1. Library & Data
library(MASS) # lda()
library(nnet) # multinom()
library(tidyverse) # manipulasi & visualisasi
library(kableExtra) # tabel rapi
library(MVN) # uji normalitas multivariat
library(biotools) # Box's M Test
library(caret) # confusionMatrix()
df <- read.csv("penguins_size.csv", stringsAsFactors = TRUE)
# Cleaning: pilih variabel relevan, hapus NA
df_clean <- df %>%
select(species, culmen_length_mm, culmen_depth_mm,
flipper_length_mm, body_mass_g) %>%
na.omit()
# Distribusi kelas
table(df_clean$species)
##
## Adelie Chinstrap Gentoo
## 151 68 123
2. Statistika Deskriptif
df_clean %>%
group_by(species) %>%
summarise(
n = n(),
Mean_CulLen = round(mean(culmen_length_mm), 2),
SD_CulLen = round(sd(culmen_length_mm), 2),
Mean_CulDep = round(mean(culmen_depth_mm), 2),
SD_CulDep = round(sd(culmen_depth_mm), 2),
Mean_Flip = round(mean(flipper_length_mm), 2),
SD_Flip = round(sd(flipper_length_mm), 2),
Mean_Mass = round(mean(body_mass_g), 2),
SD_Mass = round(sd(body_mass_g), 2)
) %>%
kable(caption = "Statistika Deskriptif per Spesies",
col.names = c("Spesies", "n",
"Mean", "SD", "Mean", "SD",
"Mean", "SD", "Mean", "SD")) %>%
kable_styling(bootstrap_options = c("striped", "hover"), full_width = TRUE) %>%
add_header_above(c(" " = 2,
"Culmen Length (mm)" = 2,
"Culmen Depth (mm)" = 2,
"Flipper Length (mm)"= 2,
"Body Mass (g)" = 2))
Statistika Deskriptif per Spesies
|
|
Culmen Length (mm)
|
Culmen Depth (mm)
|
Flipper Length (mm)
|
Body Mass (g)
|
|
Spesies
|
n
|
Mean
|
SD
|
Mean
|
SD
|
Mean
|
SD
|
Mean
|
SD
|
|
Adelie
|
151
|
38.79
|
2.66
|
18.35
|
1.22
|
189.95
|
6.54
|
3700.66
|
458.57
|
|
Chinstrap
|
68
|
48.83
|
3.34
|
18.42
|
1.14
|
195.82
|
7.13
|
3733.09
|
384.34
|
|
Gentoo
|
123
|
47.50
|
3.08
|
14.98
|
0.98
|
217.19
|
6.48
|
5076.02
|
504.12
|
# Distribusi spesies
df_clean %>%
count(species) %>%
mutate(pct = round(n / sum(n) * 100, 1),
label = paste0(species, "\n", n, " (", pct, "%)")) %>%
ggplot(aes(x = "", y = n, fill = species)) +
geom_col(width = 1, color = "white") +
coord_polar(theta = "y") +
geom_text(aes(label = label), position = position_stack(vjust = 0.5), size = 3.5) +
scale_fill_manual(values = c("#F4A460", "#6495ED", "#90EE90")) +
labs(title = "Distribusi Spesies Penguin", fill = "Spesies") +
theme_void() +
theme(plot.title = element_text(hjust = 0.5, face = "bold", size = 13))
# Boxplot variabel prediktor per spesies
df_clean %>%
pivot_longer(cols = -species, names_to = "Variabel", values_to = "Nilai") %>%
ggplot(aes(x = species, y = Nilai, fill = species)) +
geom_boxplot(alpha = 0.7, outlier.color = "red", outlier.size = 1.5) +
facet_wrap(~Variabel, scales = "free_y", ncol = 2,
labeller = as_labeller(c(
culmen_length_mm = "Culmen Length (mm)",
culmen_depth_mm = "Culmen Depth (mm)",
flipper_length_mm = "Flipper Length (mm)",
body_mass_g = "Body Mass (g)"))) +
scale_fill_manual(values = c("#F4A460", "#6495ED", "#90EE90")) +
labs(title = "Distribusi Variabel Prediktor per Spesies",
x = "Spesies", y = "Nilai", fill = "Spesies") +
theme_bw() +
theme(plot.title = element_text(hjust = 0.5, face = "bold"),
legend.position = "none")
3. Uji Asumsi
3.1 Normalitas Multivariat (Mardia’s Test)
LDA mengasumsikan data pada setiap kelompok berdistribusi normal
multivariat.
