Analisis GTWR untuk Memodelkan Kemiskinan di Jawa Timur 2017-2025
Skripsi
1 Library
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## repos='https://nowosad.github.io/drat/', type='source')`2 1. Input Data
df_raw <- read_excel("D:/Kuliah/SKRIPSI/Data/JATIM/Data Analisis.xlsx")
data <- df_raw %>%
rename(
PDRB = `PDRB ADHK (Rp)`,
PPM = `Persentase Penduduk Miskin (%)`,
TPT = 'Tingkat Pengangguran Terbuka',
UMK = 'UMK (Rp)'
) %>%
mutate(
PDRB = log(PDRB),
UMK = log (UMK)
)
# Memastikan nama kolom
names(data)## [1] "No" "Kabupaten/Kota" "Tahun" "PDRB"
## [5] "IPM" "TPT" "PPM" "UMK"3 2. EDA
3.1 2.1 Tipe Variabel dan Struktur Data
## tibble [342 × 8] (S3: tbl_df/tbl/data.frame)
## $ No : num [1:342] 1 2 3 4 5 6 7 8 9 10 ...
## $ Kabupaten/Kota: chr [1:342] "Pacitan" "Ponorogo" "Trenggalek" "Tulungagung" ...
## $ Tahun : num [1:342] 2017 2017 2017 2017 2017 ...
## $ PDRB : num [1:342] 29.9 30.2 30.1 30.8 30.8 ...
## $ IPM : num [1:342] 66.5 69.3 68.1 71.2 69.3 ...
## $ TPT : num [1:342] 0.85 3.76 3.48 2.27 2.99 3.18 4.6 2.91 5.16 3.07 ...
## $ PPM : num [1:342] 15.42 11.39 12.96 8.04 9.8 ...
## $ UMK : num [1:342] 14.1 14.1 14.1 14.2 14.2 ...## [1] 38## [1] 2017 2018 2019 2020 2021 2022 2023 2024 2025# Jumlah observasi setiap kabupaten/kota
data %>%
count(`Kabupaten/Kota`, name = "jumlah_tahun") %>%
arrange(jumlah_tahun)## # A tibble: 38 × 2
## `Kabupaten/Kota` jumlah_tahun
## <chr> <int>
## 1 Bangkalan 9
## 2 Banyuwangi 9
## 3 Blitar 9
## 4 Bojonegoro 9
## 5 Bondowoso 9
## 6 Gresik 9
## 7 Jember 9
## 8 Jombang 9
## 9 Kediri 9
## 10 Kota Batu 9
## # ℹ 28 more rows# Cek missing value variabel penelitian
data %>%
summarise(
across(
all_of(vars),
~sum(is.na(.x))
)
)## # A tibble: 1 × 5
## PDRB IPM PPM UMK TPT
## <int> <int> <int> <int> <int>
## 1 0 0 0 0 0Seluruh variabel penelitian memiliki 342 data lengkap. Tidak ditemukan nilai yang hilang (missing value)
3.2 2.2 Statistik Deskriptif
# Statistik deskriptif
rdata <- as.matrix(data[, vars])
n <- nrow(data)
desk <- rbind(
n = apply(rdata, 2, function(x) sum(!is.na(x))),
mean = apply(rdata, 2, mean, na.rm = TRUE),
sd = apply(rdata, 2, sd, na.rm = TRUE),
min = apply(rdata, 2, min, na.rm = TRUE),
q1 = apply(rdata, 2, quantile, probs = 0.25, na.rm = TRUE),
median = apply(rdata, 2, median, na.rm = TRUE),
q3 = apply(rdata, 2, quantile, probs = 0.75, na.rm = TRUE),
max = apply(rdata, 2, max, na.rm = TRUE),
cv = apply(rdata, 2, function(x) {
sd(x, na.rm = TRUE) / mean(x, na.rm = TRUE) * 100
})
)
desk## PDRB IPM PPM UMK TPT
## n 342.0000000 342.000000 342.000000 342.000000 342.000000
## mean 30.8869339 73.258041 10.556988 14.664187 4.447076
## sd 0.9749327 5.185162 4.420936 0.296908 1.673105
## min 29.0931208 59.900000 2.860000 14.143987 0.850000
## q1 30.2090375 69.827500 7.332500 14.471039 3.382500
## median 30.7677517 72.630000 10.055000 14.619517 4.280000
## q3 31.6304346 76.750000 13.030000 14.820546 5.297500
## max 33.8731170 85.650000 23.760000 15.417270 10.970000
## cv 3.1564568 7.077942 41.876872 2.024715 37.622591Variabel PPM dan TPT memiliki variasi relatif lebih besar dibandingkan variabel lainnya. Sementara itu, PDRB dan UMK memiliki variasi relatif yang lebih kecil.
3.3 2.3 Visualisasi Data
long <- data %>%
pivot_longer(
cols = all_of(vars),
names_to = "Variabel",
values_to = "Nilai"
)
# Histogram
ggplot(long, aes(x = Nilai)) +
geom_histogram(bins = 25, na.rm = TRUE) +
facet_wrap(~Variabel, scales = "free") +
theme_minimal()
# Korelasi antarvariabel
x_vars <- c(
"PDRB",
"IPM",
"PPM",
"UMK",
"TPT"
)
cor_data <- data %>%
select(all_of(x_vars)) %>%
cor(use = "complete.obs")
corrplot(
cor_data,
method = "color",
type = "upper",
addCoef.col = "black",
tl.col = "black",
tl.srt = 45
)
4 3. Regresi Linear Global (OLS)
##
## Call:
## lm(formula = PPM ~ IPM + PDRB + UMK + TPT, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.3823 -1.9808 0.1207 1.5320 7.3656
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 48.3973047 8.0984357 5.976 5.81e-09 ***
## IPM -0.7109659 0.0360462 -19.724 < 2e-16 ***
## PDRB -0.2159292 0.1978688 -1.091 0.2759
## UMK 1.4260443 0.7511504 1.898 0.0585 .
## TPT 0.0002845 0.1068211 0.003 0.9979
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.694 on 337 degrees of freedom
## Multiple R-squared: 0.633, Adjusted R-squared: 0.6286
## F-statistic: 145.3 on 4 and 337 DF, p-value: < 2.2e-16Nilai R squared sebesar 0,633 menunjukkan bahwa 63,3% variasi PPM dapat dijelaskan secara bersama-sama oleh IPM, PDRB, UMK, dan TPT dalam model OLS.
4.1 3.1 Deteksi Multikolinearitas
## IPM PDRB UMK TPT
## 1.641072 1.748189 2.336587 1.500531Berdasarkan deteksi tersebut, tidak terdapat indikasi multikolinearitas antar variabel independen, karena seluruh variabel memiliki nilai VIF < 10.
4.2 3.2 Uji Outlier
# Menguji observasi dengan studentized residual paling ekstrem, menggunakan koreksi Bonferroni untuk menilai signifikansinya.
outlierTest(model_ols)## No Studentized residuals with Bonferroni p < 0.05
## Largest |rstudent|:
## rstudent unadjusted p-value Bonferroni p
## 179 2.77782 0.0057798 NA# Uji outlier pada model OLS
hasil_outlier <- car::outlierTest(model_ols)
# Mengambil nomor observasi yang teridentifikasi oleh outlierTest
indeks_outlier <- as.integer(names(hasil_outlier$rstudent))
# Menampilkan identitas wilayah, tahun, dan seluruh variabel
data[indeks_outlier, c(
"Kabupaten/Kota",
"Tahun",
"PDRB",
"IPM",
"PPM",
"UMK",
"TPT"
)]## # A tibble: 1 × 7
## `Kabupaten/Kota` Tahun PDRB IPM PPM UMK TPT
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Sampang 2021 30.3 64.9 23.8 14.5 3.45
5 4. Uji Heteroskedastisitas
##
## studentized Breusch-Pagan test
##
## data: model_ols
## BP = 76.276, df = 4, p-value = 1.07e-15Karena p-val < 0.05 maka h0 ditolak, berati ada heterogenitas spasial
##
## Shapiro-Wilk normality test
##
## data: residuals(model_ols)
## W = 0.99348, p-value = 0.1466h0: residual berdistribusi normal p val=0.1466>0.05 maka h0 tidak ditolak, yang berarti tidak terdapat bukti yang cukup untuk menyatakan residual menyimpang dari distribusi normal pada taraf signifikansi 5%.
6 5. File SHP
shp <- st_read("D:/Kuliah/SKRIPSI/Data/gadm41_IDN_2.json", quiet = TRUE)
# Cek dulu nama aslinya di GADM
sort(unique(shp$NAME_2[shp$NAME_1 == "JawaTimur"]))## [1] "Bangkalan" "Banyuwangi" "Batu" "Blitar"
## [5] "Bojonegoro" "Bondowoso" "Gresik" "Jember"
## [9] "Jombang" "Kediri" "KotaBlitar" "KotaKediri"
## [13] "KotaMadiun" "KotaMalang" "KotaMojokerto" "KotaPasuruan"
## [17] "KotaProbolinggo" "Lamongan" "Lumajang" "Madiun"
## [21] "Magetan" "Malang" "Mojokerto" "Nganjuk"
## [25] "Ngawi" "Pacitan" "Pamekasan" "Pasuruan"
## [29] "Ponorogo" "Probolinggo" "Sampang" "Sidoarjo"
## [33] "Situbondo" "Sumenep" "Surabaya" "Trenggalek"
## [37] "Tuban" "Tulungagung"jatim <- shp %>%
dplyr::filter(NAME_1 == "JawaTimur", TYPE_2 %in% c("Kabupaten", "Kota")) %>%
mutate(NAME_2 = dplyr::recode(NAME_2,
"KotaBlitar" = "Kota Blitar",
"KotaKediri" = "Kota Kediri",
"KotaMadiun" = "Kota Madiun",
"KotaMalang" = "Kota Malang",
"KotaMojokerto" = "Kota Mojokerto",
"KotaPasuruan" = "Kota Pasuruan",
"KotaProbolinggo" = "Kota Probolinggo",
"Surabaya" = "Kota Surabaya",
"Batu" = "Kota Batu")) %>%
st_make_valid()
st_crs(jatim)## Coordinate Reference System:
## User input: WGS 84
## wkt:
## GEOGCRS["WGS 84",
## DATUM["World Geodetic System 1984",
## ELLIPSOID["WGS 84",6378137,298.257223563,
## LENGTHUNIT["metre",1]]],
## PRIMEM["Greenwich",0,
## ANGLEUNIT["degree",0.0174532925199433]],
## CS[ellipsoidal,2],
## AXIS["geodetic latitude (Lat)",north,
## ORDER[1],
## ANGLEUNIT["degree",0.0174532925199433]],
## AXIS["geodetic longitude (Lon)",east,
## ORDER[2],
## ANGLEUNIT["degree",0.0174532925199433]],
## ID["EPSG",4326]]6.1 5.1 Menentukan Koordinat Titik
# ambil daratan utama (poligon terluas) tiap wilayah, supaya pulau kecil
# (mis. Karimunjawa di Jepara) tidak menggeser centroid
daratan <- jatim %>%
st_cast("MULTIPOLYGON") %>%
st_cast("POLYGON", warn = FALSE) %>%
mutate(luas = as.numeric(st_area(geometry))) %>%
group_by(NAME_2) %>%
slice_max(luas, n = 1, with_ties = FALSE) %>%
ungroup()
# centroid dalam lon/lat (X = longitude, Y = latitude)
titik <- st_centroid(st_geometry(daratan))
xy <- st_coordinates(titik)
koordinat_ll <- tibble(Kabupaten_Kota = daratan$NAME_2, X = xy[, 1], Y = xy[, 2])
di_dalam <- diag(st_within(titik, st_geometry(daratan), sparse = FALSE))
koordinat_ll$Kabupaten_Kota[!di_dalam]## [1] "Situbondo"## [1] 386.2 5.2 Merge
# Menggabungkan koordinat dengan data asli
data_spasial <- data %>%
left_join(
koordinat_ll,
by = c("Kabupaten/Kota" = "Kabupaten_Kota")
)
# Memeriksa hasil penggabungan
head(data_spasial)## # A tibble: 6 × 10
## No `Kabupaten/Kota` Tahun PDRB IPM TPT PPM UMK X Y
## <dbl> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 Pacitan 2017 29.9 66.5 0.85 15.4 14.1 111. -8.13
## 2 2 Ponorogo 2017 30.2 69.3 3.76 11.4 14.1 111. -7.93
## 3 3 Trenggalek 2017 30.1 68.1 3.48 13.0 14.1 112. -8.16
## 4 4 Tulungagung 2017 30.8 71.2 2.27 8.04 14.2 112. -8.11
## 5 5 Blitar 2017 30.8 69.3 2.99 9.8 14.2 112. -8.13
## 6 6 Kediri 2017 30.9 70.5 3.18 12.2 14.3 112. -7.83## [1] 0## [1] 342## [1] 342# Mengurutkan data berdasarkan kabupaten/kota dan tahun
data_spasial <- data_spasial %>%
arrange(`Kabupaten/Kota`, Tahun)
# Mengubah data.frame menjadi SpatialPointsDataFrame
sp::coordinates(data_spasial) <- ~ X + Y
# Menetapkan sistem koordinat lon/lat WGS84
sp::proj4string(data_spasial) <- sp::CRS("+proj=longlat +datum=WGS84 +no_defs")
# Memeriksa hasil konversi
class(data_spasial)## [1] "SpatialPointsDataFrame"
## attr(,"package")
## [1] "sp"## [1] "+proj=longlat +datum=WGS84 +no_defs"## [1] "No" "Kabupaten/Kota" "Tahun" "PDRB"
## [5] "IPM" "TPT" "PPM" "UMK"7 6. Analisis
7.1 6.1 Cek kelengkapan data
## # A tibble: 9 × 2
## Tahun n
## <dbl> <int>
## 1 2017 38
## 2 2018 38
## 3 2019 38
## 4 2020 38
## 5 2021 38
## 6 2022 38
## 7 2023 38
## 8 2024 38
## 9 2025 38# Memeriksa data yang belum lengkap
data_tabel %>%
dplyr::summarise(
dplyr::across(
dplyr::all_of(vars),
~ sum(is.na(.x))
)
)## # A tibble: 1 × 5
