Minggu ke-7 Bagian 2 ini akan membahas mengenai: Penerapan Regresi Logistik Multinomial
Pendahuluan
Regresi logistik multinomial digunakan untuk memodelkan hubungan antara peubah respon lebih dari dua kategori dengan satu atau lebih peubah penjelas. Peubah penjelasnya bisa berupa data kontinu atau kategorik. Peubah responnya berskala nominal (tidak ada tingkatan).
Soal 1
setwd("C:\\Users\\ACER\\Downloads\\")
Jawaban Soal 1
Input Data
size <- factor(rep(c("<=2.3",">2.3"),40))
food <-factor(rep(c("Fish","Inver","Rept","Bird","Other"),rep(16,5)))
gender<-rep(factor(rep(c("Male","Female"),rep(2,2))),20)
lake<-rep(factor(rep(c("Han","Okl","Tra","Geo"),rep(4,4))),5)
counts<-c(7,4,16,3,2,13,3,0,3,8,2,0,13,9,3,8,1,0,3,0,2,7,9,1,7,6,4,1,10,0,9,1,0,0,2,1,0,6,1,0,1,6,1,0,0,0,1,0,0,1,2,2,0,0,0,1,0,3,1,0,2,1,0,0,5,2,3,3,1,0,2,0,1,5,4,0,2,2,1,1)Penentuan Referensi
size <- relevel(size, ref=">2.3")
food <- relevel(food, ref="Fish")
gender <- relevel(gender, ref="Female")
lake <- relevel(lake, ref="Geo")makan <- data.frame(lake, gender, size, food, counts)
datafood <- makan[rep(row.names(makan),counts),1:4]
head(datafood)## lake gender size food
## 1 Han Male <=2.3 Fish
## 1.1 Han Male <=2.3 Fish
## 1.2 Han Male <=2.3 Fish
## 1.3 Han Male <=2.3 Fish
## 1.4 Han Male <=2.3 Fish
## 1.5 Han Male <=2.3 Fishdim(datafood)## [1] 219 4Bagian A
library(foreign)
library(nnet)
model_1 <- multinom(food ~ lake + size, data=datafood)## # weights: 30 (20 variable)
## initial value 352.466903
## iter 10 value 271.607785
## iter 20 value 270.046051
## final value 270.040140
## convergedsummary(model_1)## Call:
## multinom(formula = food ~ lake + size, data = datafood)
##
## Coefficients:
## (Intercept) lakeHan lakeOkl lakeTra size<=2.3
## Bird -2.093358 0.6954256 -0.652622721 1.088098 -0.6306329
## Inver -1.549021 -1.6581178 0.937237973 1.122002 1.4581457
## Other -1.904343 0.8263115 0.005792737 1.516461 0.3315514
## Rept -3.314512 1.2428408 2.458913302 2.935262 -0.3512702
##
## Std. Errors:
## (Intercept) lakeHan lakeOkl lakeTra size<=2.3
## Bird 0.6622972 0.7813123 1.2020025 0.8417085 0.6424863
## Inver 0.4249185 0.6128466 0.4719035 0.4905122 0.3959418
## Other 0.5258313 0.5575446 0.7765655 0.6214371 0.4482504
## Rept 1.0530577 1.1854031 1.1181000 1.1163844 0.5800207
##
## Residual Deviance: 540.0803
## AIC: 580.0803exp(summary(model_1)$coefficients)## (Intercept) lakeHan lakeOkl lakeTra size<=2.3
## Bird 0.12327247 2.0045620 0.5206784 2.968624 0.5322548
## Inver 0.21245592 0.1904972 2.5529204 3.070995 4.2979825
## Other 0.14892051 2.2848753 1.0058095 4.556075 1.3931278
## Rept 0.03635178 3.4654441 11.6920989 18.826431 0.7037936Persamaan prediksi odds dimana alligator memilih memakan bird dibandingkan dengan fish adalah:
\[log\left ( \frac{\widehat{\pi }_B}{\widehat{\pi }_F} \right )=-2.09-0.63sz+0.7lk_H-0.65lk_O+1.09lk_T\]
Interpretasi:
- \(e^{−2.09}= 0.123\)
Untuk alligator berukuran > 2.3 m di Lake George, odds alligator memakan bird dibandingkan alligator memakan fish adalah 0.123.
- \(e{−0.63}= 0.532\)
Untuk alligator berukuran ≤ 2.3 m, odds alligator memakan bird dibandingkan fish adalah 0.532 kalinya odds alligator beukuran > 2.3 m.
- \(e^{0.7}= 2.005\)
Untuk alligator di Lake Hancock, odds alligator memakan bird dibandingkan fish adalah 2.005 kalinya odds alligator di Lake George.
- \(e^{−0.65}= 0.521\)
Untuk alligator di Lake Oklawaha, odds alligator memakan bird dibandingkan fish adalah 0.521 kalinya odds alligator di Lake George.
- \(e^{1.09}= 2.97\)
Untuk alligator di Lake Trafford, odds alligator memakan bird dibandingkan fish adalah 2.97 kalinya odds alligator di Lake George.
