PENGAJUAN HKI KATEGORI SOFTWARE...

HIU UNPAD-IGN Mindra Jaya, dkk (2018)

MoranST package 1

MANUAL BOOK PENGAJUAN HKI

KATEGORI SOFTWARE MoranST

GLOBAL AND LOCAL SPATIAL AND SPATIOTEMPORAL AUTOCORRELATIONS

Oleh I Gede Nyoman Mindra Jaya, M.Si

Bertho Tantular, M.Si Zulhanif, M.Sc

Dr. Toni Toharudin, M.Sc

Departemen Statistika Fakultas Matematika dan Ilmu Pengetahuan Alam

Universitas Padjadjaran 2018

HIU Pemetaan Penyakit Menular di Kota Bandung


MoranST package ii

Daftar Isi

Daftar Isi ............................................................................................................................ii

Kata Pengantar ................................................................................................................. iii

Pendahuluan .................................................................................................................. 1

Tujuan ............................................................................................................................. 1

Metode MoranST ........................................................................................................... 1

Referensi ........................................................................................................................ 2

Instalasi package MoranST ....................................................................................... 2

Contoh Penggunaan .................................................................................................... 3

Lampiran A ........................................................................................................................ 7


MoranST package iii

Kata Pengantar Puji Syukur kepada Tuhan yang Maha Esa, dengan ijin Nya, pembuatan Software Komputer berupa package R MoranST dapat Tim selesaikan. Package ini merupakan software yang sangat bermanfaat dalam membantu peneliti untuk menghitung dan menguji autokorelasi secara spatial dan temporal. Kami memberi nama package ini MoranST didasarkan pada statistik yang kami kembangkan adalah statistika Moran’S I yang sudah sangat umum digunakan dalam menguji dependensi spatial. Namun, statistik ini belum mampu digunakan untuk menguji dependsi spatial dan temporal secara simultan. Terimakasih kami ucapkan kepada Rektor Universitas Padjadjaran, yang telah mendanai project ini melalui program Hibah Internal Unpad dengan Nomor Kontrak: 1732 d/UN6.RKT/LT/2018. Terimakasih kepada semua Tim yang terlibat dan semua pihak yang mendukung penyelesaian package ini. Masukkan dan saran serta kritik untuk package ini dapat disampaikan melalu email: [email protected]

Tim


MoranST package 1

Pendahuluan Penelitian dalam ruang lingkup sptial dan temporal sangat berkembang pesat yang didukung oleh berbagai software computer diantaranya R, GIS, GEODA, SAS dan sofrware yang lainnya. Namun, perkembangan software seringkali tidak secepat dengan perkembangan metodologi. Sehingga, peneliti dituntut untuk mampu mengembangkan software nya sendiri. Software R adalah salah satu open source software yang sangat diminati dengan perkembangan penggunanya sangat cepat dalam 10 tahun terakhir ini. Sofware ini memberikan fasilitas kepada penggunanya untuk mengembangkan package sendiri. Dalam studi spatial dan temporal, perhitungan dan pengujian dependensi spatial dan temporal secara simultan sangat diperlukan sebagai dasar pemilihan metode yang tepat untuk data yang tersedia. Namun, sampai saat ini belum ditemukan software yang menyediakan perhitungan dan pengujian spatial dan temporal secara simultan. Pengujian secara partial dapat dengan mudah ditemukan dalam berbagai software yang disebutkan di atas. Statistik yang umumnya digunakan adalah staistik Moran’s I untuk koefisien dependensi Global dan Local Moran’s I untuk depends Local. Karena ketidaktersediaan, pengembangan software ini sangat diperlukan. Melalui project RFU 2018, software MoranST berupa package R dikembangkan oleh tim penelitian RFU. MoranST merupakan singkatan dari Moran Spatiotemporal. Package ini dikembangkan dengan tujuan melakukan perhitungan koefisien autokorelasi spatial, dan spatiotemporal. Melalui package ini peneliti dapat melakukan perhitungan dan pengujian spatial autokorelasi baik Global ataupun Local (Global Moran, dan Local Moran I) serta melakukan perhitngan spatialtemporal autokorelasi secara simultan (Global MoranST, Local MoranST) Global Moran dapat diperoleh jika dalam penelitian hanya menggunakan data spatial dengan dimensi 𝑛 × 1. Sedangkan Global MoranST diperoleh jika input data yang digunkan memiliki struktur 𝑛 × 𝑇 dengan T adalah dimensi Temporal. Package yang dikembangkan ini diberi nama package MoranST dapat diinstal dalam system operasi Windows dan Mac OS .

