library("epitools")
library("DescTools")
library("lawstat")SOAL 1
Input Data
##=====================##
# INPUT DATA
##=====================##
z.fund<-factor(rep(c("1fund","2mod","3lib"),each=4))
x.sex<-factor(rep(c("1M","2F"),each=2,times=3))
y.fav<-factor(rep(c("1fav","2opp"),times=6))
counts<-c(128,32,123,73,182,56,168,105,119,49,111,70)
data.frame(z.fund,x.sex,y.fav,counts) ## z.fund x.sex y.fav counts
## 1 1fund 1M 1fav 128
## 2 1fund 1M 2opp 32
## 3 1fund 2F 1fav 123
## 4 1fund 2F 2opp 73
## 5 2mod 1M 1fav 182
## 6 2mod 1M 2opp 56
## 7 2mod 2F 1fav 168
## 8 2mod 2F 2opp 105
## 9 3lib 1M 1fav 119
## 10 3lib 1M 2opp 49
## 11 3lib 2F 1fav 111
## 12 3lib 2F 2opp 70A.UJI MODEL INTERAKSI TIGA ARAH (SATURATED VS HOMOGENOUS)
Penentuan Kategori Referensi
##=============================##
# Penentuan kategori reference
##=============================##
x.sex<-relevel(x.sex,ref="2F")
y.fav<-relevel(y.fav,ref="2opp")
z.fund<-relevel(z.fund,ref="3lib")Model Saturated
#saturated
model<- glm(counts~ x.sex+ y.fav+ z.fund+
x.sex*y.fav+ x.sex*z.fund+ y.fav*z.fund+
x.sex*y.fav*z.fund, family=poisson("link"=log))
summary(model) ##
## Call:
## glm(formula = counts ~ x.sex + y.fav + z.fund + x.sex * y.fav +
## x.sex * z.fund + y.fav * z.fund + x.sex * y.fav * z.fund,
## family = poisson(link = log))
##
## Deviance Residuals:
## [1] 0 0 0 0 0 0 0 0 0 0 0 0
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 4.248495 0.119523 35.545 < 2e-16 ***
## x.sex1M -0.356675 0.186263 -1.915 0.05551 .
## y.fav1fav 0.461035 0.152626 3.021 0.00252 **
## z.fund1fund 0.041964 0.167285 0.251 0.80193
## z.fund2mod 0.405465 0.154303 2.628 0.00860 **
## x.sex1M:y.fav1fav 0.426268 0.228268 1.867 0.06185 .
## x.sex1M:z.fund1fund -0.468049 0.282210 -1.659 0.09721 .
## x.sex1M:z.fund2mod -0.271934 0.249148 -1.091 0.27507
## y.fav1fav:z.fund1fund 0.060690 0.212423 0.286 0.77511
## y.fav1fav:z.fund2mod 0.008969 0.196903 0.046 0.96367
## x.sex1M:y.fav1fav:z.fund1fund 0.438301 0.336151 1.304 0.19227
## x.sex1M:y.fav1fav:z.fund2mod 0.282383 0.301553 0.936 0.34905
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 2.4536e+02 on 11 degrees of freedom
## Residual deviance: 1.4655e-14 on 0 degrees of freedom
## AIC: 100.14
##
## Number of Fisher Scoring iterations: 3exp(model$coefficients)## (Intercept) x.sex1M
## 70.0000000 0.7000000
## y.fav1fav z.fund1fund
## 1.5857143 1.0428571
## z.fund2mod x.sex1M:y.fav1fav
## 1.5000000 1.5315315
## x.sex1M:z.fund1fund x.sex1M:z.fund2mod
## 0.6262231 0.7619048
## y.fav1fav:z.fund1fund y.fav1fav:z.fund2mod
## 1.0625694 1.0090090
## x.sex1M:y.fav1fav:z.fund1fund x.sex1M:y.fav1fav:z.fund2mod
## 1.5500717 1.3262868Model Homogenous
#Homogenous Model
model2 <- glm(counts~x.sex+ y.fav+ z.fund+
x.sex*y.fav+ x.sex*z.fund+ y.fav*z.fund,
family=poisson("link"=log))
summary(model2) ##
## Call:
## glm(formula = counts ~ x.sex + y.fav + z.fund + x.sex * y.fav +
## x.sex * z.fund + y.fav * z.fund, family = poisson(link = log))
##
## Deviance Residuals:
## 1 2 3 4 5 6 7 8
## 0.2996 -0.5744 -0.3002 0.3994 0.0856 -0.1530 -0.0887 0.1129
## 9 10 11 12
## -0.4085 0.6655 0.4342 -0.5281
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 4.31096 0.10522 40.972 < 2e-16 ***
## x.sex1M -0.51575 0.13814 -3.733 0.000189 ***
## y.fav1fav 0.35707 0.12658 2.821 0.004788 **
## z.fund1fund -0.06762 0.14452 -0.468 0.639854
## z.fund2mod 0.33196 0.13142 2.526 0.011540 *
## x.sex1M:y.fav1fav 0.66406 0.12728 5.217 1.81e-07 ***
## x.sex1M:z.fund1fund -0.16201 0.15300 -1.059 0.289649
## x.sex1M:z.fund2mod -0.08146 0.14079 -0.579 0.562887
## y.fav1fav:z.fund1fund 0.23873 0.16402 1.455 0.145551
## y.fav1fav:z.fund2mod 0.13081 0.14951 0.875 0.381614
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 245.361 on 11 degrees of freedom
