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aple

Approximate profile-likelihood estimator (APLE)

Description

The Approximate profile-likelihood 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 row-standardised, that is using default style="W" in nb2listw.

Usage

aple(x, listw, override_similarity_check=FALSE, useTrace=TRUE)

Arguments

`x`	a zero-mean detrended continuous variable
`listw`	a `listw` object from for example `nb2listw`
`override\_similarity\_check`	default FALSE, if TRUE - typically for row-standardised 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 of `W` 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.

Author(s)

Roger Bivand Roger.Bivand@nhh.no

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, 357-375; Li, H, Calder, C. A. and Cressie N. A. C. (2012) One-step estimation of spatial dependence parameters: Properties and extensions of the APLE statistic, Journal of Multivariate Analysis 105, 68-84.

Examples

wheat <- st_read(system.file("shapes/wheat.shp", package="spData")[1], quiet=TRUE)
nbr1 <- poly2nb(wheat, queen=FALSE)
nbrl <- nblag(nbr1, 2)
nbr12 <- nblag_cumul(nbrl)
cms0 <- with(as.data.frame(wheat), 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.data.frame(wheat),
 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"))
## Not run: 
errorsarlm(yield_detrend ~ 1, wheat, nb2listw(nbr12, style="W"))

## End(Not run)

spdep

Spatial Dependence: Weighting Schemes, Statistics

v1.1-11

GPL (>= 2)

Authors

Roger Bivand [cre, aut] (<https://orcid.org/0000-0003-2392-6140>), Micah Altman [ctb], Luc Anselin [ctb], Renato Assunção [ctb], Olaf Berke [ctb], Andrew Bernat [ctb], Guillaume Blanchet [ctb], Eric Blankmeyer [ctb], Marilia Carvalho [ctb], Bjarke Christensen [ctb], Yongwan Chun [ctb], Carsten Dormann [ctb], Stéphane Dray [ctb], Virgilio Gómez-Rubio [ctb], Martin Gubri [ctb], Rein Halbersma [ctb], Elias Krainski [ctb], Pierre Legendre [ctb], Nicholas Lewin-Koh [ctb], Angela Li [ctb], Hongfei Li [ctb], Jielai Ma [ctb], Abhirup Mallik [ctb, trl], Giovanni Millo [ctb], Werner Mueller [ctb], Hisaji Ono [ctb], Pedro Peres-Neto [ctb], Gianfranco Piras [ctb], Markus Reder [ctb], Jeff Sauer [ctb], Michael Tiefelsdorf [ctb], René Westerholt [ctb], Levi Wolf [ctb], Danlin Yu [ctb]

Initial release

2021-09-07