Kelompok : 1

Kelas : 2023 F

Anggota Kelompok:

Naufal Faiz Nugraha (23031554020)

Bagus Febriansyah Pratama (23031554144)

Otniel Glory Joseputra Pribadi (23031554151)

Rozan Adzki Yahya (23031554236)

Multinomial

1. Load Dataset

# Load the dataset
df_mltn <- read.csv("E:/Anmul-Kelompok/car_evaluation.csv")

# Display structure of the dataset
str(df_mltn)

## 'data.frame':    1728 obs. of  7 variables:
##  $ buying  : chr  "vhigh" "vhigh" "vhigh" "vhigh" ...
##  $ maint   : chr  "vhigh" "vhigh" "vhigh" "vhigh" ...
##  $ doors   : chr  "2" "2" "2" "2" ...
##  $ persons : chr  "2" "2" "2" "2" ...
##  $ lug_boot: chr  "small" "small" "small" "med" ...
##  $ safety  : chr  "low" "med" "high" "low" ...
##  $ class   : chr  "unacc" "unacc" "unacc" "unacc" ...

Penjelasan variable:
Fitur (Variabel Independen):

buying (Harga pembelian)
maint (Biaya perawatan)
doors (Jumlah pintu)
persons (Kapasitas penumpang)
lug_boot (Kapasitas bagasi)
safety (Estimasi keamanan)

Variabel Target:

class (Evaluasi keseluruhan mobil)

2. Multinomial Logistic Regression with 1 Independent Variable (IV)

# Load necessary library
library(nnet)

# Fit basic multinomial logistic regression
fit_basic <- multinom(class ~ safety, data = df_mltn)

## # weights:  16 (9 variable)
## initial  value 2395.516656 
## iter  10 value 1183.561335
## iter  20 value 1130.262427
## iter  30 value 1130.161452
## final  value 1130.152825 
## converged

# Summary of the model
summary(fit_basic)

## Call:
## multinom(formula = class ~ safety, data = df_mltn)
## 
## Coefficients:
##       (Intercept) safetylow   safetymed
## good   -1.9169216 -4.329071   0.3875256
## unacc   0.3058977 30.382690   0.3788808
## vgood  -1.1437326 -5.291423 -14.3746602
## 
## Std. Errors:
##       (Intercept)    safetylow   safetymed
## good   0.19553841 2.837316e-14   0.2634993
## unacc  0.09226088 2.306790e-11   0.1298797
## vgood  0.14243096 1.166844e-13 174.6385287
## 
## Residual Deviance: 2260.306 
## AIC: 2278.306

library(broom)
library(kableExtra)

# Tidy version of the summary with confidence intervals
tidy(fit_basic, conf.int = TRUE) %>%
  kable() %>%
  kable_styling("basic", full_width = FALSE)

y.level	term	estimate	std.error	statistic	p.value	conf.low	conf.high
good	(Intercept)	-1.9169216	0.1955384	-9.803300e+00	0.0000000	-2.3001699	-1.5336734
good	safetylow	-4.3290714	0.0000000	-1.525763e+14	0.0000000	-4.3290714	-4.3290714
good	safetymed	0.3875256	0.2634993	1.470690e+00	0.1413751	-0.1289234	0.9039747
unacc	(Intercept)	0.3058977	0.0922609	3.315574e+00	0.0009146	0.1250698	0.4867257
unacc	safetylow	30.3826900	0.0000000	1.317098e+12	0.0000000	30.3826900	30.3826900
unacc	safetymed	0.3788808	0.1298797	2.917166e+00	0.0035323	0.1243212	0.6334404
vgood	(Intercept)	-1.1437326	0.1424310	-8.030084e+00	0.0000000	-1.4228922	-0.8645731
vgood	safetylow	-5.2914234	0.0000000	-4.534818e+13	0.0000000	-5.2914234	-5.2914234
vgood	safetymed	-14.3746602	174.6385287	-8.231090e-02	0.9343995	-356.6598868	327.9105664

Interpretasi:
- safety sangat signifikan dalam memengaruhi klasifikasi mobil.
- Contoh:
- Untuk kelas “unacc”, koefisien safetylow sangat besar (30.38) → mobil dengan safety=low sangat besar kemungkinannya diklasifikasikan sebagai “unacceptable”.
- P-value < 0.05 menunjukkan koefisien signifikan.