Tujuan Sofware ini dikembangkan dengan kemampuan atau tujuan

1. Menghitung dan Menguji spatial autokorelasi menggunakan metode permutation test (Monte Carlo simulation)

2. Menghitung dan Menguji spatiotemporal autokorelasi menggunakan metode permutation test (Monte Carlo simulation)

Metode MoranST Formulasi untuk perhitungan Global Moran’s I (Lee & Li, 2016)

𝐼 =𝑛

∑ ∑ 𝑤)*+*,-

+),-

∑ ∑ 𝑤)*+*,- (𝑥) − �̅�)3𝑥* − �̅�4+

),-

∑ (𝑥) − �̅�)5+),-

Dengan n : menyatakan banyaknya unit spatial xi : menyatakan variable observasi pada lokasi ke-i wij : menyatakan element dari matrik bobot spatial W I : Koefisien Global Moran’s I


MoranST package 2

Formulasi untuk perhitungan Local Moran’s I (Lee & Li, 2016)

𝐼) =(𝑥) − �̅�)

∑ (𝑥6 − �̅�)5+6,- /𝑛

8𝑤)*

+

*,-

3𝑥* − �̅�4

Dengan Ii : Koefisien Local Moran’s I Formulasi untuk perhitungan Global MoranST I (Jaya, 2018)

𝑀𝑜𝑟𝑎𝑛𝑆𝑇 =𝑛𝑇 ∑ ∑ ∑ ∑ 𝑤>()?,*A)(𝑥)? − �̅�)3𝑥*A − �̅�4B

A,-+*,-

B?,-

+),-

∑ ∑ ∑ ∑ 𝑤>()?,*A) ∑ ∑ (𝑥)? − 𝑥)5B?

+),-

BA,-

+*,-

B?,-

+),-

Formulasi untuk perhitungan Local MoranST I (Jaya, 2018)

𝑀𝑜𝑟𝑎𝑛𝑆𝑇)? =(𝑟)? − �̅�) ∑ ∑ 𝑤>()?,*A)3𝑥*A − �̅�4B

A,-+*,-

∑ ∑ (𝑥)? − �̅�)5B?

+),- /(𝑛𝑇 − 1)

Untuk pengujian signifikansi Hipotesis: H0: 𝜌 = 0 H1: 𝜌 > 0 Melalui metode permutation test (Monte Carlo Simulation). Untuk lebih jelas lihat referensi.

Referensi Jaya, I. M. (2018). Estimation and Testing for Moran Spatial and Spatiotemporal Index. Working Paper, 1-10. Lee, J., & Li, S. (2016). Extending Moran's Index for Measuring Spatiotemporal Clustering of Geographic Events.

Geographical Analysis, 1-22.

Instalasi package MoranST Untuk dapat menggunakan package MoranST maka peneliti terlebih dahulu harus mengikuti beberapa langkah berikut:

1. Menginstal R-sofware dengan versi minimum R.3.5.0 2. Memperoleh package MoranST_0.1.0.zip untuk windows dan MoranST_0.1.0.tar.gz untuk mac OS

dengan menghubungi email: [email protected] 3. Tempatkan package MoranST di mydocument atau di Library R 4. Install package Moran’ST

a. Untuk System Operasi Windows

Pada windows R ketikkan: install.packages('C:/User/Documents/MoranST_0.1.0.zip', repos = NULL, type = "win.binary")

b. Untuk System Operasi Mac OS Pada comment lines ketikkan R CMD INSTALL MoranST_0.1.0.tar.gz


MoranST package 3

Jika tidak memperoleh package nya, maka macro R pada Lampiran A dapat digunakan dengan cara mengkopykan Macro tersebut ke windows R.

Contoh Penggunaan Pada bagian ini akan diberikan contoh penggunaan package MoranST dengan data simulasi. Dibangkitkan data dengan model pure Spatiotemporal Lag Model

𝑦)? = 𝜌8𝑤)*𝑦*?G-

+

*,-

+ 𝜀)?

