Description Usage Arguments Value Author(s) References See Also Examples

Moran's I test for spatial autocorrelation in residuals from an estimated linear model (`lm()`

). The helper function `listw2U()`

constructs a weights list object corresponding to the sparse matrix *1/2 (W + W')*

1 2 3 | ```
lm.morantest(model, listw, zero.policy=NULL, alternative = "greater",
spChk=NULL, resfun=weighted.residuals, naSubset=TRUE)
listw2U(listw)
``` |

`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 |

`naSubset` |
default TRUE to subset listw object for omitted observations in model object (this is a change from earlier behaviour, when the |

A list with class `htest`

containing the following components:

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

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

`estimate` |
the value of the observed Moran's I, its expectation and variance under the method assumption. |

`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. |

Roger Bivand Roger.Bivand@nhh.no

Cliff, A. D., Ord, J. K. 1981 Spatial processes, Pion, p. 203,

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | ```
data(oldcol)
oldcrime1.lm <- lm(CRIME ~ 1, data = COL.OLD)
oldcrime.lm <- lm(CRIME ~ HOVAL + INC, data = COL.OLD)
lm.morantest(oldcrime.lm, nb2listw(COL.nb, style="W"))
lm.LMtests(oldcrime.lm, nb2listw(COL.nb, style="W"))
lm.morantest(oldcrime.lm, nb2listw(COL.nb, style="S"))
lm.morantest(oldcrime1.lm, nb2listw(COL.nb, style="W"))
moran.test(COL.OLD$CRIME, nb2listw(COL.nb, style="W"),
randomisation=FALSE)
oldcrime.wlm <- lm(CRIME ~ HOVAL + INC, data = COL.OLD,
weights = I(1/AREA_PL))
lm.morantest(oldcrime.wlm, nb2listw(COL.nb, style="W"),
resfun=weighted.residuals)
lm.morantest(oldcrime.wlm, nb2listw(COL.nb, style="W"),
resfun=rstudent)
``` |

```
Loading required package: sp
Loading required package: Matrix
Global Moran I for regression residuals
data:
model: lm(formula = CRIME ~ HOVAL + INC, data = COL.OLD)
weights: nb2listw(COL.nb, style = "W")
Moran I statistic standard deviate = 2.9539, p-value = 0.001569
alternative hypothesis: greater
sample estimates:
Observed Moran I Expectation Variance
0.235638354 -0.033302866 0.008289408
Lagrange multiplier diagnostics for spatial dependence
data:
model: lm(formula = CRIME ~ HOVAL + INC, data = COL.OLD)
weights: nb2listw(COL.nb, style = "W")
LMErr = 5.7231, df = 1, p-value = 0.01674
Global Moran I for regression residuals
data:
model: lm(formula = CRIME ~ HOVAL + INC, data = COL.OLD)
weights: nb2listw(COL.nb, style = "S")
Moran I statistic standard deviate = 3.1745, p-value = 0.0007504
alternative hypothesis: greater
sample estimates:
Observed Moran I Expectation Variance
0.239317561 -0.033431740 0.007381982
Global Moran I for regression residuals
data:
model: lm(formula = CRIME ~ 1, data = COL.OLD)
weights: nb2listw(COL.nb, style = "W")
Moran I statistic standard deviate = 5.6754, p-value = 6.92e-09
alternative hypothesis: greater
sample estimates:
Observed Moran I Expectation Variance
0.510951264 -0.020833333 0.008779831
Moran I test under normality
data: COL.OLD$CRIME
weights: nb2listw(COL.nb, style = "W")
Moran I statistic standard deviate = 5.6754, p-value = 6.92e-09
alternative hypothesis: greater
sample estimates:
Moran I statistic Expectation Variance
0.510951264 -0.020833333 0.008779831
Global Moran I for regression residuals
data:
model: lm(formula = CRIME ~ HOVAL + INC, data = COL.OLD, weights =
I(1/AREA_PL))
weights: nb2listw(COL.nb, style = "W")
Moran I statistic standard deviate = 3.0141, p-value = 0.001289
alternative hypothesis: greater
sample estimates:
Observed Moran I Expectation Variance
0.241298974 -0.032224366 0.008235091
Global Moran I for regression residuals
data:
model: lm(formula = CRIME ~ HOVAL + INC, data = COL.OLD, weights =
I(1/AREA_PL))
weights: nb2listw(COL.nb, style = "W")
Moran I statistic standard deviate = 2.822, p-value = 0.002387
alternative hypothesis: greater
sample estimates:
Observed Moran I Expectation Variance
0.223860298 -0.032224366 0.008235091
```

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