prediktor <- df_clean %>%
select(culmen_length_mm, culmen_depth_mm, flipper_length_mm, body_mass_g)
# Handle perbedaan versi MVN
mvn_args <- names(formals(MVN::mvn))
if ("mvnTest" %in% mvn_args) {
mvn_result <- mvn(data = prediktor, mvnTest = "mardia")
} else {
mvn_result <- mvn(data = prediktor)
}
# Chi-Square Q-Q Plot (alternatif visual uji normalitas multivariat)
n <- nrow(prediktor)
p <- ncol(prediktor)
mu <- colMeans(prediktor)
S <- cov(prediktor)
d2 <- mahalanobis(prediktor, center = mu, cov = S)
q_teoritis <- qchisq(ppoints(n), df = p)
qqplot(q_teoritis, sort(d2),
main = "Chi-Square Q-Q Plot (Normalitas Multivariat)",
xlab = "Kuantil Chi-Square Teoritis",
ylab = "Jarak Mahalanobis (Data)",
pch = 19, col = "#4472C4", cex = 0.8)
abline(0, 1, col = "red", lwd = 2, lty = 2)
legend("topleft", legend = "Garis Referensi", col = "red", lwd = 2, lty = 2, bty = "n")
Jika titik-titik mendekati garis referensi, asumsi normalitas
multivariat terpenuhi.
3.2 Homogenitas Matriks Kovarians (Box’s M Test)
boxm_result <- boxM(
data = df_clean[, c("culmen_length_mm", "culmen_depth_mm",
"flipper_length_mm", "body_mass_g")],
grouping = df_clean$species
)
print(boxm_result)
##
## Box's M-test for Homogeneity of Covariance Matrices
##
## data: df_clean[, c("culmen_length_mm", "culmen_depth_mm", "flipper_length_mm", "body_mass_g")]
## Chi-Sq (approx.) = 76.795, df = 20, p-value = 1.365e-08
Jika p-value < 0.05 matriks kovarians tidak homogen; LDA tetap
cukup robust untuk sampel besar, namun QDA dapat dipertimbangkan sebagai
alternatif.
4. Split Data
set.seed(42)
idx <- createDataPartition(df_clean$species, p = 0.8, list = FALSE)
train <- df_clean[idx, ]
test <- df_clean[-idx, ]
cat("Training:", nrow(train), "| Testing:", nrow(test))
## Training: 275 | Testing: 67
5. Linear Discriminant Analysis (LDA)
5.1 Pembentukan Fungsi Diskriminan
lda_model <- lda(species ~ culmen_length_mm + culmen_depth_mm +
flipper_length_mm + body_mass_g,
data = train,
prior = as.vector(prop.table(table(train$species))))
print(lda_model)
## Call:
## lda(species ~ culmen_length_mm + culmen_depth_mm + flipper_length_mm +
## body_mass_g, data = train, prior = as.vector(prop.table(table(train$species))))
##
## Prior probabilities of groups:
## Adelie Chinstrap Gentoo
## 0.44 0.20 0.36
##
## Group means:
## culmen_length_mm culmen_depth_mm flipper_length_mm body_mass_g
## Adelie 38.79752 18.39174 190.3471 3704.132
## Chinstrap 48.80909 18.36182 195.4182 3721.364
## Gentoo 47.66061 14.99091 217.9293 5101.263
##
## Coefficients of linear discriminants:
## LD1 LD2
## culmen_length_mm -0.086609377 -0.419396547
## culmen_depth_mm 1.011226772 -0.005156790
## flipper_length_mm -0.089996132 0.013219110
## body_mass_g -0.001281395 0.001769146
##
## Proportion of trace:
## LD1 LD2
## 0.8659 0.1341
5.2 Koefisien Fungsi Diskriminan
