Saddlepoint approximation of local Moran's Ii tests
localmoran.sad.RdThe function implements Tiefelsdorf's application of the Saddlepoint
approximation to local Moran's Ii's reference distribution. If the model
object is of class "lm", global independence is assumed; if of class
"sarlm", global dependence is assumed to be represented by the spatial
parameter of that model. Tests are reported separately for each zone
selected, and may be summarised using summary.localmoransad.
Values of local Moran's Ii agree with those from localmoran(),
but in that function, the standard deviate - here the Saddlepoint
approximation - is based on the randomisation assumption.
Usage
localmoran.sad(model, select, nb, glist=NULL, style="W",
zero.policy=NULL, alternative="two.sided", spChk=NULL,
resfun=weighted.residuals, save.Vi=FALSE,
tol = .Machine$double.eps^0.5, maxiter = 1000, tol.bounds=0.0001,
save.M=FALSE, Omega = NULL)
<!-- %as.data.frame.localmoransad(x, row.names=NULL, optional=FALSE) -->
# S3 method for class 'localmoransad'
print(x, ...)
# S3 method for class 'localmoransad'
summary(object, ...)
# S3 method for class 'summary.localmoransad'
print(x, ...)
listw2star(listw, ireg, style, n, D, a, zero.policy=attr(listw, "zero.policy"))Arguments
- model
an object of class
lmreturned bylm(assuming no global spatial autocorrelation), or an object of classsarlmreturned by a spatial simultaneous autoregressive model fit (assuming global spatial autocorrelation represented by the model spatial coefficient); weights may be specified in thelmfit, but offsets should not be used- select
an integer vector of the id. numbers of zones to be tested; if missing, all zones
- nb
a list of neighbours of class
nb- glist
a list of general weights corresponding to neighbours
- style
can take values W, B, C, and S
- zero.policy
default
attr(listw, "zero.policy")as set whenlistwwas created, if attribute not set, 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
lmobject, may beresiduals,weighted.residuals,rstandard, orrstudent- save.Vi
if TRUE, return the star-shaped weights lists for each zone tested
- tol
the desired accuracy (convergence tolerance) for
uniroot- maxiter
the maximum number of iterations for
uniroot- tol.bounds
offset from bounds for
uniroot- save.M
if TRUE, save a list of left and right M products in a list for the conditional tests, or a list of the regression model matrix components
- Omega
A SAR process matrix may be passed in to test an alternative hypothesis, for example
Omega <- invIrW(listw, rho=0.1); Omega <- tcrossprod(Omega),chol()is taken internally- x
object to be printed
Details
The function implements the analytical eigenvalue calculation together with trace shortcuts given or suggested in Tiefelsdorf (2002), partly following remarks by J. Keith Ord, and uses the Saddlepoint analytical solution from Tiefelsdorf's SPSS code.
If a histogram of the probability values of the saddlepoint estimate for the assumption of global independence is not approximately flat, the assumption is probably unjustified, and re-estimation with global dependence is recommended.
No n by n matrices are needed at any point for the test assuming no global dependence, the star-shaped weights matrices being handled as listw lists. When the test is made on residuals from a spatial regression, taking a global process into account. n by n matrices are necessary, and memory constraints may be reached for large lattices.
Value
A list with class localmoransad containing "select" lists, each with
class moransad with the following components:
- statistic
the value of the saddlepoint approximation of the standard deviate of local Moran's Ii.
- p.value
the p-value of the test.
- estimate
the value of the observed local Moran's Ii.
- 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.
- internal1
Saddlepoint omega, r and u
- df
degrees of freedom
- tau
maximum and minimum analytical eigenvalues
- i
zone tested
References
Tiefelsdorf, M. 2002 The Saddlepoint approximation of Moran's I and local Moran's Ii reference distributions and their numerical evaluation. Geographical Analysis, 34, pp. 187–206.
