Chapter 17 5 Binary regression Logit and Probit

Chapter 17 5 Binary regression: Logit and Probit Models Modified Version by Woraphon Yamaka © 2016 Cengage Learning ®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. © kentoh/Shutterstock.

������� Binary regression? § ������������ Y ����������������������� ������� Y ��� ������� 2 ���� § ���������� Y ������������ (distributed normally) § ������� Y © 2016 Cengage Learning ®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use.

���������� Y X © 2016 Cengage Learning ®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use.

���������� Linear regression ? ● © 2016 Cengage Learning ®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use.

Comparing Linear Regression and Binary Regression Models Linear Regression Model 1 Binary Regression Model 0 Nonlinear models for binary response © 2016 Cengage Learning ®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use.

Logit and Probit models for Binary choice Model ● �������� Binary choice regression �� 2 ���� ��� ● 1) Logit regression 2) Probit regression ��������� (cumulative distribution function : CDF) ��������������������� � Y=1 ������ 0 -1 ��������������� � Y������� 0 -1 © 2016 Cengage Learning ®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use.

Logit and Probit distribution ● Cumulative Distribution Function : CDF ��� Logit ��� Probit © 2016 Cengage Learning ®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use.

Logit and Probit models for binary response ● Cumulative Distribution Function : CDF ��� Logit ��� Probit: (normal distribution) Logit: (logistic function) whereas ● ���������� Logit ��� Probit and © 2016 Cengage Learning ®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use.

Logit and Probit models for binary response ����� : logistic ��� normal distribution ���������� probability �������������� Y ����� 0 -1 ��� X =0, ������� p =. 50 § ������� X ������� , p ����� 1 ������� § ������� X ������� , p ����� 0 ������� © 2016 Cengage Learning ®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use.

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Logit and Probit models for binary response ● Maximum likelihood estimation ������ Logit ��� Probit ������������ yi =1 ����������������� x ��������� � yi =0 ��������� x �������� ● ������������� log-likelihood ����� Maximum likelihood estimates © 2016 Cengage Learning ®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use.

Estimation FOC SOC © 2016 Cengage Learning ®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use.

Example of the results (STATA) © 2016 Cengage Learning ®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use.

Interpretation (���� ) ● © 2016 Cengage Learning ®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use.

Problem of the traditional interpretation ����������������� BVAP ��� ��������� BVAP 0. 2 �� 0. 3 (20% 30%) ��� 0. 5 �� 0. 6 (50% 60%) ��������������������� (Black Elected) ���������� © 2016 Cengage Learning ®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use.

������������� : Marginal Effects ● ����������� partial effects ��������� (����������� ) © 2016 Cengage Learning ®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use.

������������� : Marginal Effects ���������������� • Marginal effect • Odd ratio © 2016 Cengage Learning ®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use.

������ ● ������������ Odds ratio ● Odds ratio = e(β) = e(0. 059) = 1. 061 ������ OR ������� 1 ����� x 1 ����� odds ������������� 1. 06 �������������� x ������� 6% �������� “�������������� 1 ������������ 1. 06 ��������� 6% ��������� ”. . . Odds ratio = e(β) = e((-1. 897) = 0. 15 -����� OR ���� 1 ��������� x 2 : ����������� © 2016 Cengage Learning ®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 18

������ ● ������������ Marginal effect ● β=0. 5 ����� x 1 ���������������� Y=1 ���� Pr(Y=1) ������� 0. 50 ����� 50 % �� ������������. . . ● β=-0. 5 ����� x 1 ���������������� Y=1 ���� Pr(Y=1) ������� 0. 50 ����� 50 % �� ����������. . . © 2016 Cengage Learning ®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 19

Multivariate test ● Hypothesis testing (������ maximum likelihood estimation( • t-tests and confidence intervals ��������� univariate test (������� 4 ������� ) • ������ multivariate hypotheses test ������� • Lagrange multiplier or score test • Wald test • Likelihood ratio test (������� F-test ) Chi-square distribution with q degrees of freedom Lr L ur © 2016 Cengage Learning ®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use.

Logit and Probit models for binary response ● Goodness-of-fit measures for Logit and Probit models • Percent correctly predicted Individual i‘s outcome is predicted as one if the probability for this event is larger than. 5, then percentage of correctly predicted y = 1 and y = 0 is counted • Pseudo R-squared Compare maximized log-likelihood of the model with that of a model that only contains a constant (and no explanatory variables) • Correlation based measures Look at correlation (or squared correlation) between predictions or predicted prob. and true values © 2016 Cengage Learning ®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use.

������������� ● ���� : Married women’s labor force participation ��������������� ������ ? LPM = linear Probability model or linear regression model © 2016 Cengage Learning ®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use.