aple
Approximate profilelikelihood estimator (APLE)
The Approximate profilelikelihood estimator (APLE) of the simultaneous autoregressive model's spatial dependence parameter was introduced in Li et al. (2007). It employs a correction term using the eigenvalues of the spatial weights matrix, and consequently should not be used for large numbers of observations. It also requires that the variable has a mean of zero, and it is assumed that it has been detrended. The spatial weights object is assumed to be rowstandardised, that is using default style="W"
in nb2listw
.
 Keywords
 spatial
Usage
aple(x, listw, override_similarity_check=FALSE, useTrace=TRUE)
Arguments
 x
 a zeromean detrended continuous variable
 listw
 a
listw
object from for examplenb2listw
 override\_similarity\_check
 default FALSE, if TRUE  typically for rowstandardised weights with asymmetric underlying general weights  similarity is not checked
 useTrace
 default TRUE, use trace of sparse matrix
W %*% W
(Li et al. (2010)), if FALSE, use crossproduct of eigenvalues ofW
as in Li et al. (2007)
Details
This implementation has been checked with Hongfei Li's own implementation using her data; her help was very valuable.
Value

A scalar APLE value.
References
Li, H, Calder, C. A. and Cressie N. A. C. (2007) Beyond Moran's I: testing for spatial dependence based on the spatial autoregressive model. Geographical Analysis 39, 357375; Li, H, Calder, C. A. and Cressie N. A. C. (2012) Onestep estimation of spatial dependence parameters: Properties and extensions of the APLE statistic, Journal of Multivariate Analysis 105, 6884.
See Also
Examples
example(wheat)
nbr1 < poly2nb(wheat, queen=FALSE)
nbrl < nblag(nbr1, 2)
nbr12 < nblag_cumul(nbrl)
cms0 < with(as(wheat, "data.frame"), tapply(yield, c, median))
cms1 < c(model.matrix(~ factor(c) 1, data=wheat) %*% cms0)
wheat$yield_detrend < wheat$yield  cms1
isTRUE(all.equal(c(with(as(wheat, "data.frame"),
tapply(yield_detrend, c, median))), rep(0.0, 25),
check.attributes=FALSE))
moran.test(wheat$yield_detrend, nb2listw(nbr12, style="W"))
aple(as.vector(scale(wheat$yield_detrend, scale=FALSE)), nb2listw(nbr12, style="W"))
errorsarlm(yield_detrend ~ 1, wheat, nb2listw(nbr12, style="W"))