Simulating Two‐dimensional Autocorrelated Surfaces

Haining, Robert; Griffith, Daniel A.; Bennett, Robert J.

doi:10.1111/j.1538-4632.1983.tb00785.x

Cited by 41 publications

(4 citation statements)

References 15 publications

(11 reference statements)

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“…Only 50 simulated surfaces were used due to the computer expense involved in generating and analyzing them, and no information was sought about variation in regional size or shape. Clearly, estimating the magnitude of boundary effect biases will require substantially larger simulation experiments that are of the inferential type (see Haining et al 1983).…”

Section: Discussionmentioning

confidence: 99%

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An Evaluation of Correction Techniques for Boundary Effects in Spatial Statistical Analysis: Traditional Methods

Griffith

Amrhein

1983

Geographical Analysis

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Section: Discussionmentioning

confidence: 99%

“…An alternative scheme is suggested by Haining et al (1983) that handles many of the problems associated with Goodchilds algorithm. It is designed for inferential purposes, though, and lacks many of the controls employed in the simulation experiment conducted here.…”

Section: The Simulation Experimentsmentioning

confidence: 99%

An Evaluation of Correction Techniques for Boundary Effects in Spatial Statistical Analysis: Traditional Methods

Griffith

Amrhein

1983

Geographical Analysis

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“…Spatial interpolation belongs to a family of spatial statistical procedures whose main function is to predict the spatial occurrence of data values in places that have no data from locations that have data values (see, for example, Haining, Griffith, and Bennett 1983;Getis 1991;Getis and Ord 1992;Mitasova and Mitas 1993;Mitasova et al 1995).…”

Section: Geospatial Data Analysis: Inverse Distance Weighted Algorithmentioning

confidence: 99%

Using GIS to Model and Forecast HIV/AIDS Rates in Africa, 1986–2010

Kalipeni

Zulu

2008

The Professional Geographer

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In this article we draw on the power of geographic information systems (GIS) to examine the progression of HIV/AIDS in Africa for the period from 1986 to 2003. We use GIS for two purposes: (1) to transform and interpolate a set of annual point-based HIV/AIDS rates into area data; and (2) to extract or "mine" annual HIV/AIDS prevalence rates from the interpolated area (country) level maps. Once the rates are extracted from the GIS analysis we then model and forecast them into the near future (i.e., 2004-2010) by using the UNAIDS Estimation and Projection Package (EPP) software. The article offers an alternative grounded in geospatial analysis for yielding estimates of HIV/AIDS rates in Africa. Using incomplete sets of data for the period from 1986 to 2003, mean HIV/AIDS rates are generated from spatially interpolated data and future trends are estimated. The results indicate that the HIV/AIDS epidemic for many countries in Africa has reached the saturation or maturity level as evidenced by the typical S-shaped curves in the trends over time. As a matter of fact, some countries have begun to experience a sustained decline in the rates (e.g., Uganda, Burundi, Rwanda, and Zimbabwe). Key Words: Africa, estimation and projection package (EPP), geographic information systems (GIS), geospatial data analysis, HIV/AIDS rates.En este artículo utilizamos el poder de los sistemas de información geográfica (SIG) para examinar el avance del VIH/SIDA enÁfrica en el periodo de 1986 a 2003. El SIG fue utilizado con dos propósitos: (1) transformar e interpolar en datos delárea un conjunto de tasas anuales de VIH/SIDA basado en puntos; y (2) extraer o "minar" de los mapas de nivel delárea interpolada (páıs) las tasas anuales de predominancia de VIH/SIDA. Una vez extraídas las tasas del análisis GIS, las modelamos y pronosticamos para el futuro cercano (esto es, 2004-2010) usando el programa Paquete de Cálculo y Proyección (Estimation and Projection Package) de UNAIDS. En el artículo se ofrece una alternativa basada en el análisis geoespacial para obtener cálculosaproximados de las tasas de VIH/SIDA enÁfrica. Mediante el uso de conjuntos incompletes de datos del período comprendido entre 1986 y 2003, se generan tasas medias de VIH/SIDA a partir de datos espacialmente interpolados, y se calculan aproximadamente las tendencias futuras. Los resultados indican que en muchos pá ses deÁfrica la epidemia de VIH/SIDA ha alcanzado el nivel de saturación o madurez, como lo demuestran las curvas típicas en forma de S de las tendencias a través del tiempo. De hecho, algunos páıses han The Professional Geographer, 60(1) 2008, pages 33-53 C

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“…Simulations were performed to check the models for autocorrelation effects (Ross 1997; see also Haining, Griffith, and Bennet 1983;Heagerty and Lele 1998), and regular grids were generated for this purpose. The cells were assumed to be square.…”

Section: Simulationmentioning

confidence: 99%

A Wavelet‐Based Extension of Generalized Linear Models to Remove the Effect of Spatial Autocorrelation. 基于小波扩展广义线性模型消除空间自相关的影响

Carl

Kühn

2010

Geographical Analysis

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Biogeographical studies are often based on a statistical analysis of data sampled in a spatial context. However, in many cases standard analyses such as regression models violate the assumption of independently and identically distributed errors. In this article, we show that the theory of wavelets provides a method to remove autocorrelation in generalized linear models (GLMs). Autocorrelation can be described by smooth wavelet coefficients at small scales. Therefore, data can be decomposed into uncorrelated and correlated parts. Using an appropriate linear transformation, we are able to extend GLMs to autocorrelated data. We illustrate our new method, called the wavelet-revised model (WRM), by applying it to multiple regression with response variables conforming to various distributions. Results are presented for simulated data and real biogeographical data (species counts of the plant genus Utricularia [bladderworts] in grid cells throughout Germany). The results of our WRM are compared with those of GLMs and models based on generalized estimating equations. We recommend WRMs, especially as a method that allows for spatial nonstationarity. The technique developed for lattice data is applicable without any prior knowledge of the real autocorrelation structure.

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Simulating Two‐dimensional Autocorrelated Surfaces

Cited by 41 publications

References 15 publications

An Evaluation of Correction Techniques for Boundary Effects in Spatial Statistical Analysis: Traditional Methods

An Evaluation of Correction Techniques for Boundary Effects in Spatial Statistical Analysis: Traditional Methods

Using GIS to Model and Forecast HIV/AIDS Rates in Africa, 1986–2010

A Wavelet‐Based Extension of Generalized Linear Models to Remove the Effect of Spatial Autocorrelation. 基于小波扩展广义线性模型消除空间自相关的影响

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