Regresi Logistik Biner
Studi Kasus: Prediksi Financial Distress Perusahaan
Sundarin Syifa Qolbina Suganda dan Arindy Hanum D’Coen
10 June 2026
Rumusan Masalah
Kondisi financial distress pada perusahaan publik sektor transportasi merupakan fenomena yang dapat menimbulkan kerugian bagi investor, kreditur, maupun pemangku kepentingan lainnya. Oleh karena itu, diperlukan suatu model prediksi yang mampu mengidentifikasi kemungkinan perusahaan mengalami financial distress secara dini berdasarkan indikator keuangan yang tersedia.
Berdasarkan latar belakang tersebut, rumusan masalah dalam analisis ini adalah:
- Apakah indikator keuangan yaitu current ratio (X1), debt ratio (X2), return on assets (X3), sales growth (X4), dan firm size (X5) secara simultan berpengaruh terhadap probabilitas terjadinya financial distress pada perusahaan?
- Variabel prediktor manakah yang secara parsial berpengaruh signifikan terhadap status financial distress perusahaan?
- Seberapa baik kemampuan model regresi logistik biner dalam memprediksi status financial distress perusahaan berdasarkan data pengujian?
Tujuan
Sesuai dengan rumusan masalah di atas, tujuan analisis ini adalah:
- Membangun model regresi logistik biner untuk memprediksi probabilitas financial distress perusahaan berdasarkan indikator keuangan current ratio, debt ratio, return on assets, sales growth, dan firm size.
- Mengidentifikasi variabel prediktor yang berpengaruh signifikan secara parsial terhadap status financial distress perusahaan pada taraf signifikansi α = 0,05.
- Mengevaluasi kinerja model prediksi melalui metrik klasifikasi akurasi, sensitivitas, spesifisitas, dan nilai AUC kurva ROC pada data testing.
1. Persiapan
1.1 Instalasi & Pemuatan Paket
required_packages <- c("dplyr", "ggplot2", "broom", "knitr", "scales", "readr")
missing_packages <- required_packages[
!vapply(required_packages, requireNamespace, logical(1), quietly = TRUE)
]
if (length(missing_packages) > 0) {
stop(
"Paket berikut belum tersedia: ",
paste(missing_packages, collapse = ", "),
". Silakan install terlebih dahulu."
)
}
invisible(lapply(required_packages, library, character.only = TRUE))1.2 Import Data
Data yang digunakan adalah data Financial Distress perusahaan publik yang memuat indikator-indikator keuangan sebagai prediktor dan status financial distress sebagai variabel respon biner.
raw_data <- readr::read_csv("data projek adk bismillah-3.csv",
show_col_types = FALSE)
# Periksa dimensi awal
ringkasan_data <- data.frame(
Keterangan = c("Jumlah observasi", "Jumlah variabel"),
Nilai = c(nrow(raw_data), ncol(raw_data))
)
knitr::kable(
ringkasan_data,
caption = "Ukuran dataset Financial Distress"
)| Keterangan | Nilai |
|---|---|
| Jumlah observasi | 120 |
| Jumlah variabel | 10 |
2. Eksplorasi Data
2.1 Kamus Variabel
kamus_variabel <- data.frame(
`Kode kolom` = c("X1", "X2", "X3", "X4", "X5", "Y"),
`Nama variabel analisis` = c(
"current_ratio", "debt_ratio", "roa",
"sales_growth", "firm_size", "financial_distress"
),
`Keterangan` = c(
"Current Ratio — rasio aset lancar terhadap kewajiban lancar",
"Debt Ratio — rasio total utang terhadap total aset",
"Return on Assets — laba bersih dibagi total aset",
"Sales Growth — pertumbuhan penjualan tahunan",
"Firm Size — logaritma natural total aset",
"Status financial distress: 0 = Non-distress, 1 = Distress"
),
`Tipe dalam analisis` = c(
"Numerik", "Numerik", "Numerik",
