3.1. Dataset

To fulfill the empirical target of this study, our study is based on 234 firm-year data of 98 randomly selected non-financial companies listed in Borsa Istanbul (BIST) for the period 2017–2021. These companies are selected because they have been traded on BIST for many years. Of the 234 companies in the sample, 99 are GCO and 135 are non-GCO companies. As in previous studies in this area, we exclude financial institutions due to special accounting rules [33]. Table 2 shows the sectoral classification of the sampled groups according to Economic Activities. The dataset includes 19 industrial categories in Turkey from 2017 to 2021.

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Table 2. Classifying the sample according to Economic Activity.

https://doi.org/10.1371/journal.pone.0345071.t002

The dataset of our study is based on financial (liquidity, solvency, turnover, and profitability) and non-financial (firm size and type of audit firm) 23 variables that are frequently used in previous studies on GCO estimation. The description of these variables used as estimators of the research model is presented in Table 3.

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Table 3. The research model predictors.

https://doi.org/10.1371/journal.pone.0345071.t003

3.2. Benchmarking models

3.2.1. Classification and regression tree (CART).

The CART algorithm is an algorithm based on decision trees that can be utilised for both classification and regression problems [34]. CART aims to simplify decision structures in complex data sets. The algorithm divides heterogeneous data sets into homogeneous subgroups based on a specified target variable. It recursively divides the training data into smaller subsets

using binary splits. The partitioning of data into two subsets, then repeat the process to determine the next condition of partitioning in each subset.

The CART methodology consists of three steps: (1) constructing the maximum tree; (2) selecting the optimal tree size; and (3) classifying or generating new data based on the constructed tree.

The derivation of decision rules is one of the key aspects of building CARTs. In this context, decision rules are determined using Gini rules. Gini (G) can be calculated, as expressed in Equation (1).

(1)

where n represents the number of classes, the probability of a randomly chosen element in the node being labeled as class i is p_i.

The Gini index can be calculated using the following equation when data D are classified into D₁ and D₂ by a given variable , on the basis of a given characteristic f:

(2)

3.2.2. Random forest (RF).

The RF algorithm is suggested by [35]. Random Forest (RF) allows building different models and creating classifications by training each decision tree on a different sample of observations using multiple decision trees. After several trees have been constructed, the best attributes are selected using the random subset of attributes [36]. RF is flexible and easy to use, as it can be applied to both classification and regression problems. The steps are as follows.

1. - The bagging sampling method is used to generate K training sets from the original training set M, with each set containing N samples.
2. - Train K training sets to generate K CART decision tree models
3. - For the features of a single decision tree model, the optimal split attribute of the current node is selected based on the GINI index to generate branch nodes, resulting in the creation of a single decision tree.
4. - A random forest was formed from the K decision trees generated.

In Equation (1) class and the probability identify the Gini of each of the branches at a node to decide which of the branches is more likely to be seen. Entropy governs the branching of nodes in a decision tree. Entropy is calculated by using the following function in Equation (3).

(3)

where denotes the relative frequency of the class being considered in the dataset, and n denotes the number of classes. The probability of an outcome is used to determine how the node should be branched using entropy.

3.2.3. K-nearest neighbors (KNN).

The k-nearest neighbour classifier is based on the distance metric. Minkowski and Euclidean distance metric to determine label similarity, which is the most widely used and most efficient metric for this purpose. The k-nearest neighbour (kNN) algorithm aims to identify the k-nearest neighbours of the query from the dataset and allocate a class label to the neighbourhood by label to the neighbourhood using the majority decision rule.

Suppose that in a D-dimensional space Dataset S = represents a training set with N instances from T classes. The variable denotes the class label for . [37]. The distance between the query point and the other data points must be calculated to identify which data points are closest to a given query point. Distance metrics are used to create decision boundaries that divide query points into different regions. The Euclidean distances between the given query x and each of the training instances in S are computed as follows:

(4)

Deciding can be expressed as follows:

(5)

The decision rule according to Equation (5) is: if then x on D-dimensional space for i = 1,2,..,T (probability distributions) . Order the training dataset pairs of (x), (x), …., (x)

3.2.4. Gradient-Boosting classifier (GBM).

[38] presented the gradient boosting model, which is an ensemble model of machine learning. To improve the accuracy and robustness of the final model, the model combines several weak learners. The gradient boosting model begins by creating a single leaf and constructing regression trees. Assuming that Dataset D = , the objective of gradient boosting is to obtain an approximation. A regression tree is built using an iterative process of splitting data into nodes or branches, creating smaller groups. At the beginning, all instances are placed in the same group. The data is divided into two sub-sets by testing every available predictor for every possible split [39]. The predictor aims to minimize the residual error of a given loss function and the next predictor goes on to create more trees using this method until it is no longer possible to improve the desired threshold or fit.

