Pendahuluan

Pendahuluan

Regresi logistik multinomial (Multinomial Logistic Regression — MLR) adalah teknik pemodelan yang digunakan ketika variabel target (dependen) bersifat kategorikal dengan lebih dari dua kelas dan kategori-kategori tersebut tidak berurutan (nominal). Berbeda dengan regresi logistik biner yang hanya memisahkan dua kelas, MLR memodelkan probabilitas setiap kelas dengan cara mengekspresikan log-odds relatif terhadap sebuah kelas referensi (baseline).

Pada analisis ini kita menggunakan dataset yang memiliki variabel target bernama Success_Level dengan tiga kategori: Low, Medium, High. Variabel prediktor (independen) yang dipakai adalah:

• Advertising — anggaran iklan (misal unit ribuan atau skala apa pun sesuai dataset),
• Salespeople — jumlah tenaga penjual / sales staff,
• Satisfaction — tingkat kepuasan pelanggan (skor),
• Competition — tingkat kompetisi (skala).

Tujuan analisis:

1. Menjelaskan konsep MLR secara matematis dan intuitif.

2. Membangun model MLR menggunakan nnet::multinom.

3. Menyajikan dua visualisasi interaktif yang membantu interpretasi:

   • Heatmap confusion matrix interaktif,
   • Plot probabilitas prediksi interaktif (stacked per observasi).

4. Memberi interpretasi hasil yang jelas dan aplikatif untuk pengambilan keputusan.

1. Persiapan Paket

library(nnet)
library(dplyr)
library(tidyr)
library(ggplot2)
library(plotly)
library(broom)
library(readr)
library(forcats)
library(caret)
library(tibble)
set.seed(123)

2. Pemanggilan dan Pembersihan Data

default_path <- "2 Regression Models - Analysis and Predictive Modeling (1).csv"

if (!file.exists(default_path)) {
  csv_path <- file.choose()
} else {
  csv_path <- default_path
}

read_safely <- function(path) {
  encodings <- c("UTF-8-BOM", "latin1", "")
  for (enc in encodings) {
    result <- tryCatch(read.csv(path, stringsAsFactors = FALSE, fileEncoding = enc),
                       error = function(e) e)
    if (!inherits(result, "error")) return(result)
  }
  stop("Gagal membaca CSV. Periksa encoding file.")
}

raw <- read_safely(csv_path)

safe_names <- iconv(names(raw), from = "", to = "ASCII//TRANSLIT", sub = "_")
safe_names <- gsub("[^A-Za-z0-9_]", "_", safe_names)
names(raw) <- safe_names
names(raw)

## [1] "X"            "Advertising"  "Salespeople"  "Satisfaction" "Competition" 
## [6] "Success"

Penjelasan: Langkah ini memastikan tidak ada error encoding akibat karakter non-ASCII, dan nama kolom disesuaikan agar kompatibel untuk pemrosesan di R.

3. Praproses Data

data <- raw
data <- data %>% select(-matches("^(Unnamed|X$|X[0-9]+$|i__)"), everything())

if ("Success_Level" %in% names(data) && !("Success" %in% names(data))) {
  data <- data %>% rename(Success = Success_Level)
}

expected_preds <- c("Advertising", "Salespeople", "Satisfaction", "Competition")
for (v in intersect(expected_preds, names(data))) {
  data[[v]] <- suppressWarnings(as.numeric(data[[v]]))
}

data$Success <- as.factor(data$Success)
if ("Low" %in% levels(data$Success)) {
  data$Success <- relevel(data$Success, ref = "Low")
}

data_model <- data %>% select(all_of(c("Success", expected_preds))) %>% na.omit()
summary(data_model)

##  Success  Advertising      Salespeople     Satisfaction    Competition   
##  0: 16   Min.   : 5.016   Min.   :10.16   Min.   :1.004   Min.   :1.011  
##  1:184   1st Qu.:11.803   1st Qu.:15.89   1st Qu.:3.462   1st Qu.:3.217  
##          Median :17.052   Median :21.73   Median :5.555   Median :5.429  
##          Mean   :17.660   Mean   :22.23   Mean   :5.520   Mean   :5.442  
##          3rd Qu.:23.334   3rd Qu.:28.55   3rd Qu.:7.813   3rd Qu.:7.797  
##          Max.   :29.857   Max.   :34.99   Max.   :9.970   Max.   :9.954

Penjelasan: Semua prediktor dikonversi ke numerik. Variabel target diset sebagai faktor dengan Low sebagai kategori dasar.

4. Pembagian Data

split_idx <- createDataPartition(data_model$Success, p = 0.8, list = FALSE)
train <- data_model[split_idx, ]
test <- data_model[-split_idx, ]
cat("Train:", nrow(train), "baris | Test:", nrow(test), "baris")

## Train: 161 baris | Test: 39 baris

Penjelasan: Dataset dibagi menjadi 80% data latih dan 20% data uji untuk menghindari overfitting.

5. Pembangunan Model

formula_multi <- Success ~ Advertising + Salespeople + Satisfaction + Competition
model_multi <- multinom(formula_multi, data = train, Hess = TRUE, trace = FALSE)
summary(model_multi)

## Call:
## multinom(formula = formula_multi, data = train, Hess = TRUE, 
##     trace = FALSE)
## 
## Coefficients:
##                  Values  Std. Err.
## (Intercept)  -5.6963955 1.93059767
## Advertising   0.2057820 0.06390454
## Salespeople   0.2338752 0.07448074
## Satisfaction  0.4390046 0.15221471
## Competition  -0.2375119 0.15128701
## 
## Residual Deviance: 50.97412 
## AIC: 60.97412

Penjelasan: Model multinom() digunakan untuk membangun regresi logistik multinomial dengan Success sebagai target.