"Numerik", "Numerik", "Respon biner"
),
check.names = FALSE
)
knitr::kable(
kamus_variabel,
caption = "Kamus variabel dataset Financial Distress"
)| Kode kolom | Nama variabel analisis | Keterangan | Tipe dalam analisis |
|---|---|---|---|
| X1 | current_ratio | Current Ratio — rasio aset lancar terhadap kewajiban lancar | Numerik |
| X2 | debt_ratio | Debt Ratio — rasio total utang terhadap total aset | Numerik |
| X3 | roa | Return on Assets — laba bersih dibagi total aset | Numerik |
| X4 | sales_growth | Sales Growth — pertumbuhan penjualan tahunan | Numerik |
| X5 | firm_size | Firm Size — logaritma natural total aset | Numerik |
| Y | financial_distress | Status financial distress: 0 = Non-distress, 1 = Distress | Respon biner |
2.2 Pembersihan & Penamaan Ulang Kolom
fd <- raw_data %>%
transmute(
kode_saham = `Kode Saham`,
nama_perusahaan = `Nama Perusahaan`,
tahun = Tahun,
current_ratio = `Current Ratio\n(X1)`,
debt_ratio = `Debt Ratio\n(X2)`,
roa = `ROA\n(X3)`,
sales_growth = `Sales Growth\n(X4)`,
firm_size = `Firm Size\n(X5)\n=LN(Total Aset)`,
financial_distress = factor(
`Financial Distress\n(Y)\n0=Non | 1=Distress`,
levels = c(0, 1),
labels = c("Non-distress", "Distress")
),
distress_int = as.integer(
`Financial Distress\n(Y)\n0=Non | 1=Distress`
)
) %>%
na.omit()2.3 Contoh Data
contoh_data <- fd %>%
transmute(
`Kode Saham` = kode_saham,
`Tahun` = tahun,
`Current Ratio` = current_ratio,
`Debt Ratio` = debt_ratio,
`ROA` = roa,
`Sales Growth` = sales_growth,
`Firm Size` = round(firm_size, 2),
`Status` = financial_distress
) %>%
head(8)
knitr::kable(
contoh_data,
caption = "Contoh delapan baris data setelah pembersihan"
)| Kode Saham | Tahun | Current Ratio | Debt Ratio | ROA | Sales Growth | Firm Size | Status |
|---|---|---|---|---|---|---|---|
| CMPP | 2019 | 0.4713503 | 0.9226942 | -0.0600842 | 0.5849279 | 7.87 | Distress |
| CMPP | 2020 | 0.0349001 | 1.4785397 | -0.4530505 | -0.7598748 | 8.71 | Distress |
| CMPP | 2021 | 0.0251439 | 2.0108759 | -0.4540688 | -0.6114215 | 8.55 | Distress |
| CMPP | 2022 | 0.0384977 | 2.2721673 | -0.3074482 | 5.0399361 | 8.59 | Distress |
| CMPP | 2023 | 0.0387037 | 1.4447351 | -0.1767495 | 0.7521820 | 8.72 | Distress |
| CMPP | 2024 | 0.0474417 | 1.6405457 | -0.2670981 | 0.1990943 | 8.65 | Distress |
| GIAA | 2019 | 0.3480469 | 0.8382738 | 0.0014692 | 0.0380320 | 11.03 | Non-distress |
| GIAA | 2020 | 0.1249298 | 1.1800740 | -0.2372054 | -0.6637139 | 11.93 | Non-distress |
2.4 Distribusi Kelas Respon
class_summary <- fd %>%
count(financial_distress, name = "Jumlah") %>%
mutate(Proporsi = scales::percent(Jumlah / sum(Jumlah), accuracy = 0.1)) %>%
rename(`Status Financial Distress` = financial_distress)
knitr::kable(
class_summary,
caption = "Distribusi kelas respon Financial Distress"
)| Status Financial Distress | Jumlah | Proporsi |
|---|---|---|
| Non-distress | 91 | 75.8% |
| Distress | 29 | 24.2% |
ggplot(fd, aes(x = financial_distress, fill = financial_distress)) +
geom_bar(width = 0.55, color = "white", linewidth = 0.8) +
geom_text(
stat = "count",
aes(label = after_stat(count)),
vjust = -0.4,
fontface = "bold"
) +
scale_fill_manual(values = c("Non-distress" = "#2a9d8f", "Distress" = "#e76f51")) +
labs(
title = "Distribusi Status Financial Distress",
x = NULL,
y = "Jumlah perusahaan-tahun"
) +
theme_minimal(base_size = 12) +
theme(legend.position = "none")
2.5 Eksplorasi Prediktor Numerik