Persamaan prediksi odds dimana alligator memilih memakan invertebrata dibandingkan dengan fish adalah:
\[log\left ( \frac{\widehat{\pi }_I}{\widehat{\pi }_F} \right )=-1.55+1.46sz-1.66lk_H+0.94lk_O+1.12lk_T\]
Interpretasi:
- \(e^{-1.55}= 0.21\)
Untuk alligator berukuran > 2.3 m di Lake George, odds alligator memakan invertebrata dibandingkan fish adalah 0.21.
- \(e^{1.46}= 4.3\)
Untuk alligator berukuran ≤ 2.3 m, odds alligator memakan invertebrata dibandingkan fish adalah 4.3 kalinya odds alligator beukuran > 2.3 m.
- \(e^{−1.66= 0.19\)
Untuk alligator di Lake Hancock, odds alligator memakan invertebrata dibandingkan fish adalah 0.19 kalinya odds alligator di Lake George.
- \(e^{0.94= 2.55\)
Untuk alligator di Lake Oklawaha, odds alligator memakan invertebrata dibandingkan fish adalah 2.55 kalinya odds alligator di Lake George.
- \(e^{1.12}= 3.07\)
Untuk alligator di Lake Trafford, odds alligator memakan invertebrata dibandingkan fish adalah 3.07 kalinya odds alligator di Lake George.
Persamaan prediksi odds dimana alligator memilih memakan others dibandingkan dengan fish adalah:
\[log\left ( \frac{\widehat{\pi }_O}{\widehat{\pi }_F} \right )=-1.9+0.33sz+0.83lk_H+0.01lk_O+1.52lk_T\]
Interpretasi:
- \(e^{−1.9}= 0.15\)
Untuk alligator berukuran > 2.3 m di Lake George, odds alligator memakan others dibandingkan fish adalah 0.15.
- \(e^{0.33}= 1.39\)
Untuk alligator berukuran ≤ 2.3 m, odds alligator memakan others dibandingkan fish adalah 1.39 kalinya odds alligator beukuran > 2.3 m.
- \(e^{0.83}= 2.28\)
Untuk alligator di Lake Hancock, odds alligator memakan others dibandingkan fish adalah 2.28 kalinya odds alligator di Lake George.
- \(e^{0.01}= 1.01\)
Untuk alligator di Lake Oklawaha, odds alligator memakan others dibandingkan fish adalah 1.01 kalinya odds alligator di Lake George.
- \(e^{1.52}= 4.56\)
Untuk alligator di Lake Trafford, odds alligator memakan others dibandingkan fish adalah 4.56 kalinya odds alligator di Lake George.
Persamaan prediksi odds dimana alligator memilih memakan reptile dibandingkan dengan fish adalah:
\[log\left ( \frac{\widehat{\pi }_R}{\widehat{\pi }_F} \right )=-3.31-0.35z+1.24lk_H+2.46lk_O+2.94lk_T\]
Interpretasi:
- \(e^{−3.31}= 0.036\)
Untuk alligator berukuran > 2.3 m di Lake George, odds alligator memakan reptile dibandingkan fish adalah 0.036.
- \(e^{−0.35}= 0.7\)
Untuk alligator berukuran ≤ 2.3 m, odds alligator memakan reptile dibandingkan fish adalah 0.7 kalinya odds alligator beukuran > 2.3 m.
- \(e^{1.24}= 3.47\)
Untuk alligator di Lake Hancock, odds alligator memakan reptile dibandingkan fish adalah 3.47 kalinya odds alligator di Lake George.
- \(e^{2.46}= 11.7\)
Untuk alligator di Lake Oklawaha, odds alligator memakan reptile dibandingkan fish adalah 11.7 kalinya odds alligator di Lake George.
- \(e^{2.94}= 18.83\)
Untuk alligator di Lake Trafford, odds alligator memakan reptile dibandingkan fish adalah 18.83 kalinya odds alligator di Lake George.
Bagian B
model_2 <- multinom(food ~ lake + size + gender, data=datafood)## # weights: 35 (24 variable)
## initial value 352.466903
## iter 10 value 270.967533
## iter 20 value 268.934907
## final value 268.932740
## convergedsummary(model_2)## Call:
## multinom(formula = food ~ lake + size + gender, data = datafood)
##
## Coefficients:
## (Intercept) lakeHan lakeOkl lakeTra size<=2.3 genderMale
## Bird -1.701750 0.5751767 -0.55073594 1.236877 -0.7302898 -0.6064571
## Inver -1.167210 -1.7805263 0.91314471 1.155786 1.3362563 -0.4629756
## Other -1.721273 0.7665622 0.02600333 1.557716 0.2905663 -0.2525879
## Rept -2.858940 1.1294537 2.53024455 3.061047 -0.5570885 -0.6276206
##
## Std. Errors:
## (Intercept) lakeHan lakeOkl lakeTra size<=2.3 genderMale
## Bird 0.7690488 0.7952037 1.2099728 0.8660879 0.6522819 0.6888490
## Inver 0.5337511 0.6232106 0.4761165 0.4927850 0.4111930 0.3955225
## Other 0.6313811 0.5685499 0.7777727 0.6256727 0.4599253 0.4663465
## Rept 1.1456331 1.1928006 1.1221172 1.1297303 0.6466081 0.6852751
##
## Residual Deviance: 537.8655
## AIC: 585.8655abs(model_1$edf-model_2$edf)## [1] 4qchisq(0.05, 4, lower.tail=FALSE)## [1] 9.487729- Hipotesis:
\(H_0\): peubah gender tidak berpengaruh nyata terhadap perbedaan odds bagi semua tive makanan utama alligator
