Bangor University DOCTOR of PHILOSOPHY Multivariate Analysis
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Bangor University DOCTOR OF PHILOSOPHY Multivariate analysis and survival analysis with application to company failure. Shani, Najah Turki Award date: 1991 Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal ? Take down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Download date: 05. Oct. 2021 MULTIVARIATE ANALYSIS AND SURVIVAL ANALYSIS WITH APPLICATION TO COMPANY FAILURE A Thesis submitted to the University of Wales BY NAJAH TURK! SHANI , B.Sc. , M.Sc. , FSS In candidature for the degree of PHILOSOPHIAE DOCTOR Centre for Applied Statistics, School of Mathematics, University College of North Wales, Bangor, North Wales, United Kingdom 1991 ACKNOWLEDGEMENTS I take this opportunity to express my respectful appreciation of the contributions made by several persons towards the completion of this thesis. First and foremost my supervisors, Dr. J. Y. Kassab and Professor S. Mcleay for their sustained interest, suggesting the topic, academic guidance and help with various difficulties which I have encountered during this study, all of which have contributed immensely to the quality of this research. I appreciate the support given by the Centre for Applied statistics staff and the computer laboratory staff who offered valuable and helpful comments. I would also like to thank Dr. J. Cummingham, the Deputy Chairman of the School of Mathematics, who was extremely helpful in providing facilities that were necessary for conducting this research and to the administrative staff of the Department. I wish to thank those people, specially Mr. J. Curtis, who has given me the encouragement and moral support to persevere with my studies through to completion. This research has been sponsored by the Higher Education Ministry of Iraq, whose financial assistance is gratefully acknowledged. Finally, my warmest thanks go to my brother, Mr. S. T. Shani and my sister, Mrs. H. T. Shani for their financial support and encouragement. iii SUMMARY This thesis offers an explanation of the statistical modelling of corporate financial indicators in the context where the life of a company is terminated. Whilst it is natural for companies to fail or close down, an excess of failure causes a reduction in the activity of the economy as a whole. Therefore, studies on business failure identification leading to models which may provide early warnings of impending financial crisis may make some contribution to improving economic welfare. This study considers a number of bankruptcy prediction models such as multiple discriminant analysis and logit, and then introduces survival analysis as a means of modelling corporate failure. Then, with a data set of UK companies which failed, or were taken over, or were still operating when the information was collected, we provide estimates of failure probabilities as a function of survival time, and we specify the significance of financial characteristics which are covariates of survival. Three innovative statistical methods are introduced. First, a likelihood solution is provided to the problem of takeovers and mergers in order to incorporate such events into the dichotomous outcome of failure and survival. Second, we move away from the more conventional matched pairs sampling framework to one that reflects the prior probabilities of failure and construct a sample of observations which are randomly censored, using stratified sampling to reflect the structure of the group of failed companies. The third innovation concerns the specification of survival models, which relate the hazard function to the length of survival time and to a set of financial ratios as predictors. These models also provide estimates of the rate of failure and of the parameters of the survival function. The overall adequacy of these models has been assessed using residual analysis and it has been found that the Weibull regression model fitted the data better than other parametric models. The proportional hazard model also fitted the data adequately and appears to provide a promising approach to the prediction of financial distress. Finally, the empirical analysis reported in this thesis suggests that survival models have lower classification error than discriminant and logit models. iv TABLE OF CONTENTS Page No. DECLARATION CERTIFICATE ACKNOWLEDGEMENTS SUMMARY iv TABLE OF CONTENTS LIST OF TABLES ix LIST OF FIGURES xv LIST OF APPENDICES xxv CHAPTER ONE INTRODUCTION 1.1 Objectives of the Study 3 1.2 Chapter survey 4 CHAPTER TWO BUSINESS FAILURE PREDICTION MODELS 2.1 Business Failure 7 2.2 Business Failure Definition 7 2.3 Causes of Failure 