ggplot(fd, aes(x = debt_ratio, y = roa, color = financial_distress)) +
geom_point(alpha = 0.72, size = 2.1) +
scale_color_manual(values = c("Non-distress" = "#2a9d8f", "Distress" = "#e76f51")) +
labs(
title = "Debt Ratio vs. Return on Assets",
subtitle = "Titik oranye menunjukkan perusahaan dalam kondisi financial distress",
x = "Debt Ratio (X2)",
y = "Return on Assets (X3)",
color = "Status"
) +
theme_minimal(base_size = 12)
3. Pembagian Data Training & Testing
set.seed(42)
stratified_split <- function(y, prop = 0.8) {
idx_by_class <- split(seq_along(y), y)
train_idx <- lapply(
idx_by_class,
function(idx) sample(idx, size = floor(length(idx) * prop))
)
unlist(train_idx, use.names = FALSE)
}
train_id <- stratified_split(fd$distress_int, prop = 0.8)
train_data <- fd[ train_id, ]
test_data <- fd[-train_id, ]
split_summary <- bind_rows(
train_data %>% count(financial_distress) %>% mutate(data = "Training"),
test_data %>% count(financial_distress) %>% mutate(data = "Testing")
) %>%
group_by(data) %>%
mutate(proporsi = scales::percent(n / sum(n), accuracy = 0.1)) %>%
ungroup() %>%
select(data, financial_distress, n, proporsi) %>%
rename(
Data = data,
`Status` = financial_distress,
Jumlah = n,
Proporsi = proporsi
)
knitr::kable(split_summary, caption = "Distribusi kelas pada training dan testing")| Data | Status | Jumlah | Proporsi |
|---|---|---|---|
| Training | Non-distress | 72 | 75.8% |
| Training | Distress | 23 | 24.2% |
| Testing | Non-distress | 19 | 76.0% |
| Testing | Distress | 6 | 24.0% |
4. Estimasi Model Regresi Logistik Biner
fd_fit <- glm(
distress_int ~ current_ratio + debt_ratio + roa + sales_growth + firm_size,
data = train_data,
family = binomial(link = "logit")
)
ringkasan_model <- data.frame(
Keterangan = c(
"Jumlah observasi training",
"Null deviance",
"Residual deviance",
"Derajat bebas residual",
"AIC"
),
Nilai = c(
nobs(fd_fit),
round(fd_fit$null.deviance, 3),
round(fd_fit$deviance, 3),
fd_fit$df.residual,
round(AIC(fd_fit), 3)
)
)
knitr::kable(
ringkasan_model,
caption = "Ringkasan kecocokan model regresi logistik biner"
)| Keterangan | Nilai |
|---|---|
| Jumlah observasi training | 95.000 |
| Null deviance | 105.164 |
| Residual deviance | 66.847 |
| Derajat bebas residual | 89.000 |
| AIC | 78.847 |
4.1 Tabel Koefisien & Odds Ratio
coef_table <- broom::tidy(fd_fit) %>%
mutate(
odds_ratio = exp(estimate),
ci_low = exp(estimate - 1.96 * std.error),
ci_high = exp(estimate + 1.96 * std.error)
) %>%
arrange(p.value) %>%
transmute(
`Variabel` = term,
`Koefisien (β)` = round(estimate, 4),
`Odds Ratio` = round(odds_ratio, 4),
`Selang Kepercayaan 95%` = paste0(round(ci_low, 3), " – ", round(ci_high, 3)),
`p-value` = signif(p.value, 3),
`Signifikan (α = 0.05)` = ifelse(p.value < 0.05, "Ya ✓", "Tidak")
)
knitr::kable(
coef_table,
caption = "Estimasi koefisien, odds ratio, dan uji signifikansi"
)| Variabel | Koefisien (β) | Odds Ratio | Selang Kepercayaan 95% | p-value | Signifikan (α = 0.05) |
|---|---|---|---|---|---|
| roa | -16.0189 | 0.0000 | 0 – 0.001 | 0.000289 | Ya ✓ |
| sales_growth | 1.0455 | 2.8449 | 0.484 – 16.715 | 0.247000 | Tidak |
| current_ratio | 0.0462 | 1.0473 | 0.949 – 1.156 | 0.359000 | Tidak |
| firm_size | -0.1590 | 0.8530 | 0.607 – 1.199 | 0.361000 | Tidak |
| (Intercept) | -0.6364 | 0.5292 | 0.05 – 5.552 | 0.596000 | Tidak |
| debt_ratio | -0.2399 | 0.7867 | 0.212 – 2.914 | 0.720000 | Tidak |
5. Prediksi & Evaluasi Model