\(H_1\): peubah gender berpengaruh nyata terhadap perbedaan odds bagi semua tive makanan utama alligator
- Taraf Signifikan
\(\alpha=5\%\)
- Statistik Uji
\(\bigtriangleup Deviance=540.0803-537.8655=2.2148\)
- RR
Tolak \(H_0\) jika \(\bigtriangleup Deviance > \chi ^{2}_{0.05,4}\)
- Keputusan
Karena 2.2148<9.49, maka gagal tolak \(H_0\)
- Kesimpulan
Dengan taraf nyata \(5\%\) tidak ada cukup bukti untuk mengatakan bahwa gender berpengaruh nyata terhadap perbedaan odds bagi semua tive makanan utama alligator
model_3 <- multinom(food ~ lake + gender, data=datafood)## # weights: 30 (20 variable)
## initial value 352.466903
## iter 10 value 279.421076
## iter 20 value 277.733691
## final value 277.732884
## convergedsummary(model_3)## Call:
## multinom(formula = food ~ lake + gender, data = datafood)
##
## Coefficients:
## (Intercept) lakeHan lakeOkl lakeTra genderMale
## Bird -2.12320607 0.4818741 -0.47393004 1.2811363 -0.4245404
## Inver 0.01048504 -1.7605713 0.59314476 0.9609816 -0.8577619
## Other -1.51431307 0.7842964 -0.07500933 1.4829188 -0.2871253
## Rept -3.37256725 1.1400408 2.55949903 3.0361432 -0.1834060
##
## Std. Errors:
## (Intercept) lakeHan lakeOkl lakeTra genderMale
## Bird 0.7212115 0.7960695 1.1922056 0.8381776 0.6476502
## Inver 0.3584792 0.6187324 0.4425069 0.4722548 0.3694164
## Other 0.5318941 0.5701319 0.7661014 0.6158038 0.4542938
## Rept 1.0863463 1.1945082 1.1088625 1.1134113 0.5873043
##
## Residual Deviance: 555.4658
## AIC: 595.4658abs(model_3$edf-model_2$edf)## [1] 4qchisq(0.05, 4, lower.tail=FALSE)## [1] 9.487729- Hipotesis:
\(H_0\): peubah size tidak berpengaruh nyata terhadap perbedaan odds bagi semua tive makanan utama alligator
\(H_1\): peubah size berpengaruh nyata terhadap perbedaan odds bagi semua tive makanan utama alligator
- Taraf Signifikan
\(\alpha=5\%\)
- Statistik Uji
\(\bigtriangleup Deviance=555.4658-537.8655=17.6003\)
- RR
Tolak \(H_0\) jika \(\bigtriangleup Deviance > \chi ^{2}_{0.05,4}\)
- Keputusan
Karena 17.6003>9.49, maka tolak \(H_0\)
- Kesimpulan
Dengan taraf nyata \(5\%\) ada cukup bukti untuk mengatakan bahwa size berpengaruh nyata terhadap perbedaan odds bagi semua tive makanan utama alligator
model_4 <- multinom(food ~ size + gender, data=datafood)## # weights: 20 (12 variable)
## initial value 352.466903
## iter 10 value 294.669539
## final value 294.091727
## convergedsummary(model_4)## Call:
## multinom(formula = food ~ size + gender, data = datafood)
##
## Coefficients:
## (Intercept) size<=2.3 genderMale
## Bird -1.2790620 -0.7533726 -0.61466393
## Inver -0.9638861 0.9210878 -0.09004848
## Other -1.0905582 0.2328891 -0.19634008
## Rept -1.2170166 -0.8681379 -0.03140815
##
## Std. Errors:
## (Intercept) size<=2.3 genderMale
## Bird 0.5806349 0.6439387 0.6337949
## Inver 0.4001729 0.3730328 0.3538182
## Other 0.4584432 0.4373966 0.4378935
## Rept 0.5455407 0.5629537 0.5693974
##
## Residual Deviance: 588.1835
## AIC: 612.1835abs(model_4$edf-model_2$edf)## [1] 12qchisq(0.05, 12, lower.tail=FALSE)## [1] 21.02607- Hipotesis:
\(H_0\): peubah lake tidak berpengaruh nyata terhadap perbedaan odds bagi semua tipe makanan utama alligator
\(H_1\): peubah lake berpengaruh nyata terhadap perbedaan odds bagi semua tipe makanan utama alligator
- Taraf Signifikan
\(\alpha=5\%\)
- Statistik Uji
\(\bigtriangleup Deviance=588.1835-537.8655=50.318\)
- RR
Tolak \(H_0\) jika \(\bigtriangleup Deviance > \chi ^{2}_{0.05,4}\)
- Keputusan
Karena 50.3183>21.03, maka tolak \(H_0\)
- Kesimpulan
Dengan taraf nyata \(5\%\) ada cukup bukti untuk mengatakan bahwa lake berpengaruh nyata terhadap perbedaan odds bagi semua tive makanan utama alligator
Jadi, berdasarkan hasil pengujian di atas dapat disimpulkan bahwa peubah yang berpengaruh nyata terhadap tipe makanan utama Alligator adalah peubah Lake dan peubah Size.
