ME.RdThe Moran eigenvector filtering function is intended to remove spatial autocorrelation from the residuals of generalised linear models. It uses brute force eigenvector selection to reach a subset of such vectors to be added to the RHS of the GLM model to reduce residual autocorrelation to below the specified alpha value. Since eigenvector selection only works on symmetric weights, the weights are made symmetric before the eigenvectors are found (from spdep 0.5-50).
ME(formula, data=list(), family = gaussian, weights, offset, na.action=na.fail,listw=NULL, alpha=0.05, nsim=99, verbose=NULL, stdev=FALSE, zero.policy=NULL)
| formula | a symbolic description of the model to be fit |
|---|---|
| data | an optional data frame containing the variables in the model |
| family | a description of the error distribution and link function to be used in the model |
| weights | an optional vector of weights to be used in the fitting process |
| offset | this can be used to specify an a priori known component to be included in the linear predictor during fitting |
| na.action | a function (default |
| listw | a |
| alpha | used as a stopping rule to choose all eigenvectors up to and including the one with a p-value exceeding alpha |
| nsim | number of permutations for permutation bootstrap for finding p-values |
| verbose | default NULL, use global option value; if TRUE report eigenvectors selected |
| stdev | if TRUE, p-value calculated from bootstrap permutation standard deviate using |
| zero.policy | default NULL, use global option value; if FALSE stop with error for any empty neighbour sets, if TRUE permit the weights list to be formed with zero-length weights vectors |
The eigenvectors for inclusion are chosen by calculating the empirical Moran's I values for the initial model plus each of the doubly centred symmetric spatial weights matrix eigenvectors in turn. Then the first eigenvector is chosen as that with the lowest Moran's I value. The procedure is repeated until the lowest remaining Moran's I value has a permutation-based probability value above alpha. The probability value is either Hope-type or based on using the mean and standard deviation of the permutations to calculate ZI based on the stdev argument.
An object of class Me_res:
a matrix summarising the selection of eigenvectors for inclusion, with columns:
number of selected eigenvector
permutation-based standardized deviate of Moran's I if stdev=TRUE
probability value: if stdev=TRUE of the permutation-based standardized deviate, if FALSE the Hope-type probability value, in both cases on-sided
a matrix of the selected eigenvectors in order of selection
Dray S, Legendre P and Peres-Neto PR (2005) Spatial modeling: a comprehensive framework for principle coordinate analysis of neigbbor matrices (PCNM), Ecological Modelling; Griffith DA and Peres-Neto PR (2006) Spatial modeling in ecology: the flexibility of eigenfunction spatial analyses.
Roger Bivand and Pedro Peres-Neto
#require("spdep", quietly=TRUE) data(hopkins, package="spData") hopkins_part <- hopkins[21:36,36:21] hopkins_part[which(hopkins_part > 0, arr.ind=TRUE)] <- 1 hopkins.rook.nb <- spdep::cell2nb(16, 16, type="rook") glmbase <- glm(c(hopkins_part) ~ 1, family="binomial") lw <- spdep::nb2listw(hopkins.rook.nb, style="B") set.seed(123) system.time(MEbinom1 <- ME(c(hopkins_part) ~ 1, family="binomial", listw=lw, alpha=0.05, verbose=TRUE, nsim=49)) #> eV[,2], I: 0.07978424 ZI: NA, pr(ZI): 0.04 #> eV[,54], I: 0.05704227 ZI: NA, pr(ZI): 0.12 #> user system elapsed #> 1.590 0.010 1.606 glmME <- glm(c(hopkins_part) ~ 1 + fitted(MEbinom1), family="binomial") #anova(glmME, test="Chisq") coef(summary(glmME)) #> Estimate Std. Error z value Pr(>|z|) #> (Intercept) -1.194892 0.1600429 -7.466073 8.262357e-14 #> fitted(MEbinom1)vec2 9.030818 2.5381594 3.558019 3.736629e-04 #> fitted(MEbinom1)vec54 -8.759610 2.5205844 -3.475230 5.104161e-04 anova(glmbase, glmME, test="Chisq") #> Analysis of Deviance Table #> #> Model 1: c(hopkins_part) ~ 1 #> Model 2: c(hopkins_part) ~ 1 + fitted(MEbinom1) #> Resid. Df Resid. Dev Df Deviance Pr(>Chi) #> 1 255 292.23 #> 2 253 266.27 2 25.956 2.311e-06 *** #> --- #> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 if (FALSE) { require("sf", quietly=TRUE) columbus <- st_read(system.file("shapes/columbus.shp", package="spData")[1], quiet=TRUE) #require("spdep", quietly=TRUE) col.gal.nb <- spdep::read.gal(system.file("weights/columbus.gal", package="spData")[1]) lw <- spdep::nb2listw(col.gal.nb) lmbase <- lm(CRIME ~ INC + HOVAL, data=columbus) lagcol <- SpatialFiltering(CRIME ~ 1, ~ INC + HOVAL, data=columbus, nb=col.gal.nb, style="W", alpha=0.1, verbose=TRUE) lagcol lmlag <- lm(CRIME ~ INC + HOVAL + fitted(lagcol), data=columbus) anova(lmbase, lmlag) set.seed(123) system.time(lagcol1 <- ME(CRIME ~ INC + HOVAL, data=columbus, family="gaussian", listw=lw, alpha=0.1, verbose=TRUE)) lagcol1 lmlag1 <- lm(CRIME ~ INC + HOVAL + fitted(lagcol1), data=columbus) anova(lmbase, lmlag1) set.seed(123) lagcol2 <- ME(CRIME ~ INC + HOVAL, data=columbus, family="gaussian", listw=lw, alpha=0.1, stdev=TRUE, verbose=TRUE) lagcol2 lmlag2 <- lm(CRIME ~ INC + HOVAL + fitted(lagcol2), data=columbus) anova(lmbase, lmlag2) NA.columbus <- columbus NA.columbus$CRIME[20:25] <- NA COL.ME.NA <- ME(CRIME ~ INC + HOVAL, data=NA.columbus, family="gaussian", listw=lw, alpha=0.1, stdev=TRUE, verbose=TRUE, na.action=na.exclude) COL.ME.NA$na.action summary(lm(CRIME ~ INC + HOVAL + fitted(COL.ME.NA), data=NA.columbus, na.action=na.exclude)) nc.sids <- st_read(system.file("shapes/sids.shp", package="spData")[1], quiet=TRUE) rn <- as.character(nc.sids$FIPS) ncCC89_nb <- spdep::read.gal(system.file("weights/ncCC89.gal", package="spData")[1], region.id=rn) ncCR85_nb <- spdep::read.gal(system.file("weights/ncCR85.gal", package="spData")[1], region.id=rn) glmbase <- glm(SID74 ~ 1, data=nc.sids, offset=log(BIR74), family="poisson") set.seed(123) MEpois1 <- ME(SID74 ~ 1, data=nc.sids, offset=log(BIR74), family="poisson", listw=spdep::nb2listw(ncCR85_nb, style="B"), alpha=0.2, verbose=TRUE) MEpois1 glmME <- glm(SID74 ~ 1 + fitted(MEpois1), data=nc.sids, offset=log(BIR74), family="poisson") anova(glmME, test="Chisq") anova(glmbase, glmME, test="Chisq") }