ME: Moran eigenvector GLM filtering
In spdep: Spatial Dependence: Weighting Schemes, Statistics and Models
Description
Usage
Arguments
Details
Value
Author(s)
References
See Also
Examples
Description
The 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).
Usage
1
2
Arguments
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
listw
a listw object created for example by nb2listw
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 pnorm with alternative="greater", if FALSE the Hope-type p-value
Details
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.
Value
An object of class ME_res:
selection
a matrix summarising the selection of eigenvectors for inclusion, with columns:
- Eigenvector
number of selected eigenvector
- ZI
permutation-based standardized deviate of Moran's I if stdev=TRUE
- pr(ZI)
probability value: if stdev=TRUE of the permutation-based standardized deviate, if FALSE the Hope-type probability value, in both cases on-sided
The first row is the value at the start of the search
vectors
a matrix of the selected eigenvectors in order of selection
Author(s)
Roger Bivand and Pedro Peres-Neto
References
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.
See Also
Examples
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## Not run:
example(columbus)
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(lmlag)
anova(lmbase, lmlag)
set.seed(123)
lagcol1 <- ME(CRIME ~ INC + HOVAL, data=columbus, family="gaussian",
listw=nb2listw(col.gal.nb), alpha=0.1, verbose=TRUE)
lagcol1
lmlag1 <- lm(CRIME ~ INC + HOVAL + fitted(lagcol1), data=columbus)
anova(lmlag1)
anova(lmbase, lmlag1)
set.seed(123)
lagcol2 <- ME(CRIME ~ INC + HOVAL, data=columbus, family="gaussian",
listw=nb2listw(col.gal.nb), alpha=0.1, stdev=TRUE, verbose=TRUE)
lagcol2
lmlag2 <- lm(CRIME ~ INC + HOVAL + fitted(lagcol2), data=columbus)
anova(lmlag2)
anova(lmbase, lmlag2)
example(nc.sids)
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=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")
data(hopkins)
hopkins_part <- hopkins[21:36,36:21]
hopkins_part[which(hopkins_part > 0, arr.ind=TRUE)] <- 1
hopkins.rook.nb <- cell2nb(16, 16, type="rook")
glmbase <- glm(c(hopkins_part) ~ 1, family="binomial")
set.seed(123)
MEbinom1 <- ME(c(hopkins_part) ~ 1, family="binomial",
listw=nb2listw(hopkins.rook.nb, style="B"), alpha=0.2, verbose=TRUE)
glmME <- glm(c(hopkins_part) ~ 1 + fitted(MEbinom1), family="binomial")
anova(glmME, test="Chisq")
anova(glmbase, glmME, test="Chisq")
## End(Not run)
Example output
Loading required package: sp
Loading required package: Matrix
colmbs> require(maptools)
Loading required package: maptools
Checking rgeos availability: TRUE
colmbs> columbus <- readShapePoly(system.file("etc/shapes/columbus.shp",
colmbs+ package="spdep")[1])
colmbs> col.gal.nb <- read.gal(system.file("etc/weights/columbus.gal",
colmbs+ package="spdep")[1])
Warning message:
use rgdal::readOGR or sf::st_read
Step 0 SelEvec 0 MinMi 0.2123742 ZMinMi 2.681 Pr(ZI) 0.007340246
Step 1 SelEvec 6 MinMi 0.1178225 ZMinMi 1.84512 Pr(ZI) 0.06502014
Step 2 SelEvec 4 MinMi 0.06242664 ZMinMi 1.494821 Pr(ZI) 0.1349611
Step SelEvec Eval MinMi ZMinMi Pr(ZI) R2 gamma
0 0 0 0.0000000 0.21237415 2.681000 0.007340246 0.5524040 0.00000
1 1 6 0.7161123 0.11782248 1.845120 0.065020139 0.6038801 25.46181
2 2 4 0.8682938 0.06242664 1.494821 0.134961136 0.6531288 26.68319
Analysis of Variance Table
Response: CRIME
Df Sum Sq Mean Sq F value Pr(>F)
INC 1 6502.0 6502.0 61.3749 6.988e-10 ***
HOVAL 1 921.3 921.3 8.6966 0.005089 **
fitted(lagcol) 2 1353.6 676.8 6.3884 0.003666 **
Residuals 44 4661.3 105.9
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Analysis of Variance Table
Model 1: CRIME ~ INC + HOVAL
Model 2: CRIME ~ INC + HOVAL + fitted(lagcol)