3. Multinomial Logistic Regression with Multiple Independent Variables

# Fit full multinomial logistic regression model
fit_full <- multinom(class ~ buying + maint + doors + persons + lug_boot + safety, data = df_mltn)

## # weights:  68 (48 variable)
## initial  value 2395.516656 
## iter  10 value 597.315128
## iter  20 value 467.090136
## iter  30 value 328.810480
## iter  40 value 244.612984
## iter  50 value 225.225988
## iter  60 value 224.162360
## iter  70 value 224.098885
## iter  80 value 224.087988
## iter  90 value 224.087533
## final  value 224.087526 
## converged

3.1 Interpret Relative Log Odds

# Summary output
summary(fit_full)

## Call:
## multinom(formula = class ~ buying + maint + doors + persons + 
##     lug_boot + safety, data = df_mltn)
## 
## Coefficients:
##       (Intercept) buyinglow buyingmed buyingvhigh  maintlow  maintmed
## good    -72.98492  46.65461 41.096570    8.016357 44.275659 39.476090
## unacc    70.34286  -5.02430 -3.907139    2.059538 -3.389268 -3.395281
## vgood   -83.58546  62.17300 54.746526   -8.949530 16.062733 11.340542
##       maintvhigh    doors3    doors4 doors5more   persons4 personsmore
## good  -15.139574  2.476545  3.569840   3.569871  -4.710739    -4.65662
## unacc   2.815303 -1.850896 -2.474970  -2.474970 -71.878551   -71.49822
## vgood -41.405035  4.275883  7.592428   7.592410  20.961126    22.33391
##       lug_bootmed lug_bootsmall safetylow  safetymed
## good    -3.070927     -9.435301 -19.52757  -7.969999
## unacc    1.512584      4.434169  53.67293   2.994152
## vgood   -6.412796    -32.137944 -19.60409 -37.231570
## 
## Std. Errors:
##       (Intercept) buyinglow buyingmed  buyingvhigh  maintlow  maintmed
## good    0.7059278 0.8635143 0.3687468 8.262278e-08 0.8420448 0.3745042
## unacc   0.3135998 0.5702171 0.4854407 3.744753e-01 0.4711076 0.4696660
## vgood   0.5646892 0.6400638 0.8436908 1.097143e-18 2.7185323 1.9930416
##         maintvhigh    doors3   doors4 doors5more  persons4 personsmore
## good           NaN 0.9585282 1.069365   1.069367 0.4565059   0.4706262
## unacc 4.147943e-01 0.4040376 0.427859   0.427859 0.2116368   0.2069209
## vgood 3.046022e-13 1.3524552 1.588884   1.588880 0.5365964   0.4981571
##       lug_bootmed lug_bootsmall    safetylow    safetymed
## good    0.9983513  1.961203e+00 7.482893e-14 1.601577e+00
## unacc   0.3755726  4.759416e-01 2.789120e-14 3.584065e-01
## vgood   1.3740079  9.530905e-05 2.748210e-14 1.239554e-07
## 
## Residual Deviance: 448.1751 
## AIC: 544.1751