5.1 Prediksi Probabilitas
p_train <- predict(fd_fit, newdata = train_data, type = "response")
p_test <- predict(fd_fit, newdata = test_data, type = "response")
prediction_preview <- head(
data.frame(
`Kode Saham` = test_data$kode_saham,
`Status Aktual` = test_data$financial_distress,
`Peluang Prediksi Distress` = round(p_test, 4),
check.names = FALSE
),
6
)
knitr::kable(
prediction_preview,
caption = "Contoh peluang prediksi financial distress pada data testing"
)| Kode Saham | Status Aktual | Peluang Prediksi Distress |
|---|---|---|
| CMPP | Distress | 0.9835 |
| GIAA | Non-distress | 0.0718 |
| HELI | Non-distress | 0.0716 |
| ASSA | Non-distress | 0.1161 |
| BIRD | Non-distress | 0.1012 |
| IMJS | Non-distress | 0.0929 |
5.2 Fungsi Metrik Evaluasi
safe_div <- function(num, den) {
ifelse(den == 0, NA_real_, num / den)
}
classification_metrics <- function(actual, prob, threshold = 0.5) {
pred <- as.integer(prob >= threshold)
tp <- sum(pred == 1 & actual == 1)
tn <- sum(pred == 0 & actual == 0)
fp <- sum(pred == 1 & actual == 0)
fn <- sum(pred == 0 & actual == 1)
sensitivity <- safe_div(tp, tp + fn)
specificity <- safe_div(tn, tn + fp)
precision <- safe_div(tp, tp + fp)
npv <- safe_div(tn, tn + fn)
accuracy <- safe_div(tp + tn, tp + tn + fp + fn)
data.frame(
threshold = threshold,
accuracy = accuracy,
error_rate = 1 - accuracy,
sensitivity = sensitivity,
specificity = specificity,
precision = precision,
negative_predictive_value = npv,
f1_score = safe_div(2 * precision * sensitivity, precision + sensitivity),
balanced_accuracy = (sensitivity + specificity) / 2,
false_positive_rate = 1 - specificity,
false_negative_rate = 1 - sensitivity
)
}
format_metrics_indonesia <- function(x) {
x %>%
transmute(
Threshold = threshold,
Akurasi = accuracy,
`Error rate` = error_rate,
Sensitivity = sensitivity,
Specificity = specificity,
Presisi = precision,
NPV = negative_predictive_value,
`F1-score` = f1_score,
`Balanced accuracy` = balanced_accuracy,
FPR = false_positive_rate,
FNR = false_negative_rate
)
}
confusion_matrix <- function(actual, prob, threshold = 0.5) {
pred_label <- factor(
ifelse(prob >= threshold, "Prediksi Distress", "Prediksi Non-distress"),
levels = c("Prediksi Distress", "Prediksi Non-distress")
)
actual_label <- factor(
ifelse(actual == 1, "Aktual Distress", "Aktual Non-distress"),
levels = c("Aktual Distress", "Aktual Non-distress")
)
addmargins(table(actual_label, pred_label))
}5.3 Confusion Matrix & Metrik pada Threshold 0.50
confusion_default <- confusion_matrix(test_data$distress_int, p_test, threshold = 0.5)
metrics_default <- classification_metrics(test_data$distress_int, p_test, threshold = 0.5) %>%
format_metrics_indonesia() %>%
mutate(across(where(is.numeric), round, 3))
knitr::kable(
confusion_default,
caption = "Confusion matrix testing pada threshold 0.50"
)| Prediksi Distress | Prediksi Non-distress | Sum | |
|---|---|---|---|
| Aktual Distress | 3 | 3 | 6 |
| Aktual Non-distress | 1 | 18 | 19 |
| Sum | 4 | 21 | 25 |
| Threshold | Akurasi | Error rate | Sensitivity | Specificity | Presisi | NPV | F1-score | Balanced accuracy | FPR | FNR |
|---|---|---|---|---|---|---|---|---|---|---|
| 0.5 | 0.84 | 0.16 | 0.5 | 0.947 | 0.75 | 0.857 | 0.6 | 0.724 | 0.053 | 0.5 |
6. Kurva ROC & Threshold Optimal
roc_points <- function(actual, prob) {
thresholds <- c(Inf, sort(unique(prob), decreasing = TRUE), -Inf)
out <- lapply(thresholds, function(th) {