lda_model$scaling %>%
as.data.frame() %>%
rownames_to_column("Variabel") %>%
kable(caption = "Koefisien Fungsi Diskriminan Linear", digits = 4) %>%
kable_styling(bootstrap_options = c("striped", "hover"), full_width = FALSE)
Koefisien Fungsi Diskriminan Linear
|
Variabel
|
LD1
|
LD2
|
|
culmen_length_mm
|
-0.0866
|
-0.4194
|
|
culmen_depth_mm
|
1.0112
|
-0.0052
|
|
flipper_length_mm
|
-0.0900
|
0.0132
|
|
body_mass_g
|
-0.0013
|
0.0018
|
Dengan 3 kelas, LDA menghasilkan s = g − 1 = 2 fungsi
diskriminan (LD1 dan LD2).
5.3 Proporsi Variansi yang Dijelaskan
prop_var <- lda_model$svd^2 / sum(lda_model$svd^2) * 100
data.frame(
`Fungsi Diskriminan` = c("LD1", "LD2"),
Eigenvalue = round(lda_model$svd^2, 4),
`Proporsi (%)` = round(prop_var, 2),
`Kumulatif (%)` = round(cumsum(prop_var), 2)
) %>%
kable(caption = "Proporsi Variansi yang Dijelaskan Setiap Fungsi Diskriminan") %>%
kable_styling(bootstrap_options = c("striped", "hover"), full_width = FALSE)
Proporsi Variansi yang Dijelaskan Setiap Fungsi Diskriminan
|
Fungsi.Diskriminan
|
Eigenvalue
|
Proporsi….
|
Kumulatif….
|
|
LD1
|
2088.3517
|
86.59
|
86.59
|
|
LD2
|
323.5356
|
13.41
|
100.00
|
5.4 Visualisasi LDA
lda_pred_train <- predict(lda_model, train)
lda_plot_df <- data.frame(
LD1 = lda_pred_train$x[, 1],
LD2 = lda_pred_train$x[, 2],
species = train$species
)
ggplot(lda_plot_df, aes(x = LD1, y = LD2, color = species, shape = species)) +
geom_point(size = 2.5, alpha = 0.8) +
stat_ellipse(aes(fill = species), geom = "polygon",
alpha = 0.1, level = 0.95) +
scale_color_manual(values = c("#E07B39", "#4472C4", "#5BAD5B")) +
scale_fill_manual(values = c("#E07B39", "#4472C4", "#5BAD5B")) +
labs(title = "Plot Fungsi Diskriminan Linear",
subtitle = "Pemisahan Tiga Spesies Penguin",
x = paste0("LD1 (", round(prop_var[1], 1), "%)"),
y = paste0("LD2 (", round(prop_var[2], 1), "%)"),
color = "Spesies", shape = "Spesies", fill = "Spesies") +
theme_bw() +
theme(plot.title = element_text(hjust = 0.5, face = "bold"),
plot.subtitle = element_text(hjust = 0.5))
5.5 Evaluasi Model LDA
# Prediksi
lda_pred_test <- predict(lda_model, test)
lda_pred_train_class <- predict(lda_model, train)$class
# Confusion Matrix
cm_lda <- confusionMatrix(lda_pred_test$class, test$species)
print(cm_lda)
## Confusion Matrix and Statistics
##
## Reference
## Prediction Adelie Chinstrap Gentoo
## Adelie 30 1 0
## Chinstrap 0 12 0
## Gentoo 0 0 24
##
## Overall Statistics
##
## Accuracy : 0.9851
## 95% CI : (0.9196, 0.9996)
## No Information Rate : 0.4478
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 0.9763
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: Adelie Class: Chinstrap Class: Gentoo
