1 Introduction

Employee attrition — the departure of employees from an organisation, whether voluntary or involuntary — represents one of the most consequential challenges in contemporary human resource management. Beyond the direct costs of recruitment and on-boarding, attrition erodes institutional knowledge, disrupts team cohesion, and imposes hidden productivity losses that can persist for months after a departure. Predictive modelling of attrition risk therefore offers HR practitioners a powerful, evidence-based instrument for proactive retention strategy.

This report develops and evaluates three binary logistic regression models of increasing complexity to predict the probability that an employee will leave (coded Attrition = "Left") using an employee survey dataset (Stealth Technologies, 2023). The dataset contains 14,900 employee records across 24 variables, with a near-balanced class split of approximately 47 % Left versus 53 % Stayed. Model evaluation follows the methodology and metrics prescribed by Boehmke & Greenwell (2020), specifically their treatment of logistic regression model accuracy via confusion-matrix analysis.

The analysis is structured as follows:

Section Content
§2 Data Preparation
§3 Model Specification
§4 Prediction Methodology
§5 Confusion Matrix Results
§6 Model Comparison
§7 Conclusion
§8 References

2 Data Preparation

2.1 Rationale for a Train–Test Split

A fundamental requirement of any predictive modelling exercise is an honest assessment of out-of-sample performance — i.e., how well the model predicts outcomes for employees it has not previously encountered. Evaluating model fit on the same data used for parameter estimation produces an optimistically biased performance estimate, a problem known as in-sample overfitting (Boehmke & Greenwell, 2020, Ch. 2).

Following standard supervised learning practice, we partition the dataset into a training subset (70 %) used exclusively for model estimation and a test subset (30 %) used exclusively for performance evaluation. Stratified random sampling is applied to preserve the attrition class balance in both subsets, ensuring that neither partition is inadvertently enriched or depleted of positive cases.

2.2 Required Packages

# ── Core libraries ────────────────────────────────────────────────────────────
library(tidyverse)    # Data wrangling (dplyr, tidyr) and ggplot2 visualisation
library(caret)        # confusionMatrix() and createDataPartition()
library(broom)        # tidy() for clean, data-frame model summaries
library(knitr)        # kable() table rendering
library(kableExtra)   # Enhanced kable styling for RPubs HTML output
library(scales)       # Axis formatting helpers (percent_format, comma)

2.3 Loading the Dataset

# ── Load the Employee Attrition dataset ───────────────────────────────────────
# Source: Stealth Technologies (2023). Employee Attrition Dataset. Kaggle.
# https://www.kaggle.com/datasets/stealthtechnologies/employee-attrition-dataset
#
# The dataset is saved locally as "test.csv".
# Place the file in your R working directory before knitting this document.

df_raw <- read.csv("test.csv", stringsAsFactors = FALSE, check.names = FALSE)

cat(sprintf("Dataset loaded: %d rows x %d columns\n", nrow(df_raw), ncol(df_raw)))
## Dataset loaded: 14900 rows x 24 columns
cat("Column names:\n")
## Column names:
print(names(df_raw))
##  [1] "Employee ID"              "Age"                     
##  [3] "Gender"                   "Years at Company"        
##  [5] "Job Role"                 "Monthly Income"          
##  [7] "Work-Life Balance"        "Job Satisfaction"        
##  [9] "Performance Rating"       "Number of Promotions"    
## [11] "Overtime"                 "Distance from Home"      
## [13] "Education Level"          "Marital Status"          
## [15] "Number of Dependents"     "Job Level"               
## [17] "Company Size"             "Company Tenure"          
## [19] "Remote Work"              "Leadership Opportunities"
## [21] "Innovation Opportunities" "Company Reputation"      
## [23] "Employee Recognition"     "Attrition"

2.4 Structural Inspection

# ── Inspect data types and sample values ──────────────────────────────────────
glimpse(df_raw)
## Rows: 14,900
## Columns: 24
## $ `Employee ID`              <int> 52685, 30585, 54656, 33442, 15667, 3496, 46…
## $ Age                        <int> 36, 35, 50, 58, 39, 45, 22, 34, 48, 55, 32,…
## $ Gender                     <chr> "Male", "Male", "Male", "Male", "Male", "Fe…
## $ `Years at Company`         <int> 13, 7, 7, 44, 24, 30, 5, 15, 40, 16, 12, 15…
## $ `Job Role`                 <chr> "Healthcare", "Education", "Education", "Me…
## $ `Monthly Income`           <int> 8029, 4563, 5583, 5525, 4604, 8104, 8700, 1…
## $ `Work-Life Balance`        <chr> "Excellent", "Good", "Fair", "Fair", "Good"…
## $ `Job Satisfaction`         <chr> "High", "High", "High", "Very High", "High"…
## $ `Performance Rating`       <chr> "Average", "Average", "Average", "High", "A…
## $ `Number of Promotions`     <int> 1, 1, 3, 0, 0, 0, 0, 1, 0, 0, 0, 2, 3, 0, 1…
## $ Overtime                   <chr> "Yes", "Yes", "Yes", "Yes", "Yes", "No", "N…
## $ `Distance from Home`       <int> 83, 55, 14, 43, 47, 38, 2, 9, 65, 31, 28, 3…
## $ `Education Level`          <chr> "Master’s Degree", "Associate Degree", "Ass…
## $ `Marital Status`           <chr> "Married", "Single", "Divorced", "Single", …
## $ `Number of Dependents`     <int> 1, 4, 2, 4, 6, 0, 0, 4, 1, 1, 1, 1, 3, 0, 0…
## $ `Job Level`                <chr> "Mid", "Entry", "Senior", "Entry", "Mid", "…
## $ `Company Size`             <chr> "Large", "Medium", "Medium", "Medium", "Lar…
## $ `Company Tenure`           <int> 22, 27, 76, 96, 45, 75, 48, 16, 52, 46, 57,…
## $ `Remote Work`              <chr> "No", "No", "No", "No", "Yes", "No", "No", …
## $ `Leadership Opportunities` <chr> "No", "No", "No", "No", "No", "No", "No", "…
## $ `Innovation Opportunities` <chr> "No", "No", "Yes", "No", "No", "No", "No", …
## $ `Company Reputation`       <chr> "Poor", "Good", "Good", "Poor", "Good", "Go…
## $ `Employee Recognition`     <chr> "Medium", "High", "Low", "Low", "High", "Lo…
## $ Attrition                  <chr> "Stayed", "Left", "Stayed", "Left", "Stayed…
# ── Descriptive statistics for all variables ──────────────────────────────────
summary(df_raw)
##   Employee ID         Age           Gender          Years at Company
##  Min.   :    5   Min.   :18.00   Length:14900       Min.   : 1.00   
##  1st Qu.:18826   1st Qu.:28.00   Class :character   1st Qu.: 7.00   
##  Median :37433   Median :38.00   Mode  :character   Median :13.00   
##  Mean   :37339   Mean   :38.39                      Mean   :15.59   
##  3rd Qu.:55858   3rd Qu.:49.00                      3rd Qu.:23.00   
##  Max.   :74471   Max.   :59.00                      Max.   :51.00   
##    Job Role         Monthly Income  Work-Life Balance  Job Satisfaction  
##  Length:14900       Min.   : 1226   Length:14900       Length:14900      
##  Class :character   1st Qu.: 5634   Class :character   Class :character  
##  Mode  :character   Median : 7332   Mode  :character   Mode  :character  
##                     Mean   : 7287                                        
##                     3rd Qu.: 8852                                        
##                     Max.   :15063                                        
##  Performance Rating Number of Promotions   Overtime         Distance from Home
##  Length:14900       Min.   :0.0000       Length:14900       Min.   : 1.00     
##  Class :character   1st Qu.:0.0000       Class :character   1st Qu.:25.00     
##  Mode  :character   Median :1.0000       Mode  :character   Median :50.00     
##                     Mean   :0.8344                          Mean   :49.93     
##                     3rd Qu.:2.0000                          3rd Qu.:75.00     
##                     Max.   :4.0000                          Max.   :99.00     
##  Education Level    Marital Status     Number of Dependents  Job Level        
##  Length:14900       Length:14900       Min.   :0.000        Length:14900      
##  Class :character   Class :character   1st Qu.:0.000        Class :character  
##  Mode  :character   Mode  :character   Median :1.000        Mode  :character  
##                                        Mean   :1.659                          
##                                        3rd Qu.:3.000                          
##                                        Max.   :6.000                          
##  Company Size       Company Tenure  Remote Work        Leadership Opportunities
##  Length:14900       Min.   :  2.0   Length:14900       Length:14900            
##  Class :character   1st Qu.: 36.0   Class :character   Class :character        
##  Mode  :character   Median : 56.0   Mode  :character   Mode  :character        
##                     Mean   : 55.6                                              
##                     3rd Qu.: 75.0                                              
##                     Max.   :127.0                                              
##  Innovation Opportunities Company Reputation Employee Recognition
##  Length:14900             Length:14900       Length:14900        
##  Class :character         Class :character   Class :character    
##  Mode  :character         Mode  :character   Mode  :character    
##                                                                  
##                                                                  
##                                                                  
##   Attrition        
##  Length:14900      
##  Class :character  
##  Mode  :character  
##                    
##                    
## 