pred <- as.integer(prob >= th)
tp <- sum(pred == 1 & actual == 1)
tn <- sum(pred == 0 & actual == 0)
fp <- sum(pred == 1 & actual == 0)
fn <- sum(pred == 0 & actual == 1)
sensitivity <- safe_div(tp, tp + fn)
specificity <- safe_div(tn, tn + fp)
data.frame(
threshold = th,
sensitivity = sensitivity,
specificity = specificity,
fpr = 1 - specificity,
youden = sensitivity + specificity - 1
)
})
bind_rows(out)
}
auc_value <- function(roc_df) {
roc_sorted <- roc_df %>% arrange(fpr, sensitivity)
sum(
diff(roc_sorted$fpr) *
(head(roc_sorted$sensitivity, -1) + tail(roc_sorted$sensitivity, -1)) / 2
)
}
roc_train <- roc_points(train_data$distress_int, p_train) %>% mutate(data = "Training")
roc_test <- roc_points(test_data$distress_int, p_test) %>% mutate(data = "Testing")
auc_train <- auc_value(roc_train)
auc_test <- auc_value(roc_test)
optimal_train <- roc_train %>%
filter(is.finite(threshold)) %>%
arrange(desc(youden), desc(sensitivity)) %>%
slice(1)
threshold_opt <- optimal_train$threshold[1]
test_at_opt <- roc_points(test_data$distress_int, p_test) %>%
filter(is.finite(threshold)) %>%
slice_min(abs(threshold - threshold_opt), n = 1, with_ties = FALSE) %>%
mutate(data = "Testing pada threshold optimal")auc_table <- data.frame(
Data = c("Training", "Testing"),
AUC = round(c(auc_train, auc_test), 3)
)
threshold_table <- optimal_train %>%
transmute(
`Threshold optimal` = round(threshold, 3),
Sensitivity = round(sensitivity, 3),
Specificity = round(specificity, 3),
`Indeks Youden` = round(youden, 3)
)
knitr::kable(auc_table, caption = "Nilai AUC pada data training dan testing")| Data | AUC |
|---|---|
| Training | 0.912 |
| Testing | 0.939 |
knitr::kable(threshold_table, caption = "Threshold optimal berdasarkan indeks Youden (ROC training)")| Threshold optimal | Sensitivity | Specificity | Indeks Youden |
|---|---|---|---|
| 0.266 | 0.87 | 0.903 | 0.772 |
roc_plot <- bind_rows(roc_train, roc_test)
ggplot(roc_plot, aes(x = fpr, y = sensitivity, color = data)) +
geom_path(linewidth = 1.1) +
geom_abline(intercept = 0, slope = 1, linetype = "dashed", color = "#6c757d") +
geom_point(
data = optimal_train,
aes(x = fpr, y = sensitivity),
inherit.aes = FALSE,
color = "#ffb703",
fill = "#fb8500",
shape = 21,
size = 4,
stroke = 1.2
) +
geom_point(
data = test_at_opt,
aes(x = fpr, y = sensitivity),
inherit.aes = FALSE,
color = "#8338ec",
fill = "#3a86ff",
shape = 24,
size = 4,
stroke = 1.2
) +
coord_equal() +
scale_color_manual(values = c("Training" = "#0077b6", "Testing" = "#e76f51")) +
labs(
title = "Kurva ROC Model Regresi Logistik Biner",
subtitle = paste0(
"AUC training = ", round(auc_train, 3),
"; AUC testing = ", round(auc_test, 3),
"; threshold optimal = ", round(threshold_opt, 3)
),
x = "False Positive Rate (1 – Specificity)",
y = "Sensitivity / True Positive Rate",
color = "Data"
) +
theme_minimal(base_size = 12) +
theme(legend.position = "bottom")
7. Perbandingan Threshold & Distribusi Probabilitas
7.1 Metrik pada Dua Threshold
metrics_compare <- bind_rows(
classification_metrics(test_data$distress_int, p_test, threshold = 0.5) %>%
mutate(aturan = "Threshold 0.50"),
classification_metrics(test_data$distress_int, p_test, threshold = threshold_opt) %>%
mutate(aturan = "Threshold optimal ROC")
) %>%
select(aturan, everything()) %>%
format_metrics_indonesia() %>%
bind_cols(
`Aturan klasifikasi` = c("Threshold 0.50", "Threshold optimal ROC"), .
