Abstract
Spatial lag dependence in a regression model is similar to the inclusion of a serially autoregressive term for the dependent variable in a timeseries context. However, unlike in the timeseries model, the implied covariance structure matrix from the spatial autoregressive model can have a very counterintuitive and improbable structure. A single value of spatial autocorrelation parameter can imply a large band of values of pairwise correlations among different observations of the dependent variable, when the weight matrix for the spatial model is specified exogenously. This is illustrated using cigarette sales data (1963–1992) of 46 US states. It can be seen that that two "close" neighbours can have very low implied correlations compared to distant neighbours when the weighting scheme is the firstorder contiguity matrix. However, if the weight matrix can capture the underlying dependence structure of the observations, then this unintuitive behaviour of implied correlation is corrected to a large extent. From this, the possibility of constructing the weight matrix (or the overall spatial dependence in the data) that is consistent with the underlying correlation structure of the dependent variable is explored. The suggested procedures produced very positive results indicating further research.
Original language  English (US) 

Pages (fromto)  315 
Journal  Regional Statistics 
Volume  4 
Issue number  1 
DOIs  
State  Published  2014 
Keywords
 Spatial Dependence
 Weight Matrix
 Implied Correlation Structure
 VarianceCovariance matrix
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The Improbable Nature of the Implied Correlation Matrix from Spatial Regression Models
Sen, M. (Creator) & Bera, A. K. (Creator), Harvard Dataverse, Sep 23 2015
DOI: 10.7910/DVN/GY65TP
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