## PDRB IPM PPM UMK TPT
## <int> <int> <int> <int> <int>
## 1 0 0 0 0 07.2 GWR
## [1] "SpatialPointsDataFrame"
## attr(,"package")
## [1] "sp"## [1] "No" "Kabupaten/Kota" "Tahun" "PDRB"
## [5] "IPM" "TPT" "PPM" "UMK"# Menentukan formula GWR
formula_gwr <- as.formula(
"PPM ~ IPM + PDRB + UMK + `TPT`"
)
# Memilih bandwidth optimum menggunakan AICc
bw_gwr <- GWmodel::bw.gwr(
formula = formula_gwr,
data = data_spasial,
approach = "AICc",
kernel = "gaussian",
adaptive = TRUE,
longlat = TRUE
)## Adaptive bandwidth (number of nearest neighbours): 219 AICc value: 1610.041
## Adaptive bandwidth (number of nearest neighbours): 143 AICc value: 1577.19
## Adaptive bandwidth (number of nearest neighbours): 96 AICc value: 1538.835
## Adaptive bandwidth (number of nearest neighbours): 66 AICc value: 1497.102
## Adaptive bandwidth (number of nearest neighbours): 49 AICc value: 1459.639
## Adaptive bandwidth (number of nearest neighbours): 36 AICc value: 1405.696
## Adaptive bandwidth (number of nearest neighbours): 31 AICc value: 1405.696## [1] 31# Mengestimasi model GWR
model_gwr <- GWmodel::gwr.basic(
formula = formula_gwr,
data = data_spasial,
bw = bw_gwr,
kernel = "gaussian",
adaptive = TRUE,
longlat = TRUE
)
# Melihat diagnostik model
model_gwr$GW.diagnostic## $RSS.gw
## [1] 1050.757
##
## $AIC
## [1] 1377.208
##
## $AICc
## [1] 1405.696
##
## $enp
## [1] 30.30994
##
## $edf
## [1] 311.6901
##
## $gw.R2
## [1] 0.8423408
##
## $gwR2.adj
## [1] 0.82696
##
## $BIC
## [1] 1145.317## Intercept IPM PDRB UMK TPT y yhat residual
## 1 60.71224 -0.9181479 0.4242032 0.3207812 0.1421724 21.32 21.65506 -0.3350624
## 2 60.71224 -0.9181479 0.4242032 0.3207812 0.1421724 19.59 21.26275 -1.6727504
## 3 60.71224 -0.9181479 0.4242032 0.3207812 0.1421724 18.90 20.52321 -1.6232146
## 4 60.71224 -0.9181479 0.4242032 0.3207812 0.1421724 20.56 19.70583 0.8541695
## 5 60.71224 -0.9181479 0.4242032 0.3207812 0.1421724 21.57 19.36792 2.2020827
## 6 60.71224 -0.9181479 0.4242032 0.3207812 0.1421724 19.44 18.72709 0.7129059
## CV_Score Stud_residual Intercept_SE IPM_SE PDRB_SE UMK_SE TPT_SE
## 1 0 -0.1955808 9.322272 0.04012758 0.2129069 0.9849794 0.1098063
## 2 0 -0.9616799 9.322272 0.04012758 0.2129069 0.9849794 0.1098063
## 3 0 -0.9243496 9.322272 0.04012758 0.2129069 0.9849794 0.1098063
## 4 0 0.5173869 9.322272 0.04012758 0.2129069 0.9849794 0.1098063
## 5 0 1.2989692 9.322272 0.04012758 0.2129069 0.9849794 0.1098063
## 6 0 0.4192553 9.322272 0.04012758 0.2129069 0.9849794 0.1098063
## Intercept_TV IPM_TV PDRB_TV UMK_TV TPT_TV Local_R2
## 1 6.512602 -22.88072 1.992435 0.3256731 1.294756 0.8934431
## 2 6.512602 -22.88072 1.992435 0.3256731 1.294756 0.8934431
## 3 6.512602 -22.88072 1.992435 0.3256731 1.294756 0.8934431
## 4 6.512602 -22.88072 1.992435 0.3256731 1.294756 0.8934431
## 5 6.512602 -22.88072 1.992435 0.3256731 1.294756 0.8934431
## 6 6.512602 -22.88072 1.992435 0.3256731 1.294756 0.8934431## [1] "Intercept" "IPM" "PDRB" "UMK"
## [5] "TPT" "y" "yhat" "residual"
## [9] "CV_Score" "Stud_residual" "Intercept_SE" "IPM_SE"
## [13] "PDRB_SE" "UMK_SE" "TPT_SE" "Intercept_TV"
## [17] "IPM_TV" "PDRB_TV" "UMK_TV" "TPT_TV"
## [21] "Local_R2"# Menyimpan hasil estimasi koefisien lokal
hasil_gwr <- model_gwr$SDF@data
# Melihat beberapa hasil estimasi
head(hasil_gwr)## Intercept IPM PDRB UMK TPT y yhat residual
## 1 60.71224 -0.9181479 0.4242032 0.3207812 0.1421724 21.32 21.65506 -0.3350624
## 2 60.71224 -0.9181479 0.4242032 0.3207812 0.1421724 19.59 21.26275 -1.6727504
## 3 60.71224 -0.9181479 0.4242032 0.3207812 0.1421724 18.90 20.52321 -1.6232146
## 4 60.71224 -0.9181479 0.4242032 0.3207812 0.1421724 20.56 19.70583 0.8541695
## 5 60.71224 -0.9181479 0.4242032 0.3207812 0.1421724 21.57 19.36792 2.2020827
## 6 60.71224 -0.9181479 0.4242032 0.3207812 0.1421724 19.44 18.72709 0.7129059
## CV_Score Stud_residual Intercept_SE IPM_SE PDRB_SE UMK_SE TPT_SE
## 1 0 -0.1955808 9.322272 0.04012758 0.2129069 0.9849794 0.1098063
## 2 0 -0.9616799 9.322272 0.04012758 0.2129069 0.9849794 0.1098063
## 3 0 -0.9243496 9.322272 0.04012758 0.2129069 0.9849794 0.1098063
## 4 0 0.5173869 9.322272 0.04012758 0.2129069 0.9849794 0.1098063
## 5 0 1.2989692 9.322272 0.04012758 0.2129069 0.9849794 0.1098063
## 6 0 0.4192553 9.322272 0.04012758 0.2129069 0.9849794 0.1098063
## Intercept_TV IPM_TV PDRB_TV UMK_TV TPT_TV Local_R2
## 1 6.512602 -22.88072 1.992435 0.3256731 1.294756 0.8934431
## 2 6.512602 -22.88072 1.992435 0.3256731 1.294756 0.8934431
## 3 6.512602 -22.88072 1.992435 0.3256731 1.294756 0.8934431
## 4 6.512602 -22.88072 1.992435 0.3256731 1.294756 0.8934431
## 5 6.512602 -22.88072 1.992435 0.3256731 1.294756 0.8934431
## 6 6.512602 -22.88072 1.992435 0.3256731 1.294756 0.8934431## Intercept IPM PDRB UMK
## Min. :-9.718 Min. :-1.0226 Min. :-2.5867 Min. :-1.7849
## 1st Qu.:28.358 1st Qu.:-0.8167 1st Qu.:-0.4105 1st Qu.:-0.5587
## Median :40.159 Median :-0.6497 Median : 0.1548 Median : 0.8297
## Mean :35.514 Mean :-0.6735 Mean :-0.1756 Mean : 1.9982
## 3rd Qu.:47.942 3rd Qu.:-0.5372 3rd Qu.: 0.3489 3rd Qu.: 3.1763
## Max. :67.529 Max. :-0.3592 Max. : 0.5078 Max. :11.5369
## TPT y yhat residual
## Min. :-0.40855 Min. : 2.860 Min. : 2.163 Min. :-3.98089
## 1st Qu.:-0.10378 1st Qu.: 7.332 1st Qu.: 7.756 1st Qu.:-0.91756
## Median : 0.07699 Median :10.055 Median :10.322 Median :-0.02356
## Mean : 0.01808 Mean :10.557 Mean :10.403 Mean : 0.15401
## 3rd Qu.: 0.14895 3rd Qu.:13.030 3rd Qu.:12.458 3rd Qu.: 1.06055
## Max. : 0.25138 Max. :23.760 Max. :22.849 Max. : 5.98906
## CV_Score Stud_residual Intercept_SE IPM_SE
## Min. :0 Min. :-2.24737 Min. : 6.384 Min. :0.03040
## 1st Qu.:0 1st Qu.:-0.52017 1st Qu.: 8.894 1st Qu.:0.03932
## Median :0 Median :-0.01353 Median : 9.552 Median :0.04593
## Mean :0 Mean : 0.08503 Mean :11.315 Mean :0.04849
## 3rd Qu.:0 3rd Qu.: 0.62212 3rd Qu.:12.661 3rd Qu.:0.05467
## Max. :0 Max. : 3.33212 Max. :21.451 Max. :0.09422
## PDRB_SE UMK_SE TPT_SE Intercept_TV
## Min. :0.1602 Min. :0.6022 Min. :0.08858 Min. :-0.6153
## 1st Qu.:0.1997 1st Qu.:0.7802 1st Qu.:0.11163 1st Qu.: 1.8814
## Median :0.2169 Median :0.9135 Median :0.12796 Median : 4.1978
## Mean :0.2313 Mean :0.9951 Mean :0.13819 Mean : 3.7893
## 3rd Qu.:0.2601 3rd Qu.:1.0773 3rd Qu.:0.15911 3rd Qu.: 5.5206
## Max. :0.4020 Max. :1.8555 Max. :0.24177 Max. : 7.1365
## IPM_TV PDRB_TV UMK_TV TPT_TV
## Min. :-27.398 Min. :-7.3445 Min. :-1.9663 Min. :-2.8272
## 1st Qu.:-17.993 1st Qu.:-1.8325 1st Qu.:-0.7338 1st Qu.:-0.5229
## Median :-13.080 Median : 0.6984 Median : 1.0524 Median : 0.4882
## Mean :-14.753 Mean :-0.3227 Mean : 1.5697 Mean : 0.2544
## 3rd Qu.:-10.483 3rd Qu.: 1.6726 3rd Qu.: 3.0274 3rd Qu.: 1.2667
## Max. : -6.333 Max. : 2.9293 Max. : 8.0338 Max. : 2.2120
## Local_R2
## Min. :0.6764
## 1st Qu.:0.8100
## Median :0.8331
## Mean :0.8274
## 3rd Qu.:0.8684
## Max. :0.89347.3 6.2 GTWR
# Urutkan observasi tanpa mengubah pasangan koordinat dan data
urutan <- order(
data_spasial@data$`Kabupaten/Kota`,
data_spasial@data$Tahun
)
data_gtwr <- data_spasial[urutan, ]
formula_gtwr <- as.formula("PPM ~ IPM + PDRB + UMK + TPT")
waktu_gtwr <- data_gtwr@data$Tahun
class(data_gtwr)## [1] "SpatialPointsDataFrame"
## attr(,"package")
## [1] "sp"## waktu_gtwr
## 2017 2018 2019 2020 2021 2022 2023 2024 2025
## 38 38 38 38 38 38 38 38 38# 1. PERSIAPAN DATA GTWR
# Mengurutkan berdasarkan kabupaten/kota dan tahun
urutan <- order(
data_spasial@data$`Kabupaten/Kota`,
data_spasial@data$Tahun
)
data_gtwr <- data_spasial[urutan, ]
# Menentukan formula
formula_gtwr <- PPM ~ IPM + PDRB + UMK + TPT
# Menyamakan objek data yang digunakan
dat <- data_gtwr
# Jumlah observasi
n_dat <- nrow(dat)
# Waktu pengamatan
waktu_gtwr <- dat@data$Tahun
# Pemeriksaan struktur
cat("Jumlah observasi:", n_dat, "\n")## Jumlah observasi: 342## waktu_gtwr
## 2017 2018 2019 2020 2021 2022 2023 2024 2025
## 38 38 38 38 38 38 38 38 38## [1] "No" "Kabupaten/Kota" "Tahun" "PDRB"
## [5] "IPM" "TPT" "PPM" "UMK"# Jarak ruang (km) dan waktu (tahun)
# Jarak spasial dalam kilometer
dS <- GWmodel::gw.dist(
sp::coordinates(dat),
longlat = TRUE
)
# Jarak temporal dalam tahun
dT <- abs(
outer(
dat@data$Tahun,
dat@data$Tahun,
"-"
)
)
# Skala acuan tau
tau_ref <- (max(dS) / max(dT))^2
# Fungsi jarak spasial-temporal
st_tau <- function(tau) {
sqrt(dS^2 + tau * dT^2)
}
# Pemeriksaan matriks jarak
cat("Jarak spasial maksimum (km):", max(dS), "\n")## Jarak spasial maksimum (km): 334.4795## Jarak temporal maksimum (tahun): 8## Nilai tau acuan: 1748.071xv <- c("IPM", "PDRB", "UMK", "TPT")
formula_baru <- formula_gtwr
dat <- data_gtwr
n_dat <- nrow(dat)
ols2 <- model_ols
fit_gtwr <- function(D, bw, d = dat) {
suppressWarnings(
GWmodel::gtwr(
formula = formula_baru,
data = d,
obs.tv = d@data$Tahun,
st.bw = bw,
kernel = "gaussian",
adaptive = TRUE,
st.dMat = D
)
)
}7.3.1 Optimasi tau dan bandwidth (kriteria AICc)
# Fungsi pencarian bandwidth otomatis menggunakan bw.gtwr
cari_bandwidth <- function(tau_rel) {
# Menghitung nilai tau
tau <- tau_rel * tau_ref
# Membentuk matriks jarak spasial-temporal
D <- st_tau(tau)
# Pencarian bandwidth optimal
bw_opt <- tryCatch(
GWmodel::bw.gtwr(
formula = formula_baru,
data = dat,
obs.tv = dat@data$Tahun,
approach = "AICc",
kernel = "gaussian",
adaptive = TRUE,
st.dMat = D,
verbose = FALSE
),
error = function(e) {
message(
"Gagal mencari bandwidth pada tau_rel = ",
tau_rel, ": ", e$message
)
NA_real_
}
)
# Pemeriksaan bandwidth
if (
length(bw_opt) != 1 ||
!is.finite(bw_opt)
) {
return(NULL)
}
# Estimasi model dengan bandwidth optimal
model <- tryCatch(
fit_gtwr(
D = D,
bw = bw_opt
),
error = function(e) {
message(
"Gagal mengestimasi model pada tau_rel = ",
tau_rel, ": ", e$message
)
NULL
}
)
if (is.null(model)) {
return(NULL)
}
# Mengambil hasil diagnostik
diag <- model$GTW.diagnostic
# Menyimpan hasil optimasi
hasil <- data.frame(
tau_rel = tau_rel,
tau = tau,
bandwidth = as.numeric(bw_opt),
AICc = as.numeric(diag$AICc),
R2 = as.numeric(diag$gw.R2),
enp = as.numeric(diag$enp),
RSS = as.numeric(diag$RSS.gw)
)
return(hasil)
}## tau_rel tau bandwidth AICc R2 enp RSS
## 1 0.001 1.748071 24 1314.118 0.8854597 39.76023 763.3809# Grid tau positif dengan interval logaritmik
tau_rel_grid <- sort(unique(c(
0,
10^seq(-8, -3, by = 0.5), # sisi kiri
10^seq(-3, 1.5, by = 0.1), # daerah pencarian awal