## Sensitivity 1.0000 0.9231 1.0000
## Specificity 0.9730 1.0000 1.0000
## Pos Pred Value 0.9677 1.0000 1.0000
## Neg Pred Value 1.0000 0.9818 1.0000
## Prevalence 0.4478 0.1940 0.3582
## Detection Rate 0.4478 0.1791 0.3582
## Detection Prevalence 0.4627 0.1791 0.3582
## Balanced Accuracy 0.9865 0.9615 1.0000
# Tabel Confusion Matrix rapi
cm_lda$table %>%
as.data.frame() %>%
pivot_wider(names_from = Reference, values_from = Freq) %>%
rename(Prediksi = Prediction) %>%
kable(caption = "Confusion Matrix — Linear Discriminant Analysis") %>%
kable_styling(bootstrap_options = c("striped", "hover"), full_width = FALSE) %>%
add_header_above(c(" " = 1, "Aktual" = 3))
Confusion Matrix — Linear Discriminant Analysis
|
|
Aktual
|
|
Prediksi
|
Adelie
|
Chinstrap
|
Gentoo
|
|
Adelie
|
30
|
1
|
0
|
|
Chinstrap
|
0
|
12
|
0
|
|
Gentoo
|
0
|
0
|
24
|
# APER Training & Testing
n_salah_train <- sum(lda_pred_train_class != train$species)
n_salah_test <- sum(lda_pred_test$class != test$species)
aper_train <- n_salah_train / nrow(train)
aper_test <- n_salah_test / nrow(test)
data.frame(
Data = c("Training", "Testing"),
`N Total` = c(nrow(train), nrow(test)),
`N Salah` = c(n_salah_train, n_salah_test),
`APER (%)` = round(c(aper_train, aper_test) * 100, 2),
`Akurasi (%)` = round((1 - c(aper_train, aper_test)) * 100, 2)
) %>%
kable(caption = "APER dan Akurasi Model LDA") %>%
kable_styling(bootstrap_options = c("striped", "hover"), full_width = FALSE)
APER dan Akurasi Model LDA
|
Data
|
N.Total
|
N.Salah
|
APER….
|
Akurasi….
|
|
Training
|
275
|
3
|
1.09
|
98.91
|
|
Testing
|
67
|
1
|
1.49
|
98.51
|
APER yang kecil menunjukkan fungsi diskriminan
memiliki kemampuan klasifikasi yang baik.
6. Regresi Logistik Multinomial
6.1 Pembentukan Model
# Kategori referensi = Gentoo (terbanyak kedua, sering dijadikan baseline)
train$species <- relevel(train$species, ref = "Gentoo")
test$species <- relevel(test$species, ref = "Gentoo")
multinom_model <- multinom(
species ~ culmen_length_mm + culmen_depth_mm +
flipper_length_mm + body_mass_g,
data = train,
trace = FALSE,
Hess = TRUE
)
summary(multinom_model)
## Call:
## multinom(formula = species ~ culmen_length_mm + culmen_depth_mm +
## flipper_length_mm + body_mass_g, data = train, Hess = TRUE,
## trace = FALSE)
##
## Coefficients:
## (Intercept) culmen_length_mm culmen_depth_mm flipper_length_mm
## Adelie 28.10100 -19.61744 36.333602 2.41380
## Chinstrap -21.02514 25.72737 1.335902 -1.96246
## body_mass_g
## Adelie -0.0673793
## Chinstrap -0.1910147
##
## Std. Errors:
## (Intercept) culmen_length_mm culmen_depth_mm flipper_length_mm
## Adelie 0.8292441 14.10153 20.24099 5.101465
## Chinstrap 0.9970848 15.28610 35.34625 5.513135
## body_mass_g
## Adelie 0.1515416
## Chinstrap 0.1491054
##
## Residual Deviance: 0.0007645983
## AIC: 20.00076
6.2 Estimasi Parameter
