Keith Ord

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David Seamon

Kansas State University

Anoop Chaturvedi

University of Allahabad

Armando Marques-Guedes

UNL - New University of Lisbon

John Uebersax

California Polytechnic State University at San Luis Obispo

Andrey Korotayev

National Research University Higher School of Economics

Viacheslav Kuleshov

Stockholm University

José Francisco Pessanha

UERJ - Universidade do Estado do Rio de Janeiro / Rio de Janeiro State University

Gérard-François DUMONT

Université Paris-Sorbonne (Paris IV)

Paolo Carta

University of Trento

Adebayo D Agunbiade

Olabisi Onabanjo University, Ago-Iwoye, Nigeria

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Forecasting epidemic pathways for measles in Iceland: the use of simultaneous equation and logit models

Ecology of disease, 1983

Six measles transmission chains between pairs and triplets of medical districts in Iceland are id... more Six measles transmission chains between pairs and triplets of medical districts in Iceland are identified using monthly data for the 26 years from 1945 to 1970. The years studied are divided into two halves, a calibration period (1945-1957) and a forecast period (1958-1970). Some simultaneous equation models of the chains are developed and fitted using three-stage least squares. The resulting one month ahead forecasts are presented in terms of the expected case levels and as the probability of epidemics occurring. A single equation probability model using a logistic transformation is then formulated and compared with the simultaneous equation approach. The results obtained from the Icelandic study confirm in practice the advantages theoretically expected from setting up forecasting models containing geographically based chain transmission components.

Testing for Spatial Autocorrelation Among Regression Residuals

Geographical Analysis, 2010

Testing f o r Spatial Autocorrelation Among Regression Residuals 1 NTRODUCTION A basic assumption... more Testing f o r Spatial Autocorrelation Among Regression Residuals 1 NTRODUCTION A basic assumption of least squares regression is that the error terms in the regression model are independent under the null hypothesis. To test whether this assumption has been met in regression models of time series data with normally distributed error terms and given regression structure, the d statistic of Durbin and Watson [4] is often used. Consider now a system of n counties within a country, as, for example, the counties of England and Wales. Suppose that a regression model attempting to account for, say, the county-by-county variation in per capita annual milk consumption on the basis of real personal income has been postulated. In problems of this sort, where the data have a geographic ordering, the regression model requires the error terms to be independent spatially under H,. Geary [S, SJ has made this point forcefully in the case of econometric models for several regions. It is the purpose of this paper to present a statistic, I, which can be used to test for correlation among such geographically located error terms arising from least squares regression. While the particular formulation of counties within a country is used in the remainder of the paper, I may be used to test for any postulated pattern of correlation among the error terms in any least squares regression model. In the next section, a general model is formulated from which the statistic I is derived. Since the error terms in the regression model in any practical case will be unobservable, I must be based upon the residuals from the calculated regression. These residuals are correlated under the null hypothesis whether the errors are dependent or not, and we consider three possible ways, due to Durbin and Watson [ 4 ] , Theil [ I S ] , and Moran [lo, 111 of overcoming this difficulty so that an asymptotic distribution Amdrew Clifl and Keith Ord are lecturers in geography and economics, respectively, at the University of Bristol.

Keith Ord

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