The Loss Function (L) and the Gradient Boosting Approximation Function (G) are referred to and , respectively.

Initally, a constant approximation of is determined as:

(6)

The initial prediction is typically chosen to average all target labels y. This initial prediction indicates best estimate without any feature input (X) [40]. Minimize the residual error of the given loss function:

(7)

Where t is the estimator count, with loss function calculate the difference between and .

In Equation (8). Fit a regression tree:

(8)(9)

where n represents the learning rate, a value between 0 and 1 that determines the weight of each weak model. In Equation (8), a regression tree is fitted to the current residuals in order to update the model.

3.2.5. Support vector machine.

The Support Vector Machine (SVM) is a type of neural network model that can determine the optimal solution and reduce model complexity while maintaining learning performance [41]. The Support Vector Machine (SVM) was initially developed for binary classification. However, it can also be applied to multi-class classification problems by combining multiple binary classifiers [42]. Support Vector Machines (SVM) offer important advantages in processing high, small samples and non-linear data, and exhibit high robustness and generalisation performance in solving regression and classification problems [43]. Assuming that in a D-dimensional space and let assume that there is a classification problem Dataset D = , where is input and is output and ∈ {,…,}. The objective function has been modified to enable multiclass classification to be performed simultaneously and is given by:

(10)

under these conditions.

and

where ∈ {,…,} and ∈ {,…,}/

3.2.6. Multilayer perceptron (MLP).

MLP is one of the most widely used feed-forward back-propagation artificial neural networks. The MLP is made up of a minimum of three node layers. The Input layer, Hidden layer, and Output layer (Fig 2). Neurons are the basic units that compose each layer. A neuron consists of a sum function and an activation function. Fig 2 (a) illustrates the function τ(x) and the operational principle of the neuron with confidence. Input layer variables are multiplied by their corresponding weight coefficients and then accumulated by the sum junction. The output value can be obtained from the combined summation and bias of the summation and bias using the activation function. The neuron’s operating principle can be defined through the following Equation (11) [28].

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Fig 2. Multilayer Perceptron Diagram.

https://doi.org/10.1371/journal.pone.0345071.g002

(11)

where order of the neuron is denoted by ‘i’ and order of layer presents by ‘k’. Hence, the value at the ith neuron in the kth layer is expressed by the term . The weight at the ith neuron in the kth layer is given by the term .

(12)

Fig. 2 (b) extends this concept to a multilayer network in which an input layer transmits information to two hidden layers through fully connected weighted links. Each hidden layer consists of several neurons that apply non-linear transformations to learn intermediate feature representations. The final output layer generates prediction values based on the learned representations. The arrows in the figure indicate the direction of forward information flow, while the presence of bias units ensures the model has the flexibility to shift activation thresholds. Together, these components enable the MLP to learn complex, non-linear relationships within the financial dataset used in this study.

3.2.7. Adaptive boosting (AdaBoost).

Adaptive boosting (AdaBoost) is an ensemble ML algorithm developed by [44]. It is used for the solution of problems in classification and regression. Recently, the AdaBoost model has gained popularity in various fields [45–47]. AdaBoost merges multiple weak classifiers iteratively to generate a unique strong classifier. The extent to which a weak classifier is inaccurately trained is determined by the weight assigned to each training sample [48,49]. Fig. 3 shows that ensemble learning is based on several weak classifiers by changing the sample weights of the dataset several times throughout the learning process. Dataset D = , where is input and is output vectors, N represents the number of samples. Each classifier(N) contributes to the final decision via a weighted combination, where represent non-negative scalar weights associated with each classifier. The weights indicate the relative importance or the predictive confidence of each model within the ensemble, and these may be determined based on such metrics as validation accuracy, optimization criteria or algorithm-specific learning dynamics. The final prediction is computed as a weighted aggregation of all classifier outputs, allowing the ensemble to leverage model diversity and reduce variance, bias, or overfitting effects that may arise from individual classifiers.

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Fig 3. Adaptive boosting diagram.

https://doi.org/10.1371/journal.pone.0345071.g003

First, weights are assigned to data points, and initially, all weights are equal. Where N is the total number of data points in the data set. The first weak classifier, model 1, is obtained after appropriate training. According to the classification result of the previous weak classifier, the sample weights are adjusted.