koef <- summary(multinom_model)$coefficients
se <- summary(multinom_model)$standard.errors
koef %>%
as.data.frame() %>%
rownames_to_column("Model") %>%
kable(caption = "Estimasi Koefisien (β) Model Regresi Logistik Multinomial",
digits = 4) %>%
kable_styling(bootstrap_options = c("striped", "hover"), full_width = TRUE)
Estimasi Koefisien (β) Model Regresi Logistik Multinomial
|
Model
|
(Intercept)
|
culmen_length_mm
|
culmen_depth_mm
|
flipper_length_mm
|
body_mass_g
|
|
Adelie
|
28.1010
|
-19.6174
|
36.3336
|
2.4138
|
-0.0674
|
|
Chinstrap
|
-21.0251
|
25.7274
|
1.3359
|
-1.9625
|
-0.1910
|
Kategori referensi adalah Gentoo. Model Logit 1
membandingkan Adelie vs Gentoo, Model Logit 2 membandingkan Chinstrap vs
Gentoo.
6.3 Uji Signifikansi Parameter
6.3.1 Uji Serentak (Likelihood Ratio Test / G²)
multinom_null <- multinom(species ~ 1, data = train, trace = FALSE)
lrt <- anova(multinom_null, multinom_model, test = "Chisq")
print(lrt)
## Likelihood ratio tests of Multinomial Models
##
## Response: species
## Model
## 1 1
## 2 culmen_length_mm + culmen_depth_mm + flipper_length_mm + body_mass_g
## Resid. df Resid. Dev Test Df LR stat. Pr(Chi)
## 1 548 5.780024e+02
## 2 540 7.645983e-04 1 vs 2 8 578.0016 0
Tolak H₀ jika p-value < 0.05 → minimal satu variabel prediktor
berpengaruh signifikan terhadap model.
6.3.2 Uji Parsial (Wald Test)
z_val <- koef / se
p_val <- 2 * (1 - pnorm(abs(z_val)))
# Logit 1: Adelie vs Gentoo
data.frame(
Variabel = colnames(koef),
Beta = round(koef["Adelie", ], 4),
SE = round(se["Adelie", ], 4),
Wald_Z = round(z_val["Adelie", ], 4),
P_value = round(p_val["Adelie", ], 4),
Sig = ifelse(p_val["Adelie", ] < 0.001, "***",
ifelse(p_val["Adelie", ] < 0.01, "**",
ifelse(p_val["Adelie", ] < 0.05, "*", "ns")))
) %>%
kable(caption = "Uji Parsial (Wald) — Model Logit 1: Adelie vs Gentoo",
row.names = FALSE) %>%
kable_styling(bootstrap_options = c("striped", "hover"), full_width = FALSE) %>%
footnote(general = "*** p<0.001 ** p<0.01 * p<0.05 ns = tidak signifikan")
Uji Parsial (Wald) — Model Logit 1: Adelie vs Gentoo
|
Variabel
|
Beta
|
SE
|
Wald_Z
|
P_value
|
Sig
|
|
(Intercept)
|
28.1010
|
0.8292
|
33.8875
|
0.0000
|
***
|
|
culmen_length_mm
|
-19.6174
|
14.1015
|
-1.3912
|
0.1642
|
ns
|
|
culmen_depth_mm
|
36.3336
|
20.2410
|
1.7951
|
0.0726
|
ns
|
|
flipper_length_mm
|
2.4138
|
5.1015
|
0.4732
|
0.6361
|
ns
|
|
body_mass_g
|
-0.0674
|
0.1515
|
-0.4446
|
0.6566
|
ns
|
|
Note:
|
|
*** p<0.001 ** p<0.01 * p<0.05 ns = tidak
signifikan
|
# Logit 2: Chinstrap vs Gentoo
data.frame(
Variabel = colnames(koef),
