| As a well-known generalization of the linear model, the Box-Cox (BC) model has been used extensively in applied econometrics. There are several reasons for its widespread use. First, the BC model nests as special cases the linear and semi-log models, as well as an infinite number of nonlinear models. The BC model permits a researcher to let the data determine the most appropriate functional form for a model rather than impose linearity or log-linearity arbitrarily. When theory implies some functional form for a regression equation the BC model may allow testing of the theory. More often, however, theory gives no guidelines for functional form, and the BC model provides some statistical justification for a dependent variable transformation that may otherwise be ad hoc. Second, maximum likelihood estimates for the model are easily obtained in cross-sectional or time-series settings using a grid search procedure.; There are currently few BC models appropriate for analysis of clustered data. This dissertation develops a BC model with random coefficients (BCRC) that is appropriate for clustered data, and shows how Bayesian estimates may be obtained. I discuss posterior simulation by Markov chain Monte Carlo (MCMC) methods and how marginal likelihoods and Bayes factors may be computed from the simulation output so that Bayesian model selection may be performed. The model is fit to a set of simulated data to test the performance of the sampler.; Finally, I use the BCRC model to risk-adjust the cost of providing hospital care to patients who undergo coronary artery bypass graft procedures. Data from four Midwestern hospitals are used to risk-adjust the cost of inpatient hospital care and compare the performance of the hospitals. Several important issues regarding risk adjustment are addressed, including (1) determining the most appropriate transformation of costs for the risk adjustment process, and (2) whether the hospital-level transformations are similar enough to be treated as equal. Results indicate that in these data the most appropriate transformation is inverse, and not natural log, and that the transformation is not equal across hospitals. Finally, the implication for ranking hospitals based on risk-adjusted costs is considered. |