Bagian C
new=data.frame(size=as.factor("<=2.3"),gender=as.factor("Male"),lake=as.factor("Tra"))
#model2
predict(model_2,newdata=new,"probs") ## Fish Bird Inver Other Rept
## 0.20881597 0.03446118 0.49438276 0.18417282 0.07816727Berdasarkan output dari program R peluang yang paling besar adalah aliigator tersebut akan memakan Invertebrata.
Bagian D
model_1c1 <- multinom(food ~ lake,data=datafood)## # weights: 25 (16 variable)
## initial value 352.466903
## iter 10 value 281.030560
## iter 20 value 280.583926
## final value 280.583844
## convergedsummary(model_1c1)## Call:
## multinom(formula = food ~ lake, data = datafood)
##
## Coefficients:
## (Intercept) lakeHan lakeOkl lakeTra
## Bird -2.3982809 0.6065505 -0.49188808 1.2197770
## Inver -0.5008393 -1.5137909 0.55488981 0.8263598
## Other -1.7048477 0.8686390 -0.08689071 1.4425750
## Rept -3.4962205 1.1937161 2.55175319 3.0107928
##
## Std. Errors:
## (Intercept) lakeHan lakeOkl lakeTra
## Bird 0.6031161 0.7727128 1.1912598 0.8310587
## Inver 0.2833774 0.6029744 0.4341550 0.4612870
## Other 0.4438217 0.5542879 0.7654142 0.6114775
## Rept 1.0148749 1.1817886 1.1083250 1.1099095
##
## Residual Deviance: 561.1677
## AIC: 593.1677model_1c2 <- multinom(food ~ size,data=datafood)## # weights: 15 (8 variable)
## initial value 352.466903
## iter 10 value 294.670879
## final value 294.606678
## convergedsummary(model_1c2)## Call:
## multinom(formula = food ~ size, data = datafood)
##
## Coefficients:
## (Intercept) size<=2.3
## Bird -1.727214 -0.5551882
## Inver -1.034070 0.9489120
## Other -1.241709 0.2943162
## Rept -1.241705 -0.8583649
##
## Std. Errors:
## (Intercept) size<=2.3
## Bird 0.3836949 0.6063277
## Inver 0.2910708 0.3568648
## Other 0.3148735 0.4149523
## Rept 0.3148729 0.5349960
##
## Residual Deviance: 589.2134
## AIC: 605.2134model_1c3 <- multinom(food ~ gender,data=datafood)## # weights: 15 (8 variable)
## initial value 352.466903
## iter 10 value 301.192714
## final value 301.129428
## convergedsummary(model_1c3)## Call:
## multinom(formula = food ~ gender, data = datafood)
##
## Coefficients:
## (Intercept) genderMale
## Bird -1.7635851 -0.3680370
## Inver -0.2231478 -0.3578812
## Other -0.9162928 -0.2708745
## Rept -1.7635569 0.2509570
##
## Std. Errors:
## (Intercept) genderMale
## Bird 0.4418570 0.5958549
## Inver 0.2535467 0.3339731
## Other 0.3162281 0.4153372
## Rept 0.4418517 0.5376858
##
## Residual Deviance: 602.2589
## AIC: 618.2589model_1c4 <- multinom(food ~ lake +size + gender + lake*size,
data=datafood)## # weights: 50 (36 variable)
## initial value 352.466903
## iter 10 value 265.274636
## iter 20 value 260.069949
## iter 30 value 258.937775
## iter 40 value 258.824166
## iter 50 value 258.819006
## final value 258.818962
## convergedsummary(model_1c4)## Warning in sqrt(diag(vc)): NaNs produced## Call:
## multinom(formula = food ~ lake + size + gender + lake * size,
## data = datafood)
##
## Coefficients:
## (Intercept) lakeHan lakeOkl lakeTra size<=2.3 genderMale
## Bird -2.442347 1.928711 0.6706186 2.282905 0.92900200 -0.84648228
## Inver -2.453306 -12.256978 2.7331906 3.111918 3.17363446 -0.81592590
## Other -1.688556 1.392344 -26.0432791 1.299438 0.07643898 -0.08264057
## Rept -28.472136 26.922121 28.6961637 29.221745 26.38883928 -1.07334267
## lakeHan:size<=2.3 lakeOkl:size<=2.3 lakeTra:size<=2.3
## Bird -2.6180164 -37.538905 -1.9359701
## Inver 10.0209021 -2.448568 -2.6137822
## Other -0.8062165 27.172630 0.3637365
## Rept -26.9993336 -27.961392 -27.5229971
##
## Std. Errors:
## (Intercept) lakeHan lakeOkl lakeTra size<=2.3 genderMale
## Bird 1.0695771 1.2468205 1.5193189 1.3106646 1.2892933 0.7430086
## Inver 1.0470055 0.3370560 1.1530087 1.1841238 1.0964497 0.4448919
## Other 0.6785145 0.8580021 0.4916661 0.8711876 0.8925871 0.4749617
## Rept 0.8453331 1.0511858 0.7479391 0.7710755 0.6558217 0.7692781
## lakeHan:size<=2.3 lakeOkl:size<=2.3 lakeTra:size<=2.3
## Bird 1.6535383 NaN 1.897784
## Inver 0.3370534 1.3660324 1.361887
## Other 1.1500995 0.4916661 1.258627
## Rept 1.1866462 1.2780398 1.085509
##
## Residual Deviance: 517.6379
## AIC: 589.6379model_1c5 <- multinom(food ~ lake +size + gender +lake*gender,
data=datafood)## # weights: 50 (36 variable)
