This report delves into the predictive analysis of firm growth, categorizing firms into 'fast-growing' and 'non-fast growing' using various statistical and machine learning techniques. The dataset comprises 121 variables across 57,085 observations, encompassing the financial and operational metrics of firms. Variables were categorized into distinct groups like raw financial variables, quality indicators, engineered features, and human resource-related factors. Additionally, dummy variables were generated for categorical features. Several models were developed and evaluated, primarily focusing on Logistic Regression, LASSO Regression, Random Forest, and Classification. Moreover, I decided to calculate EBTDA to identify fast-growing companies based on whether their 'ebtda_to_assets' values rank in the top 30% within their specific 'ind2_cat' and 'year' groups. • Logistic Regression and Logistic Regression with LASSO: • Models (M1 to M5) were built using different subsets of predictors. • Logistic Regression with cross-validation (LogisticRegressionCV) was used to optimize model parameters. • LASSO regression was applied for feature selection, exploring a range of lambda values. • Random Forest: • Parameters like max_features and min_samples_split were tuned using GridSearchCV. • The model's performance was evaluated using metrics like accuracy, AUC (Area Under Curve), and RMSE (Root Mean Square Error). • Among these models, the Random Forest classifier demonstrated superior performance with the highest AUC and lowest RMSE, indicating its effectiveness in balancing false positives and negatives and predicting firm growth accurately. In the results section of the predictive modelling analysis, a summary table has been created to compare the performance of different models, including Logistic Regression variants (M1 to M5), LASSO, and Random Forest. This summary focuses on the number of predictors used in each model, along with their Cross-Validation Root Mean Squared Error and Area Under Curve metrics. The Random Forest model ('randomforestprob'), utilizing 44 predictors, exhibits the most promising results with the lowest CV RMSE of 0.403 and the highest CV AUC of 0.788. This indicates a strong predictive accuracy and the model's ability to distinguish between the different classes effectively. In contrast, the Logistic Regression models (M1 to M5) show varying levels of performance. Model M1, with the fewest predictors (9), has a CV RMSE of 0.456 and a CV AUC of 0.621, while Model M4, using a considerably higher number of predictors (74), achieves a CV RMSE of 0.420 and a CV AUC of 0.743. Notably, the LASSO model, with 129 predictors, balances complexity and performance effectively, evidenced by a CV RMSE of 0.415 and a CV AUC of 0.758. These results suggest that the Random Forest model outperforms the Logistic Regression variants in this analysis, achieving higher predictive accuracy with a relatively moderate number of predictors. The LASSO model also demonstrates significant effectiveness, providing a good balance between the number of predictors used and the model's predictive power.
The effectiveness of the models was further dissected by analyzing the confusion matrix, which provided insights into the true positives, true negatives, false positives, and false negatives. This analysis was pivotal in understanding the practical implications of model predictions, especially in weighing the costs associated with incorrect predictions. The dataset was segmented into manufacturing and service firms to understand sector-specific dynamics. Distinct Random Forest models were developed for each sector. Key findings include: • Manufacturing firms had a distinct pattern in terms of the significance of predictors and performance indicators in the model. The sector-specific model offered valuable insights into the unique characteristics that drive rapid growth in the manufacturing industry, which differ from those affecting the service sector. • Service firms have a model that identifies various major predictors of growth. The service sector model exhibited distinct variations in performance compared to the manufacturing model, as indicated by the differences in RMSE and AUC. This highlights the importance of doing a sector-specific study while engaging in predictive modelling. The division into two distinct parts offered a valuable understanding of the contrasting behaviours of these industries and emphasized the significance of customized models for accurate prediction analysis.