Beta = round(koef["Chinstrap", ], 4),
SE = round(se["Chinstrap", ], 4),
Wald_Z = round(z_val["Chinstrap", ], 4),
P_value = round(p_val["Chinstrap", ], 4),
Sig = ifelse(p_val["Chinstrap", ] < 0.001, "***",
ifelse(p_val["Chinstrap", ] < 0.01, "**",
ifelse(p_val["Chinstrap", ] < 0.05, "*", "ns")))
) %>%
kable(caption = "Uji Parsial (Wald) — Model Logit 2: Chinstrap vs Gentoo",
row.names = FALSE) %>%
kable_styling(bootstrap_options = c("striped", "hover"), full_width = FALSE) %>%
footnote(general = "*** p<0.001 ** p<0.01 * p<0.05 ns = tidak signifikan")
Uji Parsial (Wald) — Model Logit 2: Chinstrap vs Gentoo
|
Variabel
|
Beta
|
SE
|
Wald_Z
|
P_value
|
Sig
|
|
(Intercept)
|
-21.0251
|
0.9971
|
-21.0866
|
0.0000
|
***
|
|
culmen_length_mm
|
25.7274
|
15.2861
|
1.6831
|
0.0924
|
ns
|
|
culmen_depth_mm
|
1.3359
|
35.3462
|
0.0378
|
0.9699
|
ns
|
|
flipper_length_mm
|
-1.9625
|
5.5131
|
-0.3560
|
0.7219
|
ns
|
|
body_mass_g
|
-0.1910
|
0.1491
|
-1.2811
|
0.2002
|
ns
|
|
Note:
|
|
*** p<0.001 ** p<0.01 * p<0.05 ns = tidak
signifikan
|
6.4 Persamaan Model
b <- round(koef, 4)
cat("**Model Logit 1 (Adelie vs Gentoo):**\n")
## **Model Logit 1 (Adelie vs Gentoo):**
cat(sprintf(
"ln(P(Adelie)/P(Gentoo)) = %.4f + %.4f*X1 + %.4f*X2 + %.4f*X3 + %.4f*X4\n",
b["Adelie","(Intercept)"], b["Adelie","culmen_length_mm"],
b["Adelie","culmen_depth_mm"], b["Adelie","flipper_length_mm"],
b["Adelie","body_mass_g"]))
## ln(P(Adelie)/P(Gentoo)) = 28.1010 + -19.6174*X1 + 36.3336*X2 + 2.4138*X3 + -0.0674*X4
cat("\n**Model Logit 2 (Chinstrap vs Gentoo):**\n")
##
## **Model Logit 2 (Chinstrap vs Gentoo):**
cat(sprintf(
"ln(P(Chinstrap)/P(Gentoo)) = %.4f + %.4f*X1 + %.4f*X2 + %.4f*X3 + %.4f*X4\n",
b["Chinstrap","(Intercept)"], b["Chinstrap","culmen_length_mm"],
b["Chinstrap","culmen_depth_mm"], b["Chinstrap","flipper_length_mm"],
b["Chinstrap","body_mass_g"]))
## ln(P(Chinstrap)/P(Gentoo)) = -21.0251 + 25.7274*X1 + 1.3359*X2 + -1.9625*X3 + -0.1910*X4
cat("\nDi mana: X1=culmen_length, X2=culmen_depth, X3=flipper_length, X4=body_mass\n")
##
## Di mana: X1=culmen_length, X2=culmen_depth, X3=flipper_length, X4=body_mass
6.5 Odds Ratio
or_adelie <- round(exp(koef["Adelie", ]), 4)
or_chinstrap <- round(exp(koef["Chinstrap", ]), 4)
data.frame(
Variabel = colnames(koef),
OR_Adelie = or_adelie,
OR_Chinstrap = or_chinstrap
) %>%
kable(caption = "Odds Ratio — Model Regresi Logistik Multinomial",
col.names = c("Variabel", "OR (Adelie vs Gentoo)", "OR (Chinstrap vs Gentoo)"),
row.names = FALSE) %>%
kable_styling(bootstrap_options = c("striped", "hover"), full_width = FALSE) %>%
footnote(general = "OR > 1: hubungan positif; OR < 1: hubungan negatif terhadap kategori tersebut dibanding Gentoo")
Odds Ratio — Model Regresi Logistik Multinomial