# Tidy version
tidy(fit_full, conf.int = TRUE) %>%
  kable() %>%
  kable_styling("basic", full_width = FALSE)

y.level	term	estimate	std.error	statistic	p.value	conf.low	conf.high
good	(Intercept)	-72.984917	0.7059278	-1.033886e+02	0.0000000	-74.3685100	-71.601324
good	buyinglow	46.654614	0.8635143	5.402877e+01	0.0000000	44.9621568	48.347071
good	buyingmed	41.096570	0.3687468	1.114493e+02	0.0000000	40.3738394	41.819300
good	buyingvhigh	8.016357	0.0000001	9.702357e+07	0.0000000	8.0163572	8.016358
good	maintlow	44.275659	0.8420448	5.258112e+01	0.0000000	42.6252816	45.926037
good	maintmed	39.476090	0.3745042	1.054089e+02	0.0000000	38.7420755	40.210105
good	maintvhigh	-15.139574	NaN	NaN	NaN	NaN	NaN
good	doors3	2.476545	0.9585282	2.583696e+00	0.0097748	0.5978644	4.355226
good	doors4	3.569840	1.0693652	3.338280e+00	0.0008430	1.4739227	5.665757
good	doors5more	3.569871	1.0693674	3.338302e+00	0.0008429	1.4739496	5.665793
good	persons4	-4.710739	0.4565059	-1.031912e+01	0.0000000	-5.6054744	-3.816004
good	personsmore	-4.656620	0.4706262	-9.894519e+00	0.0000000	-5.5790303	-3.734209
good	lug_bootmed	-3.070927	0.9983513	-3.075998e+00	0.0020980	-5.0276597	-1.114194
good	lug_bootsmall	-9.435301	1.9612026	-4.810977e+00	0.0000015	-13.2791875	-5.591415
good	safetylow	-19.527570	0.0000000	-2.609629e+14	0.0000000	-19.5275705	-19.527570
good	safetymed	-7.969999	1.6015770	-4.976345e+00	0.0000006	-11.1090325	-4.830966
unacc	(Intercept)	70.342864	0.3135998	2.243078e+02	0.0000000	69.7282201	70.957509
unacc	buyinglow	-5.024300	0.5702171	-8.811206e+00	0.0000000	-6.1419053	-3.906695
unacc	buyingmed	-3.907139	0.4854407	-8.048643e+00	0.0000000	-4.8585851	-2.955693
unacc	buyingvhigh	2.059538	0.3744753	5.499796e+00	0.0000000	1.3255796	2.793496
unacc	maintlow	-3.389268	0.4711076	-7.194255e+00	0.0000000	-4.3126222	-2.465914
unacc	maintmed	-3.395281	0.4696660	-7.229139e+00	0.0000000	-4.3158093	-2.474752
unacc	maintvhigh	2.815303	0.4147943	6.787227e+00	0.0000000	2.0023211	3.628285
unacc	doors3	-1.850896	0.4040376	-4.581000e+00	0.0000046	-2.6427952	-1.058997
unacc	doors4	-2.474970	0.4278590	-5.784546e+00	0.0000000	-3.3135587	-1.636382
unacc	doors5more	-2.474970	0.4278590	-5.784545e+00	0.0000000	-3.3135579	-1.636381
unacc	persons4	-71.878551	0.2116368	-3.396317e+02	0.0000000	-72.2933513	-71.463750
unacc	personsmore	-71.498216	0.2069209	-3.455340e+02	0.0000000	-71.9037731	-71.092658
unacc	lug_bootmed	1.512584	0.3755726	4.027407e+00	0.0000564	0.7764750	2.248693
unacc	lug_bootsmall	4.434170	0.4759416	9.316626e+00	0.0000000	3.5013411	5.366998
unacc	safetylow	53.672927	0.0000000	1.924368e+15	0.0000000	53.6729266	53.672927
unacc	safetymed	2.994152	0.3584065	8.354066e+00	0.0000000	2.2916878	3.696615
vgood	(Intercept)	-83.585464	0.5646892	-1.480203e+02	0.0000000	-84.6922347	-82.478694
vgood	buyinglow	62.173003	0.6400638	9.713563e+01	0.0000000	60.9185014	63.427506
vgood	buyingmed	54.746526	0.8436908	6.488932e+01	0.0000000	53.0929220	56.400129
vgood	buyingvhigh	-8.949530	0.0000000	-8.157122e+18	0.0000000	-8.9495303	-8.949530
vgood	maintlow	16.062733	2.7185323	5.908605e+00	0.0000000	10.7345077	21.390958
vgood	maintmed	11.340542	1.9930416	5.690068e+00	0.0000000	7.4342522	15.246832
vgood	maintvhigh	-41.405035	0.0000000	-1.359315e+14	0.0000000	-41.4050354	-41.405035
vgood	doors3	4.275883	1.3524552	3.161571e+00	0.0015692	1.6251197	6.926647
vgood	doors4	7.592428	1.5888841	4.778466e+00	0.0000018	4.4782723	10.706583
vgood	doors5more	7.592410	1.5888796	4.778468e+00	0.0000018	4.4782630	10.706557
vgood	persons4	20.961126	0.5365964	3.906311e+01	0.0000000	19.9094160	22.012835
vgood	personsmore	22.333908	0.4981571	4.483306e+01	0.0000000	21.3575377	23.310278
vgood	lug_bootmed	-6.412796	1.3740079	-4.667219e+00	0.0000031	-9.1058019	-3.719790
vgood	lug_bootsmall	-32.137944	0.0000953	-3.371972e+05	0.0000000	-32.1381304	-32.137757
vgood	safetylow	-19.604089	0.0000000	-7.133402e+14	0.0000000	-19.6040892	-19.604089
vgood	safetymed	-37.231570	0.0000001	-3.003625e+08	0.0000000	-37.2315707	-37.231570

