lm.morantest: Moran's I test for residual spatial autocorrelation

In spdep: Spatial Dependence: Weighting Schemes, Statistics and Models

Description

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')

Usage

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

Arguments

model	an object of class lm returned by lm; weights may be specified in the lm fit, but offsets should not be used
listw	a listw object created for example by nb2listw
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 get.spChkOption()
resfun	default: weighted.residuals; the function to be used to extract residuals from the lm object, may be residuals, weighted.residuals, rstandard, or rstudent
naSubset	default TRUE to subset listw object for omitted observations in model object (this is a change from earlier behaviour, when the model$na.action component was ignored, and the listw object had to be subsetted by hand)

Value

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.

Author(s)

Roger Bivand [e-mail]

References

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

See Also

lm.LMtests, lm

Examples

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)

Example output

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 

spdep documentation built on Aug. 19, 2017, 3:01 a.m.