This project assesses the effects of measurement error and develops new methods to account for measurement error in the analysis of single or multiple time series. Specifically, the investigators address these problems in the context of: i) fitting a single time series with linear and non-linear dynamic models, ii) assessing the relationship between two variables measured over time on one or more "units", with measurement error in one or both variables and serial correlation and/or contemporaneous (among unit) correlation; iii) assessing synchrony correlation among series in different locations. Throughout, this project accommodates a rich class of measurement error models allowing some combination of heteroscedasticity, possible dependence of the measurement error on the true value, correlated measurement errors and a separate estimate of the measurement error variance for each unit. These features arise in many typical applications. A variety of techniques are employed including moment approaches, likelihood methods, and the use of estimating equations.
A wide variety of important problems in ecology, environmental sciences, economics, public health and many other disciplines involve the statistical modeling of one or more variables collected over time and, perhaps, in different locations. Examples include the modeling of population densities, economic indicators, disease rates, pollution levels, temperatures, etc. over time and assessing the relationship among variables (e.g. pollution levels and disease rates or food abundance and population densities) with data collected over time and space. A common problem is that the variable(s) cannot be observed exactly and need to be estimated. In simpler settings it is known that ignoring the estimation step and its accompanying measurement error causes two serious problems. First, the amount of noise in the system is underestimated, and second, the true nature of underlying systematic relationships can be obscured or misinterpreted. In more complicated situations where the data are measured over time or are spatially related, little or nothing is known about the effects of measurement error. Utilizing theoretical developments and computer simulations, this project will provide results to guide investigators as to the impact of the use of error-prone measures, develop methods to correct for the problems caused by measurement error and ensure that our methods are applied to important real world problems.