Nilai log-odds menunjukkan arah dan kekuatan pengaruh.
Contoh:
Untuk kelas “vgood”, variabel buyinglow punya koefisien +62.17 → peluang besar mobil berkualitas sangat baik ketika harga beli rendah.

3.2 Interpret Relative Risk Ratios (Exponentiated Coefficients)

# Exponentiate coefficients
exp(coef(fit_full))

##        (Intercept)    buyinglow    buyingmed  buyingvhigh     maintlow
## good  2.009340e-32 1.827432e+20 7.047150e+17 3.030120e+03 1.693068e+19
## unacc 3.544197e+30 6.576186e-03 2.009792e-02 7.842343e+00 3.373335e-02
## vgood 5.003734e-37 1.003211e+27 5.971920e+23 1.297981e-04 9.461420e+06
##           maintmed   maintvhigh     doors3       doors4   doors5more
## good  1.393953e+17 2.660520e-07 11.9000799 3.551091e+01 3.551202e+01
## unacc 3.353114e-02 1.669823e+01  0.1570963 8.416548e-02 8.416554e-02
## vgood 8.416563e+04 1.042369e-18 71.9436502 1.983122e+03 1.983087e+03
##           persons4  personsmore lug_bootmed lug_bootsmall    safetylow
## good  8.998123e-03 9.498514e-03 0.046378139  7.985476e-05 3.305856e-09
## unacc 6.074940e-32 8.886271e-32 4.538442419  8.428210e+01 2.041060e+23
## vgood 1.268531e+09 5.006023e+09 0.001640432  1.103236e-14 3.062332e-09
##          safetymed
## good  3.456792e-04
## unacc 1.996841e+01
## vgood 6.769154e-17

# Or using tidy
tidy(fit_full, conf.int = TRUE, exponentiate = TRUE) %>%
  kable() %>%
  kable_styling("basic", full_width = FALSE)