Author
Roger Bivand Roger.Bivand@nhh.no
Examples
eire <- st_read(system.file("shapes/eire.gpkg", package="spData")[1])
#> Reading layer `eire' from data source
#> `/home/rsb/lib/r_libs/spData/shapes/eire.gpkg' using driver `GPKG'
#> Simple feature collection with 26 features and 10 fields
#> Geometry type: MULTIPOLYGON
#> Dimension: XY
#> Bounding box: xmin: -4.12 ymin: 5768 xmax: 300.82 ymax: 6119.25
#> Projected CRS: Undefined Cartesian SRS with unknown unit
row.names(eire) <- as.character(eire$names)
eire.nb <- poly2nb(eire)
lw <- nb2listw(eire.nb)
e.lm <- lm(OWNCONS ~ ROADACC, data=eire)
e.locmor <- summary(localmoran.sad(e.lm, nb=eire.nb))
e.locmor
#> Local Morans I Stand. dev. (N) Pr. (N) Saddlepoint
#> 1 Carlow 0.21699668 0.74177148 4.582258e-01 0.95074844
#> 2 Cavan -0.37257361 -0.81297374 1.583767e+00 -1.00603119
#> 3 Clare 0.23197510 0.49502499 6.205825e-01 0.67166518
#> 4 Cork 0.78193548 1.75999915 7.840795e-02 1.74761575
#> 5 Donegal -1.69064059 -1.98244914 1.952571e+00 -1.72031078
#> 6 Dublin -0.16069692 -0.15041940 1.119566e+00 -0.35212627
#> 7 Galway 1.31371473 3.34305297 8.286208e-04 2.66849536
#> 8 Kerry 0.36534866 0.58147812 5.609183e-01 0.78073279
#> 9 Kildare -0.02557544 0.15146558 8.796085e-01 0.04167665
#> 10 Kilkenny 0.57684331 1.62868431 1.033799e-01 1.70897697
#> 11 Laoghis -0.05951798 0.01724651 9.862400e-01 -0.12155465
#> 12 Leitrim 0.38484587 1.27548777 2.021367e-01 1.47227033
#> 13 Limerick 0.11817987 0.34038037 7.335701e-01 0.45727712
#> 14 Longford 1.41643200 3.10732224 1.887905e-03 2.51113769
#> 15 Louth 0.56242920 0.87665682 3.806731e-01 1.07441571
#> 16 Mayo 0.87572704 2.02375701 4.299516e-02 2.05251226
#> 17 Meath 0.00367856 0.16081712 8.722374e-01 0.12813539
#> 18 Monaghan 0.55098311 1.06684464 2.860420e-01 1.23999193
#> 19 Offaly 0.15155556 0.61933942 5.356928e-01 0.80786519
#> 20 Roscommon 2.04368839 6.66107106 2.718381e-11 4.53187292
#> 21 Sligo -0.47579871 -0.73430274 1.537236e+00 -0.94578114
#> 22 Tipperary -0.03454106 0.04843351 9.613708e-01 -0.06919691
#> 23 Waterford 0.85723423 1.98516133 4.712653e-02 1.91385108
#> 24 Westmeath 0.45138572 1.20305006 2.289569e-01 1.36017204
#> 25 Wexford 0.64371834 1.55468550 1.200210e-01 1.63188492
#> 26 Wicklow 0.02441950 0.21823347 8.272472e-01 0.21197000
#> Pr. (Sad) Expectation Variance Skewness Kurtosis Minimum
#> 1 Carlow 3.417321e-01 -0.06471134 0.14423085 -0.7895263 7.059116 -5.461326
#> 2 Cavan 3.144006e-01 -0.04030838 0.16703857 -0.4622793 6.813004 -5.567356
#> 3 Clare 5.017969e-01 -0.04219377 0.30674823 -0.3579185 6.761932 -7.406885
#> 4 Cork 8.053059e-02 -0.04363826 0.22003250 -0.4363325 6.799081 -6.360927
#> 5 Donegal 8.537596e-02 -0.11935726 0.62821008 -0.7004303 6.979051 -11.236382
#> 6 Dublin 7.247436e-01 -0.08240217 0.27093033 -0.7352902 7.009201 -7.420687
#> 7 Galway 7.619183e-03 -0.04389010 0.16491503 -0.5059997 6.838308 -5.573707
#> 8 Kerry 4.349597e-01 -0.03212369 0.46724761 -0.2212594 6.714810 -8.915104
#> 9 Kildare 9.667565e-01 -0.07623733 0.11187546 -1.0416026 7.339962 -4.999621
#> 10 Kilkenny 8.745521e-02 -0.05911601 0.15247016 -0.7040737 6.982131 -5.538889
#> 11 Laoghis 9.032517e-01 -0.06620117 0.15016408 -0.7915137 7.061015 -5.574277
#> 12 Leitrim 1.409479e-01 -0.06828680 0.12621127 -0.8864130 7.157471 -5.186756
#> 13 Limerick 6.474719e-01 -0.04172917 0.22070746 -0.4167943 6.789132 -6.348870