## Residual deviance: 1.798 on 2 degrees of freedom
## AIC: 97.934
##
## Number of Fisher Scoring iterations: 3Yang digunakan residual deviance
UJI HIPOTESIS UNTUK MENGETAHUI ADA/ TIDAK HUBUNGAN TIGA ARAH (SATURATED VS HOMOGENOUS)
#pengujian hipotesis
# Deviance of Model
Deviance.model<- model2$deviance -
model$deviance
Deviance.model## [1] 1.797977# Chi Square tabel dengan alpa = 0.05
derajat.bebas <- (2 - 0)
derajat.bebas## [1] 2chi.tabel <- qchisq((1-0.05), df=derajat.bebas)
chi.tabel## [1] 5.991465Keputusan <- ifelse(Deviance.model <= chi.tabel,"Terima", "Tolak")
Keputusan## [1] "Terima"Pada taraf nyata 5%, belum cukup bukti untuk menolak 𝐻0 atau dapat dikatakan bahwa tidak ada interaksi tiga arah antara jenis kelamin, fundamentalisme, dan pendapat mengenai hukuman mati.
Ingat, dalam membuat selisih deviance, model yang menjadi pengurang adalah model yang lebih lengkap (parameter yang lebih banyak atau derajat bebasnya lebih kecil).Makin banyak parameter, makin kecil derajat bebas nya karena derajat bebas = banyaknya amatan atau perkalian dimensi tabel kontingensi (misal: 2x2x3 = 12) - banyaknya parameter atau koefisien (lihat di output R ada berapa banyak coefficients nya termasuk intercept) .
B. UJI MODEL INTERAKSI DUA ARAH (HOMOGENOUS VS CONDITIONAL ON X)
#Conditional Association on X
model3<-glm(counts~ x.sex+ y.fav+ z.fund+
x.sex*y.fav+ x.sex*z.fund,
family=poisson("link"=log))
summary(model3) ##
## Call:
## glm(formula = counts ~ x.sex + y.fav + z.fund + x.sex * y.fav +
## x.sex * z.fund, family = poisson(link = log))
##
## Deviance Residuals:
## 1 2 3 4 5 6 7 8
## 0.60542 -1.11492 0.16142 -0.20684 0.11953 -0.21283 -0.06470 0.08220
## 9 10 11 12
## -0.74698 1.26595 -0.08912 0.11304
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 4.23495 0.08955 47.293 < 2e-16 ***
## x.sex1M -0.52960 0.13966 -3.792 0.000149 ***
## y.fav1fav 0.48302 0.08075 5.982 2.20e-09 ***
## z.fund1fund 0.07962 0.10309 0.772 0.439916
## z.fund2mod 0.41097 0.09585 4.288 1.81e-05 ***
## x.sex1M:y.fav1fav 0.65845 0.12708 5.181 2.20e-07 ***
## x.sex1M:z.fund1fund -0.12841 0.15109 -0.850 0.395405
## x.sex1M:z.fund2mod -0.06267 0.13908 -0.451 0.652274
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 245.3612 on 11 degrees of freedom
## Residual deviance: 3.9303 on 4 degrees of freedom
## AIC: 96.067
##
## Number of Fisher Scoring iterations: 4yang digunakan selanjutnya adalah Residual Deviance.
#pengujian hipotesis
# Deviance of Model
Deviance.model<- model3$deviance -
model2$deviance #model3: conditional on X, model2: homogenous
Deviance.model## [1] 2.132302# Chi Square tabel dengan alpa = 0.05
derajat.bebas <- (4 - 2)
derajat.bebas## [1] 2chi.tabel <- qchisq((1-0.05), df=derajat.bebas)
chi.tabel## [1] 5.991465Keputusan <- ifelse(Deviance.model <= chi.tabel,"Terima", "Tolak")
Keputusan## [1] "Terima"C. UJI MODEL INTERAKSI DUA ARAH (HOMOGENOUS VS CONDITIONAL ON Y)
#Conditional Association on Y
model4<-glm(counts~ x.sex+ y.fav+ z.fund+
x.sex*y.fav+ y.fav*z.fund,
family=poisson("link"=log))
summary(model4)##
## Call:
## glm(formula = counts ~ x.sex + y.fav + z.fund + x.sex * y.fav +
## y.fav * z.fund, family = poisson(link = log))
##
## Deviance Residuals:
## 1 2 3 4 5 6 7 8
## -0.13887 -0.89983 0.14286 0.64384 0.09764 -0.17120 -0.10112 0.12650
## 9 10 11 12
## 0.02418 0.99745 -0.02499 -0.77148
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 4.33931 0.09919 43.748 < 2e-16 ***
## x.sex1M -0.59345 0.10645 -5.575 2.48e-08 ***
## y.fav1fav 0.37259 0.12438 2.996 0.00274 **
## z.fund1fund -0.12516 0.13389 -0.935 0.34989
## z.fund2mod 0.30228 0.12089 2.500 0.01240 *
## x.sex1M:y.fav1fav 0.65845 0.12708 5.181 2.20e-07 ***
## y.fav1fav:z.fund1fund 0.21254 0.16205 1.312 0.18966
## y.fav1fav:z.fund2mod 0.11757 0.14771 0.796 0.42606
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 245.3612 on 11 degrees of freedom