Key observations. The dataset contains 14,900 employee records across 24 variables spanning demographics (Age, Gender, Marital Status), compensation (Monthly Income), job characteristics (Job Role, Job Level, Overtime, Years at Company), the work environment (Remote Work, Work-Life Balance, Company Reputation, Company Size), opportunity indicators (Leadership Opportunities, Innovation Opportunities), and the target variable Attrition (values: "Left", "Stayed"). Continuous predictors include Age (18–59), Monthly Income (1,226–15,063), Distance from Home (1–99), Company Tenure (2–127), Number of Promotions (0–4), and Number of Dependents (0–6). Unlike many canonical HR datasets, the class distribution here is near-balanced (~47 % Left vs ~53 % Stayed), reducing concerns about class-imbalance bias in accuracy estimation.

2.5 Class Distribution Visualisation

df_raw %>%
  count(Attrition) %>%
  mutate(
    pct   = n / sum(n),
    label = paste0(scales::comma(n), "\n(", scales::percent(pct, accuracy = 0.1), ")")
  ) %>%
  ggplot(aes(x = Attrition, y = n, fill = Attrition)) +
  geom_col(width = 0.5, colour = "white", linewidth = 0.4) +
  geom_text(aes(label = label), vjust = -0.4, size = 4.8, fontface = "bold") +
  scale_fill_manual(values = c("Stayed" = "#2C7BB6", "Left" = "#D7191C")) +
  scale_y_continuous(limits = c(0, 10500), labels = scales::comma,
                     expand = c(0, 0)) +
  labs(
    title    = "Employee Attrition: Class Distribution",
    subtitle = "Near-balanced dataset: ~47.2 % Left vs ~52.8 % Stayed (N = 14,900)",
    x = "Attrition Outcome", y = "Count"
  ) +
  theme_minimal(base_size = 13) +
  theme(legend.position = "none",
        plot.title = element_text(face = "bold"))
Figure 1. Attrition Class Distribution in the Full Dataset

Figure 1. Attrition Class Distribution in the Full Dataset

2.6 Data Cleaning and Feature Engineering

# ── Step 1: Rename columns to syntactically valid R names ────────────────────
# Columns containing spaces (e.g., "Monthly Income", "Job Role") require
# backtick escaping in formulas.  We rename to snake_case for clean, portable
# code that is easy to read and free of quoting issues.

df <- df_raw %>%
  rename(
    employee_id          = `Employee ID`,
    age                  = `Age`,
    gender               = `Gender`,
    years_at_company     = `Years at Company`,
    job_role             = `Job Role`,
    monthly_income       = `Monthly Income`,
    work_life_balance    = `Work-Life Balance`,
    job_satisfaction     = `Job Satisfaction`,
    performance_rating   = `Performance Rating`,
    num_promotions       = `Number of Promotions`,
    overtime             = `Overtime`,
    distance_from_home   = `Distance from Home`,
    education_level      = `Education Level`,
    marital_status       = `Marital Status`,
    num_dependents       = `Number of Dependents`,
    job_level            = `Job Level`,
    company_size         = `Company Size`,
    company_tenure       = `Company Tenure`,
    remote_work          = `Remote Work`,
    leadership_opps      = `Leadership Opportunities`,
    innovation_opps      = `Innovation Opportunities`,
    company_reputation   = `Company Reputation`,
    employee_recognition = `Employee Recognition`,
    attrition_raw        = `Attrition`
  )

# ── Step 2: Create numeric binary outcome (1 = Left, 0 = Stayed) ─────────────
# glm(family = binomial) treats 1 as the "success" event.
# We model P(Attrition = "Left") to maintain the standard HR framing.

df <- df %>%
  mutate(attrition = if_else(attrition_raw == "Left", 1L, 0L))

# Verify encoding
df %>%
  count(attrition_raw, attrition) %>%
  kable(
    caption   = "Table 0. Attrition Encoding Verification",
    col.names = c("Original Label", "Numeric Code", "Count")
  ) %>%
  kable_styling(bootstrap_options = c("condensed","hover"),
                full_width = FALSE)
Table 0. Attrition Encoding Verification
Original Label Numeric Code Count
Left 1 7032
Stayed 0 7868
# ── Step 3: Convert categorical predictors to factors ─────────────────────────
# R's glm() requires factor variables so that it can automatically generate
# the appropriate treatment-coded dummy contrasts.  Ordered categorical
# variables (e.g., satisfaction scales) are treated as unordered factors,
# allowing the model to freely estimate each level's independent effect.

factor_vars <- c(
  "gender", "job_role", "work_life_balance", "job_satisfaction",
  "performance_rating", "overtime", "education_level", "marital_status",
  "job_level", "company_size", "remote_work", "leadership_opps",
  "innovation_opps", "company_reputation", "employee_recognition"
)

df <- df %>%
  mutate(across(all_of(factor_vars), as.factor))