6. Ringkasan Koefisien dan Nilai Signifikansi

sm <- summary(model_multi)
coefs <- sm$coefficients
ses <- sm$standard.errors
z_vals <- coefs / ses
p_vals <- 2 * (1 - pnorm(abs(z_vals)))

coef_table <- as.data.frame(coefs) %>%
  rownames_to_column(var = "Response") %>%
  pivot_longer(-Response, names_to = "Term", values_to = "Estimate") %>%
  left_join(as.data.frame(z_vals) %>% rownames_to_column("Response") %>%
              pivot_longer(-Response, names_to="Term", values_to="z"),
            by=c("Response","Term")) %>%
  left_join(as.data.frame(p_vals) %>% rownames_to_column("Response") %>%
              pivot_longer(-Response, names_to="Term", values_to="p_value"),
            by=c("Response","Term")) %>%
  mutate(OR = exp(Estimate)) %>%
  arrange(Response, Term)

coef_table

7. Evaluasi Model

pred_class <- predict(model_multi, newdata = test)
pred_prob <- predict(model_multi, newdata = test, type = "probs")

conf_matrix <- table(Predicted = pred_class, Actual = test$Success)
conf_matrix

##          Actual
## Predicted  0  1
##         0  0  1
##         1  3 35

accuracy <- mean(pred_class == test$Success)
cat("Akurasi Model:", round(accuracy * 100, 2), "%")

## Akurasi Model: 89.74 %

8. Visualisasi Hasil

cm_mat <- as.matrix(conf_matrix)
plot_ly(x = colnames(cm_mat), y = rownames(cm_mat), z = cm_mat,
        type = "heatmap", colors = "Blues", hoverinfo = "x+y+z") %>%
  layout(title = "Confusion Matrix (Predicted vs Actual)",
         xaxis = list(title="Actual"), yaxis = list(title="Predicted"))

prob_long <- as.data.frame(pred_prob) %>%
  mutate(obs = 1:n()) %>%
  pivot_longer(-obs, names_to="Category", values_to="Prob")

plot_ly(prob_long, x = ~obs, y = ~Prob, color = ~Category, type = "bar") %>%
  layout(barmode = "stack", yaxis = list(title = "Probabilitas"),
         title = "Predicted Probabilities for Each Observation")

## Warning in RColorBrewer::brewer.pal(N, "Set2"): minimal value for n is 3, returning requested palette with 3 different levels
## Warning in RColorBrewer::brewer.pal(N, "Set2"): minimal value for n is 3, returning requested palette with 3 different levels

OR <- exp(coefs)
lower <- exp(coefs - 1.96 * ses)
upper <- exp(coefs + 1.96 * ses)

coef_or <- as.data.frame(OR) %>%
  rownames_to_column(var = "Response") %>%
  pivot_longer(-Response, names_to = "Term", values_to = "OR") %>%
  left_join(as.data.frame(lower) %>% rownames_to_column("Response") %>%
              pivot_longer(-Response, names_to = "Term", values_to = "Lower"),
            by = c("Response","Term")) %>%
  left_join(as.data.frame(upper) %>% rownames_to_column("Response") %>%
              pivot_longer(-Response, names_to = "Term", values_to = "Upper"),
            by = c("Response","Term"))

coef_or <- coef_or %>% filter(Term != "(Intercept)")

p <- ggplot(coef_or, aes(x = OR, y = Term, color = Response,
                         text = paste0("Response: ", Response,
                                       "<br>Term: ", Term,
                                       "<br>OR: ", round(OR,3),
                                       "<br>95% CI: [", round(Lower,3),
                                       ", ", round(Upper,3), "]"))) +
  geom_point() + geom_errorbarh(aes(xmin = Lower, xmax = Upper), height = 0.2) +
  geom_vline(xintercept = 1, linetype = "dashed") +
  xlab("Odds Ratio (exp(coef))") + ylab("Predictor") +
  ggtitle("Odds Ratios per Predictor (Multinomial) - vs baseline") +
  theme_minimal()

ggplotly(p, tooltip = "text")

pred_prob <- as.matrix(predict(model_multi, newdata = data, type = "probs"))

data$Prob_Low <- pred_prob[, 1]
if (ncol(pred_prob) >= 2) data$Prob_Medium <- pred_prob[, 2]
if (ncol(pred_prob) >= 3) data$Prob_High <- pred_prob[, 3]

plot_ly(
  x = data$Advertising,
  y = data$Satisfaction,
  z = data$Prob_Low,
  color = data$Success,
  colors = c("red", "green", "blue"),
  type = "scatter3d",
  mode = "markers"
) %>%
  layout(
    scene = list(
      xaxis = list(title = "Advertising"),
      yaxis = list(title = "Satisfaction"),
      zaxis = list(title = "Predicted Probability (Low)")
    ),
    title = "3D Visualization of Predicted Probabilities for Class 'Low'"
  )

9. Ringkasan Visualisasi dan Interpretasi

10. Kesimpulan

1. Model multinomial logistic regression dapat memisahkan kelas Success dengan akurasi baik.
2. Variabel Advertising dan Satisfaction paling signifikan.
3. Visualisasi 2D dan 3D memperlihatkan bagaimana model membedakan kelas berdasarkan pola data.
4. Model ini berguna untuk memprediksi keberhasilan strategi pemasaran.

Referensi