## Residual deviance: 2.9203 on 4 degrees of freedom
## AIC: 95.057
##
## Number of Fisher Scoring iterations: 4yang digunakan selanjutnya adalah Residual Deviance.
#pengujian hipotesis
# Deviance of Model
Deviance.model<- model4$deviance -
model2$deviance #model4: conditional on Y, model2: homogenous
Deviance.model## [1] 1.122315# Chi Square tabel dengan alpa = 0.05
derajat.bebas <- (4 - 2)
derajat.bebas## [1] 2chi.tabel <- qchisq((1-0.05), df=derajat.bebas)
chi.tabel## [1] 5.991465Keputusan <- ifelse(Deviance.model <= chi.tabel,"Terima", "Tolak")
Keputusan## [1] "Terima"D. UJI MODEL INTERAKSI DUA ARAH (HOMOGENOUS VS CONDITIONAL ON Z)
#Conditional Association on Y
#Conditional Association on z
model5<-glm(counts~ x.sex+ y.fav+ z.fund+
x.sex*z.fund+ y.fav*z.fund,
family=poisson("link"=log))
summary(model5) ##
## Call:
## glm(formula = counts ~ x.sex + y.fav + z.fund + x.sex * z.fund +
## y.fav * z.fund, family = poisson(link = log))
##
## Deviance Residuals:
## 1 2 3 4 5 6 7 8
## 1.3998 -2.3495 -1.3171 1.9188 1.4595 -2.2965 -1.4130 1.9781
## 9 10 11 12
## 0.7777 -1.1226 -0.7675 1.0321
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 4.12255 0.10518 39.195 < 2e-16 ***
## x.sex1M -0.07453 0.10713 -0.696 0.487
## y.fav1fav 0.65896 0.11292 5.836 5.36e-09 ***
## z.fund1fund -0.06540 0.15126 -0.432 0.665
## z.fund2mod 0.33196 0.13777 2.410 0.016 *
## x.sex1M:z.fund1fund -0.12841 0.15109 -0.850 0.395
## x.sex1M:z.fund2mod -0.06267 0.13908 -0.451 0.652
## y.fav1fav:z.fund1fund 0.21254 0.16205 1.312 0.190
## y.fav1fav:z.fund2mod 0.11757 0.14771 0.796 0.426
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 245.361 on 11 degrees of freedom
## Residual deviance: 29.729 on 3 degrees of freedom
## AIC: 123.87
##
## Number of Fisher Scoring iterations: 4yang digunakan selanjutnya adalah Residual Deviance.
#pengujian hipotesis
# Deviance of Model
Deviance.model<- model5$deviance -
model2$deviance ##model5: conditional on Z, model2: homogenous
Deviance.model## [1] 27.93095# Chi Square tabel dengan alpa = 0.05
derajat.bebas <- (3 - 2)
derajat.bebas## [1] 1chi.tabel <- qchisq((1-0.05), df=derajat.bebas)
chi.tabel## [1] 3.841459Keputusan <- ifelse(Deviance.model <= chi.tabel,"Terima", "Tolak")
Keputusan## [1] "Tolak"E. PEMILIHAN MODEL TERBAIK
#Model Terbaik
#best model
bestmodel<-glm(counts~ x.sex+ y.fav+ z.fund+
x.sex*y.fav,family=poisson("link"=log))
summary(bestmodel) ##
## Call:
## glm(formula = counts ~ x.sex + y.fav + z.fund + x.sex * y.fav,
## family = poisson(link = log))
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.32758 -0.24954 -0.01277 0.14946 1.48613
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 4.26518 0.07794 54.721 < 2e-16 ***
