Ronald P. Barry

Spatiotemporal Autoregressive Models of Neighborhood Effects

Using 70,822 observations on housing prices from 1969 to 1991 from Fairfax County Virginia, this article demonstrates the substantial benefits obtained by modeling the spatial as well as the temporal dependence of the data. Specifically, the spatiotemporal autoregression with twelve variables reduced median absolute error by 37.35% relative to an indicator-based model with twenty-six variables. One-step ahead forecasts also document the improved performance of the proposed spatiotemporal model. In addition, the article illustrates techniques for rapidly computing the estimates and shows how to compute indices for any location.

Sparse spatial autoregressions

Given local spatial error dependence, one can construct sparse spatial weight matrices. As an illustration of the power of such sparse structures, we computed a simultaneous autoregression using 20 640 observations in under 19 min despite needing to compute a 20 640 by 20 640 determinant 10 times.

A method for spatial–temporal forecasting with an application to real estate prices

Abstract Using 5243 housing price observations during 1984–92 from Baton Rouge, this manuscript demonstrates the substantial benefits obtained by modeling the spatial as well as the temporal dependence of the errors. Specifically, the spatial–temporal autoregression with 14 variables produced 46.9% less SSE than a 12-variable regression using simple indicator variables for time. More impressively, the spatial–temporal regression with 14 variables displayed 8% lower SSE than a regression using 211 variables attempting to control for the housing characteristics, time, and space via continuous and indicator variables. One-step ahead forecasts document the utility of the proposed spatial–temporal model. In addition, the manuscript illustrates techniques for rapidly computing the estimates based upon an interesting decomposition for modeling spatial and temporal effects. The decomposition maximizes the use of sparsity in some of the matrices and consequently accelerates computations. In fact, the model uses the frequent transactions in the housing market to help simplify computations. The techniques employed also have applications to other dimensions and metrics.

Monte Carlo estimates of the log determinant of large sparse matrices

Maximum likelihood estimates of parameters of some spatial models require the computation of the log-determinant of positive-definite matrices of the formI —αD. whereD is a large, sparse matrix with eigenvalues in [−1, 1] and where 0<α<1, with extremely large matrices the usual direct methods of obtaining the log-determinant require too much time and memory. We propose a Monte Carlo estimate of the log-determinant. This estimate is simple to program, very sparing in its use of memory, easily computed in parallel and can estimate log det(I-αD) for many values ofα simultaneously Using this estimator, we estimate the log-determinant for a 1,000,000 × 1,000,000 matrixD, for 100 values ofα, in 23.1 min on 133 MHz pentium with 64 MB of memory using Matlab.

Constructing and fitting models for cokriging and multivariable spatial prediction

We consider best linear unbiased prediction for multivariable data. Minimizing mean-squared-prediction errors leads to prediction equations involving either covariances or variograms. We discuss problems with multivariate extensions that include the construction of valid models and the estimation of their parameters. In this paper, we develop new methods to construct valid crossvariograms, fit them to data, and then use them for multivariable spatial prediction, including cokriging. Crossvariograms are constructed by explicitly modeling spatial data as moving averages over white noise random processes. Parameters of the moving average functions may be inferred from the variogram, and with few additional parameters, crossvariogram models are constructed. Weighted least squares is then used to fit the crossvariogram model to the empirical crossvariogram for the data. We demonstrate the method for simulated data, and show a considerable advantage of cokriging over ordinary kriging.

Microbial community analysis: a kinetic approach to constructing potential C source utilization patterns

Abstract The analysis of multiple substrate metabolism by assemblages of bacterial strains may be used to differentiate inocula from environmental samples. Biolog plates, 96-well microtiter plates containing nutrients, a single carbon test substrate in each well and a tetrazolium redox dye to monitor substrate oxidation, have been used for this purpose. One of the difficulties faced by users of this technique is determining which substrates have been metabolized. Reliance on single-time-point absorbance data for each well is problematic due to variably non-linear rates of color development for each well. Previous efforts to use color-normalized single plate readings have been successful in discriminating between environmental sample types, but substrate-use contributions to sample classifications vary depending on the duration of the plate incubation. We present a model based on the logistic equation for density-dependent population growth providing a good (low χ 2 ) fit to the sigmoidal kinetics of color development data. The kinetic parameters generated by the model can be used as surrogates for single-time-point data in constructing carbon source utilization patterns, and contribution of substrate use to sample classification does not depend on incubation time. This technique obviates the need to choose the time following inoculation to read the plate absorbance data and also provides two kinetic parameters that are invariant with respect to inoculum density. We provide a comparison of community potential substrate use analyses using single-time-point microplate data and parameters from our kinetic model.