y.level	term	estimate	std.error	statistic	p.value	conf.low	conf.high
good	(Intercept)	0.000000e+00	0.7059278	-1.033886e+02	0.0000000	0.000000e+00	0.000000e+00
good	buyinglow	1.827432e+20	0.8635143	5.402877e+01	0.0000000	3.363695e+19	9.928096e+20
good	buyingmed	7.047150e+17	0.3687468	1.114493e+02	0.0000000	3.420863e+17	1.451748e+18
good	buyingvhigh	3.030120e+03	0.0000001	9.702357e+07	0.0000000	3.030119e+03	3.030120e+03
good	maintlow	1.693068e+19	0.8420448	5.258112e+01	0.0000000	3.250308e+18	8.819101e+19
good	maintmed	1.393953e+17	0.3745042	1.054089e+02	0.0000000	6.690670e+16	2.904202e+17
good	maintvhigh	3.000000e-07	NaN	NaN	NaN	NaN	NaN
good	doors3	1.190008e+01	0.9585282	2.583696e+00	0.0097748	1.818232e+00	7.788442e+01
good	doors4	3.551091e+01	1.0693652	3.338280e+00	0.0008430	4.366329e+00	2.888066e+02
good	doors5more	3.551202e+01	1.0693674	3.338302e+00	0.0008429	4.366447e+00	2.888169e+02
good	persons4	8.998100e-03	0.4565059	-1.031912e+01	0.0000000	3.677700e-03	2.201560e-02
good	personsmore	9.498500e-03	0.4706262	-9.894519e+00	0.0000000	3.776200e-03	2.389210e-02
good	lug_bootmed	4.637810e-02	0.9983513	-3.075998e+00	0.0020980	6.554100e-03	3.281795e-01
good	lug_bootsmall	7.990000e-05	1.9612026	-4.810977e+00	0.0000015	1.700000e-06	3.729700e-03
good	safetylow	0.000000e+00	0.0000000	-2.609629e+14	0.0000000	0.000000e+00	0.000000e+00
good	safetymed	3.457000e-04	1.6015770	-4.976345e+00	0.0000006	1.500000e-05	7.978800e-03
unacc	(Intercept)	3.544197e+30	0.3135998	2.243078e+02	0.0000000	1.916820e+30	6.553216e+30
unacc	buyinglow	6.576200e-03	0.5702171	-8.811206e+00	0.0000000	2.150800e-03	2.010680e-02
unacc	buyingmed	2.009790e-02	0.4854407	-8.048643e+00	0.0000000	7.761500e-03	5.204260e-02
unacc	buyingvhigh	7.842343e+00	0.3744753	5.499796e+00	0.0000000	3.764367e+00	1.633803e+01
unacc	maintlow	3.373340e-02	0.4711076	-7.194255e+00	0.0000000	1.339840e-02	8.493120e-02
unacc	maintmed	3.353110e-02	0.4696660	-7.229139e+00	0.0000000	1.335570e-02	8.418380e-02
unacc	maintvhigh	1.669823e+01	0.4147943	6.787227e+00	0.0000000	7.406226e+00	3.764819e+01
unacc	doors3	1.570963e-01	0.4040376	-4.581000e+00	0.0000046	7.116210e-02	3.468035e-01
unacc	doors4	8.416550e-02	0.4278590	-5.784546e+00	0.0000000	3.638650e-02	1.946831e-01
unacc	doors5more	8.416550e-02	0.4278590	-5.784545e+00	0.0000000	3.638650e-02	1.946832e-01
unacc	persons4	0.000000e+00	0.2116368	-3.396317e+02	0.0000000	0.000000e+00	0.000000e+00
unacc	personsmore	0.000000e+00	0.2069209	-3.455340e+02	0.0000000	0.000000e+00	0.000000e+00
unacc	lug_bootmed	4.538442e+00	0.3755726	4.027407e+00	0.0000564	2.173796e+00	9.475341e+00
unacc	lug_bootsmall	8.428210e+01	0.4759416	9.316626e+00	0.0000000	3.315989e+01	2.142188e+02
unacc	safetylow	2.041060e+23	0.0000000	1.924368e+15	0.0000000	2.041060e+23	2.041060e+23
unacc	safetymed	1.996841e+01	0.3584065	8.354066e+00	0.0000000	9.891618e+00	4.031064e+01
vgood	(Intercept)	0.000000e+00	0.5646892	-1.480203e+02	0.0000000	0.000000e+00	0.000000e+00
vgood	buyinglow	1.003211e+27	0.6400638	9.713563e+01	0.0000000	2.861337e+26	3.517350e+27
vgood	buyingmed	5.971920e+23	0.8436908	6.488932e+01	0.0000000	1.142781e+23	3.120793e+24
vgood	buyingvhigh	1.298000e-04	0.0000000	-8.157122e+18	0.0000000	1.298000e-04	1.298000e-04
vgood	maintlow	9.461420e+06	2.7185323	5.908605e+00	0.0000000	4.591319e+04	1.949733e+09
vgood	maintmed	8.416563e+04	1.9930416	5.690068e+00	0.0000000	1.692991e+03	4.184223e+06
vgood	maintvhigh	0.000000e+00	0.0000000	-1.359315e+14	0.0000000	0.000000e+00	0.000000e+00
vgood	doors3	7.194365e+01	1.3524552	3.161571e+00	0.0015692	5.079027e+00	1.019071e+03
vgood	doors4	1.983122e+03	1.5888841	4.778466e+00	0.0000018	8.808236e+01	4.464883e+04
vgood	doors5more	1.983087e+03	1.5888796	4.778468e+00	0.0000018	8.808154e+01	4.464764e+04
vgood	persons4	1.268531e+09	0.5365964	3.906311e+01	0.0000000	4.431487e+08	3.631223e+09
vgood	personsmore	5.006023e+09	0.4981571	4.483306e+01	0.0000000	1.885649e+09	1.329000e+10
vgood	lug_bootmed	1.640400e-03	1.3740079	-4.667219e+00	0.0000031	1.110000e-04	2.423910e-02
vgood	lug_bootsmall	0.000000e+00	0.0000953	-3.371972e+05	0.0000000	0.000000e+00	0.000000e+00
vgood	safetylow	0.000000e+00	0.0000000	-7.133402e+14	0.0000000	0.000000e+00	0.000000e+00
vgood	safetymed	0.000000e+00	0.0000001	-3.003625e+08	0.0000000	0.000000e+00	0.000000e+00

