Logistic Models Are Widely Used In Economics And Other Disciplines And Are Easily Available As Part Of Many Statistical Software Packages. This Text For Graduates, Practitioners And Researchers In Economics, Medicine And Statistics, Which Was Originally Published In 2003, Explains The Theory Underlying Logit Analysis And Gives A Thorough Explanation Of The Technique Of Estimation. The Author Has Provided Many Empirical Applications As Illustrations And Worked Examples. A Large Data Set - Drawn From Dutch Car Ownership Statistics - Is Provided Online For Readers To Practise The Techniques They Have Learned. Several Varieties Of Logit Model Have Been Developed Independently In Various Branches Of Biology, Medicine And Other Disciplines. This Book Takes Its Inspiration From Logit Analysis As It Is Practised In Economics, But It Also Pays Due Attention To Developments In These Other Fields. J.s. Cramer. Includes Bibliographical References (p. 158-165) And Indexes. Cover......Page 1 Title......Page 3 Copyright......Page 4 Contents......Page 5 List of figures......Page 7 List of tables......Page 8 Preface......Page 11 1.1 The role of the logit model......Page 13 1.2 Plan of the book and further reading......Page 14 1.3 Program packages and a data set......Page 16 1.4 Notation......Page 18 2.1 The logit model for a single attribute......Page 21 2.2 Justification of the model......Page 28 2.3 The latent regression equation; probit and logit......Page 32 2.4 Applications......Page 38 3.1 Principles of maximum likelihood estimation......Page 45 3.2 Sampling considerations......Page 50 3.3 Estimation of the binary logit model......Page 52 3.4 Consequences of a binary covariate......Page 57 3.5 Estimation from categorical data......Page 59 3.6 Private car ownership and household income......Page 62 3.7 Further analysis of private car ownership......Page 66 4.1 Statistical tests in maximum likelihood theory......Page 68 4.2 The case of categorical covariates......Page 70 4.3 The Hosmer–Lemeshow test......Page 74 4.4 Some measures of fit......Page 78 5.1 Detection of outliers......Page 85 5.2 Misclassification of outcomes......Page 88 5.3 The effect of omitted variables......Page 91 6.1 A link with discriminant analysis......Page 100 6.2 One-sided sample reduction......Page 104 6.3 State-dependent sampling......Page 109 6.4 Case–control studies......Page 111 7.1 Ordered probability models......Page 116 7.2 The standard ultinomial logit model......Page 118 7.3 ML estimation of multinomial models: generalities......Page 122 7.4 Estimation of the standard multinomial logit......Page 125 7.5 Multinomial analysis of private car ownership......Page 129 7.6 A test for pooling states......Page 134 8.1 The general logit model......Page 138 8.2 McFadden’s model of random utility maximization......Page 142 8.3 The conditional logit model......Page 147 8.4 Choice of a mode of payment......Page 152 8.5 Models with correlated disturbances......Page 156 9.1 The origins of the logistic function......Page 161 9.2 The invention of probit and the advent of logit......Page 164 9.3 Other derivations......Page 168 Bibliography......Page 170 Index of authors......Page 178 Index of subjects......Page 180 Cover 1 Title 3 Copyright 4 Contents 5 List of figures 7 List of tables 8 Preface 11 1 Introduction 13 1.1 The role of the logit model 13 1.2 Plan of the book and further reading 14 1.3 Program packages and a data set 16 1.4 Notation 18 2 The binary model 21 2.1 The logit model for a single attribute 21 2.2 Justification of the model 28 2.3 The latent regression equation; probit and logit 32 2.4 Applications 38 3 Maximum likelihood estimation of the binary logit model 45 3.1 Principles of maximum likelihood estimation 45 3.2 Sampling considerations 50 3.3 Estimation of the binary logit model 52 3.4 Consequences of a binary covariate 57 3.5 Estimation from categorical data 59 3.6 Private car ownership and household income 62 3.7 Further analysis of private car ownership 66 4 Some statistical tests and measures of fit 68 4.1 Statistical tests in maximum likelihood theory 68 4.2 The case of categorical covariates 70 4.3 The Hosmer–Lemeshow test 74 4.4 Some measures of fit 78 5 Outliers, misclassification of outcomes, and omitted variables 85 5.1 Detection of outliers 85 5.2 Misclassification of outcomes 88 5.3 The effect of omitted variables 91 6 Analyses of separate samples 100 6.1 A link with discriminant analysis 100 6.2 One-sided sample reduction 104 6.3 State-dependent sampling 109 6.4 Case–control studies 111 7 The standard multinomial logit model 116 7.1 Ordered probability models 116 7.2 The standard ultinomial logit model 118 7.3 ML estimation of multinomial models: generalities 122 7.4 Estimation of the standard multinomial logit 125 7.5 Multinomial analysis of private car ownership 129 7.6 A test for pooling states 134 8 Discrete choice or random utility models 138 8.1 The general logit model 138 8.2 McFadden’s model of random utility maximization 142 8.3 The conditional logit model 147 8.4 Choice of a mode of payment 152 8.5 Models with correlated disturbances 156 9 The origins and development of the logit model 161 9.1 The origins of the logistic function 161 9.2 The invention of probit and the advent of logit 164 9.3 Other derivations 168 Bibliography 170 Index of authors 178 Index of subjects 180
Originating in economics but now used in a variety of disciplines, including medicine, epidemiology and the social sciences, this book provides accessible coverage of the theoretical foundations of the Logit model as well as its applications to concrete problems. It is written not only for economists but for researchers working in disciplines where it is necessary to model qualitative random variables. J.S. Cramer has also provided data sets on which to practice Logit analysis.
This text for graduates and practitioners explains the theory underlying logit analysis and the technique of estimation. There are many illustrations and worked examples as well as a large online data set for practice. Although inspired by economics, the book pays due attention to developments in medicine and other fields. Logit analysis is in many ways the natural complement of ordinary linear regression whenever the regressand is not a continuous variable but a state which may or may not hold, or a category in a given classification.