A decision node is created for each of the features and then the Gini index of each tree is computed. The tree with the lowest Gini index is the first node as expressed in Equation (1).

The weak learner l_i builds from the training dataset using w, which minimizes the weighted error. The weight represents the confidence () of the jth model.

Weak classifiers can be replaced with stronger ones, thanks to AdaBoost.

(14)(15)(16)(17)

3.2.8. XGBOOST.

XGBoost is an improved ML algorithm that extends the gradient-boosting decision tree algorithm. It is proficient in building boosted trees highly and is used to facilitate parallel computing. XGBoost is initially proposed by [50]. The algorithm’s key features are that it achieves high predictive power, prevents overfitting, quickly manages empty data, and effectively handles datasets with missing values. According to [50], XGBoost operates ten times faster than other popular algorithms. The main goal of XGBoost is to increase prediction accuracy by utilising the learning from previous weak learners and implementation of new weak learners, specifically designed to address and correct the remaining errors [51]. The purpose of the XGBoost algorithm is the optimisation of the target’s function.

(18)

where represents the loss function that calculates the difference between the true value and the predicted value and n represents the dimension of the feature vector. The symbol represents the regularization term that is added to the target function. The target function is to handle the complexity of the model and avoid overfitting. is the function of the jth tree. is written with the Equation (18). as follows.

(19)

is the normalisation term used to describe the complexity of the tree structure.

(20)

where T is the number of leaf nodes in the tree, determines the minimum descent value of the loss function required for node splitting, and represents the L2 regularisation term performed on the weights.

3.3. K-fold Cross-validation

In the use of ML for practical applications, over-fitting is a common problem issue. The issue of overfitting can be addressed through the use of cross-validation [52]. The model weights for the averaging prediction were determined using the fold cross-validation criterion. The model weights were chosen by minimising the sum of the squares of the prediction errors from all groups [53]. The k-fold cross-validation involves dividing the sample into equally sized K subsets and using each group as a validation sample to assess the model’s performance. Of this subset, K-1 is used to train the models and the rest is used to test them. When each unique subset has been validated once, the operation is repeated k times [15]. It is possible to get the accuracy of the K models, and the performance of the K-CV classifier model is assessed according to the average accuracy of the K models. The overall evaluation metrics of the models are computed k times, from which different ML metrics (Accuracy Score, Sensivity, Precision, F1-Score) can be calculated. Fig. 4. shows the k-fold cross-validation diagram.

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Fig 4. K-fold cross validation diagram.

https://doi.org/10.1371/journal.pone.0345071.g004

The most frequent settings of K are 5 and 10, and this corresponds to perform a leave-one-out cross-validation when K = n [53]. In this study, k is set at 10, as this is thought of as giving an unbiased estimation of the error rate of the test [54].

3.4. Hyper Tuning parameters

Hyper-parameters tuning is a significant process to determine the optimal machine learning parameters. Determining the best hyperparameters is a laborious process and takes a long time, especially when the objective functions are difficult to ascertain, or a substantial number of parameters are required to be tuned. In this study, RandomizedSearchCV is utilized for optimizing the hyperparameters that explore enabling efficiently the search space via stochastic sampling combined with k-fold cross-validation. In the Table 1A, determining the best hyperparameters were demonstrated in appendix section.

3.5. Designing hybrid systems

The initial settings are very important for the results of the ML model. The optimisation algorithms are employed to adjust the ML parameters. In our hybrid approach RF, XGB, GBM, MPL, KNN, and SVM are utilized for predicting GCO. The Adaptive Boosting (Ada), Gradient.

Boosting Machine (GBM), Random Forrest (RF), Classification and Regression Trees (CART) were used to train the RF, XGB, GBM, MPL, KNN, SVM models. Hence, a total of 24 hybrid systems were generated. Fig 5 displays the details of the hybrid system network. As illustrated in Fig 5, the hybrid model construction process that was utilised in the present study is depicted. Initially, six classical machine learning models (i.e., RF, GBM, XGB, MLP, KNN, and SVM) are trained as base learners, as illustrated at the centre of the diagram. Subsequently, each base learner is combined with one of four ensemble strategies—AdaBoost (yellow), GBM (blue), RF (red), or CART (cyan)—to generate hybrid variants. The colour-coded blocks represent the feature-selection or boosting component applied to each base model, resulting in 24 hybrid configurations in addition to the six original base models.