Dengan 𝑦)? : variable pengmatan pada lokasi i dan periode t 𝑦)?G-: variable pengmatan pada lokasi i dan periode t-1 𝜌 : lag coefficient 1. Buka program R 2. Buka script R dan ketikkan syntax melalui script ini #Simulation example library(spdep) library(MoranST) Wsim<-function(m){ x.latitude <- 1:m x.longitude <- 1:m Grid <- expand.grid(x.latitude, x.longitude) n <- nrow(Grid) #### set up distance and neighbourhood (W, based on sharing a common border) matrices distance <-array(0, c(n,n)) temp <-array(0, c(n,n)) W <-array(0, c(n,n)) for(i in 1:n) { for(j in 1:n) { temp[i,j] <- (Grid[i,1] - Grid[j,1])^2 + (Grid[i,2] - Grid[j,2])^2 distance[i,j] <- sqrt(temp[i,j]) if(temp[i,j]==1) W[i,j] <- 1 } } list(temp=temp,W=W,distance=distance) } #==== Example for n=5, and T=5 m<-5 B<-Wsim(m) W<-B$W W<-as.matrix(W) WZ<-W/rowSums(W) WN<-mat2listw(WZ) n<-nrow(W) rho=0.5 y1<-solve(diag(n)-rho*WZ)%*%rnorm(n,0,1)


MoranST package 4

y2<-0.3*y1+rnorm(n,0,1) y3<-0.2*y2+rnorm(n,0,1) y4<-0.7*y3+rnorm(n,0,1) y5<-0.8*y4+rnorm(n,0,1) y<-rbind(y1,y2,y3,y4,y5) x<-as.vector(y)

3. Struktur data input Data input merupakan vector dengan struktur sebagai berikut:

Lokasi Time Data Input A 1 X1 B 1 X2 C 1 X3 A 2 X4 B 2 X5 C 2 X6

4. Perhitungan MoranST baik global dan local dapat dilakukan sebagai berikut:

MoranSTMCResult<-MoranST.MC(x,W,nsim=100) Output

************************************************************************** * MoranST with Monte Carlo Simulation * * HIU UNPAD 2018 * * IGNM Jaya, B Tantular, Zulhanif, T Toharudin * *************************************************************************** Data input : x Weight input : W MoranST : 0.251271 p.Value : 0.00990099 ************************************************************************** Decision with an alpha level of .05 (5%) : Reject H0 [for H1:Rho > 0] **************************************************************************

