Estimating Spatial Patterns across Time: Using Hierarchical Mixed Effects Models for Variograms

• Activity Number: 312
• Type: Contributed
• Date/Time: Wednesday, August 11, 2004 : 8:30 AM to 10:20 AM
• Sponsor: General Methodology
• Author(s): Daniel G. Kehler*+ and Ransom Myers
• Companies: Dalhousie University and Dalhousie University
• Keywords: variogram ; bias ; spatio-temporal ; hierarchical mixed effect models

Abstract

In the context of spatio-temporal models, spatial information exists at multiple time intervals.Traditional methods for estimating the spatial pattern within a time period involve parametric representations in the form of variograms models. A general dependence in the spatial pattern across time can be imposed by treating variogram parameters as random effects realized from a common distribution. However, since variogram estimates at different spatial lags are often assumed to be independent observations, this can lead to an underestimation of the true parameter uncertainty, and hence an overestimation of the random effect variances. A more accurate assessment of uncertainty is obtained by dividing the data into two or more groups, and estimating multiple variograms in every year. We show, using simulations, how a hierarchical mixed effects model can accurately capture both the variogram uncertainty and correctly estimate variogram parameters in each time interval. The methods are applied to a dataset of fish recruitment in lakes by way of illustration.