Messy Data Modelling in Health Care Contingent Valuation Studies

Abstract

This study addresses the complexity in modeling contingent valuation surveys with true zeros and non-ignorable missing responses including “don’t knows†and protest responses. An endogenous switching tobit model is specified to simultaneously estimate the parameters of the latent willingness to pay (WTP) decision variable and the latent true WTP level. A Bayesian technique is developed using MCMC methods data augmentation and Metropolis Hastings algorithm with Gibbs sampling for estimating the endogenous switching tobit model. The Bayesian approach presented here is useful even for finite sample size and for models with relatively flat likelihood like sample selection models for which convergence is a problem or even if convergence is achieved correlation of the latent random errors are outside the (-1,1) range. The proposed methodology is applied to a single-bounded dichotomous choice contingent valuation model using British Eurowill data on evaluating cancer health care program. Results in this study reveal that the interview interest scores for the unresolved or missing cases are substantially high and not far from scores of “yes†respondents. The pattern in the values of socio-economic and health related variables shows that these unresolved cases are not missing completely at random so that they may actually contain valuable information at least on the willingness decision process of respondents. Inclusion of these unresolved cases is essential to modelling WTP decision and true WTP level as reflected in the higher sum of log conditional predictive ordinate(SLCPO) goodness-of-fit criterion for a cross-validation sample and higher covariance between the latent random errors of the latent self-selection or WTP decision variable and the true WTP level model. The positive covariance and correlation of the latent random errors may explain why the true WTP levels in DC contingent valuation studies are oftentimes overestimated. The model presented in this paper may also be applied to double bounded dichotomous choice models with slight modification.non-ignorable missing values, single-bounded dichotomous choice contingent valuation studies,Markov chain Monte Carlo methods