Analysis of stable isotope data : A K nearest-neighbors randomization test

The use of stable isotope analysis in ecological and wildlife studies is rapidly increasing. Studies include evaluating flow of nutrients in ecosystems and studying dietary composition of individual animals. Several mixing models have been developed to evaluate the relative contribution of different foods to the diet of consumers. All these mixing models require that all prey types will be significantly different in bivariate space. This requirement usually poses a problem in analyzing data of stable isotope ratios because sample sizes in most studies are small and seldom normally distributed. We propose a randomization test that we based on the K nearest-neighbor approach. Results from our simulations of power revealed that the K nearest-neighbor test appears to have high power even with small sample sizes and comparatively low displacement. The K nearest-neighbor test described here provides the preliminary statistical analysis necessary for the use of the mixing models, and therefore is a new, powerful tool for analyzing stable isotope data. In evaluating the test performance on data collected from American martens (Martes americana) and their prey on Chichagof Island, Southeast Alaska, we were able to reject our null hypothesis that all samples of prey were drawn from identical populations (P = 0.05). A program written in Pascal or S-Plus is available from the authors to evaluate the K nearest-neighbor statistic for several groups.

Flexible Spatial Models for Kriging and Cokriging Using Moving Averages and the Fast Fourier Transform (FFT)

Models for spatial autocorrelation and cross-correlation depend on the distance and direction separating two locations, and are constrained so that for all possible sets of locations, the covariance matrices implied from the models remain nonnegative-definite. Based on spatial correlation, optimal linear predictors can be constructed that yield complete maps of spatial fields from incomplete and noisy spatial data. This methodology is called kriging if the data are of only one variable type, and it is called cokriging if it is of two or more variable types. Historically, to satisfy the nonnegative-definite condition, cokriging has used coregionalization models for cross-variograms, even though this class of models is not very flexible. Recent research has shown that moving-average functions may be used to generate a large class of valid, flexible variogram models, and that they can also be used to generate valid cross-variograms that are compatible with component variograms. There are several problems with the moving-average approach, including large numbers of parameters and difficulties with integration. This article shows how the fast Fourier Transform (FFT) solves these problems. The flexible moving-average function that we consider is composed of many small rectangles, which eliminates the integration problem. The FFT allows us to compute the cross-variogram on a set of discrete lags; we show how to interpolate the cross-variogram for any continuous lag, which allows us to fit flexible models using standard minimization routines. Simulation examples are given to demonstrate the methods.

Assigning birds to wintering and breeding grounds using stable isotopes: lessons from two feather generations among three intercontinental migrants

AbstractGeographic origins of populations and migration patterns of several vertebrate and invertebrate species have been inferred from geographically distinct isotopes in their tissues. To test the hypothesis that feathers grown on different continents would reflect continental differences of δD in precipitation and have significantly different stable isotope ratios, we analyzed stable isotopes in two generations of feathers from three bird species (American and Pacific golden-plovers, Pluvialis dominica and P. fulva, and northern wheatears Oenantheoenanthe) that breed in North America and winter in South America, the South Pacific and Asia, and Africa. We found significant differences in stable isotope signatures between summer- and winter-grown feathers in the plovers, and our use of two generations of feathers provided similar variation to that reported in studies using larger sample sizes. In contrast to plovers, no differences were detected in isotope values between summer- and winter-grown feathers in wheatears. Discriminant analyses separated 80% of summer- and winter-grown feathers for each plover species. Nonetheless, an “assignment with exclusion” method adapted from population genetics to impart a measure of confidence in assigning individuals to groups of origin resulted in an overall accuracy among plovers of only 41%, compared with a 63% assignment accuracy when the exclusion criterion was removed. Thus, we were unable to accurately assign feathers to origin of growth on the continental scale. Moreover, using δD expectations for North America, we were unable to assign summer-grown plover feathers to within better than several thousand kilometers of their true origins. We urge researchers to carefully consider the ecology and physiology of their study organisms, statistical methodology, and the interpretation of results when using stable isotopes to infer the geographic origins of feather growth.

Long-term effects on microbial communities after a subarctic oil spill

Abstract A combination of microbial assays was used to examine soil population structure and community-level metabolism at the site of a 1976 experimental crude oil spill conducted in Alaska. Estimates of total bacterial numbers and soil C mineralization potentials were not significantly different between pristine and hydrocarbon-affected soils. In contrast, net N mineralization potential was lower, metabolically active (FDA stain) bacteria were less abundant and hydrocarbon degrading microbes were more abundant in the oiled soils. Additionally, the effects of dilution on the kinetics of community-level substrate use were examined in multiple substrate microplates. Microplate kinetic patterns varied less with dilution and by season in oiled soils. In oiled soils, absence of seasonal variation in soil C mineralization potentials, coupled with the microplate data, indicated that population diversity (evenness, richness or both) was diminished compared to the pristine soils. Further analysis of microplate data suggested that the communities surviving in the oiled soils may be considered metabolic generalists. By using several independent microbial assays, differences in soil microbial community structure attributable to oiling could be seen decades after the spill event.