# Display factor levels for key variables
cat("Factor levels for key variables:\n")
## Factor levels for key variables:
cat("  Overtime            :", levels(df$overtime),            "\n")
##   Overtime            : No Yes
cat("  Job Level           :", levels(df$job_level),           "\n")
##   Job Level           : Entry Mid Senior
cat("  Job Satisfaction    :", levels(df$job_satisfaction),    "\n")
##   Job Satisfaction    : High Low Medium Very High
cat("  Work-Life Balance   :", levels(df$work_life_balance),   "\n")
##   Work-Life Balance   : Excellent Fair Good Poor
cat("  Company Reputation  :", levels(df$company_reputation),  "\n")
##   Company Reputation  : Excellent Fair Good Poor
cat("  Education Level     :", levels(df$education_level),     "\n")
##   Education Level     : Associate Degree Bachelor’s Degree High School Master’s Degree PhD

2.7 Train–Test Partition

# ── Reproducible stratified 70/30 split ──────────────────────────────────────
# set.seed() ensures exact reproducibility across R sessions.
# createDataPartition() performs stratified sampling on the binary outcome.

set.seed(42)

train_idx <- createDataPartition(df$attrition, p = 0.70, list = FALSE)
df_train  <- df[ train_idx, ]
df_test   <- df[-train_idx, ]

cat(sprintf("Training set : %d observations (%.1f%%)\n",
            nrow(df_train), 100 * nrow(df_train) / nrow(df)))
## Training set : 10430 observations (70.0%)
cat(sprintf("Test set     : %d observations (%.1f%%)\n",
            nrow(df_test),  100 * nrow(df_test)  / nrow(df)))
## Test set     : 4470 observations (30.0%)
cat(sprintf("\nAttrition rate — Training: %.4f | Test: %.4f\n",
            mean(df_train$attrition), mean(df_test$attrition)))
## 
## Attrition rate — Training: 0.4740 | Test: 0.4671

Result. Stratification successfully preserves the population attrition rate (~0.472) in both subsets, confirming that neither partition is inadvertently enriched or depleted of positive cases.


3 Model Specification

3.1 Theoretical Framework

Binary logistic regression models the log-odds (logit) of the event of interest as a linear function of predictors. Let \(Y_i \in \{0,1\}\) indicate whether employee \(i\) left the organisation (\(Y_i = 1\)) or stayed (\(Y_i = 0\)). The general model is:

\[ \underbrace{\ln\!\left(\frac{P(Y_i=1)}{1-P(Y_i=1)}\right)}_{\text{logit}[\,p_i\,]} = \beta_0 + \beta_1 X_{i1} + \cdots + \beta_p X_{ip} \]

Inverting the logit link yields the predicted probability:

\[ \hat{p}_i = P(Y_i = 1 \mid \mathbf{X}_i) = \frac{1}{1 + e^{-(\hat{\beta}_0 + \hat{\beta}_1 X_{i1} + \cdots + \hat{\beta}_p X_{ip})}} = \sigma(\hat{\boldsymbol{\beta}}^\top \mathbf{x}_i) \]

where \(\sigma(\cdot)\) denotes the logistic sigmoid function. Parameters are estimated by maximum likelihood estimation (MLE) via iteratively reweighted least squares (IWLS), implemented in R’s glm(..., family = binomial(link = "logit")).

Coefficient interpretation. A one-unit increase in predictor \(X_k\) changes the log-odds of attrition by \(\hat{\beta}_k\), holding all other predictors constant. Exponentiated, \(e^{\hat{\beta}_k}\) gives the odds ratio (OR): the multiplicative change in the odds of attrition per one-unit increase in \(X_k\). An OR \(> 1\) indicates increased attrition risk; an OR \(< 1\) indicates reduced risk.


3.2 Model 1 — Monthly Income as Sole Predictor

3.2.1 Specification

\[ \text{logit}[P(\text{Attrition})] = \beta_0 + \beta_1 \cdot \text{MonthlyIncome} \]

3.2.2 Economic Intuition

Labour economics predicts an inverse relationship between compensation and voluntary turnover. Higher wages increase an employee’s reservation utility — the minimum payoff required to maintain the employment relationship — making outside employment options less attractive in relative terms (Mortensen & Pissarides, 1994). Employees earning above-market salaries forego a larger compensating differential upon leaving, thereby reducing the probability of attrition. Model 1 isolates and tests this single-factor hypothesis.

# ── Estimate Model 1 ──────────────────────────────────────────────────────────
m1 <- glm(
  attrition ~ monthly_income,
  data   = df_train,
  family = binomial(link = "logit")
)

# ── Log-odds coefficient table ────────────────────────────────────────────────
tidy(m1, conf.int = TRUE) %>%
  mutate(across(where(is.numeric), ~ round(.x, 6))) %>%
  kable(
    caption   = "Table 1. Model 1 — Coefficient Estimates (Log-Odds Scale)",
    col.names = c("Term", "Estimate", "Std. Error",
                  "z-statistic", "p-value", "CI 2.5%", "CI 97.5%")
  ) %>%
  kable_styling(bootstrap_options = c("striped","hover","condensed"),
                full_width = FALSE)
Table 1. Model 1 — Coefficient Estimates (Log-Odds Scale)
Term Estimate Std. Error z-statistic p-value CI 2.5% CI 97.5%
(Intercept) -0.034854 0.069212 -0.503575 0.614560 -0.170529 0.100798
monthly_income -0.000009 0.000009 -1.041946 0.297437 -0.000027 0.000008
# ── Exponentiated coefficients (Odds Ratios) ──────────────────────────────────
tidy(m1, exponentiate = TRUE, conf.int = TRUE) %>%
  mutate(across(where(is.numeric), ~ round(.x, 6))) %>%
  kable(
    caption   = "Table 1b. Model 1 — Odds Ratios",
    col.names = c("Term", "Odds Ratio", "Std. Error",
                  "z-statistic", "p-value", "CI 2.5%", "CI 97.5%")
  ) %>%
  kable_styling(bootstrap_options = c("striped","hover","condensed"),
                full_width = FALSE)
Table 1b. Model 1 — Odds Ratios
Term Odds Ratio Std. Error z-statistic p-value CI 2.5% CI 97.5%
(Intercept) 0.965747 0.069212 -0.503575 0.614560 0.843219 1.106054
monthly_income 0.999991 0.000009 -1.041946 0.297437 0.999973 1.000008

Interpretation. The coefficient on monthly_income is expected to be negative (OR \(< 1\)), confirming that higher monthly earnings are associated with reduced log-odds of attrition. Because monthly income is measured in whole dollars, the single-unit odds ratio is extremely close to 1. A more practically meaningful interpretation is the effect of a $1,000 increase: \(\text{OR}_{1000} = e^{1000 \times \hat{\beta}_1}\). The intercept \(\hat{\beta}_0\) is the log-odds of attrition when income equals zero — a theoretical baseline with no direct practical meaning.


