fcar2.m

空间统计工具箱

function [bmax, srds, prhighers, emax, logliks]=fcar2(x, y, d, detvalz, itersub)
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%  [bmax, srds, prhighers, emax, logliks]=fcar2c(x, y, d, detvalz, itersub)
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%This function computes conditional spatial autoregression (CAR or CSG). 
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%INPUTS:
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%x is a n by k matrix of independent variables. 
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%y is a n by 1 column vector of observations on the dependent variable.
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%d is a symmetric n by n spatial weight matrix. This function assumes d has a maximum eigenvalue of 1.
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%detvalz is either a iter by 2 matrix containing a vector of autoregressive parameters in the first column and 
%the associated log-determinant in the second column or a iter by 4 matrix containing a vector of autoregressive
%parameters in the first column, the associated lower bound on the log-determinant in the second column, 
%the associated log-determinant in the third column, and the associated lower bound on the log-determinant in the fourth column.
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%itersub is the number of iterations used in interpolating the sse function. As this becomes larger the results approach the exact
%ones.
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%OUTPUTS:
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%bmax is the k+1 by 1 vector of parameter estimates with the CAR regression parameter estimates as the first k elements and 
%alphamax, the global spatial dependence parameter (a scalar), as the last element.
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%srds is the k+1 by 1 vector of signed root deviances. These have a t-ratio like interpretation. If the exact log-determinant 
%(or a very close approximation) is used, this has a standard interpretation. For less precise approximations, the srds is 
%based on likelihood dominance inference and should provide lower bounds to the exact srds.
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%prhighers is a k+1 by 1 vector of estimates of obtaining a higher likelihood ratio under repeated sampling.
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%emax is n by 1 column vector of residuals in the spatially transformed space.
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%logliks is a iter by (k+2) matrix of profile log-likelihoods (first column full model, remaining columns delete-1 submodels).
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%NOTES:
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%One can square the signed root deviances to get likelihood ratios, if desired. 
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%This function uses some of the techniques discussed in:
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%Pace, R. Kelley, and James LeSage, 揕ikelihood Dominance Spatial Inference,