## initial value 352.466903
## iter 10 value 265.296842
## iter 20 value 259.530895
## iter 30 value 258.505815
## iter 40 value 258.481781
## iter 50 value 258.481314
## iter 50 value 258.481312
## iter 50 value 258.481312
## final value 258.481312
## convergedsummary(model_1c5)## Call:
## multinom(formula = food ~ lake + size + gender + lake * gender,
## data = datafood)
##
## Coefficients:
## (Intercept) lakeHan lakeOkl lakeTra size<=2.3 genderMale
## Bird -16.263542 15.4631991 16.0110863 16.5768526 -1.1908325 14.87784409
## Inver -1.046837 -2.1160620 0.8808395 0.5136922 1.5215173 -0.94732194
## Other -1.681967 0.5689054 1.3192386 2.4229579 -0.0522542 0.01106523
## Rept -2.318943 0.6134287 1.3720043 1.7963644 -0.1881737 -14.50610070
## lakeHan:genderMale lakeOkl:genderMale lakeTra:genderMale
## Bird -15.8646026 -33.5355368 -16.335073
## Inver 0.5034982 0.3048162 1.093681
## Other 0.6840401 -2.3514491 -1.347638
## Rept -7.7570090 14.5535117 14.612770
##
## Std. Errors:
## (Intercept) lakeHan lakeOkl lakeTra size<=2.3 genderMale
## Bird 0.6627872 0.6452407 1.1230758 0.9794898 0.6863823 0.5932994
## Inver 0.5534699 0.7863163 0.8191284 0.9686761 0.4618276 0.6126551
## Other 0.7978770 0.9140771 1.2081530 1.1815357 0.4926099 0.9471840
## Rept 1.0821756 1.2371499 1.5813617 1.6465079 0.6981059 0.6905281
## lakeHan:genderMale lakeOkl:genderMale lakeTra:genderMale
## Bird 1.124843e+00 2.393237e-07 1.1965529
## Inver 1.369324e+00 1.085099e+00 1.1800008
## Other 1.167883e+00 1.731244e+00 1.4487918
## Rept 9.243461e-10 9.573608e-01 0.9861938
##
## Residual Deviance: 516.9626
## AIC: 588.9626model_1c6 <- multinom(food ~ lake + size + gender +size*gender,data=datafood)## # weights: 40 (28 variable)
## initial value 352.466903
## iter 10 value 269.657367
## iter 20 value 267.859275
## iter 30 value 267.849421
## iter 30 value 267.849420
## iter 30 value 267.849420
## final value 267.849420
## convergedsummary(model_1c6)## Call:
## multinom(formula = food ~ lake + size + gender + size * gender,
## data = datafood)
##
## Coefficients:
## (Intercept) lakeHan lakeOkl lakeTra size<=2.3 genderMale
## Bird -1.610300 0.6067870 -0.4587223 1.325001 -0.9499501 -0.8219859
## Inver -1.101382 -1.7722719 0.9424647 1.184062 1.2416008 -0.5742209
## Other -1.485725 0.8147021 0.1679189 1.684913 -0.1051924 -0.6960225
## Rept -3.339082 0.9879282 2.2335485 2.778320 0.3511508 0.2037592
## size<=2.3:genderMale
## Bird 0.4491087
## Inver 0.1497835
## Other 0.6635604
## Rept -1.6862430
##
## Std. Errors:
## (Intercept) lakeHan lakeOkl lakeTra size<=2.3 genderMale
## Bird 0.8007333 0.8014123 1.2462166 0.9110709 0.9163585 0.9299201
## Inver 0.6924399 0.6288826 0.5021787 0.5131789 0.7569443 0.7911095
## Other 0.6865768 0.5726299 0.8064032 0.6559994 0.7136479 0.7714181
## Rept 1.3673993 1.2035947 1.1455785 1.1486470 1.1892358 1.1845946
## size<=2.3:genderMale
## Bird 1.3372394
## Inver 0.9344216
## Other 0.9506783
## Rept 1.6487195
##
## Residual Deviance: 535.6988
## AIC: 591.6988model_1c7 <-multinom(food~lake+size+gender+lake*size+lake*gender, data=datafood)## # weights: 65 (48 variable)
## initial value 352.466903
## iter 10 value 263.550767
## iter 20 value 252.470318
## iter 30 value 249.416728
## iter 40 value 249.182771
## iter 50 value 249.171406
## iter 60 value 249.171094
## final value 249.171077
## convergedsummary(model_1c7)## Warning in sqrt(diag(vc)): NaNs produced## Call:
## multinom(formula = food ~ lake + size + gender + lake * size +
## lake * gender, data = datafood)
##
## Coefficients:
## (Intercept) lakeHan lakeOkl lakeTra size<=2.3 genderMale