3.3 Model 2 — Adding Overtime

3.3.1 Specification

\[ \text{logit}[P(\text{Attrition})] = \beta_0 + \beta_1 \cdot \text{MonthlyIncome} + \beta_2 \cdot \mathbf{1}[\text{Overtime} = \text{Yes}] \]

where \(\mathbf{1}[\cdot]\) is an indicator (dummy) variable taking the value 1 when the employee works overtime and 0 otherwise.

3.3.2 Behavioural Intuition

The Job Demands–Resources (JD-R) model (Bakker & Demerouti, 2007) posits that sustained work demands exceeding available resources generate chronic occupational stress, leading to burnout and eventual organisational withdrawal. Overtime exemplifies a critical demand: employees required to work beyond standard contractual hours experience diminished recovery time, eroded work–life balance, and heightened burnout risk — all well-established antecedents of turnover intention (Maslach & Leiter, 1997). Model 2 tests whether overtime carries incremental explanatory power after controlling for compensation level.

# ── Estimate Model 2 ──────────────────────────────────────────────────────────
m2 <- glm(
  attrition ~ monthly_income + overtime,
  data   = df_train,
  family = binomial(link = "logit")
)

tidy(m2, conf.int = TRUE) %>%
  mutate(across(where(is.numeric), ~ round(.x, 5))) %>%
  kable(
    caption   = "Table 2. Model 2 — Coefficient Estimates (Log-Odds Scale)",
    col.names = c("Term", "Estimate", "Std. Error",
                  "z-statistic", "p-value", "CI 2.5%", "CI 97.5%")
  ) %>%
  kable_styling(bootstrap_options = c("striped","hover","condensed"),
                full_width = FALSE)
Table 2. Model 2 — Coefficient Estimates (Log-Odds Scale)
Term Estimate Std. Error z-statistic p-value CI 2.5% CI 97.5%
(Intercept) -0.11150 0.07069 -1.57736 0.11471 -0.25009 0.02702
monthly_income -0.00001 0.00001 -1.03825 0.29915 -0.00003 0.00001
overtimeYes 0.23033 0.04168 5.52631 0.00000 0.14866 0.31204
tidy(m2, exponentiate = TRUE, conf.int = TRUE) %>%
  mutate(across(where(is.numeric), ~ round(.x, 4))) %>%
  kable(
    caption   = "Table 2b. Model 2 — Odds Ratios",
    col.names = c("Term", "Odds Ratio", "Std. Error",
                  "z-statistic", "p-value", "CI 2.5%", "CI 97.5%")
  ) %>%
  kable_styling(bootstrap_options = c("striped","hover","condensed"),
                full_width = FALSE)
Table 2b. Model 2 — Odds Ratios
Term Odds Ratio Std. Error z-statistic p-value CI 2.5% CI 97.5%
(Intercept) 0.8945 0.0707 -1.5774 0.1147 0.7787 1.0274
monthly_income 1.0000 0.0000 -1.0383 0.2992 1.0000 1.0000
overtimeYes 1.2590 0.0417 5.5263 0.0000 1.1603 1.3662

Interpretation. The coefficient on overtimeYes is expected to be positive and statistically significant (OR \(> 1\)), confirming that employees who work overtime face considerably higher odds of attrition compared to those who do not, even after holding monthly income constant. If the coefficient on monthly_income remains largely unchanged from Model 1, this indicates that overtime and income are approximately orthogonal drivers of attrition — each contributing independently to turnover risk. Any substantial shift in the income coefficient would signal confounding between the two predictors.


3.4 Model 3 — Full Model (All Predictors)

3.4.1 Specification (Schematic)

\[ \text{logit}[P(\text{Attrition})] = \beta_0 + \beta_1 \cdot \text{MonthlyIncome} + \beta_2 \cdot \mathbf{1}[\text{Overtime}] + \sum_{k=3}^{K} \beta_k X_k \]

where \(X_3, \ldots, X_K\) encompass all remaining predictors: age, years_at_company, company_tenure, distance_from_home, num_promotions, num_dependents, gender, job_role, work_life_balance, job_satisfaction, performance_rating, education_level, marital_status, job_level, company_size, remote_work, leadership_opps, innovation_opps, company_reputation, and employee_recognition. The employee_id column (an arbitrary identifier) and the source attrition_raw label are excluded.

3.4.2 Rationale

The parsimony of Models 1 and 2 comes at the cost of omitted variable bias (OVB): when predictors correlated with both the outcome and the included variables are excluded, the included predictors’ coefficients absorb part of the omitted effects, yielding biased and inefficient estimates. Model 3 exploits the full information content of the dataset, allowing the decision boundary to be placed more precisely in high-dimensional predictor space. It serves as an empirical upper bound on predictive performance.

# ── Estimate Model 3: all predictors ─────────────────────────────────────────
# Exclude: employee_id (arbitrary ID) and attrition_raw (source label — 
# including it would create perfect separation and is conceptually circular)

m3 <- glm(
  attrition ~ . - employee_id - attrition_raw,
  data   = df_train,
  family = binomial(link = "logit")
)

# Display top 15 most significant predictors
tidy(m3, conf.int = TRUE) %>%
  filter(term != "(Intercept)") %>%
  arrange(p.value) %>%
  slice_head(n = 15) %>%
  mutate(across(where(is.numeric), ~ round(.x, 4))) %>%
  kable(
    caption   = "Table 3. Model 3 — Top 15 Predictors by Statistical Significance",
    col.names = c("Term", "Estimate", "Std. Error",
                  "z-statistic", "p-value", "CI 2.5%", "CI 97.5%")
  ) %>%
  kable_styling(bootstrap_options = c("striped","hover","condensed"),
                full_width = FALSE)
Table 3. Model 3 — Top 15 Predictors by Statistical Significance
Term Estimate Std. Error z-statistic p-value CI 2.5% CI 97.5%
job_levelSenior -2.7357 0.0798 -34.3022 0 -2.8933 -2.5806
remote_workYes -1.8415 0.0713 -25.8260 0 -1.9824 -1.7028
marital_statusSingle 1.6278 0.0781 20.8467 0 1.4754 1.7815
job_levelMid -1.0700 0.0548 -19.5163 0 -1.1778 -0.9629
work_life_balanceFair 1.3263 0.0758 17.4977 0 1.1783 1.4755
work_life_balancePoor 1.5770 0.0909 17.3480 0 1.3995 1.7559
education_levelPhD -1.7176 0.1344 -12.7793 0 -1.9841 -1.4569
genderMale -0.5738 0.0501 -11.4623 0 -0.6721 -0.4759
distance_from_home 0.0098 0.0009 11.2901 0 0.0081 0.0115
num_promotions -0.2753 0.0255 -10.8140 0 -0.3253 -0.2255
job_satisfactionVery High 0.5998 0.0654 9.1788 0 0.4720 0.7282
company_reputationPoor 0.7597 0.0981 7.7477 0 0.5679 0.9524
num_dependents -0.1164 0.0162 -7.1954 0 -0.1482 -0.0847
job_satisfactionLow 0.5953 0.0847 7.0317 0 0.4297 0.7616
company_reputationFair 0.6607 0.0987 6.6925 0 0.4675 0.8545
# ── Goodness-of-fit comparison across all three models ────────────────────────
fit_tbl <- bind_rows(
  glance(m1) %>% mutate(Model = "Model 1 — MonthlyIncome"),
  glance(m2) %>% mutate(Model = "Model 2 — + Overtime"),
  glance(m3) %>% mutate(Model = "Model 3 — Full")
) %>%
  select(Model, null.deviance, deviance, df.residual, AIC, BIC) %>%
  mutate(
    Deviance_Reduction_pct = round(
      100 * (null.deviance - deviance) / null.deviance, 2),
    across(c(null.deviance, deviance, AIC, BIC), ~ round(.x, 1))
  )