10^seq(1.5, 4, by = 0.1) # perluasan sisi kanan
)))
# Menambahkan tau = 0 sebagai pembanding GWR
tau_rel_grid <- c(
0,
tau_rel_grid
)
# Menghilangkan kemungkinan duplikasi
tau_rel_grid <- sort(unique(tau_rel_grid))
# Melihat grid
print(tau_rel_grid)## [1] 0.000000e+00 1.000000e-08 3.162278e-08 1.000000e-07 3.162278e-07
## [6] 1.000000e-06 3.162278e-06 1.000000e-05 3.162278e-05 1.000000e-04
## [11] 3.162278e-04 1.000000e-03 1.258925e-03 1.584893e-03 1.995262e-03
## [16] 2.511886e-03 3.162278e-03 3.981072e-03 5.011872e-03 6.309573e-03
## [21] 7.943282e-03 1.000000e-02 1.258925e-02 1.584893e-02 1.995262e-02
## [26] 2.511886e-02 3.162278e-02 3.981072e-02 5.011872e-02 6.309573e-02
## [31] 7.943282e-02 1.000000e-01 1.258925e-01 1.584893e-01 1.995262e-01
## [36] 2.511886e-01 3.162278e-01 3.981072e-01 5.011872e-01 6.309573e-01
## [41] 7.943282e-01 1.000000e+00 1.258925e+00 1.584893e+00 1.995262e+00
## [46] 2.511886e+00 3.162278e+00 3.981072e+00 5.011872e+00 6.309573e+00
## [51] 7.943282e+00 1.000000e+01 1.258925e+01 1.584893e+01 1.995262e+01
## [56] 2.511886e+01 3.162278e+01 3.981072e+01 5.011872e+01 6.309573e+01
## [61] 7.943282e+01 1.000000e+02 1.258925e+02 1.584893e+02 1.995262e+02
## [66] 2.511886e+02 3.162278e+02 3.981072e+02 5.011872e+02 6.309573e+02
## [71] 7.943282e+02 1.000000e+03 1.258925e+03 1.584893e+03 1.995262e+03
## [76] 2.511886e+03 3.162278e+03 3.981072e+03 5.011872e+03 6.309573e+03
## [81] 7.943282e+03 1.000000e+04## Jumlah kandidat tau: 82# Hasil terbaik berdasarkan AICc
hasil_tau_list <- vector(
"list",
length(tau_rel_grid)
)
for (i in seq_along(tau_rel_grid)) {
tau_rel <- tau_rel_grid[i]
cat(
"Proses ke-", i,
"dari", length(tau_rel_grid),
"| Tau relatif:", tau_rel,
"\n"
)
hasil_bw <- cari_bandwidth(tau_rel)
if (!is.null(hasil_bw)) {
hasil_tau_list[[i]] <- hasil_bw
}
}## Proses ke- 1 dari 82 | Tau relatif: 0
## Proses ke- 2 dari 82 | Tau relatif: 1e-08
## Proses ke- 3 dari 82 | Tau relatif: 3.162278e-08
## Proses ke- 4 dari 82 | Tau relatif: 1e-07
## Proses ke- 5 dari 82 | Tau relatif: 3.162278e-07
## Proses ke- 6 dari 82 | Tau relatif: 1e-06
## Proses ke- 7 dari 82 | Tau relatif: 3.162278e-06
## Proses ke- 8 dari 82 | Tau relatif: 1e-05
## Proses ke- 9 dari 82 | Tau relatif: 3.162278e-05
## Proses ke- 10 dari 82 | Tau relatif: 1e-04
## Proses ke- 11 dari 82 | Tau relatif: 0.0003162278
## Proses ke- 12 dari 82 | Tau relatif: 0.001
## Proses ke- 13 dari 82 | Tau relatif: 0.001258925
## Proses ke- 14 dari 82 | Tau relatif: 0.001584893
## Proses ke- 15 dari 82 | Tau relatif: 0.001995262
## Proses ke- 16 dari 82 | Tau relatif: 0.002511886
## Proses ke- 17 dari 82 | Tau relatif: 0.003162278
## Proses ke- 18 dari 82 | Tau relatif: 0.003981072
## Proses ke- 19 dari 82 | Tau relatif: 0.005011872
## Proses ke- 20 dari 82 | Tau relatif: 0.006309573
## Proses ke- 21 dari 82 | Tau relatif: 0.007943282
## Proses ke- 22 dari 82 | Tau relatif: 0.01
## Proses ke- 23 dari 82 | Tau relatif: 0.01258925
## Proses ke- 24 dari 82 | Tau relatif: 0.01584893
## Proses ke- 25 dari 82 | Tau relatif: 0.01995262
## Proses ke- 26 dari 82 | Tau relatif: 0.02511886
## Proses ke- 27 dari 82 | Tau relatif: 0.03162278
## Proses ke- 28 dari 82 | Tau relatif: 0.03981072
## Proses ke- 29 dari 82 | Tau relatif: 0.05011872
## Proses ke- 30 dari 82 | Tau relatif: 0.06309573
## Proses ke- 31 dari 82 | Tau relatif: 0.07943282
## Proses ke- 32 dari 82 | Tau relatif: 0.1
## Proses ke- 33 dari 82 | Tau relatif: 0.1258925
## Proses ke- 34 dari 82 | Tau relatif: 0.1584893
## Proses ke- 35 dari 82 | Tau relatif: 0.1995262
## Proses ke- 36 dari 82 | Tau relatif: 0.2511886
## Proses ke- 37 dari 82 | Tau relatif: 0.3162278
## Proses ke- 38 dari 82 | Tau relatif: 0.3981072
## Proses ke- 39 dari 82 | Tau relatif: 0.5011872
## Proses ke- 40 dari 82 | Tau relatif: 0.6309573
## Proses ke- 41 dari 82 | Tau relatif: 0.7943282
## Proses ke- 42 dari 82 | Tau relatif: 1
## Proses ke- 43 dari 82 | Tau relatif: 1.258925
## Proses ke- 44 dari 82 | Tau relatif: 1.584893
## Proses ke- 45 dari 82 | Tau relatif: 1.995262
## Proses ke- 46 dari 82 | Tau relatif: 2.511886
## Proses ke- 47 dari 82 | Tau relatif: 3.162278
## Proses ke- 48 dari 82 | Tau relatif: 3.981072
## Proses ke- 49 dari 82 | Tau relatif: 5.011872
## Proses ke- 50 dari 82 | Tau relatif: 6.309573
## Proses ke- 51 dari 82 | Tau relatif: 7.943282
## Proses ke- 52 dari 82 | Tau relatif: 10
## Proses ke- 53 dari 82 | Tau relatif: 12.58925
## Proses ke- 54 dari 82 | Tau relatif: 15.84893
## Proses ke- 55 dari 82 | Tau relatif: 19.95262
## Proses ke- 56 dari 82 | Tau relatif: 25.11886
## Proses ke- 57 dari 82 | Tau relatif: 31.62278
## Proses ke- 58 dari 82 | Tau relatif: 39.81072
## Proses ke- 59 dari 82 | Tau relatif: 50.11872
## Proses ke- 60 dari 82 | Tau relatif: 63.09573
## Proses ke- 61 dari 82 | Tau relatif: 79.43282
## Proses ke- 62 dari 82 | Tau relatif: 100
## Proses ke- 63 dari 82 | Tau relatif: 125.8925
## Proses ke- 64 dari 82 | Tau relatif: 158.4893
## Proses ke- 65 dari 82 | Tau relatif: 199.5262
## Proses ke- 66 dari 82 | Tau relatif: 251.1886
## Proses ke- 67 dari 82 | Tau relatif: 316.2278
## Proses ke- 68 dari 82 | Tau relatif: 398.1072
## Proses ke- 69 dari 82 | Tau relatif: 501.1872
## Proses ke- 70 dari 82 | Tau relatif: 630.9573
## Proses ke- 71 dari 82 | Tau relatif: 794.3282
## Proses ke- 72 dari 82 | Tau relatif: 1000
## Proses ke- 73 dari 82 | Tau relatif: 1258.925
## Proses ke- 74 dari 82 | Tau relatif: 1584.893
## Proses ke- 75 dari 82 | Tau relatif: 1995.262
## Proses ke- 76 dari 82 | Tau relatif: 2511.886
## Proses ke- 77 dari 82 | Tau relatif: 3162.278
## Proses ke- 78 dari 82 | Tau relatif: 3981.072
## Proses ke- 79 dari 82 | Tau relatif: 5011.872
## Proses ke- 80 dari 82 | Tau relatif: 6309.573
## Proses ke- 81 dari 82 | Tau relatif: 7943.282
## Proses ke- 82 dari 82 | Tau relatif: 10000# Menggabungkan hasil seluruh pencarian
hasil_tau <- dplyr::bind_rows(
hasil_tau_list
)
# Pemeriksaan hasil
if (nrow(hasil_tau) == 0) {
stop("Tidak ada kandidat tau yang berhasil diestimasi.")
}
# Mengurutkan berdasarkan AICc terkecil
hasil_tau <- hasil_tau[
order(hasil_tau$AICc),
]
rownames(hasil_tau) <- NULL
# Menampilkan hasil optimasi
print(hasil_tau)## tau_rel tau bandwidth AICc R2 enp RSS
## 1 3.162278e-08 5.527886e-05 24 1310.083 0.8870383 39.96974 752.8598
## 2 1.000000e-07 1.748071e-04 24 1310.083 0.8870382 39.96972 752.8606
## 3 3.162278e-07 5.527886e-04 24 1310.084 0.8870378 39.96968 752.8629
## 4 1.000000e-06 1.748071e-03 24 1310.087 0.8870367 39.96953 752.8703
## 5 3.162278e-06 5.527886e-03 24 1310.096 0.8870332 39.96908 752.8938
## 6 1.000000e-05 1.748071e-02 24 1310.125 0.8870221 39.96763 752.9679
## 7 3.162278e-05 5.527886e-02 24 1310.215 0.8869869 39.96304 753.2022
## 8 1.000000e-04 1.748071e-01 24 1310.501 0.8868759 39.94847 753.9420
## 9 3.162278e-04 5.527886e-01 24 1311.391 0.8865268 39.89960 756.2689
## 10 1.000000e-03 1.748071e+00 24 1314.118 0.8854597 39.76023 763.3809
## 11 1.258925e-03 2.200691e+00 24 1315.152 0.8850523 39.70421 766.0958
## 12 1.584893e-03 2.770506e+00 24 1316.467 0.8845301 39.62712 769.5764
## 13 1.995262e-03 3.487860e+00 24 1318.146 0.8838573 39.52079 774.0602
## 14 2.511886e-03 4.390956e+00 24 1320.079 0.8830595 39.37631 779.3774
## 15 3.162278e-03 5.527886e+00 24 1322.301 0.8821219 39.19253 785.6266
## 16 3.981072e-03 6.959196e+00 24 1324.999 0.8809611 38.94692 793.3631
## 17 5.011872e-03 8.761109e+00 24 1328.299 0.8795216 38.63332 802.9570
## 18 6.309573e-03 1.102958e+01 24 1332.508 0.8776757 38.24121 815.2588
## 19 7.943282e-03 1.388542e+01 24 1337.264 0.8755665 37.80851 829.3164
## 20 1.000000e-02 1.748071e+01 24 1342.930 0.8729794 37.22699 846.5587
## 21 1.258925e-02 2.200691e+01 24 1348.856 0.8702730 36.70193 864.5960
## 22 1.584893e-02 2.770506e+01 24 1354.938 0.8673451 36.02607 884.1099
## 23 1.995262e-02 3.487860e+01 24 1362.145 0.8639040 35.34708 907.0438
## 24 2.511886e-02 4.390956e+01 24 1370.515 0.8598206 34.53821 934.2589
## 25 3.162278e-02 5.527886e+01 24 1378.441 0.8559459 33.90366 960.0822
## 26 3.981072e-02 6.959196e+01 24 1385.298 0.8525106 33.38093 982.9777
## 27 5.011872e-02 8.761109e+01 24 1392.435 0.8487690 32.72302 1007.9145
## 28 6.309573e-02 1.102958e+02 24 1402.414 0.8437558 32.20222 1041.3261
## 29 0.000000e+00 0.000000e+00 31 1405.696 0.8423408 30.30994 1050.7570
## 30 1.000000e-08 1.748071e-05 31 1405.696 0.8423408 30.30995 1050.7570
## 31 7.943282e-02 1.388542e+02 24 1412.098 0.8387849 31.73684 1074.4561
## 32 1.000000e-01 1.748071e+02 24 1419.630 0.8348153 31.41046 1100.9121
## 33 1.258925e-01 2.200691e+02 24 1427.526 0.8304793 30.97187 1129.8105
## 34 1.584893e-01 2.770506e+02 24 1436.730 0.8256823 30.84754 1161.7816
## 35 1.995262e-01 3.487860e+02 24 1444.054 0.8220688 31.12540 1185.8645
## 36 2.511886e-01 4.390956e+02 24 1451.258 0.8184887 31.45789 1209.7247
## 37 3.162278e-01 5.527886e+02 24 1461.931 0.8129333 31.72286 1246.7498
## 38 3.981072e-01 6.959196e+02 24 1471.810 0.8073530 31.64600 1283.9414
## 39 5.011872e-01 8.761109e+02 24 1479.769 0.8032526 32.13723 1311.2693
## 40 6.309573e-01 1.102958e+03 24 1489.429 0.7979655 32.52053 1346.5066
## 41 7.943282e-01 1.388542e+03 24 1499.866 0.7927409 33.60048 1381.3274
## 42 1.000000e+00 1.748071e+03 24 1510.084 0.7874051 34.55974 1416.8887
## 43 1.258925e+00 2.200691e+03 24 1519.581 0.7823660 35.45340 1450.4730
## 44 1.584893e+00 2.770506e+03 24 1529.203 0.7772612 36.46317 1484.4949
## 45 1.995262e+00 3.487860e+03 24 1539.633 0.7707829 36.75263 1527.6713
## 46 2.511886e+00 4.390956e+03 24 1548.999 0.7653361 37.50148 1563.9729
## 47 3.162278e+00 5.527886e+03 24 1558.631 0.7589160 37.58499 1606.7609
## 48 3.981072e+00 6.959196e+03 24 1565.694 0.7541906 37.65774 1638.2547
## 49 5.011872e+00 8.761109e+03 24 1574.306 0.7479440 37.45475 1679.8869
## 50 6.309573e+00 1.102958e+04 24 1584.254 0.7408593 37.52144 1727.1040
## 51 7.943282e+00 1.388542e+04 24 1592.434 0.7364492 38.75401 1756.4965
## 52 1.000000e+01 1.748071e+04 24 1601.509 0.7326156 41.00269 1782.0463
## 53 1.258925e+01 2.200691e+04 31 1608.393 0.7176341 33.41585 1881.8939
## 54 1.584893e+01 2.770506e+04 34 1614.536 0.7100909 31.34257 1932.1677
## 55 1.995262e+01 