9 2.4 Survey of Failure Prediction Models 11 2.4.1 Corporate Failure Prediction Model 11 2.4.1.1 Univariate Models 12 2.4.1.2 Multivariate Models 14 2.5 Summary and Implications 41 CHAPTER THREE THE DATA SET AND EXPLORATORY ANALYSIS OF THE FINANCIAL RATIOS 3.1 The Sample 45 3.2 Collection of Financial Ratio Data 55 3.3 Mean Effects and the Influence of censoring 57 3.4 Distribution of Financial Ratios 66 3.5 Principal Component Analysis 74 3.5.1 Procedure for A principal Component Analysis 76 CHAPTER FOUR DISCRIMINANT ANALYSIS AND CLASSIFICATION OF THE "MERGED" AND "OTHER" COMPANIES 4.1 Introduction 84 4.2 Linear Discriminant Analysis 84 4.3 Stepwise Discriminant Analysis 90 4.4 Quadratic Discriminant Function 91 4.5 Application of Discriminant Analysis 94 4.6 Reclassification of the "Merged" and "Other" Companies 106 4.6.1 Stepwise Discriminant Method of Reclassification 108 4.6.2 An Alternative Method of Reclassification 110 CHAPTER FIVE A PROBABILISTIC MODEL OF FAILURE (LOGISTIC DISCRIMINATION) 5.1 Introduction 123 vi 5.2 Choice of Predictor Variables 125 5.2.1 Stepwise Regression 126 5.3 Generalised Linear Models 127 5.3.1 Prediction of Binary Variables - Logistic and Logit Models 128 5.4 Application 132 5.4.1 Stepwise Reduction of Variables 132 5.4.2 Application of the Generalised Linear Model 134 5.4.3 Prediction of Failure 137 CHAPTER SIX SURVIVAL MODELS 6.1 Introduction 140 6.2 Survival Function and Hazard Function 143 6.3 Estimation of the Survival Function 147 6.4 Parametric Models 149 6.4.1 Maximum Likelihood Estimation 155 6.4.2 Residual Analysis 156 6.5 Nonparametric Model (Proportional Hazard Model) 159 6.5.1 Model Assumptions 161 6.5.2 Maximum Likelihood Estimates 162 6.5.3 A stepwise Regression Procedure for the Selection of Variables 165 6.5.4 Residual Analysis 168 6.5.5 Estimation of the Survivor Function S(t;x) 169 6.6 Application of Methodology 173 vii 6.6.1 The Parametric Models 174 6.6.2 Nonparametric Models 216 6.6.3 Estimation the Probability of Company Failure 228 CHAPTER SEVEN SUMMARY AND CONCLUSIONS 232 APPENDICES 240 REFERENCES 254 - 267 vi ii LIST OF TABLES Table No. Title Page No. 2.1 Results of a study by Zmijewski (1984) 32 2.2 Summary of explanatory variables used in Lau's (1987) five-state financial distress prediction.. 37 2.3 Aggregate probabilistic prediction scores earned for different groups of firms for Lau's model (1987) 38 3.1 Industrial classification 46 3.2 Classification of 104 non-surviving companies... 47 3.3 Number of non-surviving companies for which data was available 49 3.4 Length of time series for non-surviving companies 50 3.5 Number of surviving companies for which data was available and the length of time series 54 3.6 List of financial ratios 56 3.7 Descriptive of distribution of financial ratios ix for survivors and non-survivors combined 68 3.8 K-S statistic test for the natural log and the square root of the ratios for survivors and non-survivors 71 3.9 Descriptive of distribution of financial ratios for non-survivors 72 3.10 Descriptive of distribution of financial ratios for survivors 73 3.11 Financial ratios and component loadings defining six financial ratio patterns for 445 non-surviving and surviving companies 82 4.1 Results of linear discriminant analysis before reclassification of "merged" and "other" companies for case a(1) (the bankrupt companies, treated as non-surviving group and surviving companies as a second group) 98 4.2 Results of linear discriminant analysis before reclassification of "merged" and "other" companies for case a(2) (the bankrupt, "merged" and "other" companies, treated as a non-surviving group and surviving companies as a second group) 99 x 4.3 Results of linear discriminant analysis before reclassification of "merged" and "other" companies for case a(1) (the bankrupt companies, treated as a non-surviving group and surviving companies as a second group) for five years prior to failure by using equal prior probabilities 104 4.4 Results of linear discriminant analysis before reclassification of "merged" and "other" companies for case a(2) (the bankrupt, "merged" and "other" companies, treated as a non-surviving group and surviving companies as a second group) for five years prior to failure by using equal prior probabilities 105 4.5 Results of linear discriminant analysis after reclassification of "merged" and "other" companies by using bankrupt and 5 others companies as a non-surviving group and the surviving and 69 others companies as surviving group 109 4.6 The results of changes in the log-likelihood when the 74 unclassified companies are added individually to the bankrupt and surviving groups for the purpose of reclassification .