Linear Probability, Logit, and Probit Models

Ordinary regression analysis is not appropriate for investigating dichotomous or otherwise "limited" dependent variables, but this volume examines three techniques -- linear probability, probit, and logit models -- which are well-suited for such data. It reviews the linear probability model and discusses alternative specifications of non-linear models. Using detailed examples, Aldrich and Nelson point out the differences among linear, logit, and probit models, and explain the assumptions associated with each.

Series Introduction

5

(2)

Acknowledgments

7

(2)

The Linear Probability Model

9

(21)

Introduction

9

(1)

Review of the Multivariate, Linear Regression Model

10

(2)

A Dichotomous Dependent Variable and the Linear Probability Model

12

(8)

A Dichotomous Response Variable with Replicated Data

20

(2)

Polytomous or Multiple Category Dependent Variables

22

(2)

The Linearity Assumption

24

(3)

The Effect of an Incorrect Linearity Assumption

27

(3)

Specification of Nonlinear Probability Models

30

(18)

Introduction

30

(1)

The General Problem of Specification

30

(1)

Alternative Nonlinear Functional Forms for the Dichotomous Case

31

(4)

Derivation of Nonlinear Transformations from a Behavioral Model

35

(2)

Nonlinear Probability Specifications for Polytomous Variables

37

(3)

Behavior of the Logit and Probit Specifications

40

(7)

Summary

47

(1)

Estimation of Probit and Logit Models for Dichotomous Dependent Variables

48

(18)

Introduction

48

(1)

Assumptions of the Models

48

(1)

Maximum Likelihood Estimation

49

(3)

Properties of Estimates

52

(2)

Interpretation of and Inference from MLE Results

54

(11)

Conclusions

65

(1)

Minimum Chi-Square Estimation and Polytomous Models

66

(12)

Introduction

66

(1)

Minimum Chi-Square Estimation for Replicated, Dichotomous Data

67

(6)

Polytomous Dependent Variables

73

(5)

Summary and Extensions

78

(7)

Introduction

78

(1)

Summary

78

(3)

Extensions

81

(4)

Notes

85

(8)

References

93

(2)

About the Authors

95

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Linear Probability, Logit, and Probit Models

Summary

Table of Contents

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