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Title: BERNOULLI REGRESSION MODELS: RE-EXAMINING STATISTICAL MODELS WITH BINARY DEPENDENT VARIABLES

Author
item Bergtold, Jason
item SPANOS, ARIS - VIRGINIA TECH.

Submitted to: Meeting Proceedings
Publication Type: Proceedings
Publication Acceptance Date: 7/24/2005
Publication Date: 7/24/2005
Citation: Bergtold, J.S., Spanos, A. 2005. Bernoulli regression models: re-examining statistical models with binary dependent variables. In: Proceedings of the American Agricultural and Applied Economics Association Annual Meeting, July 24-27, 2005, Providence, Rhode Island. Available: http://agecon.lib.umn.edu/

Interpretive Summary: Studies modeling the adoption of conservation practices often only examine if a particular practice was adopted or not. To use this information in a statistical model requires the researcher to treat this decision as binary. That is, if a person adopts the practice, then the variable representing this decision, will take a value of 1, and 0 otherwise. This binary variable then becomes the key element in a model trying to explain what social and economic factors affect the decision of a farmer or individual to adopt a particular conservation practice. In order for these models to be accurate, certain statistical requirements must be satisfied. Using the traditional statistical (or econometric) models can prove problematic, because they may give rise to a problem known as functional misspecification. That is, the form of the model is not correct, which can lead to inaccurate explanations and recommendations when using that model. This paper, re-examines the underlying statistical foundations of these types of models to address this problem. We develop a family of models, known as the Bernoulli Regression Model, that is consistent with statistical theory and guidelines for properly specifying the forms of these models. An empirical example in the paper shows that such models can provide improved predictions and recommendations concerning the adoption of conservation practices.

Technical Abstract: The classical approach for specifying statistical models with binary dependent variables in econometrics using latent variables or threshold models can leave the model misspecified, resulting in biased and inconsistent estimates as well as erroneous inferences. Furthermore, methods for trying to alleviate such problems, such as univariate generalized linear models, have not provided an adequate alternative for ensuring the statistical adequacy of such models. The purpose of this paper is to re-examine the underlying probabilistic foundations of statistical models with binary dependent variables using the probabilistic reduction approach to provide an alternative approach for model specification. This re-examination leads to the development of the Bernoulli Regression Model. Simulated and empirical examples provide evidence that the Bernoulli Regression Model can provide a superior approach for specifying statistically adequate models for dichotomous choice processes.