## Bird -26.545198 26.052061 28.139480 27.156201 0.35746095 24.32889436
## Inver -2.325022 -11.825325 3.343036 2.464092 3.39642459 -1.34474341
## Other -1.723879 1.046963 -24.458241 2.707398 0.06578482 -0.01984412
## Rept -23.134727 21.806167 23.280548 23.102673 21.98323898 -20.17051634
## lakeHan:size<=2.3 lakeOkl:size<=2.3 lakeTra:size<=2.3 lakeHan:genderMale
## Bird -2.0599485 -41.07881 -1.8707416 -25.3707049
## Inver 9.1294547 -3.19803 -2.5823130 0.9185007
## Other -0.7054789 25.78133 -0.3803866 0.6513613
## Rept -22.6845546 -23.42510 -22.7124870 -6.5400092
## lakeOkl:genderMale lakeTra:genderMale
## Bird -49.7462758 -25.988068
## Inver -0.2158311 1.066904
## Other -0.4355696 -1.489857
## Rept 19.2273535 19.910052
##
## Std. Errors:
## (Intercept) lakeHan lakeOkl lakeTra size<=2.3 genderMale
## Bird 0.7760831 0.958557 1.6265326 1.492307 1.2943109 0.8719357
## Inver 1.0551636 487.518218 1.5826690 1.569481 1.1416983 0.7209299
## Other 0.8169634 1.077639 0.6805341 1.564129 0.9248934 0.9809570
## Rept 0.8301478 1.142391 1.6281559 1.528664 0.8301478 0.8056223
## lakeHan:size<=2.3 lakeOkl:size<=2.3 lakeTra:size<=2.3 lakeHan:genderMale
## Bird 1.653312 NaN 2.189651 1.305838e+00
## Inver 487.518527 1.5483507 1.422054 1.423678e+00
## Other 1.175912 0.6805341 1.434644 1.195075e+00
## Rept 1.309035 1.5503497 1.188362 2.081841e-10
## lakeOkl:genderMale lakeTra:genderMale
## Bird NaN 1.525571
## Inver 1.336203 1.281557
## Other 1.786260 1.589410
## Rept 1.339247 1.204804
##
## Residual Deviance: 498.3422
## AIC: 594.3422model_1c8 <-multinom(food~lake+size+gender+lake*size+size*gender,data=datafood)## # weights: 55 (40 variable)
## initial value 352.466903
## iter 10 value 264.007344
## iter 20 value 258.635097
## iter 30 value 257.471456
## iter 40 value 257.268765
## iter 50 value 257.260181
## iter 60 value 257.260007
## iter 60 value 257.260005
## iter 60 value 257.260005
## final value 257.260005
## convergedsummary(model_1c8)## Call:
## multinom(formula = food ~ lake + size + gender + lake * size +
## size * gender, data = datafood)
##
## Coefficients:
## (Intercept) lakeHan lakeOkl lakeTra size<=2.3 genderMale
## Bird -2.374902 1.905770 0.7777711 2.380109 0.78737738 -1.00313562
## Inver -2.089062 -12.450905 3.7710436 4.210933 2.65814738 -2.34599930
## Other -1.684653 1.390753 -22.9574759 1.301454 0.04589109 -0.08759659
## Rept -26.119021 24.440030 25.9644059 26.459374 24.29284507 -0.63691750
## lakeHan:size<=2.3 lakeOkl:size<=2.3 lakeTra:size<=2.3
## Bird -2.5432412 -32.94969 -2.0141052
## Inver 10.3127719 -3.39441 -3.6750412
## Other -0.7904554 24.10091 0.3663241
## Rept -24.6885868 -25.43077 -24.8435013
## size<=2.3:genderMale
## Bird 0.25393402
## Inver 1.75745447
## Other 0.03952345
## Rept -1.13638396
##
## Std. Errors:
## (Intercept) lakeHan lakeOkl lakeTra size<=2.3 genderMale
## Bird 1.1116398 1.2505257 1.6186528 1.4283751 1.470820 1.1460683
## Inver 1.0663058 0.3359278 1.5774330 1.6200467 1.167156 1.3417232
## Other 0.7843509 0.8599831 0.4963547 0.9195573 1.090735 0.8394745
## Rept 1.1177932 1.0621017 0.9635959 0.9918237 1.145486 1.5602027
## lakeHan:size<=2.3 lakeOkl:size<=2.3 lakeTra:size<=2.3
## Bird 1.6767817 1.073912e-13 1.957890
## Inver 0.3359258 1.713893e+00 1.743582
## Other 1.1615493 4.963547e-01 1.283286
## Rept 1.2443446 1.359291e+00 1.229240
## size<=2.3:genderMale
## Bird 1.533010
## Inver 1.425687
## Other 1.019876
## Rept 1.957142
##
## Residual Deviance: 514.52
## AIC: 594.52model_1c9 <-multinom(food~lake+size+gender+lake*gender+size*gender,data=datafood)## # weights: 55 (40 variable)
## initial value 352.466903
## iter 10 value 264.575413
## iter 20 value 258.989840
## iter 30 value 257.785301
## iter 40 value 257.722664
## iter 50 value 257.721130
## final value 257.721117
## convergedsummary(model_1c9)## Call:
## multinom(formula = food ~ lake + size + gender + lake * gender +
## size * gender, data = datafood)
##
## Coefficients:
## (Intercept) lakeHan lakeOkl lakeTra size<=2.3 genderMale
## Bird -16.2454250 15.6026638 16.1814396 16.8103429 -1.4910019 14.7243894
## Inver -0.9882986 -2.1039274 0.8933136 0.5292055 1.4356770 -0.9763839
## Other -1.5457745 0.6835996 1.4561166 2.5972179 -0.3942057 -0.2679747
## Rept -2.6795341 0.3888810 1.1089359 1.4747671 0.5445618 -13.0797407
## lakeHan:genderMale lakeOkl:genderMale lakeTra:genderMale
## Bird -16.0142292 -32.7287883 -16.454575
## Inver 0.5012999 0.2534458 1.043671
## Other 0.5702386 -2.3683123 -1.427343
## Rept -6.8055922 13.7953320 13.964518
## size<=2.3:genderMale
## Bird 0.60936071
## Inver 0.06734568
## Other 0.55921244
## Rept -1.40622285
##
## Std. Errors:
## (Intercept) lakeHan lakeOkl lakeTra size<=2.3 genderMale
## Bird 0.7021724 0.6592361 1.1454332 1.0305022 0.9622487 0.7992739
## Inver 0.6928949 0.8027431 0.8333448 0.9877422 0.7899435 0.9277684
## Other 0.8223479 0.9407293 1.2384019 1.2313676 0.7728513 1.0714394
## Rept 1.2585713 1.2622550 1.6052792 1.6755239 1.2195085 0.9643344
## lakeHan:genderMale lakeOkl:genderMale lakeTra:genderMale
## Bird 1.129073e+00 5.670007e-07 1.206149
## Inver 1.379981e+00 1.082868e+00 1.178162
## Other 1.189446e+00 1.736694e+00 1.464333
## Rept 3.891958e-09 1.001575e+00 1.058997
## size<=2.3:genderMale
## Bird 1.3510612
## Inver 0.9707251
## Other 0.9933454
## Rept 1.6718032
##
## Residual Deviance: 515.4422
## AIC: 595.4422model_1c10 <-multinom(food~lake+size+gender+lake*size+lake*gender+size*gender, data=datafood)## # weights: 70 (52 variable)
## initial value 352.466903
## iter 10 value 261.806815
## iter 20 value 249.874155
## iter 30 value 245.251330
## iter 40 value 244.794341
## iter 50 value 244.772299
## iter 60 value 244.771293
## final value 244.771286
## convergedsummary(model_1c10)## Call:
## multinom(formula = food ~ lake + size + gender + lake * size +
## lake * gender + size * gender, data = datafood)
##
## Coefficients:
## (Intercept) lakeHan lakeOkl lakeTra size<=2.3 genderMale
## Bird -29.680243 29.103199 68.77201 39.611336 13.866329 27.422556
## Inver -2.006630 -14.493190 41.09846 40.176780 2.933473 -39.756994
## Other -1.560861 1.181926 -38.81781 3.731800 -0.534904 -0.333421
## Rept -34.044627 32.774394 21.58248 2.350668 32.774659 -14.981245
## lakeHan:size<=2.3 lakeOkl:size<=2.3 lakeTra:size<=2.3 lakeHan:genderMale
## Bird -15.3329775 -79.63494 -24.490655 -28.0806124
## Inver 11.9281761 -40.92665 -40.410530 0.7598849
## Other -0.5527564 40.50818 -0.942941 0.4179860
## Rept -33.5480948 -21.41115 -1.774053 -14.3102392
## lakeOkl:genderMale lakeTra:genderMale size<=2.3:genderMale
## Bird -88.1781781 -38.334497 -13.4362543
## Inver 0.0461318 1.299149 38.6120194
## Other -0.8036763 -2.307518 0.8491819
## Rept 26.6702270 46.387523 -31.8115065
##
## Std. Errors:
## (Intercept) lakeHan lakeOkl lakeTra size<=2.3 genderMale
## Bird 0.7070832 0.8084083 1.4658431 0.5917075 0.5509420 0.7777457
## Inver 1.0638255 0.4393419 1.0245550 1.2212504 1.2249471 0.9993125
## Other 0.8276239 1.0697093 0.7768042 2.0107535 1.2926849 1.0971195
## Rept 0.7485178 0.9206041 0.7360161 0.9455311 0.7553727 0.4517334
## lakeHan:size<=2.3 lakeOkl:size<=2.3 lakeTra:size<=2.3 lakeHan:genderMale
## Bird 0.8905558 5.432772e-11 0.7160007 1.237839e+00
## Inver 0.4393416 9.390471e-01 0.9931620 1.433917e+00
## Other 1.2294201 7.768042e-01 1.6393334 1.283608e+00
## Rept 1.0822488 9.218556e-01 0.8925133 4.926739e-13
## lakeOkl:genderMale lakeTra:genderMale size<=2.3:genderMale
## Bird 3.296180e-08 0.8287452 1.0419266
## Inver 1.413217e+00 1.3337518 0.9072072
## Other 1.997547e+00 1.9339587 1.1962097
## Rept 4.255527e-01 0.5428352 0.9846263
##
## Residual Deviance: 489.5426
## AIC: 593.5426model_1c11 <-multinom(food~lake+size+gender+lake*size+lake*gender+size*gender+lake*size*gender, data=datafood)## # weights: 85 (64 variable)
## initial value 352.466903
## iter 10 