Interpretasi:
- exp(coef) mengubah log-odds menjadi rasio risiko.
- Contoh:
- vgood:persons4 = 1.26e+09 → kemungkinan mobil “vgood” meningkat drastis saat kapasitas 4 penumpang.
- safetylow pada “unacc” = 2.04e+23 → fitur safety sangat menentukan.

3.3 Interpret Marginal Effects

# Load library
library(marginaleffects)

# Marginal effect for 'safety'
mfx_safety <- avg_comparisons(fit_full, variables = "safety", type = "probs")
mfx_safety

## 
##  Group   Contrast Estimate Std. Error      z Pr(>|z|)     S   2.5 %  97.5 %
##  acc   low - high  -0.3542    0.00923 -38.37   <0.001   Inf -0.3723 -0.3361
##  acc   med - high  -0.0417    0.01394  -2.99   0.0028   8.5 -0.0690 -0.0143
##  good  low - high  -0.0521    0.00486 -10.71   <0.001  86.5 -0.0616 -0.0426
##  good  med - high   0.0156    0.00659   2.37   0.0178   5.8  0.0027  0.0285
##  unacc low - high   0.5191    0.00831  62.50   <0.001   Inf  0.5028  0.5354
##  unacc med - high   0.1389    0.01259  11.03   <0.001  91.6  0.1142  0.1636
##  vgood low - high  -0.1128    0.00473 -23.86   <0.001 415.7 -0.1221 -0.1036
##  vgood med - high  -0.1128    0.00473 -23.86   <0.001 415.7 -0.1221 -0.1036
## 
## Term: safety
## Type:  probs

Interpretasi:
- Perubahan dari safety=high ke safety=low meningkatkan probabilitas klasifikasi ke “unacc” sebesar +51.9%.
- Untuk “good”, probabilitas turun -5.2%, menunjukkan safety sangat berpengaruh negatif.

Ordinal

1. Load Dataset

# Load the dataset
df_ord <- read.csv("E:/Anmul-Kelompok/user_knowledge_modeling.csv")

# Display structure of the dataset
str(df_ord)

## 'data.frame':    403 obs. of  6 variables:
##  $ STG: num  0 0.08 0.06 0.1 0.08 0.09 0.1 0.15 0.2 0 ...
##  $ SCG: num  0 0.08 0.06 0.1 0.08 0.15 0.1 0.02 0.14 0 ...
##  $ STR: num  0 0.1 0.05 0.15 0.08 0.4 0.43 0.34 0.35 0.5 ...
##  $ LPR: num  0 0.24 0.25 0.65 0.98 0.1 0.29 0.4 0.72 0.2 ...
##  $ PEG: num  0 0.9 0.33 0.3 0.24 0.66 0.56 0.01 0.25 0.85 ...
##  $ UNS: chr  "very_low" "High" "Low" "Middle" ...

Penjelasan variabel:
Fitur (Variabel Independen):

STG (Study Time for Goal object materials)
SCG (Study Time for Related objects with Goal object)
STR (Repetition Number of User for Goal object materials)
LPR (User Performance in Lower Assessment)
PEG (User Performance in Exam for Goal object materials)

Variabel Target:

UNS (User Knowledge Level)

2. Ordinal Logistic Regression with 1 Independent Variable (IV)

# Load necessary library
library(MASS)

# Convert the UNS variable to an ordered factor
df_ord$UNS <- factor(df_ord$UNS, ordered = TRUE)

# Fit basic ordinal logistic regression
fit_basic <- polr(UNS ~ PEG, data = df_ord, Hess = TRUE)

# Summary of the model
summary(fit_basic)

## Call:
## polr(formula = UNS ~ PEG, data = df_ord, Hess = TRUE)
## 
## Coefficients:
##     Value Std. Error t value
## PEG -5.03      0.421  -11.95
## 
## Intercepts:
##                   Value    Std. Error t value 
## High|Low           -3.5456   0.2544   -13.9367
## Low|Middle         -1.7910   0.2029    -8.8262
## Middle|Very Low     0.0635   0.2133     0.2978
## Very Low|very_low   1.0664   0.2466     4.3250
## 
## Residual Deviance: 980.4873 
## AIC: 990.4873

library(broom)
library(kableExtra)

