Based on a large number of Monte Carlo simulation experiments on a regular lattice, we compare the properties of Moran's I and Lagrange multiplier tests for spatial dependence, that is, for both spatial error autocorrelation and for a spatially lagged dependent variable. We consider both bias and power of the tests for six sample sizes, ranging from twenty-five to 225 observations, for different structures of the spatial weights matrix, for several underlying error distributions, for misspecified weights matrices, and for the situation where boundary effects are present. The results provide an indication of the sample sizes for which the asymptotic properties of the tests can be considered to hold. They also illustrate the power of the Lagrange multiplier tests to distinguish between substantive spatial dependence (spatial lag) and spatial dependence as a nuisance (error autocorrelation).

https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1538-4632.1991.tb00228.x

Properties of Tests for Spatial Dependence in Linear Regression Models

In this paper, we discuss a number of general issues that pertain to the interface between GIS and spatial analysis. In particular, we focus on the various paradigms for spatial data analysis that follow from the existence of this interface. We outline a series of questions that need to be confronted in the analysis of spatial data, and the extent to which a GIS can facilitate their resolution. We also review a number of exploratory and confirmatory techniques that we feel should form the core of a spatial analysis module for a GIS.

Spatial Statistical Analysis and Geographic Information Systems

Because of inconsistencies in the reported migration flows and large amounts of missing data, our knowledge of international migration patterns in the Europe is limited. Methods for overcoming data obstacles and harmonising international migration data, however, are improving. In this article, we provide a methodology for integrating various pieces of incomplete information together, including a partial set of harmonised migration flows, to estimate a complete set of migration flows by origin, destination, age and sex for the 31 countries in the European Union and European Free Trade Association from 2002 to 2007. The results represent a synthetic data base that can be used to inform population projections, policy decisions and migration theory.

/pdf/putting-the-pieces-of-the-puzzle-together-age-and-sex-pcfjjfe327.pdf

Putting the Pieces of the Puzzle Together: Age and Sex-Specific Estimates of Migration amongst Countries in the EU/EFTA, 2002–2007

Many landscape features are represented as polygons in GIS This paper characterizes polygon shapes with the multiplicatively weighted Voronoi (MW-Voronoi) diagram and improves its understanding The MW-Voronoi diagram's composition is implemented with topological overlay, growth simulation, and vertex calculation methods The decomposition is done by reversing a polygon to MW-Voronoi point pairs by segment It is a new approach to record, characterize, and compare polygons with form and process The implementation also serves as a geographic education and visualization tool Applications of the methods are presented with precipitation, fire polygon, and population change data

Polygon Characterization With the Multiplicatively Weighted Voronoi Diagram

Although the disaggregation of consumers is crucial in understanding the fragmented markets that are dominant in many developed countries, it is not always straightforward to carry out such disaggregation within conventional retail modelling frameworks due to the limitations of data. In particular, consumer grouping based on sampled data is not assured to link with the other statistics that are vital in estimating sampling biases and missing variables in the sampling survey. To overcome this difficulty, we propose a useful combination of spatial interaction modelling and microsimulation approaches for the reliable estimation of retail interactions based on a sample survey of consumer behaviour being linked with other areal statistics. We demonstrate this approach by building an operational retail interaction model to estimate expenditure flows from households to retail stores in a local city in Japan, Kusatsu City.

Combining microsimulation and spatial interaction models for retail location analysis

Geographical data sets sometimes contain missing observations that need to be estimated. A statistical approach to the problem is discussed for multivariate normal spatial data sets satisfying the first-order spatial Markov property with constant mean, where the information at neighboring or contiguous observed sites is used to estimate the missing values. The completed data are used to estimate the parameters of the distribution. The procedure is iterative. The approach is a special case of the Orchard and Woodbury missing information principle. The paper concludes with an illustrative empirical example using rainfall data from an area of Kansas and Nebraska. The quality of the estimates for different sites are compared.

A statistical approach to the problem of missing spatial data using a first‐order markov model

A simple graphical method for developing regression models for spatially referenced data is presented. The method supplements formal testing procedures and provides the analyst with useful information helpful in developing an understanding of data properties without the need for complex data manipulations. The paper includes a worked example and suggests directions for further work in this area.

The use of added variable plots in regression modelling with spatial data

In recent years there has been a growing concern for the development of both efficient and effective ways to handle space-time problems. Such developments should be theoretically as well as empirically oriented. Regardless of which of these two arenas one enters. the impression is quickly gained that contemporary wO, rk on dynamic and evolutionary models has not proved to be as illuminating and rewarding as first anticipated. Historically speaking. the single. most important lesson this avenue of research has provided. is that linear models are woefully inadequate when dominant non-linear trends and relationships prevail. and that independent activities and actions are all but non-existent in the real-world. Meanwhile. one prominent imp 1 ication stemming from this 1 iterature is that the easiest modelling tasks are those of specifying good dynamic space-time models. Somewhat more problematic are the statistical questions of model specification. parameter estimation. and model validation. whereas even more problematic is the operationalization of evolutionary conceptual models. A timely next step in spatial analysis would seem to be a return to basics. with a pronounced focus both on specific problems (and data) and on the mechanisms that transform phenomena through space and/or time'. It appears that these transformation mechanisms must embrace both non-linear and autoregressive formalisms. Given. also. the variety of geographic forms. they must allow for bifurcation points to emerge. too

Transformations through space and time : an analysis of nonlinear structures, bifurcation points and autoregressive dependencies

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A statistical approach to the problem of missing spatial data using a first‐order markov model

The use of added variable plots in regression modelling with spatial data

Transformations through space and time : an analysis of nonlinear structures, bifurcation points and autoregressive dependencies