Inference from Cross-Sectional and Longitudinal Data for Dynamic Behavioural Processes

Abstract

Geographers have long been aware of some of the problems encountered in attempting to determine causality from cross-sectional data. The distinction between pattern and process soon became apparent within point pattern analysis, where several alternative, but theoretically plausible, models were shown to often lead to the same cross-sectional spatial pattern. Such equifinality, as it is known, is common throughout all areas of study. Though results from such analyses may be justifiably presented as descriptions of the data, this is rarely viewed as sufficient. It is generally expected that both model form and parameter estimates should have explanatory significance. The temptation to interpret parameters is strong. In many behavioural studies of cross-sectional data, in which the models used invariably include so-called “explanatory” variables, such a temptation has frequently proved irresistible. Is such interpretation justifiable? Does a parameter estimate actually measure the impact of an explanatory variable? Formally, all statistical inference about a parameter is made conditionally upon the model being correct. In view of the potential equifinality problem, interpretation may be thought of as, at best, one of a possible set of “correct inferences”, each made from a different underlying model.