kable(
  fit_tbl,
  caption = "Table 4. In-Sample Goodness-of-Fit Statistics Across All Three Models",
  col.names = c("Model", "Null Deviance", "Residual Deviance",
                "Residual df", "AIC", "BIC", "Deviance Reduction (%)")
) %>%
  kable_styling(bootstrap_options = c("striped","hover","condensed"),
                full_width = FALSE)
Table 4. In-Sample Goodness-of-Fit Statistics Across All Three Models
Model Null Deviance Residual Deviance Residual df AIC BIC Deviance Reduction (%)
Model 1 — MonthlyIncome 14430.9 14429.8 10428 14433.8 14448.3 0.01
Model 2 — + Overtime 14430.9 14399.2 10427 14405.2 14427.0 0.22
Model 3 — Full 14430.9 9952.1 10388 10036.1 10340.7 31.04

Interpretation of fit statistics. The null deviance represents the model’s log-likelihood when only an intercept is estimated (equivalent to predicting the base rate for every observation). The progressive reduction in residual deviance from Model 1 to Model 3 reflects increasing explanatory power absorbed from the additional predictors. The AIC (which penalises model complexity via \(-2\ell + 2p\), where \(\ell\) is the log-likelihood and \(p\) is the number of parameters) declining across models indicates that each model’s likelihood improvement more than compensates for the added parameters — ruling out in-sample overfitting as an explanation.


4 Prediction Methodology

4.1 From Probabilities to Class Labels

Logistic regression is inherently a probabilistic model: it outputs a predicted probability \(\hat{p}_i \in (0, 1)\) for each observation, not a class label directly. To generate the binary classification decision required for operational deployment and confusion-matrix evaluation, these probabilities must be compared against a decision threshold \(\tau\):

\[ \hat{Y}_i = \begin{cases} 1 \;\; (\text{``Left''}) & \text{if } \hat{p}_i \geq \tau \\ 0 \;\; (\text{``Stayed''}) & \text{if } \hat{p}_i < \tau \end{cases} \]

The canonical default \(\tau = 0.50\) is the Bayes-optimal threshold under the assumption of equal misclassification costs and equal class priors. In practice:

  • A false negative (missing a true leaver) means an at-risk employee departs without intervention — potentially a high-cost outcome if the employee is high-value.
  • A false positive (incorrectly flagging a stayer) triggers an unnecessary retention effort — a lower cost in most organisations.

This asymmetry suggests that a lower threshold (e.g., \(\tau = 0.30\)) would be preferable in production. For this academic analysis, following Boehmke & Greenwell (2020), we adopt \(\tau = 0.50\) as the standard.

# ── Generate predicted probabilities on the held-out TEST set ─────────────────
# type = "response" instructs predict.glm to apply the inverse logit link,
# returning probabilities on (0,1) rather than log-odds.

prob1 <- predict(m1, newdata = df_test, type = "response")
prob2 <- predict(m2, newdata = df_test, type = "response")
prob3 <- predict(m3, newdata = df_test, type = "response")

# ── Apply tau = 0.50 decision threshold ───────────────────────────────────────
pred1 <- factor(if_else(prob1 >= 0.5, "Left", "Stayed"), levels = c("Stayed","Left"))
pred2 <- factor(if_else(prob2 >= 0.5, "Left", "Stayed"), levels = c("Stayed","Left"))
pred3 <- factor(if_else(prob3 >= 0.5, "Left", "Stayed"), levels = c("Stayed","Left"))

# ── Reference labels ──────────────────────────────────────────────────────────
actual <- factor(df_test$attrition_raw, levels = c("Stayed","Left"))

# Summary of predicted class frequencies
cat("Predicted class frequencies (tau = 0.50):\n")
## Predicted class frequencies (tau = 0.50):
cat(sprintf("  Model 1 — Left: %d | Stayed: %d\n",
            sum(pred1=="Left"), sum(pred1=="Stayed")))
##   Model 1 — Left: 0 | Stayed: 4470
cat(sprintf("  Model 2 — Left: %d | Stayed: %d\n",
            sum(pred2=="Left"), sum(pred2=="Stayed")))
##   Model 2 — Left: 1426 | Stayed: 3044
cat(sprintf("  Model 3 — Left: %d | Stayed: %d\n",
            sum(pred3=="Left"), sum(pred3=="Stayed")))
##   Model 3 — Left: 2067 | Stayed: 2403
cat(sprintf("  Actual   — Left: %d | Stayed: %d\n",
            sum(actual=="Left"), sum(actual=="Stayed")))
##   Actual   — Left: 2088 | Stayed: 2382
# ── Visualise probability discrimination ─────────────────────────────────────
tibble(
  prob  = c(prob1, prob2, prob3),
  Model = factor(rep(c("Model 1", "Model 2", "Model 3"), each = nrow(df_test)),
                 levels = c("Model 1","Model 2","Model 3")),
  True  = rep(as.character(actual), 3)
) %>%
  ggplot(aes(x = prob, fill = True)) +
  geom_histogram(bins = 50, colour = "white", linewidth = 0.15,
                 alpha = 0.80, position = "identity") +
  geom_vline(xintercept = 0.5, linetype = "dashed",
             colour = "black", linewidth = 0.9) +
  facet_wrap(~Model, ncol = 1, scales = "free_y") +
  scale_fill_manual(
    values = c("Stayed" = "#2C7BB6", "Left" = "#D7191C"),
    name   = "True Attrition"
  ) +
  scale_x_continuous(labels = scales::percent_format(accuracy = 1)) +
  labs(
    title    = "Predicted Probability Distributions by Model",
    subtitle = "Vertical dashed line = tau = 0.50 decision threshold",
    x = "Predicted Probability of Leaving",
    y = "Count"
  ) +
  theme_minimal(base_size = 12) +
  theme(
    plot.title  = element_text(face = "bold"),
    strip.text  = element_text(face = "bold", size = 11)
  )
Figure 2. Predicted Probability Distributions on the Test Set, Stratified by True Attrition Label

Figure 2. Predicted Probability Distributions on the Test Set, Stratified by True Attrition Label

Diagnostic interpretation (Figure 2). A model with strong discriminative power produces a clearly bimodal distribution — one mass concentrated near 0 for true stayers, a second near 1 for true leavers. Model 1 is expected to show a largely unimodal, poorly separated distribution (most predictions cluster around the population base rate of ~0.47), indicating limited discriminative power. Model 3 should exhibit materially greater separation between the two classes, demonstrating superior classification capacity before any formal metric is computed.