Null Distribution of Moran's ST= 0.2513

p.valueST = 0.0099Moran's I Simulation

Freq

uenc

y

0.0 0.2 0.4 0.6 0.8 1.0

010

2030

40


MoranST package 5

LocalMoranSTMCResult<-LocalMoranST.MC(x,W,nsim=100) ************************************************************************** * MoranST with Monte Carlo Simulation * * HIU UNPAD 2018 * * IGNM Jaya, B Tantular, Zulhanif, T Toharudin * *************************************************************************** Data input : x Weight input : W MoranST : 0.251271 p.Value : 0.00990099 ************************************************************************** Decision with an alpha level of .05 (5%) : Reject H0 [for H1:Rho > 0] ************************************************************************** > LocalMoranSTMCResult $LocalMoranST [,1] [,2] [,3] [,4] [,5] [1,] 0.247017501 1.71072696 -3.40833640 0.182635466 0.15628605 [2,] -1.992568025 3.14376935 3.20243766 10.877169210 7.12276131 [3,] 1.282305623 5.62126372 -0.43260545 2.481690126 2.96894020 [4,] 2.037426643 5.63018635 0.81511892 -0.193343749 0.40133523 [5,] 0.256214427 1.27193061 -0.04575960 -0.087590218 -2.71786783 [6,] -0.008208284 4.27400674 1.49665677 0.134010467 -1.63328674 [7,] -2.175673981 1.38131012 10.98535615 14.603000825 1.82915483 [8,] -1.129536663 0.26615585 1.76550888 7.178152886 -1.68593014 [9,] 0.517083837 0.70598271 0.04233331 0.862747306 1.56033150 [10,] 1.126622977 -0.42934287 -1.07720698 1.359381866 2.20601996 [11,] 0.080265931 -0.31267143 1.70602684 2.148133324 -0.03621184 [12,] 1.087358221 -0.47489967 3.88190072 8.982682977 2.71499968 [13,] 0.013021662 0.28186066 -0.12674146 1.068748729 0.36597843 [14,] -0.213527626 0.12624727 -1.05317013 0.585454254 -1.42542437 [15,] 0.351174050 -0.07268128 -0.01259812 -0.001121727 0.03387416 [16,] 5.823067186 -0.27961186 -0.35758635 -0.073903622 3.42899266 [17,] 1.553998679 -0.11175982 -0.18956924 0.976237442 3.06644897 [18,] 2.105349861 2.08022150 1.10664261 2.662899388 0.25911034 [19,] 1.231315851 3.06524297 1.41848189 3.330104083 0.26599429 [20,] -0.910321700 -0.38248696 -0.37166344 -1.154544546 -0.08659621 [21,] -0.530615032 1.10711123 1.68751651 -0.838390421 2.05072336 [22,] -0.081909368 -0.35267781 0.19053472 3.569739989 7.69780922 [23,] -0.200597767 -4.88703142 -1.56698995 0.644595647 0.18945896 [24,] 0.742517333 0.78689136 0.21572767 2.817599582 2.14778981 [25,] 0.348942009 -0.96802954 0.11492909 1.668515349 1.36794839 $p.value [,1] [,2] [,3] [,4] [,5] [1,] 0.31683168 0.13861386 0.96039604 0.43564356 0.40594059 [2,] 0.81188119 0.06930693 0.06930693 0.00990099 0.01980198 [3,] 0.16831683 0.01980198 0.64356436 0.14851485 0.06930693 [4,] 0.07920792 0.01980198 0.28712871 0.57425743 0.31683168 [5,] 0.35643564 0.16831683 0.50495050 0.60396040 0.90099010 [6,] 0.52475248 0.03960396 0.17821782 0.43564356 0.89108911 [7,] 0.87128713 0.14851485 0.00990099 0.00990099 0.13861386 [8,] 0.83168317 0.33663366 0.14851485 0.00990099 0.90099010 [9,] 0.40594059 0.23762376 0.40594059 0.25742574 0.22772277 [10,] 0.24752475 0.72277228 0.77227723 0.18811881 0.14851485 [11,] 0.55445545 0.65346535 0.19801980 0.09900990 0.64356436 [12,] 0.28712871 0.60396040 0.06930693 0.00990099 0.10891089 [13,] 0.43564356 0.38613861 0.51485149 0.18811881 0.29702970 [14,] 0.63366337 0.44554455 0.78217822 0.36633663 0.83168317 [15,] 0.26732673 0.52475248 0.47524752 0.54455446 0.53465347 [16,] 0.01980198 0.65346535 0.56435644 0.56435644 0.07920792 [17,] 0.23762376 0.56435644 0.55445545 0.19801980 0.03960396 [18,] 0.09900990 0.16831683 0.20792079 0.08910891 0.33663366 [19,] 0.13861386 0.07920792 0.18811881 0.06930693 0.44554455 [20,] 0.75247525 0.58415842 0.68316832 0.80198020 0.56435644 [21,] 0.77227723 0.24752475 0.13861386 0.76237624 0.09900990 [22,] 0.54455446 0.61386139 0.42574257 0.04950495 0.00990099 [23,] 0.64356436 0.97029703 0.88118812 0.25742574 0.25742574 [24,] 0.30693069 0.25742574 0.43564356 0.14851485 0.11881188 [25,] 0.32673267 0.76237624 0.39603960 0.10891089 0.14851485 $Decision [,1] [,2] [,3] [,4] [,5] [1,] "Accept H0" "Accept H0" "Accept H0" "Accept H0" "Accept H0" [2,] "Accept H0" "Accept H0" "Accept H0" "Reject H0" "Reject H0" [3,] "Accept H0" "Reject H0" "Accept H0" "Accept H0" "Accept H0"


MoranST package 6

[4,] "Accept H0" "Reject H0" "Accept H0" "Accept H0" "Accept H0" [5,] "Accept H0" "Accept H0" "Accept H0" "Accept H0" "Accept H0" [6,] "Accept H0" "Reject H0" "Accept H0" "Accept H0" "Accept H0" [7,] "Accept H0" "Accept H0" "Reject H0" "Reject H0" "Accept H0" [8,] "Accept H0" "Accept H0" "Accept H0" "Reject H0" "Accept H0" [9,] "Accept H0" "Accept H0" "Accept H0" "Accept H0" "Accept H0" [10,] "Accept H0" "Accept H0" "Accept H0" "Accept H0" "Accept H0" [11,] "Accept H0" "Accept H0" "Accept H0" "Accept H0" "Accept H0" [12,] "Accept H0" "Accept H0" "Accept H0" "Reject H0" "Accept H0" [13,] "Accept H0" "Accept H0" "Accept H0" "Accept H0" "Accept H0" [14,] "Accept H0" "Accept H0" "Accept H0" "Accept H0" "Accept H0" [15,] "Accept H0" "Accept H0" "Accept H0" "Accept H0" "Accept H0" [16,] "Reject H0" "Accept H0" "Accept H0" "Accept H0" "Accept H0" [17,] "Accept H0" "Accept H0" "Accept H0" "Accept H0" "Reject H0" [18,] "Accept H0" "Accept H0" "Accept H0" "Accept H0" "Accept H0" [19,] "Accept H0" "Accept H0" "Accept H0" "Accept H0" "Accept H0" [20,] "Accept H0" "Accept H0" "Accept H0" "Accept H0" "Accept H0" [21,] "Accept H0" "Accept H0" "Accept H0" "Accept H0" "Accept H0" [22,] "Accept H0" "Accept H0" "Accept H0" "Reject H0" "Reject H0" [23,] "Accept H0" "Accept H0" "Accept H0" "Accept H0" "Accept H0" [24,] "Accept H0" "Accept H0" "Accept H0" "Accept H0" "Accept H0" [25,] "Accept H0" "Accept H0" "Accept H0" "Accept H0" "Accept H0" #==================== Thank you ==============================#


