Bayesian hierarchical Tweedie spatio-temporal modeling using Hamiltonian Monte-Carlo algorithm for semi-continuous data in the context of contraceptive expenditures

Bayesian hierarchical Tweedie spatio-temporal modeling using Hamiltonian Monte-Carlo algorithm for semi-continuous data in the context of contraceptive expenditures

Space can produce variations in healthcare expenditures, even across relatively small geographic regions and suggests the need for a spatial analysis of areal data at a refined geographic scale. Also spatially sampled studies are often repeated over time. The relationship between observations collected in space and time, is often overlooked, while including a temporal or spatial correlation term is likely to improve the efficiency of the model. Another common feature in healthcare expenditures data is their semi-continuous nature. The topics for dealing with continuous data with a spike at zero is of great practical importance but it has not been given the necessary space in the literature. A popular approach is using two-part mixture models that separately model the probability of occurrence (with a binary component) and the intensity when the response is non-zero (with a continuous component). But this way is not always correct. In this paper, we develop a Bayesian hierarchical Tweedie regression model that can accommodate the excess number of zeros by combining information from occurrence and conditional-to-presence abundance, while accounting for spatial and temporal correlation simultaneously. We assess model performance via simulation in two different types of semi-continuous datasets (with high and with low spatial and temporal correlation). Separate studies were performed for a range of values for two parameters of Tweedie distribution, power parameter P which shows the proportion of zeros (1.1, 1.3, 1.7 and 1.9), and dispersion parameter (0.5 and 3). Parameters were estimated using the Hamiltonian Monte-Carlo (HMC) algorithm in the R interface of Stan with package rstan (version 2.14). We run 3 parallel HMC chains of 6000 iterations for each simulated dataset and kept only 3000 iterations per chain for the posterior sample. We compute bias (the average of posterior means minus the true values), the standard deviation of the posterior means (SD), and the coverage probability (CP) of 95% credible intervals. Simulation results suggest that in all scenarios, CP for regression parameters is more than nominal value of 95%, but in scenarios which percentage of zeros is high (when P is near to 1) gives biased estimates and low coverage probabilities just for the parameters of Tweedie distribution. It suggests that the Tweedie spatio-temporal model is applicable when a reasonable portion of response is non-zero. We apply the model to data from the Household Income and Expenditure Survey (HIES) conducted annually by the Statistical Center of Iran. We collect information on the factors influencing the average household contraceptive expenditures in the provinces of Iran for the years 2011-2018. Based on the model, divorce rate, unemployment rate, the ratio of income equity (first/last), percentage of urbanization, extended family, human development index, percentage of Muslims and percentage of immigrants were the significant factors on average household contraceptive expenditures in a province.