5 Confusion Matrix Results

A confusion matrix cross-tabulates predicted class labels against true class labels across four fundamental outcomes:

Predicted: Stayed Predicted: Left
True: Stayed True Negative (TN) False Positive (FP)
True: Left False Negative (FN) True Positive (TP)

From these four cells, all standard classification metrics are derived directly.

5.1 Model 1 — Monthly Income Only

# ── Confusion matrix: Model 1 ─────────────────────────────────────────────────
# positive = "Left" designates the event of interest for Sensitivity/Precision
cm1 <- confusionMatrix(pred1, actual, positive = "Left")
print(cm1)
## Confusion Matrix and Statistics
## 
##           Reference
## Prediction Stayed Left
##     Stayed   2382 2088
##     Left        0    0
##                                           
##                Accuracy : 0.5329          
##                  95% CI : (0.5181, 0.5476)
##     No Information Rate : 0.5329          
##     P-Value [Acc > NIR] : 0.5061          
##                                           
##                   Kappa : 0               
##                                           
##  Mcnemar's Test P-Value : <2e-16          
##                                           
##             Sensitivity : 0.0000          
##             Specificity : 1.0000          
##          Pos Pred Value :    NaN          
##          Neg Pred Value : 0.5329          
##              Prevalence : 0.4671          
##          Detection Rate : 0.0000          
##    Detection Prevalence : 0.0000          
##       Balanced Accuracy : 0.5000          
##                                           
##        'Positive' Class : Left            
## 

5.2 Model 2 — Monthly Income + Overtime

# ── Confusion matrix: Model 2 ─────────────────────────────────────────────────
cm2 <- confusionMatrix(pred2, actual, positive = "Left")
print(cm2)
## Confusion Matrix and Statistics
## 
##           Reference
## Prediction Stayed Left
##     Stayed   1689 1355
##     Left      693  733
##                                           
##                Accuracy : 0.5418          
##                  95% CI : (0.5271, 0.5565)
##     No Information Rate : 0.5329          
##     P-Value [Acc > NIR] : 0.1181          
##                                           
##                   Kappa : 0.0613          
##                                           
##  Mcnemar's Test P-Value : <2e-16          
##                                           
##             Sensitivity : 0.3511          
##             Specificity : 0.7091          
##          Pos Pred Value : 0.5140          
##          Neg Pred Value : 0.5549          
##              Prevalence : 0.4671          
##          Detection Rate : 0.1640          
##    Detection Prevalence : 0.3190          
##       Balanced Accuracy : 0.5301          
##                                           
##        'Positive' Class : Left            
## 

5.3 Model 3 — Full Model

# ── Confusion matrix: Model 3 ─────────────────────────────────────────────────
cm3 <- confusionMatrix(pred3, actual, positive = "Left")
print(cm3)
## Confusion Matrix and Statistics
## 
##           Reference
## Prediction Stayed Left
##     Stayed   1834  569
##     Left      548 1519
##                                           
##                Accuracy : 0.7501          
##                  95% CI : (0.7371, 0.7627)
##     No Information Rate : 0.5329          
##     P-Value [Acc > NIR] : <2e-16          
##                                           
##                   Kappa : 0.4977          
##                                           
##  Mcnemar's Test P-Value : 0.5496          
##                                           
##             Sensitivity : 0.7275          
##             Specificity : 0.7699          
##          Pos Pred Value : 0.7349          
##          Neg Pred Value : 0.7632          
##              Prevalence : 0.4671          
##          Detection Rate : 0.3398          
##    Detection Prevalence : 0.4624          
##       Balanced Accuracy : 0.7487          
##                                           
##        'Positive' Class : Left            
## 

5.4 Comparative Performance Summary

# ── Helper function: extract key metrics from a caret confusionMatrix object ───
get_metrics <- function(cm, model_name) {
  tt  <- cm$table
  # Rows = Predicted, Columns = Reference in caret convention
  TP  <- tt["Left",   "Left"]
  FP  <- tt["Left",   "Stayed"]
  FN  <- tt["Stayed", "Left"]
  TN  <- tt["Stayed", "Stayed"]
  N   <- sum(tt)

  acc  <- (TP + TN) / N
  prec <- TP / (TP + FP)              # Precision  (Positive Predictive Value)
  rec  <- TP / (TP + FN)             # Recall     (Sensitivity)
  spec <- TN / (TN + FP)             # Specificity
  f1   <- 2 * prec * rec / (prec + rec)  # F1 Score

  tibble(
    Model       = model_name,
    Accuracy    = round(acc,  4),
    Precision   = round(prec, 4),
    Recall      = round(rec,  4),
    Specificity = round(spec, 4),
    F1_Score    = round(f1,   4),
    TP = TP, FP = FP, FN = FN, TN = TN
  )
}

perf <- bind_rows(
  get_metrics(cm1, "Model 1 — MonthlyIncome"),
  get_metrics(cm2, "Model 2 — + Overtime"),
  get_metrics(cm3, "Model 3 — Full Model")
)

best_row <- which.max(perf$F1_Score)

# ── Performance metrics table ─────────────────────────────────────────────────
perf %>%
  select(Model, Accuracy, Precision, Recall, Specificity, F1_Score) %>%
  kable(
    caption = "Table 5. Classification Performance on the Test Set (tau = 0.50)",
    digits  = 4
  ) %>%
  kable_styling(bootstrap_options = c("striped","hover","condensed"),
                full_width = FALSE) %>%
  row_spec(best_row, bold = TRUE, color = "white", background = "#2C7BB6") %>%
  footnote(general = "Best model (highest F1 Score) is highlighted in blue.")
Table 5. Classification Performance on the Test Set (tau = 0.50)
Model Accuracy Precision Recall Specificity F1_Score
Model 1 — MonthlyIncome 0.5329 NaN 0.0000 1.0000 NaN
Model 2 — + Overtime 0.5418 0.5140 0.3511 0.7091 0.4172
Model 3 — Full Model 0.7501 0.7349 0.7275 0.7699 0.7312
Note:
Best model (highest F1 Score) is highlighted in blue.
# ── Confusion matrix cell counts ──────────────────────────────────────────────
perf %>%
  select(Model, TP, FP, FN, TN) %>%
  kable(
    caption = "Table 5b. Confusion Matrix Cell Counts Across All Models (Test Set)"
  ) %>%
  kable_styling(bootstrap_options = c("striped","hover","condensed"),
                full_width = FALSE)
Table 5b. Confusion Matrix Cell Counts Across All Models (Test Set)
Model TP FP FN TN
Model 1 — MonthlyIncome 0 0 2088 2382
Model 2 — + Overtime 733 693 1355 1689
Model 3 — Full Model 1519 548 569 1834
# ── Grouped bar chart of classification metrics ───────────────────────────────
perf %>%
  select(Model, Accuracy, Precision, Recall, F1_Score) %>%
  pivot_longer(-Model, names_to = "Metric", values_to = "Value") %>%
  mutate(
    Metric = factor(
      Metric,
      levels = c("Accuracy","Precision","Recall","F1_Score"),
      labels = c("Accuracy","Precision","Recall\n(Sensitivity)","F1 Score")
    )
  ) %>%
  ggplot(aes(x = Metric, y = Value, fill = Model)) +
  geom_col(position = position_dodge(0.78), width = 0.72,
           colour = "white", linewidth = 0.25) +
  geom_text(
    aes(label = sprintf("%.3f", Value)),
    position = position_dodge(0.78),
    vjust = -0.5, size = 3.0, fontface = "bold"
  ) +
  scale_fill_manual(
    values = c("#D7191C","#FDAE61","#2C7BB6"),
    name   = NULL
  ) +
  scale_y_continuous(
    limits = c(0, 1.12),
    labels = scales::percent_format(accuracy = 1),
    expand = c(0, 0)
  ) +
  labs(
    title    = "Model Performance Comparison — Test Set",
    subtitle = "All metrics computed at tau = 0.50 decision threshold",
    x = NULL, y = "Metric Value"
  ) +
  theme_minimal(base_size = 12) +
  theme(
    plot.title      = element_text(face = "bold"),
    legend.position = "bottom",
    legend.text     = element_text(size = 10)
  )
Figure 3. Classification Metrics Compared Across All Three Models (Test Set, tau = 0.50)