The analysis code incorporates a loss function to assess several forecasting models for the expansion of a company. The main objective of this function is to measure the financial consequences of prediction errors, specifically differentiating between the expenses related to false positives (FP) and false negatives (FN). The cost of false positives (FP) is fixed at $100,000, whereas the cost of false negatives (FN) is $60,000. The relative cost ratio, which is essential for the loss function, is determined by dividing the cost of false negatives (FN) by the cost of false positives (FP). An important component of this approach involves determining the frequency of positive cases within the training data (y_train). The prevalence rate plays a crucial role in calculating the anticipated loss during the model evaluation phase. The models, such as logistic regression models and a Random Forest classifier, undergo a K- Fold cross-validation process with 5 splits. This approach guarantees a resilient evaluation of the models' performance. During the process of cross-validation, the model makes predictions for each fold, and these predictions are then utilized to build Receiver Operating Characteristic (ROC) curves. The curves display the rates of false positives (FPR), true positives (TPR), and a variety of thresholds. A threshold that maximizes the trade-off between true positive rate (TPR) and false positive rate (FPR) is determined for each fold, taking into account the cost of false negatives and the prevalence rate. The anticipated loss for each fold is computed by taking into account the amount of false positives and false negatives at the optimal threshold, adjusting them based on their respective costs, and normalizing them by the number of observations in the fold. This calculation yields a distinct financial consequence of the forecast inaccuracies. The procedure calculates the mean of the best thresholds and projected losses for each model across all the folds, enabling a thorough assessment. More precisely, the study provides information about the threshold and anticipated loss for the fifth fold, giving ian n- depth understanding of how well the model performs on a specific portion of the data. In the last phase of this study, the most effective model, chosen based on the average anticipated loss, is utilized on a separate dataset. The Random Forest model is determined to be the optimal model in this scenario. The model is trained using the entire training dataset and subsequently employed to make predictions on the holdout data. The cross-validation results in an ideal threshold, which is then used to classify the observations based on the predictions. A confusion matrix is created based on these predictions, classifying them as true positives, true negatives, false positives, and false negatives. Subsequently, the matrix is transformed into percentage values, offering a clearer perspective on the model's ability to effectively categorize each category. To summarize, this strategy that relies on a loss function emphasizes the significance of financial consequences in predictimodellinging. It helps in choosing models that strike a balance between accuracy and economic feasibility. This method offers a more comprehensive comprehension of the efficacy of the models, surpassing traditional accuracy metrics by evaluating the monetary consequences of forecast errors.
Task 2 involves the application of predictmodellingling to distinguish and analyze manufacturing and service organizations. The dataset is classified into manufacturing and service sectors according to industry codes ('ind2'). Manufacturing businesses are categorized based on industry codes (27, 29, 28, 26, 30), and a binary variable ('manufacturing_dummy') is generated to indicate their presence. The dataset is subsequently divided into two subsets: data_manu for manufacturing companies and data_serv for service companies. An examination of these subcategories unveils diverse growth patterns: roughly 8% of manufacturing companies and 11% of service companies are categorized as 'rapid growth'. Random Forest classifiers are utilized to construct prediction models for both domains. The models are customized using variables that are relevant to each industry, such as elements relating to finance and human resources. The data for each sector is partitioned into training and holdout sets, preserving an 80-20 ratio. The Random Forest models for each sector are optimized using GridSearchCV, with a specific emphasis on tuning parameters such as 'max_features' and 'min_samples_split'. The performance of each parameter combination is assessed using accuracy, ROC AUC, and RMSE metrics. The outcomes of this optimization process are condensed, presenting the performance metrics for each set of parameters. The optimal parameters determined are utilized to train the RandomForestClassifier for every sector. The models are assessed using cross-validation, wherein a loss function is employed to compute the anticipated loss and optimal classification threshold. This takes into account the costs associated with false positives and false negatives, as well as the prevalence of positive cases in the training data. In the industrial industry, the Random Forest model, referred to as 'randomforestprob', exhibits the following performance metrics: a CV RMSE (Cross-Validation Root Mean Squared Error) of 0.427, a CV AUC (Cross-Validation Area Under the Curve) of 0.69, and an average optimal threshold of 0.699. The anticipated loss for Fold 5 in this model is 15.059. In the service sector, the 'randomforestprob' model produces a cross-validated root mean squared error (CV RMSE) of 0.403, a cross-validated area under the curve (CV AUC) of 0.785, and an average optimal threshold of 0.563. The anticipated loss for Fold 5 is significantly reduced to 0.278. Subsequently, the remaining data for each sector is utilized to conduct a more comprehensive evaluation of the model's effectiveness. The Random Forest model applied to manufacturing enterprises has an RMSE (Root Mean Square Error) of 0.441, an AUC (Area Under the Curve) of 0.68, and an expected loss of 14.882 when evaluated on the holdout data. The holdout data for service firms yields an RMSE of 0.403, an AUC of 0.792, and a little greater anticipated loss of 0.291. Ultimately, confusion matrices are produced for every sector, providing a breakdown of the proportions of accurate positive predictions, accurate negative predictions, inaccurate positive predictions, and inaccurate negative predictions. These matrices offer a comprehensive perspective on the model's predicted precision in categorizing companies into 'rapid growth' and 'not fast growth' groups within each industry. To summarize, this investigation provides a thorough perspective on the unique patterns of growth in the manufacturing and service sectors utilizing Random Forest models. The performance indicators of the models, such as RMSE, AUC, and anticipated loss, offer vital insights into their ability to accurately predict and classify organizations according to their growth patterns, as well as their financial ramifications.
The analysis effectively utilized a range of statistical andmachine-learningg techniques to forecast the expansion of the company. The Random Forest model proved to be the most efficient, demonstrating exceptional performance in both the industrial and service industries. This study emphasizes the needto dog sector-specific analysis in predictive momodellingnd provides a strong framework for future analyses in related fields. Additional investigation could focus on enhancing the predicted