R: Approximate profile-likelihood estimator (APLE)

aple {spdep} | R Documentation

## 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.

### See Also

`nb2listw`, `aple.mc`, `aple.plot`

### 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"))

[Package spdep version 0.6-13 Index]