Advancement of Methods for Ecological Inference

分析聚合数据在许多不同的上下文中都很有用。然而，估计是不平凡的，没有可靠的方法存在。回归或相关等标准技术表现不佳（Robinson, 1950; Goodman, 1953）。最近，King（1997）提出了一个变参数模型。虽然这个模型比标准的OLS模型更有效，但它不能解释参数和回归量（聚集偏差）之间相关性的中心问题。在任何聚合数据模型中都必须解决聚合偏差问题。该项目通过切换回归模型的框架来解决这个问题，其中状态定义变量可能是确定性的或随机的，并测量宏观层面单元的同质性。虽然这个规范是可行的，但是如何实现这样一个模型还不清楚。初步工作表明，时间序列方法测试参数常数是有用的，在这方面。本研究通过发展评估聚合数据结构变化的形式化方法，探索和分析了聚合数据参数恒常性的不同测试方法。除了采用协变量方法外，本研究还探讨了混合分布的拟合。拟合混合模型涉及许多关键方面，包括选择分布类型、混合程度、拟合诊断和状态数。

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.