## x.sex1M -0.59345 0.10645 -5.575 2.48e-08 ***
## y.fav1fav 0.48302 0.08075 5.982 2.20e-09 ***
## z.fund1fund 0.01986 0.07533 0.264 0.792
## z.fund2mod 0.38130 0.06944 5.491 4.00e-08 ***
## x.sex1M:y.fav1fav 0.65845 0.12708 5.181 2.20e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 245.3612 on 11 degrees of freedom
## Residual deviance: 4.6532 on 6 degrees of freedom
## AIC: 92.79
##
## Number of Fisher Scoring iterations: 4Dari summary model diatas terlihat bahwa best model memiliki AIC yang lebih rendah dibandingkan saturated, homogeneous, dan conditional model
F. INTERPRETASI KOEFISIEN MODEL TERBAIK
#interpretasi
data.frame(koef=bestmodel$coefficients,
exp_koef=exp(bestmodel$coefficients))## koef exp_koef
## (Intercept) 4.26517861 71.1776316
## x.sex1M -0.59344782 0.5524194
## y.fav1fav 0.48302334 1.6209677
## z.fund1fund 0.01985881 1.0200573
## z.fund2mod 0.38129767 1.4641834
## x.sex1M:y.fav1fav 0.65845265 1.9318008G. NILAI DUGAAN MODEL TERBAIK
#fitted
data.frame(Fund=z.fund,sex=x.sex,favor=
y.fav,counts=counts,
fitted=bestmodel$fitted.values)## Fund sex favor counts fitted
## 1 1fund 1M 1fav 128 125.59539
## 2 1fund 1M 2opp 32 40.10855
## 3 1fund 2F 1fav 123 117.69079
## 4 1fund 2F 2opp 73 72.60526
## 5 2mod 1M 1fav 182 180.27878
## 6 2mod 1M 2opp 56 57.57155
## 7 2mod 2F 1fav 168 168.93257
## 8 2mod 2F 2opp 105 104.21711
## 9 3lib 1M 1fav 119 123.12582
## 10 3lib 1M 2opp 49 39.31990
## 11 3lib 2F 1fav 111 115.37664
## 12 3lib 2F 2opp 70 71.17763Keterangan: nilai miyu_ijk akan sama apapun referensi dari kategori peubahnya yang kita gunakan.
SOAL 2
Input Data
##=====================##
# INPUT DATA
##=====================##
z.fav<-factor(rep(c("1s_agr","2agr","3dis","4s_dis"),each=6))
x.sex<-factor(rep(c("1M","2F"),each=3,times=4))
y.race<-factor(rep(c("1white","2black","3other"),times=8))
counts<-c(96,16,3,71,30,6,172,17,23,174,34,13,59,1,13,96,3,10,
15,2,1,35,2,5)
data.frame(z.fav,x.sex,y.race,counts) ## z.fav x.sex y.race counts
## 1 1s_agr 1M 1white 96
## 2 1s_agr 1M 2black 16
## 3 1s_agr 1M 3other 3
## 4 1s_agr 2F 1white 71
## 5 1s_agr 2F 2black 30
## 6 1s_agr 2F 3other 6
## 7 2agr 1M 1white 172
## 8 2agr 1M 2black 17
## 9 2agr 1M 3other 23
## 10 2agr 2F 1white 174
## 11 2agr 2F 2black 34
## 12 2agr 2F 3other 13
## 13 3dis 1M 1white 59
## 14 3dis 1M 2black 1
## 15 3dis 1M 3other 13
## 16 3dis 2F 1white 96
## 17 3dis 2F 2black 3
## 18 3dis 2F 3other 10
## 19 4s_dis 1M 1white 15
## 20 4s_dis 1M 2black 2
## 21 4s_dis 1M 3other 1
## 22 4s_dis 2F 1white 35
## 23 4s_dis 2F 2black 2
## 24 4s_dis 2F 3other 5A.UJI MODEL INTERAKSI TIGA ARAH (SATURATED VS HOMOGENOUS)
Penentuan Kategori Referensi
##=============================##
# Penentuan kategori reference
##=============================##
x.sex<-relevel(x.sex,ref="2F")
y.race<-relevel(y.race,ref="3other")
z.fav<-relevel(z.fav,ref="4s_dis")Model Saturated
#saturated
model<- glm(counts~ x.sex+ y.race+ z.fav+
x.sex*y.race+ x.sex*z.fav+ y.race*z.fav+
x.sex*y.race*z.fav, family=poisson("link"=log))