Res.Df RSS Df Sum of Sq F Pr(>F)
1 46 6014.9
2 44 4661.3 2 1353.6 6.3884 0.003666 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
eV[,6], I: 0.1178225 ZI: NA, pr(ZI): 0.07
eV[,4], I: 0.06242664 ZI: NA, pr(ZI): 0.19
Eigenvector ZI pr(ZI)
0 NA NA 0.04
1 6 NA 0.07
2 4 NA 0.19
Analysis of Variance Table
Response: CRIME
Df Sum Sq Mean Sq F value Pr(>F)
INC 1 6502.0 6502.0 61.3749 6.988e-10 ***
HOVAL 1 921.3 921.3 8.6966 0.005089 **
fitted(lagcol1) 2 1353.6 676.8 6.3884 0.003666 **
Residuals 44 4661.3 105.9
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Analysis of Variance Table
Model 1: CRIME ~ INC + HOVAL
Model 2: CRIME ~ INC + HOVAL + fitted(lagcol1)
Res.Df RSS Df Sum of Sq F Pr(>F)
1 46 6014.9
2 44 4661.3 2 1353.6 6.3884 0.003666 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
eV[,6], I: 0.1178225 ZI: 1.672528, pr(ZI): 0.0472101
eV[,4], I: 0.06242664 ZI: 0.9968862, pr(ZI): 0.1594099
Eigenvector ZI pr(ZI)
0 NA 2.3241331 0.01005918
1 6 1.6725283 0.04721010
2 4 0.9968862 0.15940988
Analysis of Variance Table
Response: CRIME
Df Sum Sq Mean Sq F value Pr(>F)
INC 1 6502.0 6502.0 61.3749 6.988e-10 ***
HOVAL 1 921.3 921.3 8.6966 0.005089 **
fitted(lagcol2) 2 1353.6 676.8 6.3884 0.003666 **
Residuals 44 4661.3 105.9
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Analysis of Variance Table
Model 1: CRIME ~ INC + HOVAL
Model 2: CRIME ~ INC + HOVAL + fitted(lagcol2)
Res.Df RSS Df Sum of Sq F Pr(>F)
1 46 6014.9
2 44 4661.3 2 1353.6 6.3884 0.003666 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
nc.sds> require(maptools)
nc.sds> nc.sids <- readShapePoly(system.file("etc/shapes/sids.shp", package="spdep")[1],
nc.sds+ ID="FIPSNO", proj4string=CRS("+proj=longlat +ellps=clrk66"))
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
nc.sds> rn <- sapply(slot(nc.sids, "polygons"), function(x) slot(x, "ID"))
nc.sds> ncCC89_nb <- read.gal(system.file("etc/weights/ncCC89.gal", package="spdep")[1],
nc.sds+ region.id=rn)
nc.sds> ncCR85_nb <- read.gal(system.file("etc/weights/ncCR85.gal", package="spdep")[1],
nc.sds+ region.id=rn)
nc.sds> ## Not run:
nc.sds> ##D plot(nc.sids, border="grey")
nc.sds> ##D plot(ncCR85_nb, coordinates(nc.sids), add=TRUE, col="blue")
nc.sds> ##D plot(nc.sids, border="grey")
nc.sds> ##D plot(ncCC89_nb, coordinates(nc.sids), add=TRUE, col="blue")
nc.sds> ## End(Not run)
nc.sds>
nc.sds>
nc.sds>
Warning message:
use rgdal::readOGR or sf::st_read
eV[,1], I: 0.1327384 ZI: NA, pr(ZI): 0.01
eV[,8], I: 0.06936385 ZI: NA, pr(ZI): 0.11
eV[,4], I: 0.03584503 ZI: NA, pr(ZI): 0.27
Eigenvector ZI pr(ZI)
0 NA NA 0.01
1 1 NA 0.01
2 8 NA 0.11
3 4 NA 0.27
Analysis of Deviance Table
Model: poisson, link: log
Response: SID74
Terms added sequentially (first to last)
Df Deviance Resid. Df Resid. Dev Pr(>Chi)
NULL 99 203.34
fitted(MEpois1) 3 32.499 96 170.84 4.108e-07 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Analysis of Deviance Table
Model 1: SID74 ~ 1
Model 2: SID74 ~ 1 + fitted(MEpois1)
Resid. Df Resid. Dev Df Deviance Pr(>Chi)
1 99 203.34
2 96 170.84 3 32.499 4.108e-07 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
eV[,2], I: 0.08451491 ZI: NA, pr(ZI): 0.03
eV[,8], I: 0.06530444 ZI: NA, pr(ZI): 0.06
eV[,55], I: 0.04982992 ZI: NA, pr(ZI): 0.11
eV[,1], I: 0.03004852 ZI: NA, pr(ZI): 0.24
Analysis of Deviance Table
Model: binomial, link: logit
Response: c(hopkins_part)
Terms added sequentially (first to last)
Df Deviance Resid. Df Resid. Dev Pr(>Chi)
NULL 255 292.23
fitted(MEbinom1) 4 32.335 251 259.89 1.634e-06 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
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
2 251 259.89 4 32.335 1.634e-06 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
spdep documentation built on Aug. 19, 2017, 3:01 a.m.