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Fig 5. Hybrid model diagram.

https://doi.org/10.1371/journal.pone.0345071.g005

4.1. Evaluation metrics

To evaluate the study’s performance, we constructed a confusion matrix consisting of true positives (tp), false positives (fp), true negatives (tn), and false negatives (fn). The most commonly used metric for performance assessment is the accuracy score. In this study, our model performs binary class classification, so the assessment metrics consider two classes, and the equation is as follows:

(21)

(22)

(23)

(24)

4.2. Comparison between classical and hybrid models

This phase describes the details of the hybrid and classical ML models used in this study. As mentioned, we are dealing with a binary classification problem, using a set of predictor features as inputs. The hybrid and classical models aim to categorise the firms in the dataset as GCO or non-GCO. The results of the classical benchmark models are evaluated using all 23 variables. The evaluation of model performance using acc_score will not be complicated since there is no imbalance in the dataset. As shown in Table 4, balanced data distribution prevented distortion of evaluation metrics such as accuracy and F1-score, allowing the hybrid models’ gains to be attributed to algorithmic structure rather than class imbalance correction.The performance of six classical machine learning models was assessed by looking at Table 4, which denotes the performance values measured on test data using 10-fold cross-validation. The Table 4 shows that RF provides the most accurate predictions and the lowest accuracy score was received by SVM among classical ML models.

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Table 4. Performance evaluation of basic classical models (%).

https://doi.org/10.1371/journal.pone.0345071.t004

The primary objective of his study is to develop appropriate hybrid systems. Table 5 presents the parameters adopted by the models to create hybrid systems. This study uses RF, AdaBoost, GBM, and CART, as models to choose important variables, remove noise, and boost model accuracy. Table 5 reveals that the model suggesting the most variables is RF and the model suggesting the fewest variables is GBM.

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Table 5. The list of variables selected by models.

https://doi.org/10.1371/journal.pone.0345071.t005

In this section, the success of the models with the inputs provided by the ML is evaluated. Thus, It has been determined which hybrid model is the best. Fig 6 displays the feature selection models that are combined with the base classical models. The merging of the AdaBoost models with the basic models is indicated by the red dots, blue dots denote where None-feature seleciton has merged with the base, CART that has merged with the base models is indicated by purple dots, grey dots indicate RF base models, and yellow dots indicate GBM which have merged with the base models in Fig 6. Fig 6 demonstrates that the first five hybrid models achieved higher accuracy scores than the base model, which had the highest accuracy score among the basic models. Again, Fig 6 shows that the last five hybrid models get lower accuracy scores than the base model, which had the lowest accuracy score among the basic models. The choice of a hybrid model does not always lead to better results. As illustrated in Table A1 (in the appendix) and Fig 6., certain traditional models such as XGB and RF achieved higher accuracy than some hybrid variants (e.g., SVM-Ada, SVM-GBM). These experimental results illustrate that performance improvements are not guaranteed as a result of hybridisation. This aligns with prior research reporting that hybrid models may introduce redundancy or overfitting when model components are poorly matched [2,4]. While hybrid models are regularly developed to improve predictive precision, prior research and our trial outcomes (see Table A1 and Fig 6) show that their superiority is dependent on the circumstances.

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Fig 6. Performance evaluation of all models.

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Examining the initial five models that generate the most accurate prediction accuracy score in Fig 6, we observe that the feature selection algorithms used include ADA and CART. It was noted that six variables were used by CART and seven by RF. The hybrid model FR-SVM, which received the lowest prediction score among the hybrid models, made predictions using four variables.

Fig 7 shows the effect of the most effective parameters on hybrid systems after they have been determined using ML models. Looking at Fig 7, it is obvious that without features selection the results are highly volatile. It is clear that the features that are selected by the cart model are the more stable ones. The predictive ability of the basic models is similar when using features, as adopted by the cart model. The use of AdaBoost in hybrid models can result in extreme prediction values, as illustrated by the points in Fig 7. Fig 7 shows the variability of accuracy scores across feature selection strategies used in the hybrid benchmark models. Error bars shown in box plots represent the distribution of model accuracies from repeated cross-validation folds. Wider error bars indicate higher variability and hence less stable performance across folds, on the otherhand narrower error bars reflect more consistent prediction behavior. As seen in the AdaBoost-based hybrids, the error bars are significantly wider, indicating that the features selected by AdaBoost exhibit higher volatility, causing accuracy values to fluctuate more significantly across folds. This instability suggests that AdaBoost-driven feature weighting is sensitive to sampling differences, conducting to less generalizable results. Conversely, the use of CART-based feature selection shows much more precise error bars, pointing out that CART produces more consistent and reproducible feature subsets. The RF and GBM feature selectors fall between these two extremes. While both provide occasional peaks of high accuracy, their wider interquartile ranges indicate that performance can vary significantly depending on the training layer. The error bar patterns demonstrated in Fig 7 show that CART generated hybrid configurations with the highest consistency. On the otherhand, AdaBoost, while occasionally producing fairly accurate results, tends to introduce more variance.

