Estimating Explained Variation of a Latent Scale Dependent Variable Underlying a Binary Indicator of Event Occurrence

• Activity Number: 392
• Type: Contributed
• Date/Time: Tuesday, August 5, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Dinesh Sharma*+ and Amanda Miller and Caroline Hollingsworth
• Companies: James Madison University and James Madison University and James Madison University
• Keywords: Logistic Regression ; Measure of Explained Variation ; Latent Scale Dependent Variable ; Multilevel non-linear model ; McFadden's R^2 ; Chapman-Richards model

Abstract

The coefficient of determinant, also known as the R^2 statistic, is widely used as a measure of the proportion of explained variation in the context of a linear regression model. In many real life events, interests may lie on measuring the proportion of explained variation, ?^2 , of a latent scale dependent variable U which follows a multiple regression model. But in practice, U may not be observable and is represented by its binary proxy. In such situations, use of logistic regression analysis is a popular choice. Many analogues to R^2 type statistics have been proposed to measure explained variation in the context of logistic regression. McFadden's R^2 measure stands out from others because of its intuitive interpretation and its independence on the proportion of success in the sample. It, however, severely underestimates the proportion of explained variation of the underlying linear model. In this research we present a method for estimating the explained variation for the underlying linear model using the McFadden's R^2 statistics. When used in a real life dataset, our method estimated ?^2 of the underlying model within an acceptable margin of error.