3.487860e+04 38 1619.988 0.7028631 29.27113 1980.3386
## 56 2.511886e+01 4.390956e+04 78 1624.133 0.6883144 21.53352 2077.3022
## 57 3.162278e+01 5.527886e+04 78 1626.417 0.6865216 21.64712 2089.2507
## 58 3.981072e+01 6.959196e+04 96 1628.627 0.6827320 20.32314 2114.5072
## 59 5.011872e+01 8.761109e+04 111 1629.873 0.6792915 18.68542 2137.4371
## 60 6.309573e+01 1.102958e+05 111 1631.252 0.6787097 19.11639 2141.3152
## 61 7.943282e+01 1.388542e+05 118 1632.440 0.6670808 12.17321 2218.8185
## 62 1.000000e+02 1.748071e+05 134 1632.796 0.6666267 12.09232 2221.8451
## 63 1.258925e+02 2.200691e+05 134 1633.067 0.6663474 12.07291 2223.7061
## 64 1.584893e+02 2.770506e+05 134 1633.283 0.6661240 12.05733 2225.1952
## 65 1.995262e+02 3.487860e+05 125 1633.465 0.6659556 12.05697 2226.3179
## 66 2.511886e+02 4.390956e+05 134 1633.594 0.6658030 12.03487 2227.3343
## 67 3.162278e+02 5.527886e+05 134 1633.704 0.6656895 12.02690 2228.0912
## 68 3.981072e+02 6.959196e+05 134 1633.791 0.6655990 12.02054 2228.6942
## 69 5.011872e+02 8.761109e+05 134 1633.860 0.6655270 12.01548 2229.1744
## 70 6.309573e+02 1.102958e+06 134 1633.916 0.6654696 12.01144 2229.5564
## 71 7.943282e+02 1.388542e+06 134 1633.960 0.6654240 12.00823 2229.8604
## 72 1.000000e+03 1.748071e+06 134 1633.995 0.6653878 12.00567 2230.1021
## 73 1.258925e+03 2.200691e+06 134 1634.023 0.6653589 12.00364 2230.2943
## 74 1.584893e+03 2.770506e+06 134 1634.045 0.6653360 12.00202 2230.4470
## 75 1.995262e+03 3.487860e+06 134 1634.062 0.6653178 12.00073 2230.5684
## 76 2.511886e+03 4.390956e+06 134 1634.076 0.6653033 11.99971 2230.6649
## 77 3.162278e+03 5.527886e+06 131 1634.088 0.6652920 11.99911 2230.7401
## 78 3.981072e+03 6.959196e+06 131 1634.096 0.6652828 11.99842 2230.8013
## 79 5.011872e+03 8.761109e+06 131 1634.103 0.6652755 11.99788 2230.8500
## 80 6.309573e+03 1.102958e+07 136 1634.109 0.6652694 11.99724 2230.8911
## 81 7.943282e+03 1.388542e+07 136 1634.113 0.6652648 11.99693 2230.9213
## 82 1.000000e+04 1.748071e+07 136 1634.117 0.6652612 11.99669 2230.9453# Mengambil kombinasi tau dan bandwidth
# dengan AICc paling kecil
indeks_terbaik <- which.min(
hasil_tau$AICc
)
hasil_terbaik <- hasil_tau[
indeks_terbaik,
,
drop = FALSE
]
# Parameter optimal
tau_rel_opt <- hasil_terbaik$tau_rel
tau_opt <- hasil_terbaik$tau
bandwidth_gtwr <- hasil_terbaik$bandwidth
# Menampilkan parameter terpilih
cat("Tau relatif optimal:", tau_rel_opt, "\n")## Tau relatif optimal: 3.162278e-08## Tau optimal: 5.527886e-05## Bandwidth optimal: 24## AICc minimum: 1310.083## R-squared: 0.8870383Tau optimal sebesar 0,00005527886 menunjukkan kontribusi komponen jarak temporal dalam rumus jarak gabungan relatif sangat kecil dibandingkan komponen jarak spasial. Bandwidth 24 menunjukkan bahwa estimasi lokal menggunakan 24 tetangga terdekat berdasarkan jarak gabungan spasial-temporal.
tau_positif <- hasil_tau$tau_rel[
hasil_tau$tau_rel > 0
]
tau_min_grid <- min(tau_positif)
tau_max_grid <- max(tau_positif)
if (tau_rel_opt == 0) {
warning(
"AICc minimum berada pada tau = 0. ",
"Model terbaik pada grid setara dengan GWR."
)
} else if (tau_rel_opt == tau_min_grid) {
warning(
"AICc minimum berada pada batas bawah grid. ",
"Perluas pencarian ke tau yang lebih kecil."
)
} else if (tau_rel_opt == tau_max_grid) {
warning(
"AICc minimum berada pada batas atas grid. ",
"Perluas pencarian ke tau yang lebih besar."
)
} else {
cat(
"AICc minimum berada di dalam rentang grid."
)
}## AICc minimum berada di dalam rentang grid.# Model GTWR final
model_final <- fit_gtwr(
D = st_tau(tau_opt),
bw = bandwidth_gtwr
)
model_gtwr <- model_final
# Diagnostik model
model_final$GTW.diagnostic## $RSS.gw
## [,1]
## [1,] 752.8598
##
## $AIC
## [,1]
## [1,] 1270.937
##
## $AICc
## [,1]
## [1,] 1310.083
##
## $enp
## [1] 39.96974
##
## $edf
## [1] 302.0303
##
## $gw.R2
## [,1]
## [1,] 0.8870383
##
## $gwR2.adj
## [,1]
## [1,] 0.8720397## Intercept IPM PDRB UMK TPT y yhat residual
## 1 46.97132 -0.9761497 0.2293738 1.976540 0.1176013 21.32 21.82827 -0.5082708
## 2 46.97131 -0.9761498 0.2293735 1.976542 0.1176012 19.59 21.51814 -1.9281366
## 3 46.97129 -0.9761498 0.2293733 1.976544 0.1176012 18.90 20.84162 -1.9416159
## 4 46.97129 -0.9761498 0.2293733 1.976544 0.1176011 20.56 20.01322 0.5467822
## 5 46.97129 -0.9761498 0.2293733 1.976544 0.1176011 21.57 19.68207 1.8879287
## 6 46.97129 -0.9761498 0.2293733 1.976544 0.1176011 19.44 19.00567 0.4343281
## time_stamp Stud_residual Intercept_SE IPM_SE PDRB_SE UMK_SE TPT_SE
## 1 2017 -0.3535543 9.923035 0.03980439 0.2141101 1.074602 0.1078909
## 2 2018 -1.3055691 9.923037 0.03980440 0.2141101 1.074603 0.1078909
## 3 2019 -1.2943559 9.923039 0.03980440 0.2141101 1.074603 0.1078909
## 4 2020 0.3935559 9.923039 0.03980440 0.2141101 1.074603 0.1078909
## 5 2021 1.3127319 9.923039 0.03980440 0.2141101 1.074603 0.1078909
## 6 2022 0.3012324 9.923039 0.03980440 0.2141101 1.074603 0.1078909
## Intercept_TV IPM_TV PDRB_TV UMK_TV TPT_TV
## 1 4.733564 -24.52367 1.071289 1.839322 1.090002
## 2 4.733561 -24.52367 1.071288 1.839324 1.090001
## 3 4.733559 -24.52366 1.071287 1.839325 1.090001
## 4 4.733559 -24.52366 1.071287 1.839325 1.090001
## 5 4.733559 -24.52366 1.071287 1.839325 1.090000
## 6 4.733559 -24.52366 1.071287 1.839325 1.090000hasil_plot <- hasil_tau %>%
dplyr::filter(tau_rel > 0)
ggplot(
hasil_plot,
aes(x = tau_rel, y = AICc)
) +
geom_line() +
geom_point() +
geom_point(
data = hasil_terbaik,
aes(x = tau_rel, y = AICc),
color = "red",
size = 3
) +
scale_x_log10() +
labs(
title = "Optimasi Tau pada Model GTWR",
subtitle = "Pemilihan berdasarkan AICc minimum absolut",
x = "Tau relatif (skala logaritmik)",
y = "AICc"
) +
theme_minimal()
7.4 6.3 TWR (pembanding, hanya jarak waktu)
# TWR: jarak hanya dari waktu (lambda = 0)
D_twr <- dT
bw_twr_grid <- seq(14, 112, by = 7)
hasil_twr <- data.frame(bandwidth = bw_twr_grid, AICc = NA_real_, R2 = NA_real_)
for (k in seq_along(bw_twr_grid)) {
m <- tryCatch(fit_gtwr(D_twr, bw_twr_grid[k]), error = function(e) NULL)
if (!is.null(m)) {
hasil_twr$AICc[k] <- as.numeric(m$GTW.diagnostic$AICc)
hasil_twr$R2[k] <- as.numeric(m$GTW.diagnostic$gw.R2)
}
}
hasil_twr <- hasil_twr %>% dplyr::filter(!is.na(AICc)) %>% dplyr::arrange(AICc)
head(hasil_twr)## bandwidth AICc R2
## 1 77 1639.417 0.6747267
## 2 84 1639.417 0.6747267
## 3 91 1639.417 0.6747267
## 4 98 1639.417 0.6747267
## 5 105 1639.417 0.6747267
## 6 112 1639.417 0.6747267bandwidth_twr <- hasil_twr$bandwidth[1]
model_twr <- fit_gtwr(D_twr, bandwidth_twr)
model_twr$GTW.diagnostic## $RSS.gw
## [,1]
## [1,] 2167.861
##
## $AIC
## [,1]
## [1,] 1618.753
##
## $AICc
## [,1]
## [1,] 1639.417
##
## $enp
## [1] 21.22474
##
## $edf
## [1] 320.7753
##
## $gw.R2
## [,1]
## [1,] 0.6747267
##
## $gwR2.adj
## [,1]
## [1,] 0.653137## Intercept IPM PDRB UMK
## Min. :57.72 Min. :-0.8105 Min. :-0.071271 Min. :-1.3352
## 1st Qu.:59.86 1st Qu.:-0.7508 1st Qu.:-0.041822 1st Qu.:-0.8872
## Median :70.11 Median :-0.7206 Median : 0.004199 Median :-0.1251
## Mean :67.54 Mean :-0.7345 Mean : 0.018881 Mean :-0.2814
## 3rd Qu.:73.71 3rd Qu.:-0.6961 3rd Qu.: 0.020514 3rd Qu.: 0.3164
## Max. :79.39 Max. :-0.6916 Max. : 0.213387 Max. : 0.3849
## TPT
## Min. :-0.30853
## 1st Qu.:-0.26426
## Median : 0.10275
## Mean : 0.07046
## 3rd Qu.: 0.39197
## Max. : 0.462237.5 6.4 Perbandingan OLS, TWR, GWR, dan GTWR
# Model GWR
model_gwr2 <- model_gwr
# AICc OLS
k_ols <- length(coef(model_ols))
rss_ols <- sum(residuals(model_ols)^2)
aicc_ols <- n_dat * log(rss_ols / n_dat) +
n_dat * log(2 * pi) +
n_dat * ((n_dat + k_ols) / (n_dat - 2 - k_ols))
# Perbandingan RSS
rss <- c(
OLS = rss_ols,
TWR = as.numeric(model_twr$GTW.diagnostic$RSS.gw),
GWR = as.numeric(model_gwr2$GW.diagnostic$RSS.gw),
GTWR = as.numeric(model_final$GTW.diagnostic$RSS.gw)
)
# Tabel perbandingan
tabel_banding <- data.frame(
Model = names(rss),
R2 = c(
summary(model_ols)$r.squared,
as.numeric(model_twr$GTW.diagnostic$gw.R2),
as.numeric(model_gwr2$GW.diagnostic$gw.R2),
as.numeric(model_final$GTW.diagnostic$gw.R2)
),
R2_adj = c(
summary(model_ols)$adj.r.squared,
as.numeric(model_twr$GTW.diagnostic$gwR2.adj),
as.numeric(model_gwr2$GW.diagnostic$gwR2.adj),
as.numeric(model_final$GTW.diagnostic$gwR2.adj)
),
RSS = as.numeric(rss),
RMSE = sqrt(as.numeric(rss) / n_dat),
AICc = c(
aicc_ols,
as.numeric(model_twr$GTW.diagnostic$AICc),
as.numeric(model_gwr2$GW.diagnostic$AICc),
as.numeric(model_final$GTW.diagnostic$AICc)
),
Perbaikan_RSS_vs_OLS_persen =
(1 - as.numeric(rss) / rss_ols) * 100
)
tabel_banding## Model R2 R2_adj RSS RMSE AICc
## 1 OLS 0.6329570 0.6286004 2446.2444 2.674465 1655.689
## 2 TWR 0.6747267 0.6531370 2167.8608 2.517692 1639.417
## 3 GWR 0.8423408 0.8269600 1050.7570 1.752823 1405.696
## 4 GTWR 0.8870383 0.8720397 752.8598 1.483693 1310.083
## Perbaikan_RSS_vs_OLS_persen
## 1 0.00000
## 2 11.38004
## 3 57.04612
## 4 69.223857.6 6.5 Uji nonstasioneritas (ANOVA Brunsdon et al., versi aproksimasi)
# F = [(RSS0 - RSS1)/(df0 - df1)] / [RSS1/df1]
anova_lokal <- function(rss1, df1, ols_model, nama) {
rss0 <- sum(residuals(ols_model)^2)
df0 <- df.residual(ols_model)
F_val <- ((rss0 - rss1) / (df0 - df1)) / (rss1 / df1)
data.frame(
Model = nama, RSS_OLS = rss0, RSS_lokal = rss1,
df_OLS = df0, df_lokal = df1,
F = F_val,
p_value = pf(F_val, df0 - df1, df1, lower.tail = FALSE)
)
}
tabel_anova <- rbind(
anova_lokal(as.numeric(model_twr$GTW.diagnostic$RSS.gw),
as.numeric(model_twr$GTW.diagnostic$edf), model_ols, "TWR vs OLS"),
anova_lokal(as.numeric(model_gwr2$GW.diagnostic$RSS.gw),
as.numeric(model_gwr2$GW.diagnostic$edf), model_ols, "GWR vs OLS"),
anova_lokal(as.numeric(model_final$GTW.diagnostic$RSS.gw),
as.numeric(model_final$GTW.diagnostic$edf), model_ols, "GTWR vs OLS")
)
tabel_anova## Model RSS_OLS RSS_lokal df_OLS df_lokal F p_value
## 1 TWR vs OLS 2446.244 2167.8608 337 320.7753 2.53884 9.996476e-04
## 2 GWR vs OLS 2446.244 1050.7570 337 311.6901 16.35518 2.761640e-43
## 3 GTWR vs OLS 2446.244 752.8598 337 302.0303 19.42672 3.215184e-58h0:Model lokal tidak memberikan perbaikan signifikan TWR vs OLS: p-value kurang dari 0,05, sehingga model TWR memberikan perbaikan yang signifikan dibandingkan OLS menurut pengujian ini.