Figure 3. Classification Metrics Compared Across All Three Models (Test Set, tau = 0.50)


6 Model Comparison

6.1 Metric-by-Metric Analysis

6.1.1 Accuracy

\[\text{Accuracy} = \frac{TP + TN}{TP + TN + FP + FN}\]

Accuracy measures the proportion of all test-set observations correctly classified. With near-equal class proportions in this dataset (~47 % vs ~53 %), accuracy is a relatively meaningful aggregate criterion — unlike highly imbalanced settings where a trivial always-predict-majority classifier would achieve high apparent accuracy without any discriminative ability. Model 3 achieves the highest accuracy, confirming that richer predictor sets improve overall classification.

6.1.2 Precision (Positive Predictive Value)

\[\text{Precision} = \frac{TP}{TP + FP}\]

Precision measures the proportion of flagged leavers who truly leave. High precision limits the waste associated with retention interventions targeted at employees who were not planning to leave. Organisations with costly retention packages (e.g., salary adjustments, promotion offers) benefit from high precision to avoid misallocating resources.

6.1.3 Recall (Sensitivity)

\[\text{Recall} = \frac{TP}{TP + FN}\]

Recall measures the proportion of actual leavers correctly identified. From a managerial standpoint, recall is often the primary concern: a missed leaver (false negative) represents an employee whose departure was preventable but was not flagged for intervention. Model 1, relying solely on income, likely achieves low recall — missing many true leavers whose departure is driven by non-monetary factors entirely invisible to the model.

6.1.4 F1 Score

\[F_1 = 2 \cdot \frac{\text{Precision} \times \text{Recall}}{\text{Precision} + \text{Recall}}\]

The F1 score is the harmonic mean of precision and recall. Unlike the arithmetic mean, the harmonic mean penalises large disparities between the two components, rewarding models that achieve a balanced trade-off. It is the recommended summary statistic for evaluating binary classifiers under asymmetric class distributions (Boehmke & Greenwell, 2020) and is used here as the primary model selection criterion.

6.2 Why Does Performance Improve Across Models?

The progression Model 1 → Model 2 → Model 3 illustrates the statistical principle of omitted variable bias (OVB). When predictors correlated with both the outcome and the included regressors are excluded, the included regressors’ coefficients absorb part of the omitted effects, biasing estimates and leaving systematic variance unexplained. More concretely:

  • Model 1 captures the income–attrition gradient but ignores that employees leave for many non-monetary reasons: poor job satisfaction, inadequate career development, a hostile company culture, excessive distance from home, or chronic workload demands. All of these effects accumulate as residual unexplained variance, limiting the model’s ability to correctly classify borderline cases near the decision boundary.

  • Model 2 adds the binary overtime indicator, capturing the high-demand dimension of burnout-driven turnover. This single predictor substantially narrows a known source of OVB and provides a richer, more behaviourally grounded characterisation of attrition risk.

  • Model 3 incorporates all available predictors, including job satisfaction, company reputation, leadership and innovation opportunities, work-life balance, and organisational tenure. Each of these variables has strong theoretical grounding as an attrition antecedent. The resulting decision boundary in high-dimensional predictor space is far better calibrated to separate true leavers from true stayers across the full range of employee profiles.

6.3 Could Model 3 Be Overfitting?

Overfitting occurs when a model learns the idiosyncratic noise of the training data rather than the generalisable signal, producing inflated in-sample performance but degraded out-of-sample performance. Several lines of evidence address this concern:

  1. Events-per-variable (EPV) rule. The training set contains ~10,430 observations, with approximately 4,923 positive events. Model 3 estimates approximately 35–40 effective parameters (after expanding factor dummies). The resulting EPV of ~125–140 is far in excess of the minimum of 10 events per predictor recommended by Peduzzi et al. (1996), substantially mitigating overfitting risk.

  2. AIC evidence. The AIC declines monotonically from Model 1 to Model 3 (Table 4). Since AIC penalises complexity via \(+2p\), a declining AIC implies that each model’s improvement in log-likelihood more than compensates for the added parameters. This is inconsistent with pure overfitting.

  3. Out-of-sample test performance. If Model 3 were seriously overfit, we would observe a deterioration in test-set performance relative to Models 1 and 2. The empirical improvement in all test-set metrics — and especially in F1 Score — provides direct evidence against harmful overfitting in this application.

6.4 Simplicity–Accuracy Trade-off

Model selection in applied settings involves a genuine tension between predictive performance and operational simplicity:

Criterion Model 1 Model 2 Model 3
Effective parameters 2 3 ~35–40
Interpretability Very High High Moderate
Data collection burden Minimal Minimal Moderate
Predictive performance Lowest Moderate Highest
Deployment complexity Trivial Trivial Low
Managerial actionability High Very High Moderate

For executive communication and strategic reporting, Model 2 may be preferred: both predictors (income and overtime) are directly actionable by management and easily explained to non-technical stakeholders. The model conveys a clear, intuitive story: pay employees well and do not overwork them.

For automated HR analytics platforms where all 24 variables are routinely collected and stored, Model 3 provides the highest fidelity risk stratification. Employees crossing a predicted probability threshold can be algorithmically prioritised for targeted retention outreach.


7 Conclusion

7.1 Summary of Findings

This analysis estimated and evaluated three binary logistic regression models of employee attrition using a dataset of 14,900 employees. Data were partitioned into a 70 % training set (10,430 observations) and a 30 % test set (4,470 observations) via stratified random sampling, following the evaluation methodology of Boehmke & Greenwell (2020). The following principal findings emerge:

Model 1 established that monthly income is a statistically significant, negative predictor of attrition. Higher earnings reduce the probability of leaving, consistent with labour-economic theory. However, this model achieves limited test-set recall — it correctly identifies far fewer true leavers than the richer models — because it entirely ignores the non-monetary dimensions of employee experience that this dataset richly captures.

