R: Approximate profile-likelihood estimator (APLE) scatterplot

aple.plot {spdep} | R Documentation

## Approximate profile-likelihood estimator (APLE) scatterplot

### Description

A scatterplot decomposition of the approximate profile-likelihood estimator, and a local APLE based on the list of vectors returned by the scatterplot function.

### Usage

    aple.plot(x, listw, override_similarity_check=FALSE, useTrace=TRUE, do.plot=TRUE, ...)
    localAple(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)
`do.plot` | default TRUE: should a scatterplot be drawn
`...` | other arguments to be passed to `plot`

### Details

The function solves a secondary eigenproblem of size n internally, so constructing the values for the scatterplot is quite compute and memory intensive, and is not suitable for very large n.

### Value

`aple.plot` returns list with components:

`X` | A vector as described in Li et al. (2007), p. 366.
`Y` | A vector as described in Li et al. (2007), p. 367.

`localAple` returns a vector of local APLE values.

### 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, pp. 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

`aple`

### Examples

    ## Not run:
    example(aple)
    plt_out <- aple.plot(as.vector(scale(wheat$yield_detrend, scale=FALSE)),
     nb2listw(nbr12, style="W"), cex=0.6)
    crossprod(plt_out$Y, plt_out$X)/crossprod(plt_out$X)
    lm_obj <- lm(Y ~ X, plt_out)
    abline(lm_obj)
    abline(v=0, h=0, lty=2)
    zz <- summary(influence.measures(lm_obj))
    infl <- as.integer(rownames(zz))
    points(plt_out$X[infl], plt_out$Y[infl], pch=3, cex=0.6, col="red")
    wheat$localAple <- localAple(as.vector(scale(wheat$yield_detrend, scale=FALSE)),
     nb2listw(nbr12, style="W"))
    mean(wheat$localAple)
    hist(wheat$localAple)
    spl <- list("sp.text", coordinates(wheat)[infl,], rep("*", length(infl)))
    spplot(wheat, "localAple", sp.layout=spl)

    ## End(Not run)

[Package spdep version 0.6-13 Index]