# Differences between moran.test and lm.morantest

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## Differences between moran.test and lm.morantest

Hello everybody:

Currently I am working on a paper in which we need to analyze the presence of possible spatial correlation in the data. With this aim I am running some tests in R. I am a little bit confused about the differences between moran.test and lm.morantest R functions. The problem I face to is that when I run moran.test on my  regression residuals the result is totally different from the one I obtain when I use lm.morantest with the lm regression object (please, see below the different outputs I get and after it a reproducible example). In particular, whereas the observed Moran I is the same, the expectation and variance differ dramatically, getting opposite conclusions. I would appreciate very much if someone could clarify for me which is the cause behind this. By the way, I also run LM tests (LMerr, RLMerr, LMlag and RLMlag) not rejecting the null hypothesis in any of them (all p-values are higher than 0.7), which is in clear contradiction with the lm.morantest… how is this possible?

MY PARTICULAR CASE

reg.OLS <- lm(y~z1+z2+z3+z4+z5+z6+z7+z8+z9+z10, data=datos)

moran.test(resid(reg.OLS),alternative="two.sided", W_n)

Moran I test under randomisation

data:  resid(reg.OLS)

weights: W_n

Moran I statistic standard deviate = 0.4434, p-value = 0.6575

alternative hypothesis: two.sided

sample estimates:

Moran I statistic       Expectation          Variance

1.596378e-05     -3.595829e-04      7.173448e-07

moran.lm <-lm.morantest(reg.OLS, W_n, alternative="two.sided")

print(moran.lm)

Global Moran I for regression residuals

data:

model: lm(formula = y ~ z1 + z2 + z3 + z4 + z5 + z6 + z7 + z8 + z9 + z10

, data = datos)

weights: W_n

Moran I statistic standard deviate = 11.649, p-value < 2.2e-16

alternative hypothesis: two.sided

sample estimates:

Observed Moran I      Expectation         Variance

1.596378e-05    -1.913005e-03     2.741816e-08

A REPRODUCIBLE EXAMPLE

library(spdep)

data(oldcol)

oldcrime.lm <- lm(CRIME ~ HOVAL + INC + OPEN + PLUMB + DISCBD + PERIM, data = COL.OLD)

moran.test(resid(oldcrime.lm), nb2listw(COL.nb, style="W"))

Moran I test under randomisation

data:  resid(oldcrime.lm)

weights: nb2listw(COL.nb, style = "W")

Moran I statistic standard deviate = 1.2733, p-value = 0.1015

alternative hypothesis: greater

sample estimates:

Moran I statistic       Expectation          Variance

0.096711162      -0.020833333       0.008521765

lm.morantest(oldcrime.lm, nb2listw(COL.nb, style="W"))

Global Moran I for regression residuals

data:

model: lm(formula = CRIME ~ HOVAL + INC + OPEN + PLUMB + DISCBD +

PERIM, data = COL.OLD)

weights: nb2listw(COL.nb, style = "W")

Moran I statistic standard deviate = 1.6668, p-value = 0.04777

alternative hypothesis: greater

sample estimates:

Observed Moran I      Expectation         Variance

0.096711162     -0.052848581      0.008050938

Thanks a lot in advance and sorry for the inconvenience.

Javi

 JAVIER GARCÍA  Departamento de Economía Aplicada III (Econometría y Estadística)Facultad de Economía y Empresa (Sección Sarriko)Avda. Lehendakari Aguirre 8348015 BILBAOT.: +34 601 7126 F.: +34 601 3754

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