#> 14 Longford 1.203427e-02 -0.04055162 0.21985521 -0.4059156 6.783792 -6.324457
#> 15 Louth 2.826364e-01 -0.04386717 0.47831137 -0.2983105 6.738631 -9.149779
#> 16 Mayo 4.011990e-02 -0.10340651 0.23408152 -0.9804377 7.264328 -7.165847
#> 17 Meath 8.980418e-01 -0.04799533 0.10324707 -0.6949022 6.974408 -4.551176
#> 18 Monaghan 2.149784e-01 -0.04136950 0.30828917 -0.3501006 6.758633 -7.415047
#> 19 Offaly 4.191682e-01 -0.04662212 0.10238870 -0.6782821 6.960676 -4.519986
#> 20 Roscommon 5.846302e-06 -0.04435301 0.09826301 -0.6591526 6.945294 -4.414164
#> 21 Sligo 3.442602e-01 -0.11041170 0.24760301 -1.0156782 7.307311 -7.409091
#> 22 Tipperary 9.448329e-01 -0.04872132 0.08571886 -0.7716947 7.042300 -4.198353
#> 23 Waterford 5.563919e-02 -0.05435079 0.21086415 -0.5533724 6.868342 -6.353514
#> 24 Westmeath 1.737755e-01 -0.04181671 0.16806722 -0.4779156 6.821788 -5.599610
#> 25 Wexford 1.027037e-01 -0.05432673 0.20159596 -0.5654870 6.876461 -6.225016
#> 26 Wicklow 8.321304e-01 -0.07022471 0.18808122 -0.7515626 7.023792 -6.198974
#> Maximum omega sad.r sad.u
#> 1 Carlow 3.908254 0.071122863 0.71853146 0.84900467
#> 2 Cavan 4.599954 -0.051532330 -0.69003582 -0.85816092
#> 3 Clare 6.394234 0.031939551 0.46982957 0.51656357
#> 4 Cork 5.313609 0.083281515 1.43928884 2.24323856
#> 5 Donegal 8.371808 -0.039371561 -1.39288713 -2.19776923
#> 6 Dublin 5.443035 -0.010354512 -0.14127218 -0.14554367
#> 7 Galway 4.520344 0.134873939 2.39189491 4.63522665
#> 8 Kerry 8.144135 0.028431952 0.54051534 0.61545648
#> 9 Kildare 3.169925 0.018723213 0.14926096 0.14688325
#> 10 Kilkenny 4.120105 0.105365819 1.40668493 2.15214600
#> 11 Laoghis 3.985449 0.001724096 0.01660985 0.01657177
#> 12 Leitrim 3.547872 0.109608339 1.18229964 1.66578026
#> 13 Limerick 5.347370 0.027585567 0.32820959 0.34241163
#> 14 Longford 5.351218 0.108368224 2.22687206 4.19385821
#> 15 Louth 8.096967 0.037745731 0.78968254 0.98878788
#> 16 Mayo 4.684091 0.105317102 1.75922892 2.94711915
#> 17 Meath 3.399289 0.020074178 0.15693992 0.15623206
#> 18 Monaghan 6.422179 0.053418031 0.94193428 1.24723730
#> 19 Offaly 3.401055 0.071432961 0.59871278 0.67858124
#> 20 Roscommon 3.349691 0.357114199 4.33885200 10.02517077
#> 21 Sligo 4.759210 -0.036185300 -0.60775394 -0.74635955
#> 22 Tipperary 3.029041 0.006482570 0.04683010 0.04657633
#> 23 Waterford 5.049095 0.093409563 1.61022194 2.62552879
#> 24 Westmeath 4.596009 0.080097979 1.05978192 1.45704611
#> 25 Wexford 4.921174 0.085478829 1.32647942 1.98902088
#> 26 Wicklow 4.513581 0.020437514 0.21417067 0.21406975
mean(e.locmor[,1])
#> [1] 0.3366057
sum(e.locmor[,1])/Szero(lw)
#> [1] 0.3366057
lm.morantest(e.lm, lw)
#>
#> Global Moran I for regression residuals
#>
#> data:
#> model: lm(formula = OWNCONS ~ ROADACC, data = eire)
#> weights: lw
#>
#> Moran I statistic standard deviate = 3.2575, p-value = 0.0005619
#> alternative hypothesis: greater
#> sample estimates:
#> Observed Moran I Expectation Variance
#> 0.33660565 -0.05877741 0.01473183
#>
# note equality for mean() only when the sum of weights equals
# the number of observations (thanks to Juergen Symanzik)
hist(e.locmor[,"Pr. (Sad)"])
e.wlm <- lm(OWNCONS ~ ROADACC, data=eire, weights=RETSALE)
e.locmorw1 <- summary(localmoran.sad(e.wlm, nb=eire.nb, resfun=weighted.residuals))
e.locmorw1