summary(model) ##
## Call:
## glm(formula = counts ~ x.sex + y.race + z.fav + x.sex * y.race +
## x.sex * z.fav + y.race * z.fav + x.sex * y.race * z.fav,
## family = poisson(link = log))
##
## Deviance Residuals:
## [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.6094 0.4472 3.599 0.00032 ***
## x.sex1M -1.6094 1.0954 -1.469 0.14177
## y.race1white 1.9459 0.4781 4.070 4.7e-05 ***
## y.race2black -0.9163 0.8367 -1.095 0.27344
## z.fav1s_agr 0.1823 0.6055 0.301 0.76334
## z.fav2agr 0.9555 0.5262 1.816 0.06941 .
## z.fav3dis 0.6931 0.5477 1.266 0.20569
## x.sex1M:y.race1white 0.7621 1.1381 0.670 0.50307
## x.sex1M:y.race2black 1.6094 1.4832 1.085 0.27788
## x.sex1M:z.fav1s_agr 0.9163 1.3038 0.703 0.48220
## x.sex1M:z.fav2agr 2.1800 1.1491 1.897 0.05781 .
## x.sex1M:z.fav3dis 1.8718 1.1734 1.595 0.11067
## y.race1white:z.fav1s_agr 0.5250 0.6398 0.821 0.41187
## y.race2black:z.fav1s_agr 2.5257 0.9487 2.662 0.00776 **
## y.race1white:z.fav2agr 0.6482 0.5579 1.162 0.24529
## y.race2black:z.fav2agr 1.8777 0.8980 2.091 0.03652 *
## y.race1white:z.fav3dis 0.3159 0.5822 0.542 0.58748
## y.race2black:z.fav3dis -0.2877 1.0646 -0.270 0.78698
## x.sex1M:y.race1white:z.fav1s_agr 0.2327 1.3490 0.172 0.86306
## x.sex1M:y.race2black:z.fav1s_agr -1.5449 1.6721 -0.924 0.35552
## x.sex1M:y.race1white:z.fav2agr -1.3442 1.1947 -1.125 0.26050
## x.sex1M:y.race2black:z.fav2agr -2.8731 1.5520 -1.851 0.06413 .
## x.sex1M:y.race1white:z.fav3dis -1.5113 1.2245 -1.234 0.21714
## x.sex1M:y.race2black:z.fav3dis -2.9704 1.9262 -1.542 0.12305
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 1.2482e+03 on 23 degrees of freedom
## Residual deviance: 3.7303e-14 on 0 degrees of freedom
## AIC: 157
##
## Number of Fisher Scoring iterations: 3exp(model$coefficients)## (Intercept) x.sex1M
## 5.00000000 0.20000000
## y.race1white y.race2black
## 7.00000000 0.40000000
## z.fav1s_agr z.fav2agr
## 1.20000000 2.60000000
## z.fav3dis x.sex1M:y.race1white
## 2.00000000 2.14285714
## x.sex1M:y.race2black x.sex1M:z.fav1s_agr
## 5.00000000 2.50000000
## x.sex1M:z.fav2agr x.sex1M:z.fav3dis
## 8.84615385 6.50000000
## y.race1white:z.fav1s_agr y.race2black:z.fav1s_agr
## 1.69047619 12.50000000
## y.race1white:z.fav2agr y.race2black:z.fav2agr
## 1.91208791 6.53846154
## y.race1white:z.fav3dis y.race2black:z.fav3dis
## 1.37142857 0.75000000
## x.sex1M:y.race1white:z.fav1s_agr x.sex1M:y.race2black:z.fav1s_agr
## 1.26197183 0.21333333
## x.sex1M:y.race1white:z.fav2agr x.sex1M:y.race2black:z.fav2agr
## 0.26073630 0.05652174
## x.sex1M:y.race1white:z.fav3dis x.sex1M:y.race2black:z.fav3dis
## 0.22061966 0.05128205Model Homogenous
#Homogenous Model
model2 <- glm(counts~ x.sex+ y.race+ z.fav+
x.sex*y.race+ x.sex*z.fav+ y.race*z.fav,
family=poisson("link"=log))
summary(model2) ##
## Call:
## glm(formula = counts ~ x.sex + y.race + z.fav + x.sex * y.race +
## x.sex * z.fav + y.race * z.fav, family = poisson(link = log))
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.23956 -0.36301 0.00067 0.28922 1.32392
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.3201 0.4299 3.071 0.002136 **
## x.sex1M -0.5064 0.3584 -1.413 0.157676
## y.race1white 2.2340 0.4421 5.053 4.35e-07 ***
## y.race2black -0.1265 0.6548 -0.193 0.846783
## z.fav1s_agr -0.1222 0.5490 -0.223 0.823806
## z.fav2agr 1.3815 0.4600 3.003 0.002669 **
## z.fav3dis 1.1680 0.4765 2.451 0.014241 *
## x.sex1M:y.race1white -0.3368 0.2489 -1.353 0.175958
## x.sex1M:y.race2black -1.0423 0.3207 -3.250 0.001154 **
## x.sex1M:z.fav1s_agr 1.0467 0.3160 3.313 0.000924 ***
## x.sex1M:z.fav2agr 0.8539 0.2993 2.853 0.004332 **
## x.sex1M:z.fav3dis 0.4126 0.3210 1.285 0.198645
## y.race1white:z.fav1s_agr 0.8860 0.5555 1.595 0.110685
## y.race2black:z.fav1s_agr 2.2840 0.7488 3.050 0.002289 **
## y.race1white:z.fav2agr 0.2123 0.4697 0.452 0.651277
## y.race2black:z.fav2agr 0.9518 0.6869 1.386 0.165863
## y.race1white:z.fav3dis -0.1796 0.4877 -0.368 0.712663
## y.race2black:z.fav3dis -1.2538 0.8457 -1.482 0.138218
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 1248.1895 on 23 degrees of freedom
## Residual deviance: 8.6165 on 6 degrees of freedom
## AIC: 153.62
##
## Number of Fisher Scoring iterations: 5Yang digunakan residual deviance
UJI HIPOTESIS UNTUK MENGETAHUI ADA/ TIDAK HUBUNGAN TIGA ARAH (SATURATED VS HOMOGENOUS)
Ho : Tidak ada interaksi 3 arah
H1 : Ada interaksi 3 arah
#pengujian hipotesis
# Deviance of Model
Deviance.model<- model2$deviance - model$deviance
Deviance.model## [1] 8.616541model2$df.residual## [1] 6# Chi Square tabel dengan alpa = 0.05
derajat.bebas <- (model2$df.residual - model$df.residual)
derajat.bebas## [1] 6chi.tabel <- qchisq((1-0.05), df=derajat.bebas)
chi.tabel## [1] 12.59159Keputusan <- ifelse(Deviance.model <= chi.tabel,"Terima", "Tolak")
Keputusan## [1] "Terima"Pada taraf nyata 5%, belum cukup bukti untuk menolak 𝐻0 atau dapat dikatakan bahwa tidak ada interaksi tiga arah antara jenis kelamin, ras, dan pendapat/mendukung untuk memukul sebagai pendisiplinan anak.
