On the linear in probability model for binary data

Area of Science:

• Statistics
• Sociology

Background:

• Binary response data analysis often employs models linear in the logistic transform of probabilities.
• Standard methods can sometimes obscure direct empirical interpretation of underlying parameters.

Purpose of the Study:

• To evaluate the advantages and disadvantages of simple least-squares estimates for binary response data.
• To explore the utility of linear probability models for parameter interpretation.

Main Methods:

• Analysis of binary response data using simple least-squares estimation.
• Comparison with models linear in the logistic transform of probabilities.
• Illustration through a sociological study.

Main Results:

• Simple least-squares estimates can offer a more direct empirical interpretation of parameters.
• The linear representation of probabilities has specific advantages and disadvantages.

Conclusions:

• Least-squares estimates provide a valuable alternative for analyzing binary response data, particularly when direct parameter interpretation is desired.
• The choice of model depends on the specific goals of the analysis and the nature of the data.