Mixed model estimation for discrete longitudinal and/or spatially correlated data from small areas

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Approaches for assessing attributes associated with each of a number of small groups of individuals comprising a larger group are investigated.  These small groups may be defined by a small geographic area within a larger one, or by classifying individuals in the large group according to some trait such as age.  Attributes to be considered are counts and the proportion of individuals within each group possessing a particular characteristic.    The approaches to be investigated are motivated in part by a study on infant mortality rates in the various health areas (the small groups) in British Columbia, in which the annual number of deaths in each area were recorded over ten years.  These methods must acknowledge that the data consist of repeated observations on the same area, and their geographic proximity.  Of particular interest is the forecasting of mortality counts for health areas in future years.  The proposed methods will also be applied to data on disease cases (measles, for example) at a specific location and time, with a view towards forecasting trends and outbreaks of epidemics.    Methods for studies where the attribute  for each small group is a proportion of individuals that possess a particular characteristic will also be investigated.  Of importance is that the methods must acknowledge that a proportion is bounded between zero and one.  My past research has included an assessment of a seven year smoking prevention study conducted in elementary and high schools.  Of present interest is to consider methods for forecasting the proportion of smokers at each school (the small groups) at specific time points.  To do so, the proposed approaches must acknowledge that the data comprise repeated observations over time, and that students at the same school will likely be more similar regarding smoking behavior than students attending different schools.  The proposed methods will also be applied to data from a cancer study to investigate the factors that motivate the choice of surgery type, and to data reflecting wheezing status in children.    Finally, the proposed methods will also be developed to accommodate missing data; in other words, for situations where the information for the small group over time is incomplete.