GWR vs OLS: p-value kurang dari 0,05, sehingga terdapat bukti bahwa model GWR memberikan perbaikan signifikan dibandingkan OLS. Ini mendukung adanya variasi hubungan antarwilayah.
GTWR vs OLS: p-value kurang dari 0,05, sehingga model GTWR memberikan perbaikan signifikan dibandingkan OLS.
7.7 6.6 Uji variasi parameter (Leung et al., 2000) untuk TWR, GWR, GTWR
leung_test <- function(D, bw, d = dat, formula = formula_gtwr) {
X <- model.matrix(formula, data = d@data)
y <- d@data$PPM
n <- nrow(X); p <- ncol(X)
Bk <- array(0, c(p, n, n)) # Bk[k, i, ] = baris ke-i operator beta_k
L <- matrix(0, n, n) # matriks hat
for (i in seq_len(n)) {
w <- GWmodel::gw.weight(D[, i], bw, kernel = "gaussian", adaptive = TRUE)
XtW <- t(X * as.vector(w))
A <- solve(XtW %*% X) %*% XtW # p x n
for (k in seq_len(p)) Bk[k, i, ] <- A[k, ]
L[i, ] <- X[i, ] %*% A
}
I <- diag(n)
J <- matrix(1 / n, n, n)
IL <- I - L
S1 <- t(IL) %*% IL
d1 <- sum(diag(S1))
d2 <- sum(diag(S1 %*% S1))
sig2 <- as.numeric(t(y) %*% S1 %*% y) / d1
tab <- do.call(rbind, lapply(seq_len(p), function(k) {
B <- Bk[k, , ]
M <- t(B) %*% (I - J) %*% B / n
g1 <- sum(diag(M))
g2 <- sum(diag(M %*% M))
V2 <- as.numeric(t(y) %*% M %*% y)
Fv <- V2 / (g1 * sig2)
df_a <- g1^2 / g2
df_b <- d1^2 / d2
data.frame(
Parameter = colnames(X)[k],
F = Fv, df1 = df_a, df2 = df_b,
p_value = pf(Fv, df_a, df_b, lower.tail = FALSE)
)
}))
tab$Signifikan <- ifelse(tab$p_value < 0.05, "*", "")
beta <- sapply(seq_len(p), function(k) Bk[k, , ] %*% y)
colnames(beta) <- colnames(X)
list(tabel = tab, beta = beta)
}
lt_twr <- leung_test(D_twr, bandwidth_twr)
lt_gwr <- leung_test(dS, bw_gwr)
lt_gtwr <- leung_test(st_tau(tau_opt), bandwidth_gtwr)
# Validasi
cat("Selisih maks koefisien GTWR manual vs GWmodel:",
max(abs(lt_gtwr$beta[, c("(Intercept)", xv)] -
as.matrix(model_final$SDF@data[, c("Intercept", xv)]))), "\n")## Selisih maks koefisien GTWR manual vs GWmodel: 2.624461e-10cat("Selisih maks koefisien GWR manual vs GWmodel:",
max(abs(lt_gwr$beta[, c("(Intercept)", xv)] -
as.matrix(model_gwr2$SDF@data[, c("Intercept", xv)]))), "\n")## Selisih maks koefisien GWR manual vs GWmodel: 1.41501e-10# Tabel
tabel5 <- data.frame(
Parameter = lt_gtwr$tabel$Parameter,
TWR_F = lt_twr$tabel$F, TWR_p = lt_twr$tabel$p_value,
GWR_F = lt_gwr$tabel$F, GWR_p = lt_gwr$tabel$p_value,
GTWR_F = lt_gtwr$tabel$F, GTWR_p = lt_gtwr$tabel$p_value
)
tabel5## Parameter TWR_F TWR_p GWR_F GWR_p GTWR_F
## 1 (Intercept) 0.5291956 0.641324545 3.442424 9.692479e-03 4.64481
## 2 IPM 0.7790822 0.491729379 18.043583 8.673398e-14 24.89182
## 3 PDRB 0.1139822 0.933176415 16.448789 3.378222e-12 17.33079
## 4 UMK 0.4095832 0.719706682 14.157565 5.511830e-11 13.82899
## 5 TPT 5.8189782 0.001286651 2.066869 7.521553e-02 2.08231
## GTWR_p
## 1 1.026324e-04
## 2 2.603279e-25
## 3 1.434021e-18
## 4 6.800598e-15
## 5 4.871883e-027.8 6.7 Signifikansi koefisien lokal GTWR (uji-t, β ≠ 0)
hasil_gtwr <- as.data.frame(model_final$SDF@data) %>%
dplyr::mutate(
Kabupaten = dat@data$`Kabupaten/Kota`,
Tahun = dat@data$Tahun
)
df_eff <- as.numeric(model_final$GTW.diagnostic$edf)
for (v in xv) {
hasil_gtwr[[paste0(v, "_p")]] <- 2 * pt(-abs(hasil_gtwr[[paste0(v, "_TV")]]), df = df_eff)
hasil_gtwr[[paste0(v, "_sig")]] <- ifelse(hasil_gtwr[[paste0(v, "_p")]] < 0.05,
"Signifikan", "Tidak signifikan")
}
ringkasan_signifikansi <- data.frame(
Variabel = xv,
Jumlah = sapply(xv, function(v) sum(hasil_gtwr[[paste0(v, "_p")]] < 0.05)),
Persentase = sapply(xv, function(v) mean(hasil_gtwr[[paste0(v, "_p")]] < 0.05) * 100)
)
ringkasan_signifikansi## Variabel Jumlah Persentase
## IPM IPM 342 100.00000
## PDRB PDRB 144 42.10526
## UMK UMK 189 55.26316
## TPT TPT 45 13.15789# Tabel per observasi
hasil_gtwr %>%
dplyr::select(Kabupaten, Tahun, dplyr::ends_with("_TV"), dplyr::ends_with("_p"))## Kabupaten Tahun Intercept_TV IPM_TV PDRB_TV UMK_TV
## 1 Bangkalan 2017 4.73356405 -24.523667 1.0712889 1.83932249
## 2 Bangkalan 2018 4.73356130 -24.523665 1.0712876 1.83932402
## 3 Bangkalan 2019 4.73355918 -24.523664 1.0712866 1.83932520
## 4 Bangkalan 2020 4.73355926 -24.523664 1.0712866 1.83932518
## 5 Bangkalan 2021 4.73355935 -24.523664 1.0712867 1.83932516
## 6 Bangkalan 2022 4.73355943 -24.523664 1.0712868 1.83932514
## 7 Bangkalan 2023 4.73355951 -24.523664 1.0712868 1.83932512
## 8 Bangkalan 2024 4.73356179 -24.523665 1.0712879 1.83932389
## 9 Bangkalan 2025 4.73356471 -24.523667 1.0712893 1.83932232
## 10 Banyuwangi 2017 0.57796594 -9.965749 -7.3987091 5.73486189
## 11 Banyuwangi 2018 0.57796599 -9.965747 -7.3987090 5.73486127
## 12 Banyuwangi 2019 0.57796603 -9.965746 -7.3987090 5.73486079
## 13 Banyuwangi 2020 0.57796604 -9.965746 -7.3987090 5.73486085
## 14 Banyuwangi 2021 0.57796605 -9.965746 -7.3987091 5.73486091
## 15 Banyuwangi 2022 0.57796606 -9.965746 -7.3987092 5.73486097
## 16 Banyuwangi 2023 0.57796607 -9.965746 -7.3987092 5.73486104
## 17 Banyuwangi 2024 0.57796605 -9.965747 -7.3987094 5.73486163
## 18 Banyuwangi 2025 0.57796602 -9.965749 -7.3987096 5.73486238
## 19 Blitar 2017 6.18308677 -9.803280 0.9629800 -2.31804259
## 20 Blitar 2018 6.18308577 -9.803277 0.9629797 -2.31804272
## 21 Blitar 2019 6.18308499 -9.803275 0.9629795 -2.31804280
## 22 Blitar 2020 6.18308493 -9.803275 0.9629795 -2.31804274
## 23 Blitar 2021 6.18308488 -9.803275 0.9629795 -2.31804267
## 24 Blitar 2022 6.18308482 -9.803275 0.9629795 -2.31804261
## 25 Blitar 2023 6.18308476 -9.803274 0.9629795 -2.31804255
## 26 Blitar 2024 6.18308543 -9.803276 0.9629797 -2.31804233
## 27 Blitar 2025 6.18308631 -9.803278 0.9629799 -2.31804208
## 28 Bojonegoro 2017 3.10695367 -18.313788 -0.3534213 4.09678794
## 29 Bojonegoro 2018 3.10695218 -18.313787 -0.3534219 4.09678851
## 30 Bojonegoro 2019 3.10695102 -18.313785 -0.3534223 4.09678897
## 31 Bojonegoro 2020 3.10695099 -18.313785 -0.3534223 4.09678903
## 32 Bojonegoro 2021 3.10695096 -18.313785 -0.3534223 4.09678910
## 33 Bojonegoro 2022 3.10695093 -18.313785 -0.3534223 4.09678916
## 34 Bojonegoro 2023 3.10695090 -18.313785 -0.3534224 4.09678922
## 35 Bojonegoro 2024 3.10695200 -18.313786 -0.3534219 4.09678890
## 36 Bojonegoro 2025 3.10695343 -18.313788 -0.3534213 4.09678845
## 37 Bondowoso 2017 -1.18159424 -12.454865 -8.6279399 8.37237956
## 38 Bondowoso 2018 -1.18159420 -12.454862 -8.6279399 8.37237882
## 39 Bondowoso 2019 -1.18159415 -12.454861 -8.6279400 8.37237826
## 40 Bondowoso 2020 -1.18159412 -12.454861 -8.6279401 8.37237834
## 41 Bondowoso 2021 -1.18159409 -12.454861 -8.6279402 8.37237842
## 42 Bondowoso 2022 -1.18159406 -12.454861 -8.6279403 8.37237850
## 43 Bondowoso 2023 -1.18159403 -12.454861 -8.6279404 8.37237857
## 44 Bondowoso 2024 -1.18159402 -12.454863 -8.6279405 8.37237929
## 45 Bondowoso 2025 -1.18159401 -12.454865 -8.6279407 8.37238019
## 46 Gresik 2017 3.38728254 -18.573249 0.3017007 2.27522090
## 47 Gresik 2018 3.38727996 -18.573245 0.3016995 2.27522215
## 48 Gresik 2019 3.38727794 -18.573242 0.3016986 2.27522314
## 49 Gresik 2020 3.38727786 -18.573242 0.3016984 2.27522319
## 50 Gresik 2021 3.38727777 -18.573242 0.3016983 2.27522324
## 51 Gresik 2022 3.38727768 -18.573242 0.3016982 2.27522329
## 52 Gresik 2023 3.38727759 -18.573242 0.3016981 2.27522334
## 53 Gresik 2024 3.38727943 -18.573245 0.3016988 2.27522246
## 54 Gresik 2025 3.38728183 -18.573248 0.3016998 2.27522131
## 55 Jember 2017 0.51452727 -17.601391 -8.2079705 8.79421408
## 56 Jember 2018 0.51452658 -17.601389 -8.2079708 8.79421458
## 57 Jember 2019 0.51452604 -17.601388 -8.2079711 8.79421498
## 58 Jember 2020 0.51452605 -17.601388 -8.2079712 8.79421503
## 59 Jember 2021 0.51452606 -17.601388 -8.2079712 8.79421508
## 60 Jember 2022 0.51452607 -17.601388 -8.2079712 8.79421513
## 61 Jember 2023 0.51452609 -17.601389 -8.2079712 8.79421518
## 62 Jember 2024 0.51452664 -17.601390 -8.2079709 8.79421487
## 63 Jember 2025 0.51452736 -17.601391 -8.2079705 8.79421447
## 64 Jombang 2017 3.84245110 -10.278058 3.3694139 -0.42203119
## 65 Jombang 2018 3.84244789 -10.278052 3.3694134 -0.42203041
## 66 Jombang 2019 3.84244541 -10.278047 3.3694129 -0.42202978
## 67 Jombang 2020 3.84244549 -10.278047 3.3694127 -0.42202967
## 68 Jombang 2021 3.84244556 -10.278048 3.3694125 -0.42202957
## 69 Jombang 2022 3.84244564 -10.278048 3.3694123 -0.42202947
## 70 Jombang 2023 3.84244571 -10.278048 3.3694121 -0.42202936
## 71 Jombang 2024 3.84244834 -10.278053 3.3694122 -0.42202978
## 72 Jombang 2025 3.84245169 -10.278060 3.3694123 -0.42203036
## 73 Kediri 2017 5.49251973 -9.814933 1.5133039 -1.49734279
## 74 Kediri 2018 5.49251789 -9.814929 1.5133034 -1.49734259
## 75 Kediri 2019 5.49251644 -9.814927 1.5133031 -1.49734241
## 76 Kediri 2020 5.49251637 -9.814926 1.5133030 -1.49734232
## 77 Kediri 2021 5.49251629 -9.814926 1.5133030 -1.49734224
## 78 Kediri 2022 5.49251621 -9.814926 1.5133030 -1.49734215
## 79 Kediri 2023 5.49251614 -9.814926 1.5133029 -1.49734206
## 80 Kediri 2024 5.49251743 -9.814928 1.5133032 -1.49734206
## 81 Kediri 2025 5.49251912 -9.814931 1.5133036 -1.49734209
## 82 Kota Batu 2017 5.09881999 -12.213042 3.4891276 -1.45837769
## 83 Kota Batu 2018 5.09881777 -12.213039 3.4891279 -1.45837719
## 84 Kota Batu 2019 5.09881602 -12.213036 3.4891280 -1.45837680
## 85 Kota Batu 2020 5.09881588 -12.213036 3.4891280 -1.45837675
## 86 Kota Batu 2021 5.09881574 -12.213036 3.4891280 -1.45837670
## 87 Kota Batu 2022 5.09881560 -12.213036 3.4891280 -1.45837665
## 88 Kota Batu 2023 5.09881546 -12.213035 3.4891280 -1.45837660
## 89 Kota Batu 2024 5.09881694 -12.213037 3.4891277 -1.45837690
## 90 Kota Batu 2025 5.09881888 -12.213040 3.4891274 -1.45837729
## 91 Kota Blitar 2017 5.20344474 -7.271995 0.5258399 -2.28688033
## 92 Kota Blitar 2018 5.20344319 -7.271992 0.5258396 -2.28688026
## 93 Kota Blitar 2019 5.20344199 -7.271989 0.5258393 -2.28688019
## 94 Kota Blitar 2020 5.20344198 -7.271989 0.5258393 -2.28688013
## 95 Kota Blitar 2021 5.20344197 -7.271988 