Linear probability, logit, and probit models / John H. Aldrich, Forrest D. Nelson.

Format:

Book

Author/Creator:

Aldrich, John H., 1947-

Contributor:

Nelson, Forrest D.

Series:

Quantitative applications in the social sciences ; no. 07-045.

Sage university papers series. Quantitative applications in the social sciences ; no. 07-045

Language:

English

Subjects (All):

Probabilities.

Logits.

Probits.

Physical Description:

95 pages : illustrations ; 22 cm.

Place of Publication:

Beverly Hills : Sage Publications, [1984]

Summary:

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.

Contents:

1. The Linear Probability Model 9

1.1 Review of the Multivariate, Linear Regression Model 10

1.2 A Dichotomous Dependent Variable and the Linear Probability Model 12

1.3 A Dichotomous Response Variable with Replicated Data 20

1.4 Polytomous or Multiple Category Dependent Variables 22

1.5 The Linearity Assumption 24

1.6 The Effect of an Incorrect Linearity Assumption 27

2. Specification of Nonlinear Probability Models 30

2.1 The General Problem of Specification 30

2.2 Alternative Nonlinear Functional Forms for the Dichotomous Case 31

2.3 Derivation of Nonlinear Transformations from a Behavioral Model 35

2.4 Nonlinear Probability Specifications for Polytomous Variables 37

2.5 Behavior of the Logit and Probit Specifications 40

3. Estimation of Probit and Logit Models for Dichotomous Dependent Variables 48

3.1 Assumptions of the Models 48

3.2 Maximum Likelihood Estimation 49

3.3 Properties of Estimates 52

3.4 Interpretation of and Inference from MLE Results 54

4. Minimum Chi-Square Estimation and Polytomous Models 66

4.1 Minimum Chi-Square Estimation for Replicated, Dichotomous Data 67

4.2 Polytomous Dependent Variables 73

5. Summary and Extensions 78

5.2 Extension 81.

Notes:

Bibliography: pages 93-94.

ISBN:

0803921330

OCLC:

11728938