MoranST package 7

LAMPIRAN A. MACRO PROGRAM #=======================================================================================================# # @ @ @@@@@@ @@@@@@ @@@@@@ @@ @ @@@@@@ @@@@@@@ # # @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ # # @ @ @ @ @ @ @ @ @ @ @ @ @ @ # # @ @ @ @ @@@@@@ @@@@@@ @ @ @ @@@@@@ @ # # @ @ @ @ @ @ @ @ @ @@ @ @ # # @ @ @ @ @ @ @ @ @ @ @ @ # # @ @ @@@@@@ @ @ @ @ @ @ @@@@@@ @ # # # # # # Syntax R Moran's I for Spatiotemporal Data # # MoranST # # Update 1 July 2018. # # # # by: # # I Gede Nyoman Mindra Jaya, S.Si., M.Si. ([email protected]) # # Bertho Tantular, S.Si, M.Si. ([email protected]) # # Zulhanif, S.Si, M.Sc. ([email protected]) # # Dr. Toni Toharudin, M.Sc. ([email protected]) # # # # Article: # # IGNM Jaya, et al. 2018. Estimation and Testing For Spatiotemporal Moran's I # #=======================================================================================================# #======================================== Start Function of Moran ST ===================================# MoranST.MC<-function(x,W,nsim){ library(abind) library(spdep) if (!is.matrix(W)) stop(paste(deparse(substitute(W)), "is not a numeric matrix")) if (!is.numeric(x)) stop(paste(deparse(substitute(x)), "is not a numeric vector")) if (missing(nsim)) stop("nsim must be given") xname <- deparse(substitute(x)) wname <- deparse(substitute(W)) ### MoranST MoranST<-function (x, W) { n<-nrow(W) T<-length(x)/n x<-matrix(x,n,T) if (n != nrow(x)) stop("objects of different length") M<-0 w1<-0 SS<-0 for( i in 1:n){ for( j in 1:T){ SS<-SS+(x[i,j]-mean(x))^2 for( k in 1:n){ for( h in 1:T){ if (j==h) { w<-W[i,k] } else if ((i==k)& (abs(j-h)==1)) { w<-1 } else w<-0 M<-M +(w*(x[i,j]-mean(x))*(x[k,h]-mean(x))) w1<-w1+w } } } } MoranST<-n*T*M/(w1*SS) return(MoranST) } ### Calculating p.value Moran<-MoranST(x,W) sim <- replicate(nsim, MoranST(sample(x), W))


