| Nested logit models have been widely estimated by maximum likelihood estimation. A key issue is inference on the coefficient of the inclusive variable, because this coefficient provides an insight into the decision making process of the economic agent and the degree of substitution between the available choices. In theory, this coefficient needs to be within the unit interval. When this constraint is violated, the data is deemed inconsistent with random utility maximization. Constraining this coefficient within the unit interval is not a solution since, in many applications, the estimate hits one of the bounds (0 or 1) and is often unable to make inference because the constrained maximum likelihood estimation procedures do not produce standard error estimates.; I study nested logit models under a Bayesian framework, and present a new Markov Chain Monte Carlo algorithm to estimate such models. The algorithm is designed block-wise, and is a single channel Metropolis-Hastings algorithm. Bayesian framework has two advantages: (1) it provides posterior probability density functions of coefficients, and (2) it allows imposition of constraints on coefficients much more easily than maximum likelihood estimation. The algorithm is applied to ambulatory health care data to analyze the choices of physicians in treating patients diagnosed with depression. |