|
Variabel
|
OR (Adelie vs Gentoo)
|
OR (Chinstrap vs Gentoo)
|
|
(Intercept)
|
1.599955e+12
|
0.000000e+00
|
|
culmen_length_mm
|
0.000000e+00
|
1.490229e+11
|
|
culmen_depth_mm
|
6.018423e+15
|
3.803400e+00
|
|
flipper_length_mm
|
1.117630e+01
|
1.405000e-01
|
|
body_mass_g
|
9.348000e-01
|
8.261000e-01
|
|
Note:
|
|
OR > 1: hubungan positif; OR < 1: hubungan negatif
terhadap kategori tersebut dibanding Gentoo
|
6.6 Evaluasi Model Multinomial
multinom_pred <- predict(multinom_model, newdata = test, type = "class")
cm_multi <- confusionMatrix(multinom_pred, test$species)
print(cm_multi)
## Confusion Matrix and Statistics
##
## Reference
## Prediction Gentoo Adelie Chinstrap
## Gentoo 24 1 0
## Adelie 0 28 1
## Chinstrap 0 1 12
##
## Overall Statistics
##
## Accuracy : 0.9552
## 95% CI : (0.8747, 0.9907)
## No Information Rate : 0.4478
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 0.9295
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: Gentoo Class: Adelie Class: Chinstrap
## Sensitivity 1.0000 0.9333 0.9231
## Specificity 0.9767 0.9730 0.9815
## Pos Pred Value 0.9600 0.9655 0.9231
## Neg Pred Value 1.0000 0.9474 0.9815
## Prevalence 0.3582 0.4478 0.1940
## Detection Rate 0.3582 0.4179 0.1791
## Detection Prevalence 0.3731 0.4328 0.1940
## Balanced Accuracy 0.9884 0.9532 0.9523
# Tabel confusion matrix rapi
cm_multi$table %>%
as.data.frame() %>%
pivot_wider(names_from = Reference, values_from = Freq) %>%
rename(Prediksi = Prediction) %>%
kable(caption = "Confusion Matrix — Regresi Logistik Multinomial") %>%
kable_styling(bootstrap_options = c("striped", "hover"), full_width = FALSE) %>%
add_header_above(c(" " = 1, "Aktual" = 3))
Confusion Matrix — Regresi Logistik Multinomial
|
|
Aktual
|
|
Prediksi
|
Gentoo
|
Adelie
|
Chinstrap
|
|
Gentoo
|
24
|
1
|
0
|
|
Adelie
|
0
|
28
|
1
|
|
Chinstrap
|
0
|
1
|
12
|
# APER Multinomial
multinom_pred_train <- predict(multinom_model, newdata = train, type = "class")
n_salah_multi_train <- sum(multinom_pred_train != train$species)
n_salah_multi_test <- sum(multinom_pred != test$species)
aper_multi_train <- n_salah_multi_train / nrow(train)
aper_multi_test <- n_salah_multi_test / nrow(test)
data.frame(
Data = c("Training", "Testing"),
`N Total` = c(nrow(train), nrow(test)),
`N Salah` = c(n_salah_multi_train, n_salah_multi_test),
`APER (%)` = round(c(aper_multi_train, aper_multi_test) * 100, 2),
`Akurasi (%)` = round((1 - c(aper_multi_train, aper_multi_test)) * 100, 2)
) %>%
kable(caption = "APER dan Akurasi Model Regresi Logistik Multinomial") %>%
kable_styling(bootstrap_options = c("striped", "hover"), full_width = FALSE)
APER dan Akurasi Model Regresi Logistik Multinomial
|
Data
|
N.Total
|
N.Salah
|
APER….