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Description Usage Arguments Details Value Author(s) References See Also Examples
Description
The 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).
Usage
1 2 |
Arguments
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 |
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 |
Details
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.
Value
An object of class ME_res:
selection |
a matrix summarising the selection of eigenvectors for inclusion, with columns:
The first row is the value at the start of the search |
vectors |
a matrix of the selected eigenvectors in order of selection |
Author(s)
Roger Bivand and Pedro Peres-Neto
References
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.
See Also
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 | ## Not run:
example(columbus)
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(lmlag)
anova(lmbase, lmlag)
set.seed(123)
lagcol1 <- ME(CRIME ~ INC + HOVAL, data=columbus, family="gaussian",
listw=nb2listw(col.gal.nb), alpha=0.1, verbose=TRUE)
lagcol1
lmlag1 <- lm(CRIME ~ INC + HOVAL + fitted(lagcol1), data=columbus)
anova(lmlag1)
anova(lmbase, lmlag1)
set.seed(123)
lagcol2 <- ME(CRIME ~ INC + HOVAL, data=columbus, family="gaussian",
listw=nb2listw(col.gal.nb), alpha=0.1, stdev=TRUE, verbose=TRUE)
lagcol2
lmlag2 <- lm(CRIME ~ INC + HOVAL + fitted(lagcol2), data=columbus)
anova(lmlag2)
anova(lmbase, lmlag2)
example(nc.sids)
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=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")
data(hopkins)
hopkins_part <- hopkins[21:36,36:21]
hopkins_part[which(hopkins_part > 0, arr.ind=TRUE)] <- 1
hopkins.rook.nb <- cell2nb(16, 16, type="rook")
glmbase <- glm(c(hopkins_part) ~ 1, family="binomial")
set.seed(123)
MEbinom1 <- ME(c(hopkins_part) ~ 1, family="binomial",
listw=nb2listw(hopkins.rook.nb, style="B"), alpha=0.2, verbose=TRUE)
glmME <- glm(c(hopkins_part) ~ 1 + fitted(MEbinom1), family="binomial")
anova(glmME, test="Chisq")
anova(glmbase, glmME, test="Chisq")
## End(Not run)
|
Example output
Loading required package: sp
Loading required package: Matrix
colmbs> require(maptools)
Loading required package: maptools
Checking rgeos availability: TRUE
colmbs> columbus <- readShapePoly(system.file("etc/shapes/columbus.shp",
colmbs+ package="spdep")[1])
colmbs> col.gal.nb <- read.gal(system.file("etc/weights/columbus.gal",
colmbs+ package="spdep")[1])
Warning message:
use rgdal::readOGR or sf::st_read
Step 0 SelEvec 0 MinMi 0.2123742 ZMinMi 2.681 Pr(ZI) 0.007340246
Step 1 SelEvec 6 MinMi 0.1178225 ZMinMi 1.84512 Pr(ZI) 0.06502014
Step 2 SelEvec 4 MinMi 0.06242664 ZMinMi 1.494821 Pr(ZI) 0.1349611
Step SelEvec Eval MinMi ZMinMi Pr(ZI) R2 gamma
0 0 0 0.0000000 0.21237415 2.681000 0.007340246 0.5524040 0.00000
1 1 6 0.7161123 0.11782248 1.845120 0.065020139 0.6038801 25.46181
2 2 4 0.8682938 0.06242664 1.494821 0.134961136 0.6531288 26.68319
Analysis of Variance Table
Response: CRIME
Df Sum Sq Mean Sq F value Pr(>F)
INC 1 6502.0 6502.0 61.3749 6.988e-10 ***
HOVAL 1 921.3 921.3 8.6966 0.005089 **
fitted(lagcol) 2 1353.6 676.8 6.3884 0.003666 **
Residuals 44 4661.3 105.9
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Analysis of Variance Table
Model 1: CRIME ~ INC + HOVAL
Model 2: CRIME ~ INC + HOVAL + fitted(lagcol)
Res.Df RSS Df Sum of Sq F Pr(>F)
1 46 6014.9
2 44 4661.3 2 1353.6 6.3884 0.003666 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
eV[,6], I: 0.1178225 ZI: NA, pr(ZI): 0.07
eV[,4], I: 0.06242664 ZI: NA, pr(ZI): 0.19