B. UJI MODEL INTERAKSI DUA ARAH (HOMOGENOUS VS CONDITIONAL ON X)
Ho : Tidak ada interaksi antara Y dan Z
H1 : Ada interaksi Y dan Z
#Conditional Association on X
model3<-glm(counts~ x.sex+ y.race+ z.fav+
x.sex*y.race+ x.sex*z.fav,
family=poisson("link"=log))
summary(model3) ##
## Call:
## glm(formula = counts ~ x.sex + y.race + z.fav + x.sex * y.race +
## x.sex * z.fav, family = poisson(link = log))
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -3.9335 -0.6256 0.0552 0.6367 3.2840
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.0923 0.2261 4.831 1.36e-06 ***
## x.sex1M -0.5486 0.3596 -1.526 0.127119
## y.race1white 2.4032 0.1791 13.420 < 2e-16 ***
## y.race2black 0.7077 0.2095 3.378 0.000731 ***
## z.fav1s_agr 0.9352 0.1821 5.136 2.81e-07 ***
## z.fav2agr 1.6605 0.1683 9.865 < 2e-16 ***
## z.fav3dis 0.9537 0.1816 5.251 1.51e-07 ***
## x.sex1M:y.race1white -0.2573 0.2449 -1.050 0.293510
## x.sex1M:y.race2black -0.8131 0.3109 -2.615 0.008922 **
## x.sex1M:z.fav1s_agr 0.9194 0.3121 2.946 0.003221 **
## x.sex1M:z.fav2agr 0.8057 0.2977 2.707 0.006794 **
## x.sex1M:z.fav3dis 0.4464 0.3197 1.396 0.162674
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 1248.190 on 23 degrees of freedom
## Residual deviance: 59.495 on 12 degrees of freedom
## AIC: 192.5
##
## Number of Fisher Scoring iterations: 5yang digunakan selanjutnya adalah residual deviance
#pengujian hipotesis
# Deviance of Model
Deviance.model<- model3$deviance - model2$deviance
#model3: conditional on X, model2: homogenous
Deviance.model## [1] 50.87895# Chi Square tabel dengan alpa = 0.05
derajat.bebas <- (model3$df.residual - model2$df.residual)
derajat.bebas## [1] 6chi.tabel <- qchisq((1-0.05), df=derajat.bebas)
chi.tabel## [1] 12.59159Keputusan <- ifelse(Deviance.model <= chi.tabel,"Terima", "Tolak")
Keputusan## [1] "Tolak"Pada taraf nyata 5%, cukup bukti untuk menolak 𝐻0 atau dapat dikatakan bahwa interaksi YZ signifikan (ada interaksi dua arah antara ras dengan pendapat/mendukung untuk memukul sebagai pendisiplinan anak.