MoranST package 8

p.value <- mean((all <- c(Moran,sim) >= Moran)) hist(sim, main=paste("Null Distribution of Moran's ST=",round(Moran,4)), sub=paste("p.valueST =", round(p.value, 4)),xlab="Moran's I Simulation", xlim=range(all),col="blue") abline(v = Moran, col="#903030", lty=3, lwd=2) Decision<-ifelse(p.value<=0.05,paste("Reject H0"), paste("Accept H0")) Result<-list(MoranST=Moran,p.value=p.value,Simulation=sim) cat("**************************************************************************" ,"\n* MoranST with Monte Carlo Simulation *" ,"\n* HIU UNPAD 2018 *" ,"\n* IGNM Jaya, B Tantular, Zulhanif, T Toharudin *" ,"\n***************************************************************************" ,"\n","Data input : ", xname ,"\n","Weight input : ", wname ,"\n","MoranST : ", Moran ,"\n","p.Value : ", p.value ,"\n**************************************************************************" ,"\n","Decision with an alpha level of .05 (5%) :", Decision, "[for H1:Rho > 0]" ,"\n**************************************************************************" ,"\n") return(Result) } #======================================= End of Function Moran ST =======================================# #======================================== Start Function of Local Moran ST ==============================# LocalMoranST.MC<-function (x, W,nsim) { #### Global MoranST MoranST.MCA<-function(x,W,nsim){ library(abind) library(spdep) if (!is.matrix(W)) stop(paste(deparse(substitute(W)), "is not a numeric matrix")) if (!is.numeric(x)) stop(paste(deparse(substitute(x)), "is not a numeric vector")) if (missing(nsim)) stop("nsim must be given") xname <- deparse(substitute(x)) wname <- deparse(substitute(W)) ### MoranST MoranST<-function (x, W) { n<-nrow(W) T<-length(x)/n x<-matrix(x,n,T) if (n != nrow(x)) stop("objects of different length") M<-0 w1<-0 SS<-0 for( i in 1:n){ for( j in 1:T){ SS<-SS+(x[i,j]-mean(x))^2 for( k in 1:n){ for( h in 1:T){ if (j==h) { w<-W[i,k] } else if ((i==k)& (abs(j-h)==1)) { w<-1 } else w<-0 M<-M +(w*(x[i,j]-mean(x))*(x[k,h]-mean(x))) w1<-w1+w } } } } MoranST<-n*T*M/(w1*SS) return(MoranST) } Moran<-MoranST(x,W) sim <- replicate(nsim, MoranST(sample(x), W)) p.value <- mean((all <- c(Moran,sim) >= Moran)) Decision<-ifelse(p.value<=0.05,paste("Reject H0"), paste("Accept H0"))


MoranST package 9

Result<-list(MoranST=Moran,p.value=p.value,Decision=Decision, Simulation=sim) return(Result) } #== End of Function Global Moran ST ===============# #== Start of Function Local MoranST ===============# library(abind) library(spdep) if (!is.matrix(W)) stop(paste(deparse(substitute(W)), "is not a numeric matrix")) if (!is.numeric(x)) stop(paste(deparse(substitute(x)), "is not a numeric vector")) if (missing(nsim)) stop("nsim must be given") xname <- deparse(substitute(x)) wname <- deparse(substitute(W)) ### LocalMoranST LocalMoranST<-function (x, W) { n<-nrow(W) T<-length(x)/n nT<-n*T x<-matrix(x,n,T) if (n != nrow(x)) stop("objects of different length") LocalST<-matrix(0,n,T) M<-matrix(0,n,T) for( i in 1:n){ for( j in 1:T){ for( k in 1:n){ for( h in 1:T){ if (j==h) { w<-W[i,k] } else if ((i==k)& (abs(j-h)==1)) { w<-1 } else w<-0 M[k,h]<-(w*(x[k,h]-mean(x))) SM<-sum(M) } SS<-sum((x-mean(x))^2) LocalST[i,j]<-(x[i,j]-mean(x))*SM/(SS/nT) } } } return(LocalST) } #### Calculating p.value Moran<-MoranST.MCA(x,W,nsim)$Moran p.valueG<-MoranST.MCA(x,W,nsim)$p.value DecisionG<-MoranST.MCA(x,W,nsim)$Decision LocalST<-LocalMoranST(x,W) sim <- replicate(nsim, LocalMoranST(sample(x), W)) p.value <- rowMeans((all <- abind(replicate(1,LocalST),sim) >= replicate(nsim+1,LocalST)),dim=2) Decision<-ifelse(p.value<=0.05,paste("Reject H0"), paste("Accept H0")) Result<-list(LocalMoranST=LocalST,p.value=p.value,Decision=Decision) cat("***************************************************************************" ,"\n* Global MoranST with Monte Carlo Simulation *" ,"\n* HIU UNPAD 2018 *" ,"\n* IGNM Jaya, B Tantular, Zulhanif, T Toharudin *" ,"\n****************************************************************************" ,"\n","Data input : ", xname ,"\n","Weight input : ", wname ,"\n","Global MoranST : ", Moran ,"\n","Global p.Value : ", p.valueG ,"\n***************************************************************************" ,"\n","Decision with an alpha level of .05 (5%) :", DecisionG, "[for H1:Rho > 0]" ,"\n***************************************************************************" ,"\n" ,"\n***************************************************************************" ,"\n* Statistics of Local MoranST with Monte Carlo Simulation *" ,"\n***************************************************************************" ,"\n") return(Result) } #================================= End of Function Global & Local Moran ST ============================#

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