#> Local Morans I Stand. dev. (N) Pr. (N) Saddlepoint
#> 1 Carlow 0.160490657 0.41009538 6.817360e-01 0.57729730
#> 2 Cavan -0.144663771 -0.27825575 1.219184e+00 -0.45305168
#> 3 Clare 0.301676582 0.59021701 5.550452e-01 0.78987327
#> 4 Cork 1.520488153 3.49016956 4.827142e-04 2.83665634
#> 5 Donegal -0.435899664 -0.44665946 1.344879e+00 -0.67136090
#> 6 Dublin -0.340222996 -0.60886675 1.457387e+00 -0.85658016
#> 7 Galway 1.469009037 3.64546192 2.669119e-04 2.82274510
#> 8 Kerry 0.268957279 0.49517211 6.204786e-01 0.66861012
#> 9 Kildare 0.002996577 0.12659200 8.992633e-01 0.09978249
#> 10 Kilkenny 0.497968801 1.20610829 2.277757e-01 1.34091379
#> 11 Laoghis -0.026328708 -0.01713904 1.013674e+00 -0.06511750
#> 12 Leitrim 0.277306386 0.80644537 4.199861e-01 1.01176491
#> 13 Limerick 0.263122939 0.67591893 4.990921e-01 0.87759628
#> 14 Longford 0.605211711 1.23874274 2.154408e-01 1.35375850
#> 15 Louth 0.359469683 0.53572990 5.921452e-01 0.73280188
#> 16 Mayo 1.742480472 3.68118786 2.321499e-04 3.01500163
#> 17 Meath -0.112171618 -0.26680698 1.210382e+00 -0.45470531
#> 18 Monaghan 0.241044892 0.46013751 6.454175e-01 0.64094159
#> 19 Offaly 0.129191178 0.40988983 6.818868e-01 0.57205532
#> 20 Roscommon 1.469671750 4.39927211 1.086146e-05 3.13215267
#> 21 Sligo 0.095559559 0.31036587 7.562827e-01 0.38503064
#> 22 Tipperary 0.088352646 0.39958273 6.894639e-01 0.52592105
#> 23 Waterford 1.212658861 2.69846035 6.966104e-03 2.29292584
#> 24 Westmeath 0.256165310 0.61222265 5.403905e-01 0.81620859
#> 25 Wexford 0.619197906 1.31967483 1.869436e-01 1.42553832
#> 26 Wicklow 0.006531073 0.13142161 8.954418e-01 0.10986725
#> Pr. (Sad) Expectation Variance Skewness Kurtosis Minimum
#> 1 Carlow 0.563738639 -0.01840558 0.19029731 -0.1986977 6.709176 -5.665283
#> 2 Cavan 0.650511526 -0.02184465 0.19482455 -0.2329761 6.717975 -5.769371
#> 3 Clare 0.429601786 -0.02782578 0.31166901 -0.2346279 6.718435 -7.299407
#> 4 Cork 0.004558865 -0.07147410 0.20805228 -0.7280203 7.002789 -6.495227
#> 5 Donegal 0.501990650 -0.07638800 0.64784767 -0.4450323 6.803659 -10.931345
#> 6 Dublin 0.391676955 -0.11187469 0.14065367 -1.3324828 7.767845 -5.846924
#> 7 Galway 0.004761441 -0.04407925 0.17227545 -0.4973247 6.833103 -5.688263
#> 8 Kerry 0.503744214 -0.05644300 0.43184063 -0.4031537 6.782459 -8.859407
#> 9 Kildare 0.920517009 -0.04145378 0.12329287 -0.5519841 6.867423 -4.857131
#> 10 Kilkenny 0.179948446 -0.02321457 0.18672759 -0.2528322 6.723714 -5.669156
#> 11 Laoghis 0.948080445 -0.01882531 0.19166504 -0.2024943 6.710081 -5.689691
#> 12 Leitrim 0.311650473 -0.03314655 0.14819776 -0.4041387 6.782933 -5.190860
#> 13 Limerick 0.380162847 -0.04800976 0.21188592 -0.4885390 6.827925 -6.298874
#> 14 Longford 0.175813436 -0.01321709 0.24923967 -0.1247567 6.694960 -6.392250
#> 15 Louth 0.463679274 -0.02272663 0.50895713 -0.1500895 6.699098 -9.179410
#> 16 Mayo 0.002569779 -0.09458039 0.24904116 -0.8745463 7.144787 -7.272523
#> 17 Meath 0.649321260 -0.02548973 0.10555100 -0.3685280 6.766525 -4.353122
#> 18 Monaghan 0.521560632 -0.02333303 0.33012248 -0.1912612 6.707452 -7.451275
#> 19 Offaly 0.567284497 -0.01927989 0.13120470 -0.2505068 6.723017 -4.750083
#> 20 Roscommon 0.001735296 -0.02385522 0.11525625 -0.3302939 6.750604 -4.517676
#> 21 Sligo 0.700214717 -0.06927688 0.28207107 -0.6087587 6.906925 -7.416881
