An O (N) parallel method of computing the Log-Jacobian of the variable transformation for models with spatial interaction on a lattice

Oleg A. Smirnov, Luc E. Anselin

Research output: Contribution to journalArticle

16 Scopus citations


A parallel method for computing the log of the Jacobian of variable transformations in models of spatial interactions on a lattice is developed. The method is shown to be easy to implement in parallel and distributed computing environments. The advantages of parallel computations are significant even in computer systems with low numbers of processing units, making it computationally efficient in a variety of settings. The non-iterative method is feasible for any sparse spatial weights matrix since the computations involved impose modest memory requirements for storing intermediate results. The method has a linear computational complexity for datasets with a finite Hausdorff dimension. It is shown that most geo-spatial data satisfy this requirement. Asymptotic properties of the method are illustrated using simulated data, and the method is deployed for obtaining maximum likelihood estimates for the spatial autoregressive model using data for the US economy.

Original languageEnglish (US)
Pages (from-to)2980-2988
Number of pages9
JournalComputational Statistics and Data Analysis
Issue number8
StatePublished - Jun 15 2009


ASJC Scopus subject areas

  • Statistics and Probability
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

Cite this