default event times. The study found that adding a frailty term significantly improved the models, thus indicating the presence of unobserved heterogeneity. The major policy recommendation is for the regulator to institute appropriate policy frameworks to allow robust and complete credit information sharing and reporting as doing so will significantly improve the functioning of the credit market

A Data-driven Statistical Approach to Customer Behaviour Analysis and Modelling in Online Freemium Games

The video games industry is one of the most attractive and lucrative segments in the entertainment and digital media, with big business of more than $150 billion worldwide. A popular approach in this industry is the online freemium model, wherein the game is downloadable free of cost, while advanced and bonus content have optional charges. Monetisation is through micro payments by customers and the focus is on maintaining average revenue per user and lifetime value of players. The overall aim of this research is to develop suitable data-driven methods to gain insight about customer behaviour in online freemium games, with a view to providing recommendations for successful business in this industry.Three important aspects of user behaviour are modelled in this research - engagement, time until defection, and number of micro transactions made. A multiple logistic regression using penalised likelihood approach is found to be most suitable for modelling and demonstrates good fit and accuracy for assigning observations to engaged and non-engaged categories. Cox’s proportional hazards model is adopted to analyse time to defection, and a negative binomial zero-inflated model results in the best fit to the data on micro payments. Cluster analysis techniques are used to classify the wide variety of customers based on their gameplay styles, and social network models are developed to identify prominent ‘actors’ based on social interactions. Some of the significant predictors of engagement and monetisation are amount of premium in-game currency, success in missions and competency in virtual fights, and quantity of virtual resources used in the game.This research offers extensive insight into what drives the reputation, virality and commercial viability of freemium games. In particular it helps to fill a gap in understanding the behaviour of online game players by demonstrating the effectiveness of applying a data analytic approach. It gives more insight into the determinants of player behaviour than relying on observational studies or those based on survey research. Additionally, it refines statistical models and demonstrates their implementation in R to new and complex data types representing online customer behaviours

Strategic Categorization, Category Bundle, and Typecasting: Three Essays on Product Categorization

Categories are social agreements about the meanings of labels applied to products. Categories serve as the basis for market interaction: audiences use categories to make sense of the products offered to them, producers apply product categories in marketing activities to reach their target customers, and market intermediaries refer to prototypical categories in assessing the quality of products. As a widely used sociocognitive concept, categorization has accrued prominence in research and practice, with researchers investigating the social and economic impacts of categorization and practitioners probing superior categorization strategies that optimize their economic returns. However, current strategic management and organization theory research has achieved limited success in expounding on how organizations strategically manipulate category labels to acquire excess returns and how audiences process categorical information in assessing the products to which they are exposed. This dissertation joins the ongoing dialogue on categorization and contributes to the literature by offering three essays that respectively address three understudied questions. First, how do producers manipulate the categorical perception of the audiences for their offerings? Second, how do audiences handle the interconnected relationships between categories when they classify products in the market? Last, how do the market identities imposed on market candidates persistently affect their career development? I chose the feature film industry in North America (Canada and the U.S.) as the empirical setting for my dissertation, since a dominant category system, film genres, significantly affects the market success of all film market participants. The genre labels associated with a film shape moviegoers consumption decisions, and the categorical perception of moviegoers of an actor/actress has considerable impacts on the actors/actresss career advancement. Using a gigantic database of feature film projects that were exhibited in theaters in the U.S. and Canada from 1990 to 2015, I construct three unique datasets that are respectively used to test my hypotheses and answer my research questions at the film, genre, and actor levels. I summarize my key findings as follows. This dissertation contributes to category, labor market, and strategic management research

Essays on Commercial Banking: Survival, Performance, and Heterogeneous Technologies

In the first chapter, we focus on explaining the U.S. commercial banking failures during the recent financial crisis. We employ the semi-parametric mixture hazard model (MHM) with both continuous and discrete time specifications to first, distinguish between troubled and healthy banks and second, to estimate the probability and the timing of their failure. We combine the MHM with the stochastic frontier model (SFM) to explore the role of managerial inefficiency on a bank's longer term viability. We find that the discrete-time MHM which takes the managerial inefficiencies into account fits well and dominates other competing specifications by accurately predicting the timing of failures both in and out of the sample. The second chapter explores a new class of flexible cross-sectional parametric SFMs that impose an unobservable bound on the inefficiency term. We consider 11 doubly truncated normal, truncated half-normal, and truncated exponential distributions to model the inefficiencies. We extend the models to the panel data setting and specify a time-varying inefficiency bound. We apply these models to analyze the performance of the U.S. commercial banking industry during 1984-2009. In the third chapter, we address the issue of the "wrong" skewness of the least squares residuals that often arises in applied studies using the traditional SFM. Findings of "wrong" skewness imply that the SFM is misspecified and all firms are fully efficient. Based on doubly truncated normal distribution that displays both positive and negative skewness, we prove that "wrong" skewness does not necessarily imply that the SFM model is misspecified. The fourth chapter investigates the existence of heterogeneous technologies in the U.S. commercial banking industry through the threshold effects estimation techniques, modified to allow for time-varying effects. We employ the total assets as a threshold variable and determine seven distinct technology-groups. In the fifth chapter, we describe the commercial banking data that are extracted from the quarterly Consolidated Reports of Condition and Income (Call Reports). We detail the construction of the key variables used in this thesis, which mainly contain output quantities, input quantities and prices, bank-specific structural and geographical characteristics, as well as a number of measures of risk