#> 22 Tipperary 0.598943063 -0.03719246 0.09871568 -0.5534442 6.868390 -4.347214
#> 23 Waterford 0.021852275 -0.04027429 0.21558757 -0.4070996 6.784366 -6.264083
#> 24 Westmeath 0.414380842 -0.01522814 0.19650786 -0.1618342 6.701275 -5.716689
#> 25 Wexford 0.154001651 -0.02786850 0.24041626 -0.2674357 6.728234 -6.450174
#> 26 Wicklow 0.912514660 -0.04751424 0.16911517 -0.5404006 6.859847 -5.677417
#> Maximum omega sad.r sad.u
#> 1 Carlow 5.223549 0.033637462 0.38794383 0.41751442
#> 2 Cavan 5.245099 -0.022294725 -0.26091513 -0.27432856
#> 3 Clare 6.631589 0.035302524 0.54866959 0.62630505
#> 4 Cork 4.779848 0.134384022 2.56890121 5.11058941
#> 5 Donegal 9.098033 -0.017507303 -0.40402088 -0.45010348
#> 6 Dublin 3.161931 -0.040828131 -0.50710580 -0.60543071
#> 7 Galway 4.630361 0.138454493 2.55314856 5.08170760
#> 8 Kerry 7.504775 0.027195108 0.47167584 0.51758880
#> 9 Kildare 3.862240 0.014230854 0.12280697 0.12246022
#> 10 Kilkenny 5.112007 0.071351828 1.03314661 1.41988761
#> 11 Laoghis 5.237883 -0.001502568 -0.01645549 -0.01646868
#> 12 Leitrim 4.395343 0.066207108 0.74158109 0.90609823
#> 13 Limerick 5.146640 0.050265468 0.63703133 0.74253221
#> 14 Longford 6.075040 0.060534639 1.04112815 1.44165700
#> 15 Louth 8.633971 0.025231866 0.49793592 0.55971045
#> 16 Mayo 5.002594 0.135902733 2.75603129 5.62669411
#> 17 Meath 3.741368 -0.028724497 -0.24912602 -0.26221742
#> 18 Monaghan 6.891283 0.028042744 0.43280552 0.47360371
#> 19 Offaly 4.287365 0.040883462 0.38909358 0.41780262
#> 20 Roscommon 3.945151 0.180270100 2.87643937 6.00202551
#> 21 Sligo 5.754236 0.023145822 0.30299868 0.31062426
#> 22 Tipperary 3.454595 0.048932861 0.38768333 0.40902706
#> 23 Waterford 5.297500 0.101874758 1.99944904 3.59542986
#> 24 Westmeath 5.351214 0.044919886 0.56403221 0.65024353
#> 25 Wexford 5.781330 0.066083430 1.11524637 1.57637406
#> 26 Wicklow 4.537075 0.012609906 0.12748740 0.12720134
e.locmorw2 <- summary(localmoran.sad(e.wlm, nb=eire.nb, resfun=rstudent))
e.locmorw2
#> Local Morans I Stand. dev. (N) Pr. (N) Saddlepoint
#> 1 Carlow 0.121997164 0.32185426 0.7475631028 0.45871930
#> 2 Cavan -0.110588620 -0.20105599 1.1593452023 -0.34808741
#> 3 Clare 0.308759283 0.60290381 0.5465726820 0.80379674
#> 4 Cork 1.404203115 3.23522979 0.0012154487 2.69598105
#> 5 Donegal -0.421182109 -0.42837428 1.3316213558 -0.65187732
#> 6 Dublin -0.443534307 -0.88433550 1.6234848706 -1.05167518
#> 7 Galway 1.376190254 3.42183495 0.0006220006 2.70663064
#> 8 Kerry 0.241623387 0.45357724 0.6501331373 0.61515126
#> 9 Kildare 0.008842913 0.14324202 0.8860990418 0.12690939
#> 10 Kilkenny 0.382893124 0.93980330 0.3473184643 1.12810394
#> 11 Laoghis -0.019904450 -0.00246494 1.0019667357 -0.04176107
#> 12 Leitrim 0.200483743 0.60688769 0.5439254449 0.80241456
#> 13 Limerick 0.238810092 0.62310059 0.5332184222 0.81824678
#> 14 Longford 0.466942853 0.96178354 0.3361583457 1.14088225
#> 15 Louth 0.271710988 0.41271732 0.6798137369 0.58520655
#> 16 Mayo 1.705850161 3.60778634 0.0003088206 2.97346461
#> 17 Meath -0.160603054 -0.41587901 1.3225014587 -0.63254531
#> 18 Monaghan 0.181378604 0.35629110 0.7216225742 0.50697175
#> 19 Offaly 0.107919508 0.35116431 0.7254650854 0.49312417
#> 20 Roscommon 1.249826037 3.75170355 0.0001756371 2.81402777
#> 21 Sligo 0.079431883 0.27999953 0.7794778655 0.33741411