Eigenvector ZI pr(ZI)
0 NA NA 0.04
1 6 NA 0.07
2 4 NA 0.19
Analysis of Variance Table
Response: CRIME
Df Sum Sq Mean Sq F value Pr(>F)
INC 1 6502.0 6502.0 61.3749 6.988e-10 ***
HOVAL 1 921.3 921.3 8.6966 0.005089 **
fitted(lagcol1) 2 1353.6 676.8 6.3884 0.003666 **
Residuals 44 4661.3 105.9
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Analysis of Variance Table
Model 1: CRIME ~ INC + HOVAL
Model 2: CRIME ~ INC + HOVAL + fitted(lagcol1)
Res.Df RSS Df Sum of Sq F Pr(>F)
1 46 6014.9
2 44 4661.3 2 1353.6 6.3884 0.003666 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
eV[,6], I: 0.1178225 ZI: 1.672528, pr(ZI): 0.0472101
eV[,4], I: 0.06242664 ZI: 0.9968862, pr(ZI): 0.1594099
Eigenvector ZI pr(ZI)
0 NA 2.3241331 0.01005918
1 6 1.6725283 0.04721010
2 4 0.9968862 0.15940988
Analysis of Variance Table
Response: CRIME
Df Sum Sq Mean Sq F value Pr(>F)
INC 1 6502.0 6502.0 61.3749 6.988e-10 ***
HOVAL 1 921.3 921.3 8.6966 0.005089 **
fitted(lagcol2) 2 1353.6 676.8 6.3884 0.003666 **
Residuals 44 4661.3 105.9
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Analysis of Variance Table
Model 1: CRIME ~ INC + HOVAL
Model 2: CRIME ~ INC + HOVAL + fitted(lagcol2)
Res.Df RSS Df Sum of Sq F Pr(>F)
1 46 6014.9
2 44 4661.3 2 1353.6 6.3884 0.003666 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
nc.sds> require(maptools)
nc.sds> nc.sids <- readShapePoly(system.file("etc/shapes/sids.shp", package="spdep")[1],
nc.sds+ ID="FIPSNO", proj4string=CRS("+proj=longlat +ellps=clrk66"))
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
nc.sds> rn <- sapply(slot(nc.sids, "polygons"), function(x) slot(x, "ID"))
nc.sds> ncCC89_nb <- read.gal(system.file("etc/weights/ncCC89.gal", package="spdep")[1],
nc.sds+ region.id=rn)
nc.sds> ncCR85_nb <- read.gal(system.file("etc/weights/ncCR85.gal", package="spdep")[1],
nc.sds+ region.id=rn)
nc.sds> ## Not run:
nc.sds> ##D plot(nc.sids, border="grey")
nc.sds> ##D plot(ncCR85_nb, coordinates(nc.sids), add=TRUE, col="blue")
nc.sds> ##D plot(nc.sids, border="grey")
nc.sds> ##D plot(ncCC89_nb, coordinates(nc.sids), add=TRUE, col="blue")
nc.sds> ## End(Not run)
nc.sds>
nc.sds>
nc.sds>
Warning message:
use rgdal::readOGR or sf::st_read
eV[,1], I: 0.1327384 ZI: NA, pr(ZI): 0.01
eV[,8], I: 0.06936385 ZI: NA, pr(ZI): 0.11
eV[,4], I: 0.03584503 ZI: NA, pr(ZI): 0.27
Eigenvector ZI pr(ZI)
0 NA NA 0.01
1 1 NA 0.01
2 8 NA 0.11
3 4 NA 0.27
Analysis of Deviance Table
Model: poisson, link: log
Response: SID74
Terms added sequentially (first to last)
Df Deviance Resid. Df Resid. Dev Pr(>Chi)
NULL 99 203.34
fitted(MEpois1) 3 32.499 96 170.84 4.108e-07 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Analysis of Deviance Table
Model 1: SID74 ~ 1
Model 2: SID74 ~ 1 + fitted(MEpois1)
Resid. Df Resid. Dev Df Deviance Pr(>Chi)
1 99 203.34
2 96 170.84 3 32.499 4.108e-07 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
eV[,2], I: 0.08451491 ZI: NA, pr(ZI): 0.03
eV[,8], I: 0.06530444 ZI: NA, pr(ZI): 0.06
eV[,55], I: 0.04982992 ZI: NA, pr(ZI): 0.11
eV[,1], I: 0.03004852 ZI: NA, pr(ZI): 0.24
Analysis of Deviance Table
Model: binomial, link: logit
Response: c(hopkins_part)
Terms added sequentially (first to last)
Df Deviance Resid. Df Resid. Dev Pr(>Chi)
NULL 255 292.23
fitted(MEbinom1) 4 32.335 251 259.89 1.634e-06 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
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
2 251 259.89 4 32.335 1.634e-06 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
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