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</o:shapelayout></xml><![endif]--></head><body lang=ES link=blue vlink=purple><div class=WordSection1><p class=MsoNormal style='background:white'><span style='font-size:14.0pt;color:black'>Hello everybody:<o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:14.0pt;color:black'><o:p> </o:p></span></p><p class=MsoNormal style='text-align:justify;background:white'><span style='font-size:14.0pt;color:black'>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?<o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:14.0pt;color:black'><o:p> </o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:14.0pt;color:black'><o:p> </o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:14.0pt;color:black'>MY PARTICULAR CASE <o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:14.0pt;color:black'> <o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'>reg.OLS <- lm(y~z1+z2+z3+z4+z5+z6+z7+z8+z9+z10, data=datos)<o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'> <o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'>moran.test(resid(reg.OLS),alternative="two.sided", W_n)<o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'> <o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'> Moran I test under randomisation<o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'> <o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'>data: resid(reg.OLS) <o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'>weights: W_n <o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'> <o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'>Moran I statistic standard deviate = 0.4434, p-value = 0.6575<o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'>alternative hypothesis: two.sided<o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'>sample estimates:<o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'>Moran I statistic Expectation Variance <o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'> 1.596378e-05 -3.595829e-04 7.173448e-07<o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'> <o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'> <o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'> <o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'>moran.lm <-lm.morantest(reg.OLS, W_n, alternative="two.sided")<o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'>print(moran.lm)<o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'> <o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'> Global Moran I for regression residuals<o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'> <o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'>data: <o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'>model: lm(formula = y ~ z1 + z2 + z3 + z4 + z5 + z6 + z7 + z8 + z9 + z10<o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'>, data = datos)<o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'>weights: W_n<o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'> <o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'>Moran I statistic standard deviate = 11.649, p-value < 2.2e-16<o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'>alternative hypothesis: two.sided<o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'>sample estimates:<o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'>Observed Moran I Expectation Variance <o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'> 1.596378e-05 -1.913005e-03 2.741816e-08<o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:14.0pt;color:black'> <o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:14.0pt;color:black'><o:p> </o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:14.0pt;color:black'>A REPRODUCIBLE EXAMPLE<o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:14.0pt;color:black'> <o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:14.0pt;color:black'><o:p> </o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'>library(spdep)<o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'> <o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'>data(oldcol)<o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'> <o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'>oldcrime.lm <- lm(CRIME ~ HOVAL + INC + OPEN + PLUMB + DISCBD + PERIM, data = COL.OLD)<o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'><o:p> </o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'>moran.test(resid(oldcrime.lm), nb2listw(COL.nb, style="W"))<o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'><o:p> </o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'> Moran I test under randomisation<o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'><o:p> </o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'>data: resid(oldcrime.lm) <o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'>weights: nb2listw(COL.nb, style = "W") <o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'><o:p> </o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'>Moran I statistic standard deviate = 1.2733, p-value = 0.1015<o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'>alternative hypothesis: greater<o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'>sample estimates:<o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'>Moran I statistic Expectation Variance <o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'> 0.096711162 -0.020833333 0.008521765<o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'><o:p> </o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'><o:p> </o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'>lm.morantest(oldcrime.lm, nb2listw(COL.nb, style="W"))<o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'><o:p> </o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'> Global Moran I for regression residuals<o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'><o:p> </o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'>data: <o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'>model: lm(formula = CRIME ~ HOVAL + INC + OPEN + PLUMB + DISCBD +<o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'>PERIM, data = COL.OLD)<o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'>weights: nb2listw(COL.nb, style = "W")<o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'><o:p> </o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'>Moran I statistic standard deviate = 1.6668, p-value = 0.04777<o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'>alternative hypothesis: greater<o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'>sample estimates:<o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'>Observed Moran I Expectation Variance <o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Courier New";color:black'> 0.096711162 -0.052848581 0.008050938 <o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:14.0pt;color:black'><o:p> </o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:14.0pt;color:black'> <o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:14.0pt;color:black'>Thanks a lot in advance and sorry for the inconvenience.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:14.0pt'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:14.0pt'>Javi<o:p></o:p></span></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><o:p> </o:p></p><table class=MsoNormalTable border=0 cellspacing=3 cellpadding=0 width="86%" style='width:86.58%;background:white'><tr><td style='padding:3.75pt 3.75pt 3.75pt 3.75pt'></td></tr><tr><td width="99%" style='width:99.04%;background:black;padding:3.75pt 3.75pt 3.75pt 3.75pt'><table class=MsoNormalTable border=0 cellspacing=3 cellpadding=0 width="100%" style='width:100.0%'><tr><td width="55%" style='width:55.0%;padding:.75pt .75pt .75pt .75pt'><p class=MsoNormal><b><span style='font-size:8.5pt;font-family:"Verdana","sans-serif";color:white;mso-fareast-language:ES'>JAVIER GARCÍA </span></b><b><span style='font-size:8.5pt;font-family:"Verdana","sans-serif";color:white;mso-fareast-language:ES'><o:p></o:p></span></b></p><p class=MsoNormal><b><span style='font-size:8.5pt;font-family:"Verdana","sans-serif";color:white;mso-fareast-language:ES'><o:p> </o:p></span></b></p><p class=MsoNormal><b><span style='font-size:8.5pt;font-family:"Verdana","sans-serif";color:white;mso-fareast-language:ES'>Departamento de Economía Aplicada III (Econometría y Estadística)<o:p></o:p></span></b></p><p class=MsoNormal><b><span style='font-size:8.5pt;font-family:"Verdana","sans-serif";color:white;mso-fareast-language:ES'>Facultad de Economía y Empresa (Sección Sarriko)</span></b><span style='color:#1F497D;mso-fareast-language:ES'><br></span><span style='font-size:7.0pt;font-family:"Verdana","sans-serif";color:white;mso-fareast-language:ES'>Avda. Lehendakari Aguirre 83</span><span style='font-size:7.0pt;color:#1F497D;mso-fareast-language:ES'><o:p></o:p></span></p><p class=MsoNormal><span style='font-size:7.0pt;font-family:"Verdana","sans-serif";color:white;mso-fareast-language:ES'>48015 BILBAO<br><b>T.: +34 601 7126</b> <b>F.: +34 601 3754</b><br></span><span style='color:#1F497D;mso-fareast-language:ES'><a href="http://www.ehu.es/"><b><span style='font-size:7.0pt;font-family:"Verdana","sans-serif";color:white'>www.ehu.es</span></b></a> </span><span style='font-size:12.0pt;color:#1F497D;mso-fareast-language:ES'><o:p></o:p></span></p></td><td width="45%" valign=top style='width:45.0%;padding:.75pt .75pt .75pt .75pt'><p class=MsoNormal align=right style='text-align:right'><span style='color:#1F497D;mso-fareast-language:ES'><img border=0 width=482 height=74 id="Imagen_x0020_1" src="cid:image001.gif@01D3081D.E1A72DE0" alt="http://www.unibertsitate-hedakuntza.ehu.es/p268-content/es/contenidos/informacion/manual_id_corp/es_manual/images/firma_email_upv_euskampus_bilingue.gif"></span><span style='font-size:12.0pt;color:#1F497D;mso-fareast-language:ES'><o:p></o:p></span></p></td></tr></table></td></tr></table><p class=MsoNormal><span style='mso-fareast-language:ES'><o:p> </o:p></span></p><p class=MsoNormal><o:p> </o:p></p></div></body></html>