# Tidy version of the summary with confidence intervals
tidy(fit_basic, conf.int = TRUE) %>%
  kable() %>%
  kable_styling("basic", full_width = FALSE)

term	estimate	std.error	statistic	conf.low	conf.high	coef.type
PEG	-5.0300645	0.4209646	-11.9489011	-5.869162	-4.21746	coefficient
High\|Low	-3.5455722	0.2544062	-13.9366585	NA	NA	scale
Low\|Middle	-1.7910226	0.2029215	-8.8261822	NA	NA	scale
Middle\|Very Low	0.0635231	0.2133103	0.2977966	NA	NA	scale
Very Low\|very_low	1.0664483	0.2465762	4.3250257	NA	NA	scale

Interpretasi:
- PEG memiliki pengaruh negatif signifikan (koef = -5.03, p < 0.001)
- Artinya, semakin tinggi nilai ujian PEG, semakin besar peluang masuk kategori UNS yang lebih tinggi.

3. Ordinal Logistic Regression with Multiple Independent Variables

# Fit full ordinal logistic regression model
fit_full <- polr(UNS ~ STG + SCG + STR + LPR + PEG,
               data = df_ord, Hess = TRUE)

LPR dan PEG memiliki koefisien negatif signifikan, menurunkan peluang masuk kategori rendah (pengetahuan meningkat).
Variabel lain seperti SCG, STR, dan STG tidak signifikan (p > 0.05).

3.1 Interpret Relative Log Odds

# Summary output
summary(fit_full)

## Call:
## polr(formula = UNS ~ STG + SCG + STR + LPR + PEG, data = df_ord, 
##     Hess = TRUE)
## 
## Coefficients:
##       Value Std. Error  t value
## STG  0.2283     0.4918   0.4642
## SCG -0.5580     0.4845  -1.1516
## STR  0.1046     0.4096   0.2555
## LPR -3.5800     0.4318  -8.2900
## PEG -5.6935     0.4577 -12.4385
## 
## Intercepts:
##                   Value    Std. Error t value 
## High|Low           -5.6482   0.4331   -13.0415
## Low|Middle         -3.6504   0.3810    -9.5813
## Middle|Very Low    -1.5322   0.3637    -4.2125
## Very Low|very_low  -0.3507   0.3661    -0.9579
## 
## Residual Deviance: 897.9469 
## AIC: 915.9469

# Tidy version
tidy(fit_full, conf.int = TRUE) %>%
  kable() %>%
  kable_styling("basic", full_width = FALSE)

term	estimate	std.error	statistic	conf.low	conf.high	coef.type
STG	0.2282968	0.4917878	0.4642180	-0.7410857	1.1893214	coefficient
SCG	-0.5579528	0.4845045	-1.1515947	-1.5141430	0.3875627	coefficient
STR	0.1046400	0.4095556	0.2554965	-0.6983297	0.9088211	coefficient
LPR	-3.5799523	0.4318379	-8.2900376	-4.4424867	-2.7477296	coefficient
PEG	-5.6934772	0.4577302	-12.4385008	-6.6078809	-4.8118616	coefficient
High\|Low	-5.6481945	0.4330929	-13.0415319	NA	NA	scale
Low\|Middle	-3.6503755	0.3809896	-9.5812997	NA	NA	scale
Middle\|Very Low	-1.5321805	0.3637200	-4.2125269	NA	NA	scale
Very Low\|very_low	-0.3507019	0.3661202	-0.9578873	NA	NA	scale

LPR dan PEG memiliki koefisien negatif signifikan, menurunkan peluang masuk kategori rendah (pengetahuan meningkat).
Variabel lain seperti SCG, STR, dan STG tidak signifikan (p > 0.05).