) %>%
select(`Aturan klasifikasi`, everything()) %>%
mutate(across(where(is.numeric), round, 3))
confusion_opt <- confusion_matrix(test_data$distress_int, p_test, threshold = threshold_opt)
knitr::kable(
metrics_compare,
caption = "Perbandingan metrik testing pada dua aturan threshold"
)| Aturan klasifikasi | Threshold | Akurasi | Error rate | Sensitivity | Specificity | Presisi | NPV | F1-score | Balanced accuracy | FPR | FNR |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Threshold 0.50 | 0.500 | 0.84 | 0.16 | 0.500 | 0.947 | 0.75 | 0.857 | 0.600 | 0.724 | 0.053 | 0.500 |
| Threshold optimal ROC | 0.266 | 0.88 | 0.12 | 0.667 | 0.947 | 0.80 | 0.900 | 0.727 | 0.807 | 0.053 | 0.333 |
| Prediksi Distress | Prediksi Non-distress | Sum | |
|---|---|---|---|
| Aktual Distress | 4 | 2 | 6 |
| Aktual Non-distress | 1 | 18 | 19 |
| Sum | 5 | 20 | 25 |
7.2 Distribusi Probabilitas Prediksi
test_prob_plot <- test_data %>%
mutate(peluang_distress = p_test)
ggplot(test_prob_plot, aes(x = peluang_distress, fill = financial_distress)) +
geom_density(alpha = 0.55, color = "white", linewidth = 0.7) +
geom_vline(
xintercept = threshold_opt,
color = "#fb8500",
linewidth = 1.2,
linetype = "dashed"
) +
annotate(
"label",
x = threshold_opt,
y = Inf,
label = paste0("threshold = ", round(threshold_opt, 3)),
vjust = 1.4,
fill = "#fff3b0",
color = "#5f370e",
label.size = 0
) +
scale_fill_manual(values = c("Non-distress" = "#2a9d8f", "Distress" = "#e76f51")) +
labs(
title = "Distribusi Peluang Prediksi Financial Distress pada Data Testing",
x = "Peluang prediksi distress",
y = "Kepadatan",
fill = "Status aktual"
) +
theme_minimal(base_size = 12)
8. Kesimpulan
## Model regresi logistik biner diestimasi menggunakan 95 observasi training dari total 120 observasi.
##
## Nilai AUC pada data testing sebesar 0.939 menunjukkan kemampuan diskriminasi model terhadap perusahaan dalam kondisi financial distress dan non-distress.
##
## Threshold optimal berdasarkan indeks Youden pada kurva ROC training adalah 0.266.Berdasarkan hasil analisis:
- AUC testing = 0.939 — kemampuan diskriminasi model.
- Threshold optimal = 0.266 — diperoleh dari maksimum indeks Youden pada kurva ROC data training.
- Variabel yang signifikan secara statistik (α = 0,05) dapat dilihat pada tabel koefisien di Bagian 4.1.
Laporan dibuat otomatis menggunakan R Markdown.