|
Akurasi….
|
|
Training
|
275
|
0
|
0.00
|
100.00
|
|
Testing
|
67
|
3
|
4.48
|
95.52
|
7. Perbandingan LDA vs Regresi Logistik Multinomial
data.frame(
Aspek = c("Metode", "Asumsi Utama", "Variabel Dependen",
"APER Testing (%)", "Akurasi Testing (%)", "Kelebihan"),
LDA = c("Linear Discriminant Analysis",
"Normalitas multivariat & homogenitas kovarians",
"Nominal ≥ 2 kategori",
paste0(round(aper_test * 100, 2), "%"),
paste0(round((1 - aper_test) * 100, 2), "%"),
"Interpretasi geometris jelas, visualisasi mudah"),
Multinomial = c("Regresi Logistik Multinomial",
"Tidak memerlukan normalitas prediktor",
"Nominal ≥ 3 kategori",
paste0(round(aper_multi_test * 100, 2), "%"),
paste0(round((1 - aper_multi_test) * 100, 2), "%"),
"Lebih fleksibel, menghasilkan odds ratio")
) %>%
kable(caption = "Perbandingan LDA dan Regresi Logistik Multinomial",
col.names = c("Aspek", "LDA", "Multinomial Logistik")) %>%
kable_styling(bootstrap_options = c("striped", "hover"), full_width = TRUE)
Perbandingan LDA dan Regresi Logistik Multinomial
|
Aspek
|
LDA
|
Multinomial Logistik
|
|
Metode
|
Linear Discriminant Analysis
|
Regresi Logistik Multinomial
|
|
Asumsi Utama
|
Normalitas multivariat & homogenitas kovarians
|
Tidak memerlukan normalitas prediktor
|
|
Variabel Dependen
|
Nominal ≥ 2 kategori
|
Nominal ≥ 3 kategori
|
|
APER Testing (%)
|
1.49%
|
4.48%
|
|
Akurasi Testing (%)
|
98.51%
|
95.52%
|
|
Kelebihan
|
Interpretasi geometris jelas, visualisasi mudah
|
Lebih fleksibel, menghasilkan odds ratio
|
8. Kesimpulan
cat(sprintf(
"LDA Multinomial:
- Menghasilkan 2 fungsi diskriminan (LD1: %.2f%%, LD2: %.2f%%)
- APER Training: %.2f%% | APER Testing: %.2f%%
- Akurasi Testing: %.2f%%
Regresi Logistik Multinomial:
- Kategori referensi: Gentoo
- Menghasilkan 2 persamaan logit (Adelie vs Gentoo, Chinstrap vs Gentoo)
- APER Training: %.2f%% | APER Testing: %.2f%%
- Akurasi Testing: %.2f%%
",
prop_var[1], prop_var[2],
aper_train * 100, aper_test * 100, (1 - aper_test) * 100,
aper_multi_train * 100, aper_multi_test * 100, (1 - aper_multi_test) * 100
))
## LDA Multinomial:
## - Menghasilkan 2 fungsi diskriminan (LD1: 86.59%, LD2: 13.41%)
## - APER Training: 1.09% | APER Testing: 1.49%
## - Akurasi Testing: 98.51%
##
## Regresi Logistik Multinomial:
## - Kategori referensi: Gentoo
## - Menghasilkan 2 persamaan logit (Adelie vs Gentoo, Chinstrap vs Gentoo)
## - APER Training: 0.00% | APER Testing: 4.48%
## - Akurasi Testing: 95.52%