C. UJI MODEL INTERAKSI DUA ARAH (HOMOGENOUS VS CONDITIONAL ON Y)
Ho : Tidak ada interaksi antara X dan Z
H1 : Ada interaksi X dan Z
#Conditional Association on Y
model4<-glm(counts~ x.sex+ y.race+ z.fav+
x.sex*y.race+ y.race*z.fav,
family=poisson("link"=log))
summary(model4)##
## Call:
## glm(formula = counts ~ x.sex + y.race + z.fav + x.sex * y.race +
## y.race * z.fav, family = poisson(link = log))
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.9398 -0.6296 0.0079 0.6122 1.7862
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.01405 0.42728 2.373 0.01763 *
## x.sex1M 0.16252 0.23326 0.697 0.48598
## y.race1white 2.25109 0.45148 4.986 6.16e-07 ***
## y.race2black -0.04761 0.66146 -0.072 0.94262
## z.fav1s_agr 0.40547 0.52705 0.769 0.44171
## z.fav2agr 1.79176 0.44096 4.063 4.84e-05 ***
## z.fav3dis 1.34373 0.45842 2.931 0.00338 **
## x.sex1M:y.race1white -0.25730 0.24494 -1.050 0.29351
## x.sex1M:y.race2black -0.81311 0.31094 -2.615 0.00892 **
## y.race1white:z.fav1s_agr 0.80051 0.55115 1.452 0.14638
## y.race2black:z.fav1s_agr 2.03688 0.74129 2.748 0.00600 **
## y.race1white:z.fav2agr 0.14266 0.46619 0.306 0.75960
## y.race2black:z.fav2agr 0.75377 0.68121 1.107 0.26850
## y.race1white:z.fav3dis -0.21233 0.48641 -0.437 0.66245
## y.race2black:z.fav3dis -1.34373 0.84270 -1.595 0.11081
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 1248.190 on 23 degrees of freedom
## Residual deviance: 26.557 on 9 degrees of freedom
## AIC: 165.56
##
## Number of Fisher Scoring iterations: 5#pengujian hipotesis
# Deviance of Model
Deviance.model<- model4$deviance - model2$deviance
#model4: conditional on Y, model2: homogenous
Deviance.model## [1] 17.94087# Chi Square tabel dengan alpa = 0.05
derajat.bebas <- (model4$df.residual - model2$df.residual)
derajat.bebas## [1] 3chi.tabel <- qchisq((1-0.05), df=derajat.bebas)
chi.tabel## [1] 7.814728Keputusan <- ifelse(Deviance.model <= chi.tabel,"Terima", "Tolak")
Keputusan## [1] "Tolak"Pada taraf nyata 5%, cukup bukti untuk menolak 𝐻0 atau dapat dikatakan bahwa interaksi XZ signifikan (ada interaksi dua arah antara jenis kelamin dengan pendapat/mendukung untuk memukul sebagai pendisiplinan anak).
D. UJI MODEL INTERAKSI DUA ARAH (HOMOGENOUS VS CONDITIONAL ON Z)
Ho : Tidak ada interaksi antara X dan Y
H1 : Ada interaksi X dan Y
#Conditional Association on z
model5<-glm(counts~ x.sex+ y.race+ z.fav+
x.sex*z.fav+ y.race*z.fav,
family=poisson("link"=log))
summary(model5) ##
## Call:
## glm(formula = counts ~ x.sex + y.race + z.fav + x.sex * z.fav +
## y.race * z.fav, family = poisson(link = log))
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.7064 -0.6946 0.0000 0.6878 1.5769
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.43508 0.41690 3.442 0.000577 ***
## x.sex1M -0.84730 0.28172 -3.008 0.002633 **
## y.race1white 2.12026 0.43205 4.907 9.23e-07 ***
## y.race2black -0.40547 0.64550 -0.628 0.529909
## z.fav1s_agr 0.03229 0.53830 0.060 0.952165
## z.fav2agr 1.47586 0.45145 3.269 0.001079 **
## z.fav3dis 1.18775 0.47007 2.527 0.011513 *
## x.sex1M:z.fav1s_agr 0.91940 0.31210 2.946 0.003221 **
## x.sex1M:z.fav2agr 0.80572 0.29767 2.707 0.006794 **
## x.sex1M:z.fav3dis 0.44641 0.31975 1.396 0.162674
## y.race1white:z.fav1s_agr 0.80051 0.55115 1.452 0.146382
## y.race2black:z.fav1s_agr 2.03688 0.74129 2.748 0.006001 **
## y.race1white:z.fav2agr 0.14266 0.46619 0.306 0.759602
## y.race2black:z.fav2agr 0.75377 0.68121 1.107 0.268504
## y.race1white:z.fav3dis -0.21233 0.48641 -0.437 0.662453
## y.race2black:z.fav3dis -1.34373 0.84270 -1.595 0.110811
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 1248.190 on 23 degrees of freedom
## Residual deviance: 21.687 on 8 degrees of freedom
## AIC: 162.69
##
## Number of Fisher Scoring iterations: 4#pengujian hipotesis
# Deviance of Model
Deviance.model<- model5$deviance - model2$deviance
#model5: conditional on Z, model2: homogenous
Deviance.model## [1] 13.07038# Chi Square tabel dengan alpa = 0.05
derajat.bebas <- (model5$df.residual - model2$df.residual)
derajat.bebas## [1] 2chi.tabel <- qchisq((1-0.05), df=derajat.bebas)
chi.tabel## [1] 5.991465Keputusan <- ifelse(Deviance.model <= chi.tabel,"Terima", "Tolak")
Keputusan## [1] "Tolak"Pada taraf nyata 5%, cukup bukti untuk menolak 𝐻0 atau dapat dikatakan bahwa interaksi XY signifikan (ada interaksi dua arah antara jenis kelamin dengan ras).
E. PEMILIHAN MODEL TERBAIK
Karena terdapat interaksi YZ, XZ, dan XY maka model terbaiknya adalah model homogenous.
