Advancement of Methods for Ecological Inference

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Analyzing aggregate data is useful in many different contexts. However, estimation is non-trivial and no reliable methods exist. Standard techniques such as regression or correlation perform poorly (Robinson, 1950; Goodman, 1953). Recently, King (1997) has proposed a varying parameter model. While this model is more efficient than a standard OLS model, it is not able to account for the central problem of correlation between the parameters and the regressors (aggregation bias). The aggregation bias problem must be addressed in any aggregate data model. This project addresses the problem through the framework of switching regression models where the state-defining variable may be deterministic or stochastic and measures homogeneity across the macro-level units. While this specification is viable, it is unclear how to implement such a model. Preliminary work has shown that time-series methods of testing parameter constancy are useful in this regard. This research explores and analyzes different methods of testing for parameter constancy in aggregate data through developing formal methods of assessing structural shifts in aggregate data. In addition to pursuing the covariate approach, the research also explores the fitting of mixture distributions. Fitting a mixture model involves many crucial aspects, including choosing the type of distribution, the degree of mixture, diagnostics for fit, and number of states.