#> 22 Tipperary 0.085153638 0.38940098 0.6969795442 0.51126046
#> 23 Waterford 1.022922345 2.28982205 0.0220316342 2.06385578
#> 24 Westmeath 0.201539331 0.48899468 0.6248454598 0.67791734
#> 25 Wexford 0.481114325 1.03805702 0.2992435100 1.21094348
#> 26 Wicklow -0.011694661 0.08710223 0.9305902563 0.03786608
#> Pr. (Sad) Expectation Variance Skewness Kurtosis Minimum
#> 1 Carlow 0.646435751 -0.01840558 0.19029731 -0.1986977 6.709176 -5.665283
#> 2 Cavan 0.727774542 -0.02184465 0.19482455 -0.2329761 6.717975 -5.769371
#> 3 Clare 0.421514374 -0.02782578 0.31166901 -0.2346279 6.718435 -7.299407
#> 4 Cork 0.007018166 -0.07147410 0.20805228 -0.7280203 7.002789 -6.495227
#> 5 Donegal 0.514480318 -0.07638800 0.64784767 -0.4450323 6.803659 -10.931345
#> 6 Dublin 0.292948602 -0.11187469 0.14065367 -1.3324828 7.767845 -5.846924
#> 7 Galway 0.006796983 -0.04407925 0.17227545 -0.4973247 6.833103 -5.688263
#> 8 Kerry 0.538454834 -0.05644300 0.43184063 -0.4031537 6.782459 -8.859407
#> 9 Kildare 0.899012117 -0.04145378 0.12329287 -0.5519841 6.867423 -4.857131
#> 10 Kilkenny 0.259276027 -0.02321457 0.18672759 -0.2528322 6.723714 -5.669156
#> 11 Laoghis 0.966689166 -0.01882531 0.19166504 -0.2024943 6.710081 -5.689691
#> 12 Leitrim 0.422313193 -0.03314655 0.14819776 -0.4041387 6.782933 -5.190860
#> 13 Limerick 0.413216288 -0.04800976 0.21188592 -0.4885390 6.827925 -6.298874
#> 14 Longford 0.253918927 -0.01321709 0.24923967 -0.1247567 6.694960 -6.392250
#> 15 Louth 0.558408841 -0.02272663 0.50895713 -0.1500895 6.699098 -9.179410
#> 16 Mayo 0.002944584 -0.09458039 0.24904116 -0.8745463 7.144787 -7.272523
#> 17 Meath 0.527030613 -0.02548973 0.10555100 -0.3685280 6.766525 -4.353122
#> 18 Monaghan 0.612174643 -0.02333303 0.33012248 -0.1912612 6.707452 -7.451275
#> 19 Offaly 0.621924855 -0.01927989 0.13120470 -0.2505068 6.723017 -4.750083
#> 20 Roscommon 0.004892500 -0.02385522 0.11525625 -0.3302939 6.750604 -4.517676
#> 21 Sligo 0.735804747 -0.06927688 0.28207107 -0.6087587 6.906925 -7.416881
#> 22 Tipperary 0.609168686 -0.03719246 0.09871568 -0.5534442 6.868390 -4.347214
#> 23 Waterford 0.039031392 -0.04027429 0.21558757 -0.4070996 6.784366 -6.264083
#> 24 Westmeath 0.497824103 -0.01522814 0.19650786 -0.1618342 6.701275 -5.716689
#> 25 Wexford 0.225917068 -0.02786850 0.24041626 -0.2674357 6.728234 -6.450174
#> 26 Wicklow 0.969794461 -0.04751424 0.16911517 -0.5404006 6.859847 -5.677417
#> Maximum omega sad.r sad.u
#> 1 Carlow 5.223549 0.0272472954 0.306852385 0.321490350
#> 2 Cavan 5.245099 -0.0166242430 -0.190223798 -0.196022741
#> 3 Clare 6.631589 0.0358559846 0.559584155 0.641527095
#> 4 Cork 4.779848 0.1283688794 2.421993662 4.702934834
#> 5 Donegal 9.098033 -0.0169574018 -0.388662370 -0.430528174
#> 6 Dublin 3.161931 -0.0507848831 -0.696824139 -0.892299501
#> 7 Galway 4.630361 0.1333224875 2.431707338 4.745166958
#> 8 Kerry 7.504775 0.0252982005 0.433626352 0.469138111
#> 9 Kildare 3.862240 0.0161278548 0.139072871 0.138837812
#> 10 Kilkenny 5.112007 0.0622219791 0.835166590 1.066654825
#> 11 Laoghis 5.237883 -0.0002164925 -0.002368023 -0.002368244
#> 12 Leitrim 4.395343 0.0543844388 0.571625643 0.652237768
#> 13 Limerick 5.146640 0.0473787285 0.590605630 0.675595582
#> 14 Longford 6.075040 0.0528365356 0.840671447 1.082014178
#> 15 Louth 8.633971 0.0204960239 0.389078238 0.419930705
