Logistic regression analyses for indirect data

ABSTRACT

The article’s topic is logistic regression for direct data on the covariates, but indirect data on the endogenous variable. The indirect data may result from a privacy-protecting survey procedure for sensitive characteristics or from statistical disclosure control. Various procedures to generate the indirect data exist. However, we show that it is possible to develop a general approach for logistic regression analyses with indirect data that covers many procedures. We first derive a general algorithm for the maximum likelihood estimation and a general procedure for variance estimation. Subsequently, lots of examples demonstrate the broad applicability of our general framework.

KEYWORDS:

• Item count technique
• Missing data
• Non-randomized response
• Randomized response
• Sensitive question
• Statistical disclosure control.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62D05
• 62J12
• 90-08

Acknowledgments

The author thanks the editor, an associate editor, and two referees for the review of this manuscript and their comments and suggestions to improve the manuscript.