#Model Terbaik adalah model homogenous
#best model
bestmodel<-glm(counts~ x.sex+ y.race+ z.fav+ x.sex*y.race+ x.sex*z.fav+ y.race*z.fav,
family=poisson("link"=log))
summary(bestmodel) ##
## Call:
## glm(formula = counts ~ x.sex + y.race + z.fav + x.sex * y.race +
## x.sex * z.fav + y.race * z.fav, family = poisson(link = log))
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.23956 -0.36301 0.00067 0.28922 1.32392
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.3201 0.4299 3.071 0.002136 **
## x.sex1M -0.5064 0.3584 -1.413 0.157676
## y.race1white 2.2340 0.4421 5.053 4.35e-07 ***
## y.race2black -0.1265 0.6548 -0.193 0.846783
## z.fav1s_agr -0.1222 0.5490 -0.223 0.823806
## z.fav2agr 1.3815 0.4600 3.003 0.002669 **
## z.fav3dis 1.1680 0.4765 2.451 0.014241 *
## x.sex1M:y.race1white -0.3368 0.2489 -1.353 0.175958
## x.sex1M:y.race2black -1.0423 0.3207 -3.250 0.001154 **
## x.sex1M:z.fav1s_agr 1.0467 0.3160 3.313 0.000924 ***
## x.sex1M:z.fav2agr 0.8539 0.2993 2.853 0.004332 **
## x.sex1M:z.fav3dis 0.4126 0.3210 1.285 0.198645
## y.race1white:z.fav1s_agr 0.8860 0.5555 1.595 0.110685
## y.race2black:z.fav1s_agr 2.2840 0.7488 3.050 0.002289 **
## y.race1white:z.fav2agr 0.2123 0.4697 0.452 0.651277
## y.race2black:z.fav2agr 0.9518 0.6869 1.386 0.165863
## y.race1white:z.fav3dis -0.1796 0.4877 -0.368 0.712663
## y.race2black:z.fav3dis -1.2538 0.8457 -1.482 0.138218
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 1248.1895 on 23 degrees of freedom
## Residual deviance: 8.6165 on 6 degrees of freedom
## AIC: 153.62
##
## Number of Fisher Scoring iterations: 5Dari summary model diatas terlihat bahwa best model memiliki AIC yang lebih rendah dibandingkan saturated dan conditional model
F. INTERPRETASI KOEFISIEN MODEL TERBAIK
#interpretasi
data.frame(koef=bestmodel$coefficients,
exp_koef=exp(bestmodel$coefficients))## koef exp_koef
## (Intercept) 1.3201108 3.7438360
## x.sex1M -0.5064447 0.6026343
## y.race1white 2.2340153 9.3372825
## y.race2black -0.1265188 0.8811576
## z.fav1s_agr -0.1222374 0.8849383
## z.fav2agr 1.3815186 3.9809424
## z.fav3dis 1.1680493 3.2157136
## x.sex1M:y.race1white -0.3367854 0.7140620
## x.sex1M:y.race2black -1.0422655 0.3526548
## x.sex1M:z.fav1s_agr 1.0467430 2.8483588
## x.sex1M:z.fav2agr 0.8538990 2.3487871
## x.sex1M:z.fav3dis 0.4126187 1.5107688
## y.race1white:z.fav1s_agr 0.8860333 2.4254893
## y.race2black:z.fav1s_agr 2.2839521 9.8153952
## y.race1white:z.fav2agr 0.2122983 1.2365167
## y.race2black:z.fav2agr 0.9518044 2.5903794
## y.race1white:z.fav3dis -0.1795930 0.8356102
## y.race2black:z.fav3dis -1.2537900 0.2854210G. NILAI DUGAAN MODEL TERBAIK
#fitted
data.frame(favor=z.fav,sex=x.sex,race=y.race,counts=counts,
fitted=bestmodel$fitted.values)## favor sex race counts fitted
## 1 1s_agr 1M 1white 96 91.9674549
## 2 1s_agr 1M 2black 16 17.3456089
## 3 1s_agr 1M 3other 3 5.6869361
## 4 1s_agr 2F 1white 71 75.0325451
## 5 1s_agr 2F 2black 30 28.6543911
## 6 1s_agr 2F 3other 6 3.3130639
## 7 2agr 1M 1white 172 173.9228497
## 8 2agr 1M 2black 17 16.9811459
## 9 2agr 1M 3other 23 21.0960043
## 10 2agr 2F 1white 174 172.0771503
## 11 2agr 2F 2black 34 34.0188541
## 12 2agr 2F 3other 13 14.9039957
## 13 3dis 1M 1white 59 61.0669498
## 14 3dis 1M 2black 1 0.9721547
## 15 3dis 1M 3other 13 10.9608955
## 16 3dis 2F 1white 96 93.9330502
## 17 3dis 2F 2black 3 3.0278453
## 18 3dis 2F 3other 10 12.0391045
## 19 4s_dis 1M 1white 15 15.0427455
## 20 4s_dis 1M 2black 2 0.7010905
## 21 4s_dis 1M 3other 1 2.2561640
## 22 4s_dis 2F 1white 35 34.9572545
## 23 4s_dis 2F 2black 2 3.2989095
## 24 4s_dis 2F 3other 5 3.7438360Keterangan: nilai miyu_ijk akan sama apapun referensi dari kategori peubahnya yang kita gunakan.