Determining optimal neighborhood size for ecological studies using leave-one-out cross validation

There has been a growing interest in ecological research assuming that the neighborhood where people reside may influence their health status [1,2] as much as personal risk factors like age and gender [3-6]. Several factors have stimulated interest in ecological research. Chief among them are studies of the determinants of health [7,8] which recognize that social influences on health operate through neighborhoods [1,2]. The emergence of multilevel analytical methods permits investigators to quantify the health effects of neighborhoods [8,9]. The growing concern about confidentiality of individual health data [10,11] has also motivated investigators to examine alternative methods for observational studies. Interest in ecological research is also due to ease, as risk factors are often not available at the individual level or may not be obtained or acquired from pre-existing sources (e.g., census or aggregated survey data).An ecological variable most commonly refers to a set of individual level attributes which have been aggregated up to the areal level (e.g., percent poor, diabetes prevalence). Defining the neighborhood boundaries in which variables are aggregated greatly influences the results of statistical analyses [12] due to the modifiable areal unit problem (MAUP). The MAUP is a potential source of error, in particular when point-based measures of spatial phenomena are aggregated to an aerial unit which can affect spatial studies that utilize aggregate data sources [13]. For example, census data may be aggregated into census enumeration districts, or villages, communities, or any other spatial partition, thus, the areal units are modifiable. The MAUP problem has been addressed in the area of spatial crime analysis, where the areal units used in many geographical studies are arbitrary, modifiable, and subject to the whims and fancies of whoever is doing, or did, the aggregating [14]. However, the implications of aggregating strategies are often overlooked [15,16]