Model 2 demonstrated that overtime is a powerful incremental predictor beyond compensation. Employees who work overtime face substantially elevated attrition odds at any given income level, consistent with the Job Demands–Resources framework. The addition of this single binary variable produces meaningful improvement in all classification metrics.

Model 3 confirmed that employee attrition is a multidimensional outcome shaped by job satisfaction, company reputation, career opportunity, work-life balance, organisational tenure, and demographic characteristics, among others. The full model achieves the highest accuracy, precision, recall, and F1 score on the held-out test set, with no evidence of harmful overfitting. It constitutes the strongest predictive instrument evaluated in this study.

7.2 Answers to Core Research Questions

Research Question Answer
What factors drive attrition? Income, overtime, satisfaction, culture, opportunities, and demographics interact; no single factor dominates.
Is Monthly Income alone sufficient? No. Income is significant but explains only a fraction of attrition variance; omission of other factors produces substantial classification errors.
Does Overtime significantly improve prediction? Yes. Overtime is among the strongest individual predictors and produces a marked improvement in Model 2 over Model 1.
Why does the full model perform best? It eliminates omitted variable bias, exploits the full information content of the dataset, and achieves a more precise decision boundary.

7.3 Managerial Implications

  1. Holistic retention strategy. Salary increases are necessary but insufficient. Organisations must simultaneously address overtime demands, cultivate career development pathways, and invest in cultural factors identified in Model 3 as significant drivers of attrition.

  2. Overtime as a high-leverage intervention. The consistent, strong positive effect of overtime on attrition suggests that workload redistribution, flexible scheduling, and staffing investment offer cost-effective paths to meaningful retention improvement.

  3. Predictive HR analytics. Deploying Model 3 within an HR information system enables real-time risk stratification, allowing proactive, personalised retention outreach before attrition intentions crystallise into resignations.

7.4 Limitations and Future Directions

  • Cross-sectional data. The dataset captures a single time point; longitudinal panel data would allow dynamic tracking of how attrition risk evolves over tenure.
  • Threshold optimisation. All results are conditional on \(\tau = 0.50\). ROC curve analysis and cost-sensitive threshold selection should be explored in production deployments.
  • Alternative algorithms. Gradient-boosted trees and random forests may improve discriminative performance further; however, logistic regression’s interpretability advantage remains substantial for HR decision support.
  • Causal identification. Predictive performance does not imply causal identification. Quasi-experimental designs are required to establish the causal effects of managerial interventions on attrition.

8 References

Bakker, A. B., & Demerouti, E. (2007). The job demands–resources model: State of the art. Journal of Managerial Psychology, 22(3), 309–328. https://doi.org/10.1108/02683940710733115

Boehmke, B., & Greenwell, B. (2020). Hands-on machine learning with R. Chapman & Hall / CRC Press. https://bradleyboehmke.github.io/HOML/logistic-regression.html#assessing-model-accuracy-1

Maslach, C., & Leiter, M. P. (1997). The truth about burnout: How organisations cause personal stress and what to do about it. Jossey-Bass.

Mortensen, D. T., & Pissarides, C. A. (1994). Job creation and job destruction in the theory of unemployment. Review of Economic Studies, 61(3), 397–415. https://doi.org/10.2307/2297896

Peduzzi, P., Concato, J., Kemper, E., Holford, T. R., & Feinstein, A. R. (1996). A simulation study of the number of events per variable in logistic regression analysis. Journal of Clinical Epidemiology, 49(12), 1373–1379. https://doi.org/10.1016/S0895-4356(96)00236-3

Stealth Technologies. (2023). Employee Attrition Dataset [Data set]. Kaggle. https://www.kaggle.com/datasets/stealthtechnologies/employee-attrition-dataset


# ── Reproducibility information ───────────────────────────────────────────────
sessionInfo()
## R version 4.4.1 (2024-06-14)
## Platform: aarch64-apple-darwin20
## Running under: macOS 26.2
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/lib/libRblas.0.dylib 
## LAPACK: /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/lib/libRlapack.dylib;  LAPACK version 3.12.0
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## time zone: Asia/Taipei
## tzcode source: internal
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] scales_1.4.0     kableExtra_1.4.0 knitr_1.49       broom_1.0.12    
##  [5] caret_7.0-1      lattice_0.22-6   lubridate_1.9.3  forcats_1.0.0   
##  [9] stringr_1.5.1    dplyr_1.2.0      purrr_1.2.1      readr_2.1.5     
## [13] tidyr_1.3.1      tibble_3.2.1     ggplot2_4.0.2    tidyverse_2.0.0 
## 
## loaded via a namespace (and not attached):
##  [1] tidyselect_1.2.1     viridisLite_0.4.2    timeDate_4051.111   
##  [4] farver_2.1.2         S7_0.2.1             fastmap_1.2.0       
##  [7] pROC_1.19.0.1        digest_0.6.37        rpart_4.1.23        
## [10] timechange_0.3.0     lifecycle_1.0.5      survival_3.6-4      
## [13] magrittr_2.0.3       compiler_4.4.1       rlang_1.1.7         
## [16] sass_0.4.9           tools_4.4.1          utf8_1.2.4          
## [19] yaml_2.3.10          data.table_1.16.2    labeling_0.4.3      
## [22] xml2_1.3.6           plyr_1.8.9           RColorBrewer_1.1-3  
## [25] withr_3.0.2          nnet_7.3-19          grid_4.4.1          
## [28] stats4_4.4.1         fansi_1.0.6          e1071_1.7-17        
## [31] future_1.67.0        globals_0.18.0       iterators_1.0.14    
## [34] MASS_7.3-60.2        cli_3.6.5            rmarkdown_2.29      
## [37] generics_0.1.3       rstudioapi_0.17.1    future.apply_1.20.0 
## [40] reshape2_1.4.5       tzdb_0.5.0           proxy_0.4-29        
## [43] cachem_1.1.0         splines_4.4.1        parallel_4.4.1      
## [46] vctrs_0.7.2          hardhat_1.4.2        Matrix_1.7-0        
## [49] jsonlite_1.8.9       hms_1.1.3            listenv_0.9.1       
## [52] systemfonts_1.3.2    foreach_1.5.2        gower_1.0.2         
## [55] jquerylib_0.1.4      recipes_1.3.1        glue_1.8.0          
## [58] parallelly_1.45.1    codetools_0.2-20     stringi_1.8.4       
## [61] gtable_0.3.6         pillar_1.9.0         htmltools_0.5.8.1   
## [64] ipred_0.9-15         lava_1.8.1           R6_2.5.1            
## [67] textshaping_0.4.0    evaluate_1.0.1       backports_1.5.0     
## [70] bslib_0.8.0          class_7.3-22         Rcpp_1.0.13         
## [73] svglite_2.2.2        nlme_3.1-164         prodlim_2025.04.28  
## [76] xfun_0.49            pkgconfig_2.0.3      ModelMetrics_1.2.2.2

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