value 260.145098
## iter 20 value 247.220833
## iter 30 value 244.162621
## iter 40 value 243.815027
## iter 50 value 243.801406
## iter 60 value 243.800899
## iter 60 value 243.800898
## iter 60 value 243.800898
## final value 243.800898
## convergedsummary(model_1c11)## Call:
## multinom(formula = food ~ lake + size + gender + lake * size +
## lake * gender + size * gender + lake * size * gender, data = datafood)
##
## Coefficients:
## (Intercept) lakeHan lakeOkl lakeTra size<=2.3 genderMale
## Bird -23.659137 23.253776 45.302701 18.666966 -5.1636921 21.461986
## Inver -2.079465 -12.135591 23.723299 41.083525 3.1778456 -32.399336
## Other -2.079548 2.079581 -19.265751 -6.158001 0.9806851 0.575526
## Rept -29.481972 28.383330 8.903792 8.739972 28.3828917 -9.045851
## lakeHan:size<=2.3 lakeOkl:size<=2.3 lakeTra:size<=2.3 lakeHan:genderMale
## Bird 3.489575 -44.628018 9.462975 -22.443051
## Inver 9.363311 -23.723138 -41.488498 -0.378315
## Other -2.654656 19.959036 7.950245 -1.268768
## Rept -29.363666 -8.903379 -8.333677 -13.270796
## lakeOkl:genderMale lakeTra:genderMale size<=2.3:genderMale
## Bird -68.65129 -17.450651 5.489023
## Inver 10.13646 -6.892404 31.038624
## Other -14.17904 7.192033 -1.348468
## Rept 28.85082 29.500163 -21.726694
## lakeHan:size<=2.3:genderMale lakeOkl:size<=2.3:genderMale
## Bird -29.234803 0.4598397
## Inver 1.466961 -9.8742203
## Other 3.379153 14.6644729
## Rept 4.422985 -19.9036846
## lakeTra:size<=2.3:genderMale
## Bird -44.1067826
## Inver 8.4069123
## Other -8.2112240
## Rept 0.8663284
##
## Std. Errors:
## (Intercept) lakeHan lakeOkl lakeTra size<=2.3 genderMale
## Bird 0.7076713 0.8055881 1.2170267 0.5899784 0.5605073 0.7643122
## Inver 1.0606630 0.4583132 0.6686450 0.6394553 1.2527514 0.6124146
## Other 1.0607033 1.3385692 0.7359783 0.9350246 1.5679312 1.3176434
## Rept 0.7713307 0.9140028 0.7471843 0.8686971 0.7713308 0.4213413
## lakeHan:size<=2.3 lakeOkl:size<=2.3 lakeTra:size<=2.3 lakeHan:genderMale
## Bird 0.9039139 9.842819e-12 0.7030400 1.229372e+00
## Inver 0.4583076 8.466216e-01 0.7271145 7.348490e-01
## Other 1.8764086 7.359783e-01 0.9350246 1.775630e+00
## Rept 1.0804467 9.296716e-01 0.9101667 9.906137e-10
## lakeOkl:genderMale lakeTra:genderMale size<=2.3:genderMale
## Bird 4.851911e-10 0.8268938 1.0437480
## Inver 6.900638e-01 0.7756274 0.7546887
## Other 1.029998e+00 0.9350246 1.9095632
## Rept 4.222621e-01 0.4827984 0.5984610
## lakeHan:size<=2.3:genderMale lakeOkl:size<=2.3:genderMale
## Bird 9.598235e-11 9.920193e-15
## Inver 7.348490e-01 9.390853e-01
## Other 2.408691e+00 1.029998e+00
## Rept 9.081705e-18 4.538504e-10
## lakeTra:size<=2.3:genderMale
## Bird 1.471557e-14
## Inver 8.139676e-01
## Other 1.352559e+00
## Rept 5.984610e-01
##
## Residual Deviance: 487.6018
## AIC: 615.6018model_1c1$deviance## [1] 561.1677model_1c2$deviance## [1] 589.2134model_1c3$deviance## [1] 602.2589model_1c4$deviance## [1] 517.6379model_1c5$deviance## [1] 516.9626model_1c6$deviance## [1] 535.6988model_1c7$deviance## [1] 498.3422model_1c8$deviance## [1] 514.52model_1c9$deviance## [1] 515.4422model_1c10$deviance## [1] 489.5426model_1c11$deviance## [1] 487.6018model_1c1$edf## [1] 16model_1c2$edf## [1] 8model_1c3$edf## [1] 8model_1c4$edf## [1] 36model_1c5$edf## [1] 36model_1c6$edf## [1] 28model_1c7$edf## [1] 48model_1c8$edf## [1] 40model_1c9$edf## [1] 40model_1c10$edf## [1] 52model_1c11$edf## [1] 64model_1c1$AIC## [1] 593.1677model_1c2$AIC## [1] 605.2134model_1c3$AIC## [1] 618.2589model_1c4$AIC## [1] 589.6379model_1c5$AIC## [1] 588.9626model_1c6$AIC## [1] 591.6988model_1c7$AIC## [1] 594.3422model_1c8$AIC## [1] 594.52model_1c9$AIC## [1] 595.4422model_1c10$AIC## [1] 593.5426model_1c11$AIC## [1] 615.6018Jadi, dapat disimpulkan bahwa model terbaik adalah model dengan peubah bebas size dan lake (Model 4). Hal ini juga dapat dipastikan dengan nilai AIC yang lebih kecil dibandingkan dengan model lainnya.