Simple, multiple and multiway correspondence analysis applied to spatial census-based population microsimulation studies using R

As a bivariate and multivariate multidimensional exploratory method, simple and multiple correspondence analyses have been used successfully in social science for survey or questionnaire results descriptions. Nonetheless, the complexity of social interactions including health status indicators, with also the need to take into account the spatial and temporal realm of the survey, may incline to look at variable associations in a multiway approach instead of a two-way matrix analysis. This means for example, that interaction of order three between the spatial configuration (say the Output Areas of an urban zone), the set of categorical variables (say selected from a census survey) and the evolution (say every 5 years over a 30 years period) would be considered in order to differentiate spatio-temporal associations across categorical variables. For census-based spatial simulation models such as microsimulations, exhibiting this kind of properties is useful as forecasts moves of population characteristics to be considered for healthcare policy scenario analysis. In this paper it is shown how to run this type of analysis within R using a package dedicated to multiway analysis (the R package PTAk), that is, working on multi-entry array data using an algorithm extending classical multidimensional analysis. A didactic approach from two-way analyses to multiway ones, of the same dataset generated from a population spatial simulation model allows a critical demonstration of the potential of the different t methods. Particular attention is also given to the different choices of spatial units and the scale variation effect within a nested administrative zoning system that can be analysed by a correspondence analysis with respect to a model (extending the approach using the independence model) and which can be done for a simple, multiple of multiway correspondence analysis.