The function implements Tiefelsdorf's application of the Saddlepoint approximation to global Moran's I's reference distribution.

1 2 3 4 5 6 7 8 9 10 | ```
lm.morantest.sad(model, listw, zero.policy=NULL, alternative="greater",
spChk=NULL, resfun=weighted.residuals, tol=.Machine$double.eps^0.5,
maxiter=1000, tol.bounds=0.0001, zero.tol = 1e-07, Omega=NULL,
save.M=NULL, save.U=NULL)
## S3 method for class 'moransad'
print(x, ...)
## S3 method for class 'moransad'
summary(object, ...)
## S3 method for class 'summary.moransad'
print(x, ...)
``` |

`model` |
an object of class |

`listw` |
a |

`zero.policy` |
default NULL, use global option value; if TRUE assign zero to the lagged value of zones without neighbours, if FALSE assign NA |

`alternative` |
a character string specifying the alternative hypothesis, must be one of greater (default), less or two.sided. |

`spChk` |
should the data vector names be checked against the spatial objects for identity integrity, TRUE, or FALSE, default NULL to use |

`resfun` |
default: weighted.residuals; the function to be used to extract residuals from the |

`tol` |
the desired accuracy (convergence tolerance) for |

`maxiter` |
the maximum number of iterations for |

`tol.bounds` |
offset from bounds for |

`zero.tol` |
tolerance used to find eigenvalues close to absolute zero |

`Omega` |
A SAR process matrix may be passed in to test an alternative hypothesis, for example |

`save.M` |
return the full M matrix for use in |

`save.U` |
return the full U matrix for use in |

`x` |
object to be printed |

`object` |
object to be summarised |

`...` |
arguments to be passed through |

The function involves finding the eigenvalues of an n by n matrix, and numerically finding the root for the Saddlepoint approximation, and should therefore only be used with care when n is large.

A list of class `moransad`

with the following components:

`statistic` |
the value of the saddlepoint approximation of the standard deviate of global Moran's I. |

`p.value` |
the p-value of the test. |

`estimate` |
the value of the observed global Moran's I. |

`alternative` |
a character string describing the alternative hypothesis. |

`method` |
a character string giving the method used. |

`data.name` |
a character string giving the name(s) of the data. |

`internal1` |
Saddlepoint omega, r and u |

`internal2` |
f.root, iter and estim.prec from |

`df` |
degrees of freedom |

`tau` |
eigenvalues (excluding zero values) |

Roger Bivand Roger.Bivand@nhh.no

Tiefelsdorf, M. 2002 The Saddlepoint approximation of Moran's I and local Moran's Ii reference distributions and their numerical evaluation. Geographical Analysis, 34, pp. 187–206.

`lm.morantest`

1 2 3 4 5 6 7 8 9 10 11 12 | ```
require(maptools)
eire <- readShapePoly(system.file("etc/shapes/eire.shp", package="spdep")[1],
ID="names", proj4string=CRS("+proj=utm +zone=30 +ellps=airy +units=km"))
eire.nb <- poly2nb(eire)
#data(eire)
e.lm <- lm(OWNCONS ~ ROADACC, data=eire)
lm.morantest(e.lm, nb2listw(eire.nb))
lm.morantest.sad(e.lm, nb2listw(eire.nb))
summary(lm.morantest.sad(e.lm, nb2listw(eire.nb)))
e.wlm <- lm(OWNCONS ~ ROADACC, data=eire, weights=RETSALE)
lm.morantest(e.wlm, nb2listw(eire.nb), resfun=rstudent)
lm.morantest.sad(e.wlm, nb2listw(eire.nb), resfun=rstudent)
``` |

Questions? Problems? Suggestions? Tweet to @rdrrHQ or email at ian@mutexlabs.com.

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