#> 16 Mayo 5.002594 0.1340509166 2.712635049 5.503894365
#> 17 Meath 3.741368 -0.0415411327 -0.379736494 -0.417998694
#> 18 Monaghan 6.891283 0.0226076552 0.338579266 0.358443998
#> 19 Offaly 4.287365 0.0357600182 0.335019324 0.353243066
#> 20 Roscommon 3.945151 0.1623235556 2.543240406 5.063795948
#> 21 Sligo 5.754236 0.0209568244 0.273376649 0.278204612
#> 22 Tipperary 3.454595 0.0478130890 0.377982061 0.397511387
#> 23 Waterford 5.297500 0.0941811771 1.762051071 2.998984773
#> 24 Westmeath 5.351214 0.0379323563 0.457473561 0.506014991
#> 25 Wexford 5.781330 0.0582538352 0.911459483 1.197527949
#> 26 Wicklow 4.537075 0.0083101099 0.084281843 0.083952776
run <- FALSE
if (requireNamespace("spatialreg", quietly=TRUE)) run <- TRUE
if (run) {
e.errorsar <- spatialreg::errorsarlm(OWNCONS ~ ROADACC, data=eire,
listw=lw)
if (packageVersion("spatialreg") < "1.1.7")
spatialreg::print.sarlm(e.errorsar)
else
print(e.errorsar)
}
#>
#> Call:
#> spatialreg::errorsarlm(formula = OWNCONS ~ ROADACC, data = eire,
#> listw = lw)
#> Type: error
#>
#> Coefficients:
#> lambda (Intercept) ROADACC
#> 0.783970989 2.892719569 0.002800913
#>
#> Log likelihood: -64.12465
if (run) {
lm.target <- lm(e.errorsar$tary ~ e.errorsar$tarX - 1)
Omega <- tcrossprod(spatialreg::invIrW(lw, rho=e.errorsar$lambda))
e.clocmor <- summary(localmoran.sad(lm.target, nb=eire.nb, Omega=Omega))
e.clocmor
}
#> Local Morans I Stand. dev. (N) Pr. (N) Saddlepoint Pr. (Sad)
#> 1 Carlow 0.17958462 -0.5947094 1.4479623 -0.01890335 0.9849182097
#> 2 Cavan -0.24752628 -0.9775195 1.6716880 -1.30903979 0.1905208730
#> 3 Clare -0.27901334 -0.9987481 1.6820833 -1.41535136 0.1569655035
#> 4 Cork 0.37808655 -0.5304596 1.4042067 0.06399747 0.9489722431
#> 5 Donegal -1.01894688 -1.4634181 1.8566470 -1.88871177 0.0589304608
#> 6 Dublin -0.18171297 -0.9790853 1.6724621 -1.11436913 0.2651208631
#> 7 Galway 1.02193390 0.9527103 0.3407369 1.44844014 0.1474939944
#> 8 Kerry -0.94967914 -1.1410950 1.7461696 -2.37909992 0.0173549707
#> 9 Kildare 0.07005053 -0.6531380 1.4863327 -0.10338270 0.9176592421
#> 10 Kilkenny 0.43022231 -0.3097714 1.2432652 0.46873471 0.6392592765
#> 11 Laoghis -0.12239133 -0.9818401 1.6738214 -0.97718184 0.3284791346
#> 12 Leitrim -0.24203970 -0.9591963 1.6625401 -1.53246533 0.1254076470
#> 13 Limerick -0.03214546 -0.7729433 1.5604441 -0.80301568 0.4219656705
#> 14 Longford 0.38307454 -0.4899146 1.3758057 0.16621954 0.8679841832
#> 15 Louth 0.21301552 -0.6509309 1.4849089 -0.21224290 0.8319175422
#> 16 Mayo 0.93971200 0.3895188 0.6968924 1.15011408 0.2500968882
#> 17 Meath 0.12484415 -0.6182203 1.4635699 -0.09720926 0.9225602152
#> 18 Monaghan -0.16109919 -0.8608004 1.6106520 -1.20575831 0.2279106933
#> 19 Offaly -0.00632492 -0.7740865 1.5611204 -0.33915072 0.7344961920
#> 20 Roscommon 1.02089429 0.6454801 0.5186161 1.21215474 0.2254531515
#> 21 Sligo -2.01629233 -1.8957526 1.9420072 -3.59571732 0.0003234989
#> 22 Tipperary -0.10810709 -0.9082666 1.6362626 -1.09721448 0.2725476427
#> 23 Waterford 0.44099279 -0.3488980 1.2728341 0.41219202 0.6801986841
#> 24 Westmeath -0.06329661 -0.8267635 1.5916289 -0.81444158 0.4153920274
#> 25 Wexford 0.30764883 -0.5219835 1.3983182 0.12395154 0.9013536461
#> 26 Wicklow -0.01696406 -0.7708237 1.5591886 -0.68244661 0.4949565907
#> Expectation Variance Skewness Kurtosis Minimum Maximum