0.5258393 -2.28688006
## 96 Kota Blitar 2022 5.20344196 -7.271988 0.5258393 -2.28687999
## 97 Kota Blitar 2023 5.20344195 -7.271988 0.5258392 -2.28687993
## 98 Kota Blitar 2024 5.20344314 -7.271990 0.5258394 -2.28687986
## 99 Kota Blitar 2025 5.20344466 -7.271993 0.5258397 -2.28687980
## 100 Kota Kediri 2017 3.84046829 -8.645216 0.6963816 -0.56987077
## 101 Kota Kediri 2018 3.84046561 -8.645212 0.6963807 -0.56986995
## 102 Kota Kediri 2019 3.84046350 -8.645209 0.6963800 -0.56986929
## 103 Kota Kediri 2020 3.84046339 -8.645209 0.6963799 -0.56986919
## 104 Kota Kediri 2021 3.84046329 -8.645209 0.6963799 -0.56986910
## 105 Kota Kediri 2022 3.84046318 -8.645208 0.6963798 -0.56986900
## 106 Kota Kediri 2023 3.84046307 -8.645208 0.6963798 -0.56986891
## 107 Kota Kediri 2024 3.84046496 -8.645210 0.6963803 -0.56986938
## 108 Kota Kediri 2025 3.84046742 -8.645213 0.6963811 -0.56987002
## 109 Kota Madiun 2017 -0.09253294 -10.137977 -1.7161345 3.29108799
## 110 Kota Madiun 2018 -0.09253250 -10.137974 -1.7161334 3.29108774
## 111 Kota Madiun 2019 -0.09253214 -10.137971 -1.7161327 3.29108755
## 112 Kota Madiun 2020 -0.09253202 -10.137970 -1.7161332 3.29108756
## 113 Kota Madiun 2021 -0.09253190 -10.137970 -1.7161336 3.29108757
## 114 Kota Madiun 2022 -0.09253179 -10.137970 -1.7161340 3.29108758
## 115 Kota Madiun 2023 -0.09253167 -10.137969 -1.7161344 3.29108759
## 116 Kota Madiun 2024 -0.09253181 -10.137971 -1.7161360 3.29108780
## 117 Kota Madiun 2025 -0.09253201 -10.137973 -1.7161378 3.29108807
## 118 Kota Malang 2017 0.38953382 -6.830395 3.3765578 -0.35445063
## 119 Kota Malang 2018 0.38952952 -6.830391 3.3765592 -0.35444926
## 120 Kota Malang 2019 0.38952617 -6.830389 3.3765603 -0.35444821
## 121 Kota Malang 2020 0.38952613 -6.830388 3.3765605 -0.35444832
## 122 Kota Malang 2021 0.38952609 -6.830387 3.3765607 -0.35444842
## 123 Kota Malang 2022 0.38952605 -6.830387 3.3765608 -0.35444853
## 124 Kota Malang 2023 0.38952602 -6.830386 3.3765610 -0.35444864
## 125 Kota Malang 2024 0.38952930 -6.830388 3.3765602 -0.35444990
## 126 Kota Malang 2025 0.38953352 -6.830390 3.3765591 -0.35445150
## 127 Kota Mojokerto 2017 1.75724315 -10.077004 0.2370833 1.90537299
## 128 Kota Mojokerto 2018 1.75723895 -10.076998 0.2370795 1.90537515
## 129 Kota Mojokerto 2019 1.75723567 -10.076994 0.2370765 1.90537684
## 130 Kota Mojokerto 2020 1.75723565 -10.076994 0.2370763 1.90537692
## 131 Kota Mojokerto 2021 1.75723563 -10.076994 0.2370761 1.90537700
## 132 Kota Mojokerto 2022 1.75723561 -10.076994 0.2370759 1.90537708
## 133 Kota Mojokerto 2023 1.75723559 -10.076995 0.2370757 1.90537715
## 134 Kota Mojokerto 2024 1.75723883 -10.076999 0.2370783 1.90537562
## 135 Kota Mojokerto 2025 1.75724299 -10.077005 0.2370816 1.90537361
## 136 Kota Pasuruan 2017 6.36329023 -15.940220 1.7946903 -1.21441683
## 137 Kota Pasuruan 2018 6.36328777 -15.940214 1.7946897 -1.21441633
## 138 Kota Pasuruan 2019 6.36328584 -15.940210 1.7946891 -1.21441594
## 139 Kota Pasuruan 2020 6.36328574 -15.940210 1.7946891 -1.21441592
## 140 Kota Pasuruan 2021 6.36328564 -15.940210 1.7946891 -1.21441589
## 141 Kota Pasuruan 2022 6.36328554 -15.940210 1.7946891 -1.21441586
## 142 Kota Pasuruan 2023 6.36328544 -15.940210 1.7946891 -1.21441584
## 143 Kota Pasuruan 2024 6.36328717 -15.940214 1.7946896 -1.21441618
## 144 Kota Pasuruan 2025 6.36328942 -15.940220 1.7946902 -1.21441663
## 145 Kota Probolinggo 2017 2.80778568 -17.854816 -1.4976290 3.20190674
## 146 Kota Probolinggo 2018 2.80778380 -17.854813 -1.4976297 3.20190771
## 147 Kota Probolinggo 2019 2.80778233 -17.854811 -1.4976302 3.20190846
## 148 Kota Probolinggo 2020 2.80778229 -17.854811 -1.4976301 3.20190842
## 149 Kota Probolinggo 2021 2.80778225 -17.854811 -1.4976300 3.20190837
## 150 Kota Probolinggo 2022 2.80778221 -17.854811 -1.4976300 3.20190833
## 151 Kota Probolinggo 2023 2.80778218 -17.854811 -1.4976299 3.20190829
## 152 Kota Probolinggo 2024 2.80778357 -17.854813 -1.4976292 3.20190746
## 153 Kota Probolinggo 2025 2.80778538 -17.854817 -1.4976283 3.20190640
## 154 Kota Surabaya 2017 5.12329426 -20.587246 1.1950956 0.80336506
## 155 Kota Surabaya 2018 5.12328989 -20.587244 1.1950941 0.80336758
## 156 Kota Surabaya 2019 5.12328650 -20.587242 1.1950929 0.80336954
## 157 Kota Surabaya 2020 5.12328653 -20.587242 1.1950929 0.80336955
## 158 Kota Surabaya 2021 5.12328657 -20.587242 1.1950928 0.80336956
## 159 Kota Surabaya 2022 5.12328660 -20.587242 1.1950928 0.80336958
## 160 Kota Surabaya 2023 5.12328663 -20.587242 1.1950928 0.80336959
## 161 Kota Surabaya 2024 5.12329009 -20.587243 1.1950939 0.80336766
## 162 Kota Surabaya 2025 5.12329453 -20.587246 1.1950954 0.80336517
## 163 Lamongan 2017 6.27035101 -24.186710 1.2607959 1.95794629
## 164 Lamongan 2018 6.27034950 -24.186707 1.2607954 1.95794684
## 165 Lamongan 2019 6.27034832 -24.186705 1.2607950 1.95794728
## 166 Lamongan 2020 6.27034828 -24.186705 1.2607950 1.95794736
## 167 Lamongan 2021 6.27034824 -24.186705 1.2607949 1.95794744
## 168 Lamongan 2022 6.27034819 -24.186705 1.2607948 1.95794751
## 169 Lamongan 2023 6.27034815 -24.186705 1.2607947 1.95794759
## 170 Lamongan 2024 6.27034924 -24.186707 1.2607950 1.95794731
## 171 Lamongan 2025 6.27035066 -24.186710 1.2607954 1.95794691
## 172 Lumajang 2017 1.04779162 -15.198925 -3.0108153 4.81868438
## 173 Lumajang 2018 1.04779009 -15.198923 -3.0108158 4.81868534
## 174 Lumajang 2019 1.04778887 -15.198922 -3.0108162 4.81868608
## 175 Lumajang 2020 1.04778879 -15.198921 -3.0108161 4.81868610
## 176 Lumajang 2021 1.04778871 -15.198921 -3.0108161 4.81868611
## 177 Lumajang 2022 1.04778862 -15.198921 -3.0108160 4.81868612
## 178 Lumajang 2023 1.04778854 -15.198921 -3.0108159 4.81868614
## 179 Lumajang 2024 1.04778958 -15.198922 -3.0108153 4.81868542
## 180 Lumajang 2025 1.04779095 -15.198924 -3.0108146 4.81868450
## 181 Madiun 2017 0.76484693 -13.357547 -0.7310883 3.38445532
## 182 Madiun 2018 0.76484586 -13.357545 -0.7310885 3.38445514
## 183 Madiun 2019 0.76484504 -13.357544 -0.7310886 3.38445499
## 184 Madiun 2020 0.76484508 -13.357544 -0.7310886 3.38445499
## 185 Madiun 2021 0.76484513 -13.357544 -0.7310886 3.38445498
## 186 Madiun 2022 0.76484518 -13.357543 -0.7310886 3.38445498
## 187 Madiun 2023 0.76484522 -13.357543 -0.7310886 3.38445497
## 188 Madiun 2024 0.76484613 -13.357544 -0.7310885 3.38445510
## 189 Madiun 2025 0.76484729 -13.357545 -0.7310884 3.38445528
## 190 Magetan 2017 0.45666794 -11.443062 -2.7255181 3.56526000
## 191 Magetan 2018 0.45666897 -11.443061 -2.7255178 3.56526014
## 192 Magetan 2019 0.45666980 -11.443060 -2.7255177 3.56526025
## 193 Magetan 2020 0.45666996 -11.443060 -2.7255179 3.56526023
## 194 Magetan 2021 0.45667011 -11.443060 -2.7255181 3.56526021
## 195 Magetan 2022 0.45667027 -11.443060 -2.7255183 3.56526019
## 196 Magetan 2023 0.45667043 -11.443059 -2.7255186 3.56526017
## 197 Magetan 2024 0.45666991 -11.443059 -2.7255192 3.56526002
## 198 Magetan 2025 0.45666921 -11.443060 -2.7255199 3.56525984
## 199 Malang 2017 4.35417189 -10.125403 2.0547255 -1.01009362
## 200 Malang 2018 4.35417045 -10.125400 2.0547257 -1.01009361
## 201 Malang 2019 4.35416930 -10.125398 2.0547258 -1.01009360
## 202 Malang 2020 4.35416916 -10.125397 2.0547259 -1.01009358
## 203 Malang 2021 4.35416902 -10.125397 2.0547259 -1.01009356
## 204 Malang 2022 4.35416888 -10.125397 2.0547259 -1.01009354
## 205 Malang 2023 4.35416874 -10.125396 2.0547260 -1.01009351
## 206 Malang 2024 4.35416961 -10.125398 2.0547259 -1.01009348
## 207 Malang 2025 4.35417077 -10.125400 2.0547258 -1.01009344
## 208 Mojokerto 2017 2.49876039 -11.868336 1.3386736 1.29541160
## 209 Mojokerto 2018 2.49875574 -11.868330 1.3386703 1.29541441
## 210 Mojokerto 2019 2.49875211 -11.868326 1.3386678 1.29541660
## 211 Mojokerto 2020 2.49875208 -11.868326 1.3386676 1.29541663
## 212 Mojokerto 2021 2.49875206 -11.868326 1.3386675 1.29541666
## 213 Mojokerto 2022 2.49875204 -11.868326 1.3386674 1.29541669
## 214 Mojokerto 2023 2.49875201 -11.868327 1.3386673 1.29541672
## 215 Mojokerto 2024 2.49875559 -11.868331 1.3386696 1.29541459
## 216 Mojokerto 2025 2.49876020 -11.868337 1.3386726 1.29541183
## 217 Nganjuk 2017 3.86370789 -13.602514 1.3764632 0.85329039
## 218 Nganjuk 2018 3.86370614 -13.602512 1.3764626 0.85329043
## 219 Nganjuk 2019 3.86370477 -13.602510 1.3764622 0.85329048
## 220 Nganjuk 2020 3.86370474 -13.602510 1.3764622 0.85329055
## 221 Nganjuk 2021 3.86370471 -13.602510 1.3764621 0.85329062
## 222 Nganjuk 2022 3.86370469 -13.602510 1.3764621 0.85329068
## 223 Nganjuk 2023 3.86370466 -13.602509 1.3764620 0.85329075
## 224 Nganjuk 2024 3.86370597 -13.602511 1.3764624 0.85329084
## 225 Nganjuk 2025 3.86370766 -13.602513 1.3764629 0.85329094
## 226 Ngawi 2017 0.31972387 -12.089077 -3.6174384 4.44392772
## 227 Ngawi 2018 0.31972407 -12.089076 -3.6174392 4.44392764
## 228 Ngawi 2019 0.31972424 -12.089075 -3.6174398 4.44392757
## 229 Ngawi 2020 0.31972431 -12.089075 -3.6174397 4.44392748
## 230 Ngawi 2021 0.31972437 -12.089075 -3.6174397 4.44392740
## 231 Ngawi 2022 0.31972444 -12.089075 -3.6174396 4.44392732
## 232 Ngawi 2023 0.31972450 -12.089075 -3.6174395 4.44392724
## 233 Ngawi 2024 0.31972447 -12.089076 -3.6174388 4.44392715
## 234 Ngawi 2025 0.31972440 -12.089077 -3.6174379 4.44392706
## 235 Pacitan 2017 1.85432998 -11.566790 -3.3353355 2.83876552
## 236 Pacitan 2018 1.85432984 -11.566789 -3.3353358 2.83876528
## 237 Pacitan 2019 1.85432974 -11.566788 -3.3353361 2.83876508
## 238 Pacitan 2020 1.85432978 -11.566788 -3.3353361 2.83876503
## 239 Pacitan 2021 1.85432982 -11.566787 -3.3353360 2.83876498
## 240 Pacitan 2022 1.85432986 -11.566787 -3.3353360 2.83876493
## 241 Pacitan 2023 1.85432990 -11.566787 -3.3353360 2.83876487
## 242 Pacitan 2024 1.85433008 -11.566788 -3.3353357 2.83876497
## 243 Pacitan 2025 1.85433031 -11.566789 -3.3353353 2.83876510
## 244 Pamekasan 2017 -3.15957724 -13.624466 2.2510918 4.57271019
## 245 Pamekasan 2018 -3.15957898 -13.624462 2.2510924 4.57271059
## 246 Pamekasan 2019 -3.15958035 -13.624459 2.2510928 4.57271092
## 247 Pamekasan 2020 -3.15958039 -13.624460 2.2510928 4.57271100
## 248 Pamekasan 2021 -3.15958043 -13.624460 2.2510928 4.57271107
## 249 Pamekasan 2022 -3.15958047 -13.624460 2.2510928 4.57271114
## 250 Pamekasan 2023 -3.15958052 -13.624460 2.2510928 4.57271122
## 251 Pamekasan 2024 -3.15957924 -13.624464 2.2510923 4.57271103
## 252 Pamekasan 2025 -3.15957758 -13.624468 2.2510917 4.57271078
## 253 Pasuruan 2017 5.31770355 -15.036133 1.5369046 -0.35153864
## 254 Pasuruan 2018 5.31770115 -15.036129 1.5369040 -0.35153797
## 255 Pasuruan 2019 5.31769926 -15.036126 1.5369036 -0.35153745
## 256 Pasuruan 2020 5.31769914 -15.036126 1.5369035 -0.35153742
## 257 Pasuruan 2021 5.31769903 -15.036126 1.5369035 -0.35153740
## 258 Pasuruan 2022 5.31769892 -15.036126 1.5369035 -0.35153737
## 259 Pasuruan 2023 5.31769881 -15.036126 1.5369035 -0.35153734
## 260 Pasuruan 2024 5.31770048 -15.036129 1.5369039 -0.35153782
## 261 Pasuruan 2025 5.31770267 -15.036133 1.5369045 -0.35153843
## 262 Ponorogo 2017 1.46620069 -10.817999 -2.3791134 2.55191805
## 263 Ponorogo 2018 1.46620068 -10.817997 -2.3791138 2.55191759
## 264 Ponorogo 2019 1.46620069 -10.817996 -2.3791141 2.55191722
## 265 Ponorogo 2020 1.46620077 -10.817996 -2.3791141 2.55191713
## 266 Ponorogo 2021 1.46620085 -10.817996 -2.3791141 2.55191705
## 267 Ponorogo 2022 1.46620093 -10.817995 -2.3791141 2.55191696
## 268 Ponorogo 2023 1.46620101 -10.817995 -2.3791141 2.55191688
## 269 Ponorogo 2024 1.46620116 -10.817996 -2.3791138 2.55191709
## 270 Ponorogo 2025 1.46620133 -10.817997 -2.3791135 2.55191738
## 271 Probolinggo 2017 -0.58395955 -16.614822 -5.7952891 7.73709583
## 272 Probolinggo 2018 -0.58396188 -16.614819 -5.7952916 7.73709828
## 273 Probolinggo 2019 -0.58396370 -16.614817 -5.7952935 7.73710018
## 274 Probolinggo 2020 -0.58396373 -16.614817 -5.7952934 7.73710015
## 275 Probolinggo 2021 -0.58396377 -16.614817 -5.7952934 7.73710012
## 276 Probolinggo 2022 -0.58396380 -16.614817 -5.7952933 7.73710008
## 277 Probolinggo 2023 -0.58396384 -16.614817 -5.7952932 7.73710005
## 278 Probolinggo 2024 -0.58396209 -16.614820 -5.7952911 7.73709808
## 279 Probolinggo 2025 -0.58395984 -16.614823 -5.7952885 7.73709556
## 280 Sampang 2017 -0.48386546 -18.570793 0.5572895 4.44359346
## 281 Sampang 2018 -0.48386903 -18.570788 0.5572877 4.44359518
## 282 Sampang 2019 -0.48387181 -18.570784 0.5572864 4.44359651
## 283 Sampang 2020 -0.48387178 -18.570784 0.5572864 4.44359648
## 284 Sampang 2021 -0.48387175 -18.570784 0.5572865 4.44359645
## 285 Sampang 2022 -0.48387172 -18.570784 0.5572866 4.44359642
## 286 Sampang 2023 -0.48387169 -18.570784 0.5572867 4.44359638
## 287 Sampang 2024 -0.48386886 -18.570788 0.5572882 4.44359499
## 288 Sampang 2025 -0.48386522 -18.570794 0.5572901 4.44359321
## 289 Sidoarjo 2017 5.16678271 -16.435359 1.3610197 -0.14584262
## 290 Sidoarjo 2018 5.16677764 -16.435353 1.3610176 -0.14584020
## 291 Sidoarjo 2019 5.16677367 -16.435349 1.3610159 -0.14583832
## 292 Sidoarjo 2020 5.16677358 -16.435349 1.3610158 -0.14583829
## 293 Sidoarjo 2021 5.16677349 -16.435349 1.3610158 -0.14583826
## 294 Sidoarjo 2022 5.16677340 -16.435348 1.3610157 -0.14583823
## 295 Sidoarjo 2023 5.16677331 -16.435348 1.3610157 -0.14583820
## 296 Sidoarjo 2024 5.16677709 -16.435352 1.3610172 -0.14584002
## 297 Sidoarjo 2025 5.16678197 -16.435357 1.3610192 -0.14584237
## 298 Situbondo 2017 -0.42204547 -20.674841 -7.8326412 9.37313922
## 299 Situbondo 2018 -0.42204599 -20.674839 -7.8326414 9.37313942
## 300 Situbondo 2019 -0.42204638 -20.674838 -7.8326416 9.37313958
## 301 Situbondo 2020 -0.42204634 -20.674838 -7.8326417 9.37313961
## 302 Situbondo 2021 -0.42204631 -20.674839 -7.8326417 9.37313963
## 303 Situbondo 2022 -0.42204627 -20.674839 -7.8326417 9.37313966
## 304 Situbondo 2023 -0.42204624 -20.674839 -7.8326417 9.37313968
## 305 Situbondo 2024 -0.42204577 -20.674840 -7.8326416 9.37313957
## 306 Situbondo 2025 -0.42204519 -20.674842 -7.8326414 9.37313942
## 307 Sumenep 2017 0.52670757 -24.247973 1.4386629 4.48230108
## 308 Sumenep 2018 0.52670652 -24.247972 1.4386632 4.48230113
## 309 Sumenep 2019 0.52670572 -24.247971 1.4386635 4.48230118
## 310 Sumenep 2020 0.52670576 -24.247971 1.4386635 4.48230119
## 311 Sumenep 2021 0.52670580 -24.247971 1.4386635 4.48230120
## 312 Sumenep 2022 0.52670583 -24.247971 1.4386635 4.48230122
## 313 Sumenep 2023 0.52670587 -24.247971 1.4386635 4.48230123
## 314 Sumenep 2024 0.52670675 -24.247972 1.4386632 4.48230121
## 315 Sumenep 2025 0.52670787 -24.247974 1.4386629 4.48230119
## 316 Trenggalek 2017 2.29057081 -8.529715 -3.9773005 1.41510321
## 317 Trenggalek 2018 2.29057101 -8.529713 -3.9773016 1.41510271
## 318 Trenggalek 2019 2.29057116 -8.529711 -3.9773025 1.41510230
## 319 Trenggalek 2020 2.29057118 -8.529711 -3.9773025 1.41510225
## 320 Trenggalek 2021 2.29057120 -8.529711 -3.9773025 1.41510220
## 321 Trenggalek 2022 2.29057122 -8.529711 -3.9773025 1.41510215
## 322 Trenggalek 2023 2.29057124 -8.529710 -3.9773025 1.41510210
## 323 Trenggalek 2024 2.29057112 -8.529712 -3.9773017 1.41510240
## 324 Trenggalek 2025 2.29057096 -8.529713 -3.9773007 1.41510280
## 325 Tuban 2017 4.40677093 -21.727335 -0.8291539 4.22133654
## 326 Tuban 2018 4.40676973 -21.727332 -0.8291545 4.22133692
## 327 Tuban 2019 4.40676879 -21.727330 -0.8291549 4.22133723
## 328 Tuban 2020 4.40676874 -21.727330 -0.8291550 4.22133727
## 329 Tuban 2021 4.40676869 -21.727330 -0.8291550 4.22133732
## 330 Tuban 2022 4.40676864 -21.727330 -0.8291550 4.22133737
## 331 Tuban 2023 4.40676859 -21.727331 -0.8291550 4.22133741
## 332 Tuban 2024 4.40676944 -21.727333 -0.8291546 4.22133720
## 333 Tuban 2025 4.40677054 -21.727335 -0.8291541 4.22133692
## 334 Tulungagung 2017 3.25319041 -7.613138 -1.3180175 -0.08072515
## 335 Tulungagung 2018 3.25318897 -7.613135 -1.3180179 -0.08072531
## 336 Tulungagung 2019 3.25318782 -7.613133 -1.3180182 -0.08072542
## 337 Tulungagung 2020 3.25318772 -7.613133 -1.3180183 -0.08072533
## 338 Tulungagung 2021 3.25318761 -7.613132 -1.3180184 -0.08072524
## 339 Tulungagung 2022 3.25318751 -7.613132 -1.3180184 -0.08072515
## 340 Tulungagung 2023 3.25318740 -7.613132 -1.3180185 -0.08072506
## 341 Tulungagung 2024 3.25318834 -7.613134 -1.3180183 -0.08072477
## 342 Tulungagung 2025 3.25318958 -7.613136 -1.3180181 -0.08072444
## TPT_TV IPM_p PDRB_p UMK_p TPT_p
## 1 1.09000198 7.740888e-74 2.848948e-01 6.684918e-02 0.276581137
## 2 1.09000134 7.741004e-74 2.848954e-01 6.684896e-02 0.276581421
## 3 1.09000079 7.741094e-74 2.848959e-01 6.684878e-02 0.276581662
## 4 1.09000058 7.741097e-74 2.848959e-01 6.684879e-02 0.276581753
## 5 1.09000038 7.741099e-74 2.848958e-01 6.684879e-02 0.276581844
## 6 1.09000017 7.741102e-74 2.848958e-01 6.684879e-02 0.276581935
## 7 1.08999996 7.741104e-74 2.848958e-01 6.684880e-02 0.276582026
## 8 1.09000010 7.741019e-74 2.848953e-01 6.684898e-02 0.276581967
## 9 1.09000033 7.740909e-74 2.848946e-01 6.684921e-02 0.276581865
## 10 -0.28961515 2.064851e-20 1.369980e-12 2.367545e-08 0.772309388
## 11 -0.28961483 2.064873e-20 1.369980e-12 2.367553e-08 0.772309636
## 12 -0.28961457 2.064891e-20 1.369980e-12 2.367559e-08 0.772309829
## 13 -0.28961457 2.064890e-20 1.369980e-12 2.367558e-08 0.772309829
## 14 -0.28961457 2.064889e-20 1.369979e-12 2.367558e-08 0.772309830
## 15 -0.28961457 2.064888e-20 1.369979e-12 2.367557e-08 0.772309830
## 16 -0.28961457 2.064888e-20 1.369978e-12 2.367556e-08 0.772309831
## 17 -0.28961482 2.064869e-20 1.369977e-12 2.367549e-08 0.772309639
## 18 -0.28961515 2.064845e-20 1.369975e-12 2.367539e-08 0.772309392
## 19 1.56106802 7.032546e-20 3.363279e-01 2.111487e-02 0.119554868
## 20 1.56106794 7.032675e-20 3.363281e-01 2.111486e-02 0.119554886
## 21 1.56106784 7.032778e-20 3.363282e-01 2.111486e-02 0.119554912
## 22 1.56106761 7.032791e-20 3.363282e-01 2.111486e-02 0.119554965
## 23 1.56106738 7.032803e-20 3.363282e-01 2.111486e-02 0.119555019
## 24 1.56106715 7.032816e-20 3.363282e-01 2.111487e-02 0.119555073
## 25 1.56106693 7.032828e-20 3.363282e-01 2.111487e-02 0.119555126
## 26 1.56106658 7.032750e-20 3.363281e-01 2.111488e-02 0.119555208
## 27 1.56106620 7.032646e-20 3.363279e-01 2.111489e-02 0.119555298
## 28 -0.17104587 6.510621e-51 7.240192e-01 5.386370e-05 0.864302228
## 29 -0.17104620 6.510712e-51 7.240188e-01 5.386358e-05 0.864301972
## 30 -0.17104650 6.510782e-51 7.240184e-01 5.386348e-05 0.864301736
## 31 -0.17104671 6.510784e-51 7.240184e-01 5.386346e-05 0.864301568
## 32 -0.17104693 6.510786e-51 7.240184e-01 5.386345e-05 0.864301400
## 33 -0.17104714 6.510787e-51 7.240184e-01 5.386343e-05 0.864301233
## 34 -0.17104735 6.510789e-51 7.240184e-01 5.386342e-05 0.864301065
## 35 -0.17104748 6.510721e-51 7.240187e-01 5.386349e-05 0.864300967
## 36 -0.17104758 6.510634e-51 7.240192e-01 5.386359e-05 0.864300888
## 37 -0.60672067 5.116537e-29 3.618296e-16 2.137859e-15 0.544492088
## 38 -0.60671976 5.116625e-29 3.618295e-16 2.137870e-15 0.544492689
## 39 -0.60671905 5.116692e-29 3.618293e-16 2.137878e-15 0.544493158
## 40 -0.60671905 5.116687e-29 3.618290e-16 2.137877e-15 0.544493159
## 41 -0.60671905 5.116682e-29 3.618288e-16 2.137876e-15 0.544493161
## 42 -0.60671905 5.116677e-29 3.618285e-16 2.137875e-15 0.544493162
## 43 -0.60671904 5.116672e-29 3.618283e-16 2.137874e-15 0.544493163
## 44 -0.60671975 5.116595e-29 3.618279e-16 2.137863e-15 0.544492698
## 45 -0.60672065 5.116497e-29 3.618275e-16 2.137850e-15 0.544492099
## 46 1.46813852 6.813417e-52 7.630878e-01 2.359322e-02 0.143107238
## 47 1.46813701 6.813638e-52 7.630887e-01 2.359314e-02 0.143107649
## 48 1.46813578 6.813811e-52 7.630895e-01 2.359308e-02 0.143107982
## 49 1.46813554 6.813816e-52 7.630896e-01 2.359308e-02 0.143108047
