Spatio-temporal Modeling of the Longitudinal Pm2.5 Data with Missing Values

Airborne particulate matter has become an important topic of epidemiological and environmental studies in the last decade when it was understood that the particulate matter is an important determinant of deaths, especially in the elderly, even though the biological mechanisms of its effect are not quite clear yet. The United States Environmental Protection Agency regulates the admissible levels of PM10 and PM2.5, the indicators of the concentration of the particulate matter of sizes 10 and 2.5 μm, respectively. The federal standard for PM2.5, the particulate matter size studied in this paper, was introduced in 1996, and states that “(a) the threeyear average of the annual 98th percentile of PM2.5 concentration measurements at any monitoring site should not exceed 50 μg per cubic meter of ambient air, and (b) the arithmetic mean (over one or multiple monitoring sites in the region) of sitespecific three-year averages of daily PM2.5 concentration measurements should not exceed 15 μg per cubic meter” (Cox 2000). The EPA has also outlined a number of research topics related to the particulate matter, and one of the statistical questions raised is, “Can spatial interpolation methods provide more accurate estimates of individual exposures to particulate air pollution?” (Cox 2000). A further step can be made to incorporate the temporal dimension of the data, especially as long as this is the natural way data comes from monitoring stations. Such data is known as the repeated measurement, or longitudinal, or panel, data. A common problem for such data sets though is the