#> 1 Carlow 0.8594106 1.3067303 2.362830 10.416149 6.743373e-17 20.625856
#> 2 Cavan 1.1247112 1.9706416 2.347202 10.347468 1.645654e+00 25.347414
#> 3 Clare 1.2679076 2.3989670 2.334022 10.287656 2.485514e+00 27.944268
#> 4 Cork 1.2841620 2.9175890 2.362830 10.416149 -2.406699e-16 30.819888
#> 5 Donegal 1.7253177 3.5165365 2.172101 9.492322 8.227735e+00 33.179890
#> 6 Dublin 0.9462667 1.3272768 2.331563 10.276363 1.928660e+00 20.781740
#> 7 Galway 0.4507425 0.3594525 2.362830 10.416149 1.587770e-16 10.817821
#> 8 Kerry 2.6933183 10.1923447 2.307813 10.165571 7.170614e+00 57.469026
#> 9 Kildare 0.5337376 0.5040110 2.362830 10.416149 -6.444628e-18 12.809701
#> 10 Kilkenny 0.7317135 0.9472545 2.362830 10.416149 5.035617e-16 17.561125
#> 11 Laoghis 0.6035313 0.5466372 2.336004 10.296727 1.143655e+00 13.341096
#> 12 Leitrim 1.2258675 2.3419747 2.347302 10.347916 1.788145e+00 27.632674
#> 13 Limerick 1.5147254 4.0050955 2.362668 10.415466 2.341575e-01 36.119253
#> 14 Longford 1.0996747 2.1395031 2.362830 10.416149 5.674463e-16 26.392192
#> 15 Louth 1.5875248 4.4588771 2.362830 10.416149 4.309554e-16 38.100594
#> 16 Mayo 0.6190019 0.6779043 2.362830 10.416149 -2.035156e-16 14.856045
#> 17 Meath 0.7025948 0.8733620 2.362830 10.416149 -7.624840e-18 16.862274
#> 18 Monaghan 1.5519577 3.9603958 2.357838 10.394611 1.306155e+00 35.940829
#> 19 Offaly 0.3048481 0.1615939 2.362560 10.415009 6.073803e-02 7.255616
#> 20 Roscommon 0.5492905 0.5338125 2.362830 10.416149 9.144870e-16 13.182973
#> 21 Sligo 2.3130311 5.2152695 1.886102 7.938452 1.739456e+01 38.118185
#> 22 Tipperary 0.7147979 0.8208668 2.354040 10.377921 7.922254e-01 16.362924
#> 23 Waterford 0.8228671 1.1979644 2.362830 10.416149 1.408133e-15 19.748811
#> 24 Westmeath 0.8426747 1.2007879 2.360962 10.408167 4.379239e-01 19.786270
#> 25 Wexford 1.0063848 1.7918953 2.362830 10.416149 1.028640e-17 24.153236
#> 26 Wicklow 0.9927147 1.7157589 2.362598 10.415171 1.833509e-01 23.641801
#> omega sad.r sad.u
#> 1 Carlow -0.017838447 -0.38297869 -0.33313448
#> 2 Cavan -0.066132684 -1.21593175 -1.36168605
#> 3 Clare -0.066612498 -1.30513958 -1.50704646
#> 4 Cork -0.010368850 -0.33915229 -0.29581081
#> 5 Donegal -0.045800559 -1.66568212 -2.41507712
#> 6 Dublin -0.056683668 -1.03296356 -1.12358099
#> 7 Galway 0.031762997 1.14153962 1.62047125
#> 8 Kerry -0.079689480 -2.19374456 -3.29442701
#> 9 Kildare -0.025051491 -0.36678693 -0.33300845
#> 10 Kilkenny 0.003214928 0.09217307 0.09542846
#> 11 Laoghis -0.065438986 -0.89335507 -0.96282454
#> 12 Leitrim -0.092395573 -1.43474097 -1.65069014
#> 13 Limerick -0.047140362 -0.97737323 -0.82423542
#> 14 Longford -0.007176482 -0.22762630 -0.20810767
#> 15 Louth -0.018552546 -0.58005974 -0.46861210
#> 16 Mayo 0.019992304 0.84088281 1.09059594
#> 17 Meath -0.026958325 -0.44558661 -0.38151850
#> 18 Monaghan -0.062388996 -1.21509194 -1.20138917
#> 19 Offaly -0.044380046 -0.41568118 -0.40266554
#> 20 Roscommon 0.023338184 0.88169755 1.17993235
#> 21 Sligo -0.131646728 -3.40243100 -6.56750200
#> 22 Tipperary -0.089378129 -1.06748205 -1.10190609
#> 23 Waterford 0.001151041 0.03534520 0.03581914
#> 24 Westmeath -0.058470593 -0.88397327 -0.83127666
#> 25 Wexford -0.009550496 -0.26689930 -0.24045996
#> 26 Wicklow -0.050401553 -0.84395069 -0.73641410
if (run) {
hist(e.clocmor[,"Pr. (Sad)"])
}