3.2 Interpret Relative Risk Ratios (Exponentiated Coefficients)

# Exponentiate coefficients
exp(coef(fit_full))

##         STG         SCG         STR         LPR         PEG 
## 1.256458149 0.572379649 1.110310835 0.027877028 0.003367862

# Or using tidy
tidy(fit_full, conf.int = TRUE, exponentiate = TRUE) %>%
  kable() %>%
  kable_styling("basic", full_width = FALSE)

term	estimate	std.error	statistic	conf.low	conf.high	coef.type
STG	1.2564581	0.4917878	0.4642180	0.4765962	3.2848512	coefficient
SCG	0.5723796	0.4845045	-1.1515947	0.2199967	1.4733853	coefficient
STR	1.1103108	0.4095556	0.2554965	0.4974155	2.4813955	coefficient
LPR	0.0278770	0.4318379	-8.2900376	0.0117666	0.0640732	coefficient
PEG	0.0033679	0.4577302	-12.4385008	0.0013497	0.0081327	coefficient
High\|Low	0.0035239	0.4330929	-13.0415319	NA	NA	scale
Low\|Middle	0.0259814	0.3809896	-9.5812997	NA	NA	scale
Middle\|Very Low	0.2160640	0.3637200	-4.2125269	NA	NA	scale
Very Low\|very_low	0.7041936	0.3661202	-0.9578873	NA	NA	scale

Interpretasi:
- PEG = 0.0034 → Setiap peningkatan PEG mengurangi risiko berada di kategori rendah sebesar 99.66%.
- LPR = 0.0279 → Semakin tinggi nilai LPR, peluang pengetahuan rendah juga turun.

3.3 Interpret Marginal Effects

# Load library
library(marginaleffects)

# Marginal effect for 'PEG'
mfx_peg <- avg_comparisons(fit_full, variables = "PEG", type = "probs")
mfx_peg

## 
##     Group Estimate Std. Error      z Pr(>|z|)     S   2.5 %  97.5 %
##  High       0.6784     0.0165  41.08   <0.001   Inf  0.6460  0.7107
##  Low       -0.2668     0.0193 -13.79   <0.001 141.3 -0.3048 -0.2289
##  Middle    -0.2730     0.0194 -14.09   <0.001 147.3 -0.3110 -0.2350
##  Very Low  -0.0802     0.0142  -5.65   <0.001  25.9 -0.1080 -0.0523
##  very_low  -0.0584     0.0108  -5.40   <0.001  23.9 -0.0796 -0.0372
## 
## Term: PEG
## Type:  probs 
## Comparison: +1

Interpretasi:
- Peningkatan 1 unit PEG meningkatkan probabilitas kategori “High” sebesar 67.8%.
- Sebaliknya, menurunkan probabilitas “Low” dan “Middle” secara signifikan.

Kesimpulan

Untuk MLR, variabel safety, persons, buying, dan maint sangat berpengaruh.
Untuk OLR, PEG dan LPR adalah faktor paling dominan dalam menentukan tingkat pengetahuan.

Seluruh model menunjukkan konvergensi baik dan hasil yang valid. Evaluasi melalui log-odds, RRR, dan marginal effects memberikan pemahaman komprehensif terhadap pengaruh variabel dalam model.

MLR-OLR_Case

Kelompok-1_2023F

2025-04-28

Kelompok : 1

Kelas : 2023 F

Anggota Kelompok:

Naufal Faiz Nugraha (23031554020)

Bagus Febriansyah Pratama (23031554144)

Otniel Glory Joseputra Pribadi (23031554151)

Rozan Adzki Yahya (23031554236)

Multinomial

1. Load Dataset

2. Multinomial Logistic Regression with 1 Independent Variable (IV)

3. Multinomial Logistic Regression with Multiple Independent Variables

3.1 Interpret Relative Log Odds

3.2 Interpret Relative Risk Ratios (Exponentiated Coefficients)

3.3 Interpret Marginal Effects

Ordinal

1. Load Dataset

2. Ordinal Logistic Regression with 1 Independent Variable (IV)

3. Ordinal Logistic Regression with Multiple Independent Variables

3.1 Interpret Relative Log Odds

3.2 Interpret Relative Risk Ratios (Exponentiated Coefficients)

3.3 Interpret Marginal Effects

Kesimpulan