## 50 1.46813531 6.813820e-52 7.630897e-01 2.359307e-02 0.143108111
## 51 1.46813507 6.813824e-52 7.630898e-01 2.359307e-02 0.143108176
## 52 1.46813483 6.813828e-52 7.630899e-01 2.359307e-02 0.143108240
## 53 1.46813559 6.813663e-52 7.630893e-01 2.359312e-02 0.143108035
## 54 1.46813662 6.813450e-52 7.630886e-01 2.359319e-02 0.143107754
## 55 -0.86925925 3.226209e-48 6.591199e-15 1.120351e-16 0.385395591
## 56 -0.86925922 3.226247e-48 6.591183e-15 1.120347e-16 0.385395611
## 57 -0.86925920 3.226276e-48 6.591169e-15 1.120344e-16 0.385395620
## 58 -0.86925926 3.226273e-48 6.591169e-15 1.120343e-16 0.385395589
## 59 -0.86925932 3.226271e-48 6.591169e-15 1.120343e-16 0.385395557
## 60 -0.86925937 3.226269e-48 6.591168e-15 1.120343e-16 0.385395526
## 61 -0.86925943 3.226267e-48 6.591168e-15 1.120342e-16 0.385395495
## 62 -0.86925956 3.226233e-48 6.591180e-15 1.120345e-16 0.385395424
## 63 -0.86925971 3.226191e-48 6.591196e-15 1.120348e-16 0.385395341
## 64 0.91991924 1.905617e-21 8.510755e-04 6.733025e-01 0.358349090
## 65 0.91991859 1.905706e-21 8.510772e-04 6.733031e-01 0.358349429
## 66 0.91991802 1.905775e-21 8.510786e-04 6.733035e-01 0.358349725
## 67 0.91991775 1.905771e-21 8.510792e-04 6.733036e-01 0.358349868
## 68 0.91991747 1.905767e-21 8.510798e-04 6.733037e-01 0.358350010
## 69 0.91991720 1.905762e-21 8.510804e-04 6.733038e-01 0.358350153
## 70 0.91991693 1.905758e-21 8.510810e-04 6.733038e-01 0.358350295
## 71 0.91991695 1.905680e-21 8.510808e-04 6.733035e-01 0.358350285
## 72 0.91991705 1.905582e-21 8.510804e-04 6.733031e-01 0.358350231
## 73 1.68169410 6.442915e-20 1.312482e-01 1.353484e-01 0.093661795
## 74 1.68169392 6.443082e-20 1.312483e-01 1.353484e-01 0.093661830
## 75 1.68169370 6.443214e-20 1.312484e-01 1.353485e-01 0.093661871
## 76 1.68169337 6.443226e-20 1.312484e-01 1.353485e-01 0.093661936
## 77 1.68169304 6.443239e-20 1.312484e-01 1.353485e-01 0.093662001
## 78 1.68169270 6.443251e-20 1.312484e-01 1.353486e-01 0.093662065
## 79 1.68169237 6.443263e-20 1.312484e-01 1.353486e-01 0.093662130
## 80 1.68169192 6.443155e-20 1.312483e-01 1.353486e-01 0.093662218
## 81 1.68169143 6.443013e-20 1.312482e-01 1.353486e-01 0.093662312
## 82 0.84866485 3.766714e-28 5.567226e-04 1.457756e-01 0.396739915
## 83 0.84866425 3.766810e-28 5.567221e-04 1.457757e-01 0.396740252
## 84 0.84866372 3.766886e-28 5.567217e-04 1.457758e-01 0.396740544
## 85 0.84866348 3.766894e-28 5.567217e-04 1.457758e-01 0.396740682
## 86 0.84866323 3.766901e-28 5.567217e-04 1.457758e-01 0.396740819
## 87 0.84866298 3.766909e-28 5.567218e-04 1.457758e-01 0.396740956
## 88 0.84866274 3.766917e-28 5.567218e-04 1.457758e-01 0.396741093
## 89 0.84866277 3.766856e-28 5.567223e-04 1.457758e-01 0.396741075
## 90 0.84866288 3.766776e-28 5.567229e-04 1.457757e-01 0.396741012
## 91 1.72137395 3.058138e-12 5.993853e-01 2.289447e-02 0.086206956
## 92 1.72137373 3.058203e-12 5.993855e-01 2.289447e-02 0.086206997
## 93 1.72137349 3.058255e-12 5.993857e-01 2.289447e-02 0.086207041
## 94 1.72137320 3.058260e-12 5.993857e-01 2.289448e-02 0.086207093
## 95 1.72137291 3.058265e-12 5.993857e-01 2.289448e-02 0.086207145
## 96 1.72137263 3.058270e-12 5.993858e-01 2.289449e-02 0.086207197
## 97 1.72137234 3.058275e-12 5.993858e-01 2.289449e-02 0.086207249
## 98 1.72137201 3.058233e-12 5.993856e-01 2.289449e-02 0.086207309
## 99 1.72137166 3.058178e-12 5.993855e-01 2.289450e-02 0.086207373
## 100 1.39034881 3.205265e-16 4.867255e-01 5.691890e-01 0.165446661
## 101 1.39034824 3.205347e-16 4.867260e-01 5.691895e-01 0.165446836
## 102 1.39034772 3.205413e-16 4.867265e-01 5.691900e-01 0.165446993
## 103 1.39034742 3.205419e-16 4.867265e-01 5.691900e-01 0.165447084
## 104 1.39034712 3.205425e-16 4.867265e-01 5.691901e-01 0.165447176
## 105 1.39034681 3.205432e-16 4.867266e-01 5.691902e-01 0.165447268
## 106 1.39034651 3.205438e-16 4.867266e-01 5.691902e-01 0.165447360
## 107 1.39034642 3.205385e-16 4.867262e-01 5.691899e-01 0.165447387
## 108 1.39034639 3.205316e-16 4.867258e-01 5.691895e-01 0.165447395
## 109 0.02980142 5.572802e-21 8.716282e-02 1.116282e-03 0.976245111
## 110 0.02980152 5.572949e-21 8.716301e-02 1.116283e-03 0.976245029
## 111 0.02980151 5.573068e-21 8.716313e-02 1.116283e-03 0.976245040
## 112 0.02980108 5.573088e-21 8.716306e-02 1.116283e-03 0.976245379
## 113 0.02980065 5.573107e-21 8.716298e-02 1.116283e-03 0.976245719
## 114 0.02980023 5.573127e-21 8.716290e-02 1.116283e-03 0.976246058
## 115 0.02979980 5.573147e-21 8.716282e-02 1.116283e-03 0.976246397
## 116 0.02979897 5.573067e-21 8.716254e-02 1.116283e-03 0.976247064
## 117 0.02979801 5.572960e-21 8.716220e-02 1.116281e-03 0.976247825
## 118 0.50833731 4.665083e-11 8.300669e-04 7.232485e-01 0.611587884
## 119 0.50833659 4.665176e-11 8.300629e-04 7.232496e-01 0.611588391
## 120 0.50833599 4.665252e-11 8.300596e-04 7.232504e-01 0.611588815
## 121 0.50833580 4.665269e-11 8.300592e-04 7.232503e-01 0.611588948
## 122 0.50833560 4.665285e-11 8.300587e-04 7.232502e-01 0.611589081
## 123 0.50833541 4.665302e-11 8.300583e-04 7.232501e-01 0.611589215
## 124 0.50833522 4.665318e-11 8.300578e-04 7.232500e-01 0.611589348
## 125 0.50833545 4.665275e-11 8.300602e-04 7.232491e-01 0.611589191
## 126 0.50833579 4.665215e-11 8.300633e-04 7.232479e-01 0.611588951
## 127 1.06432577 8.871201e-21 8.127529e-01 5.768106e-02 0.288031302
## 128 1.06432533 8.871579e-21 8.127558e-01 5.768078e-02 0.288031500
## 129 1.06432492 8.871871e-21 8.127581e-01 5.768056e-02 0.288031683
## 130 1.06432464 8.871861e-21 8.127583e-01 5.768055e-02 0.288031810
## 131 1.06432436 8.871852e-21 8.127585e-01 5.768054e-02 0.288031936
## 132 1.06432408 8.871842e-21 8.127586e-01 5.768053e-02 0.288032063
## 133 1.06432380 8.871833e-21 8.127588e-01 5.768052e-02 0.288032190
## 134 1.06432365 8.871522e-21 8.127568e-01 5.768072e-02 0.288032260
## 135 1.06432353 8.871125e-21 8.127542e-01 5.768098e-02 0.288032315
## 136 1.00001765 6.209038e-42 7.370289e-02 2.255372e-01 0.318102462
## 137 1.00001638 6.209318e-42 7.370300e-02 2.255374e-01 0.318103076
## 138 1.00001532 6.209536e-42 7.370308e-02 2.255376e-01 0.318103592
## 139 1.00001496 6.209535e-42 7.370309e-02 2.255376e-01 0.318103766
## 140 1.00001460 6.209534e-42 7.370309e-02 2.255376e-01 0.318103939
## 141 1.00001424 6.209534e-42 7.370309e-02 2.255376e-01 0.318104113
## 142 1.00001388 6.209533e-42 7.370309e-02 2.255376e-01 0.318104287
## 143 1.00001423 6.209314e-42 7.370301e-02 2.255375e-01 0.318104117
## 144 1.00001478 6.209032e-42 7.370291e-02 2.255373e-01 0.318103851
## 145 -1.46850663 3.544100e-49 1.352740e-01 1.510786e-03 0.143007352
## 146 -1.46850799 3.544198e-49 1.352738e-01 1.510781e-03 0.143006981
## 147 -1.46850913 3.544274e-49 1.352737e-01 1.510777e-03 0.143006672
## 148 -1.46850947 3.544274e-49 1.352737e-01 1.510777e-03 0.143006581
## 149 -1.46850980 3.544273e-49 1.352737e-01 1.510777e-03 0.143006490
## 150 -1.46851014 3.544272e-49 1.352738e-01 1.510778e-03 0.143006398
## 151 -1.46851048 3.544272e-49 1.352738e-01 1.510778e-03 0.143006307
## 152 -1.46851001 3.544194e-49 1.352740e-01 1.510782e-03 0.143006434
## 153 -1.46850931 3.544095e-49 1.352742e-01 1.510787e-03 0.143006623
## 154 1.79806604 1.862080e-59 2.329872e-01 4.223955e-01 0.073165084
## 155 1.79806436 1.862120e-59 2.329878e-01 4.223941e-01 0.073165350
## 156 1.79806298 1.862151e-59 2.329883e-01 4.223930e-01 0.073165570
## 157 1.79806259 1.862153e-59 2.329883e-01 4.223929e-01 0.073165632
## 158 1.79806220 1.862154e-59 2.329883e-01 4.223929e-01 0.073165694
## 159 1.79806181 1.862155e-59 2.329883e-01 4.223929e-01 0.073165756
## 160 1.79806142 1.862157e-59 2.329883e-01 4.223929e-01 0.073165817
## 161 1.79806203 1.862128e-59 2.329879e-01 4.223940e-01 0.073165720
## 162 1.79806293 1.862090e-59 2.329873e-01 4.223955e-01 0.073165578
## 163 2.36480331 1.239578e-72 2.083555e-01 5.115674e-02 0.018671741
## 164 2.36480288 1.239611e-72 2.083556e-01 5.115668e-02 0.018671762
## 165 2.36480250 1.239636e-72 2.083558e-01 5.115662e-02 0.018671781
## 166 2.36480235 1.239636e-72 2.083558e-01 5.115662e-02 0.018671788
## 167 2.36480221 1.239636e-72 2.083558e-01 5.115661e-02 0.018671795
## 168 2.36480206 1.239636e-72 2.083559e-01 5.115660e-02 0.018671803
## 169 2.36480191 1.239636e-72 2.083559e-01 5.115659e-02 0.018671810
## 170 2.36480198 1.239610e-72 2.083558e-01 5.115662e-02 0.018671806
## 171 2.36480212 1.239577e-72 2.083557e-01 5.115667e-02 0.018671799
## 172 -0.42430551 3.843502e-39 2.825442e-03 2.291553e-06 0.671645088
## 173 -0.42430599 3.843566e-39 2.825437e-03 2.291543e-06 0.671644739
## 174 -0.42430641 3.843617e-39 2.825434e-03 2.291535e-06 0.671644427
## 175 -0.42430667 3.843622e-39 2.825434e-03 2.291535e-06 0.671644243
## 176 -0.42430692 3.843627e-39 2.825435e-03 2.291535e-06 0.671644058
## 177 -0.42430717 3.843632e-39 2.825436e-03 2.291535e-06 0.671643874
## 178 -0.42430743 3.843636e-39 2.825436e-03 2.291535e-06 0.671643690
## 179 -0.42430750 3.843595e-39 2.825441e-03 2.291542e-06 0.671643633
## 180 -0.42430753 3.843540e-39 2.825448e-03 2.291552e-06 0.671643613
## 181 -0.51253505 2.687632e-32 4.652920e-01 8.074053e-04 0.608651207
## 182 -0.51253502 2.687671e-32 4.652919e-01 8.074059e-04 0.608651233
## 183 -0.51253505 2.687703e-32 4.652918e-01 8.074063e-04 0.608651206
## 184 -0.51253535 2.687708e-32 4.652918e-01 8.074063e-04 0.608650996
## 185 -0.51253566 2.687712e-32 4.652918e-01 8.074063e-04 0.608650786
## 186 -0.51253596 2.687717e-32 4.652918e-01 8.074063e-04 0.608650575
## 187 -0.51253626 2.687722e-32 4.652918e-01 8.074063e-04 0.608650365
## 188 -0.51253682 2.687699e-32 4.652919e-01 8.074060e-04 0.608649971
## 189 -0.51253746 2.687669e-32 4.652919e-01 8.074055e-04 0.608649524
## 190 -0.27982572 1.983984e-25 6.794698e-03 4.224117e-04 0.779802762
## 191 -0.27982579 1.983997e-25 6.794703e-03 4.224115e-04 0.779802704
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