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Fig 7. Effect of feature selection on accuracy score among benchmark models.

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One of the most important metrics is recall (sensitivity), which explains how many of the predictions we made were positive. In cases where the cost of a false negative is high, the sensitivity score is also a metric that will assist us. It should be as high as it can be. In this study, the information generated for the auditor’s report. If the model marks an accepted GCO as non-GCO, the consequences of a situation pose a problem for a company. Hybrid models, which are Ada-RF, CART-XGB, None-RF, and Ada-GBM, have 94.00%, 92.94%, 91.94%, and 91.94% the highest predicted precision scores, respectively. None-KNN got the lowest recall value, 68.33%.

Fig 8 and 9 show the net performance patterns across the 30 benchmarks and the hybrid model configuration. The reviewer expressed concern about false negatives, which lead to significant audit costs. The emphasis is on recall and F1-score metrics. Accuracy is less important. These figures show that models with good recall performance also tend to have high F1-scores, making them better suited for continuous business forecasting. The main aim of continuous business forecasting is to prevent financially distressed companies from being incorrectly classified as healthy.

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Fig 8. Recall comparasion of benchmark and hybrid machine learning models.

https://doi.org/10.1371/journal.pone.0345071.g008

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Fig 9. F1-score comparasion of benchmark and hybrid machine learning models.

https://doi.org/10.1371/journal.pone.0345071.g009

In both models, the top rankings for recall and F1-score are consistently held by AdaBoost-based hybrid models (e.g., Ada–RF, Ada–GBM, Ada–XGB).These models outperform most of the baseline non-hybrid models, achieving recall values above 0.93 and F1-scores above 0.92. This model reflects AdaBoost’s ability to iteratively reweight misclassified observations, which appears particularly advantageous for capturing early signals of distress. Because distressed firms are generally more difficult to classify, AdaBoost’s focus on misclassified samples is likely to make it more sensitive.

When considering accuracy alone, no discernible performance difference emerges. This is also seen in the lower-ranked models in Fig 8 and 9. These models demonstrate relatively high accuracy thanks to the balanced nature of the dataset. However, recall values fall below 0.82, indicating a higher risk of false negatives. This distinction is critical for audit practitioners and regulators because a model with slightly lower accuracy but higher recall is more reliable in identifying firms requiring further investigation. This means both figures highlight the importance of using recall and F1-score as key evaluation metrics in the context of ongoing business.

According to Fig 8 and 9, the results show that hybrid boosting and hybrid tree-assisted models, particularly AdaBoost- and CART-based combinations, provide the strongest performance in identifying distressed firms. These experimantal results demonstrate the suitability of ensemble-assisted hybrid approaches for audit risk applications. In these cases, avoiding false negatives is more important than maximizing overall classification accuracy.

The harmonic average of the precision and recall values is another important metric, the F1 score. The reason to use harmonic averaging rather than simple averaging is to avoid ignoring extreme cases. The main reason for the use of the F1 Score value instead of the Accuracy value is to avoid incorrect model selection in unbalanced data sets. The 5 models with the highest F1 scores are Ada-RF, Ada-GBM, None-XGB, CART-XGB, and Ada-XGB, 93.04%, 92.88%, 92.14%, 91.19%, and 90.93, respectively. Again, the hybrid model RF-Ada had the highest f1.

The actual and predicted values in a classification problem are shown in the confusion matrix table. The Fig 6 above was made using a confusion matrix table. The key details of the study are contained in Fig 10. The most used metrics for classifying ML problems have been evaluated. In this text, it focused on the evaluation indices: accuracy, precision, recall, and F-measure.

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Fig 10. Performance heatmaps for benchmark and hybrid models across four metrics.

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As we mentioned above, the five models with the highest validation scores are hybrid models. Accuracy is a metric that is commonly used to evaluate the performance of a model, but it is not a sufficient measure on its own, especially with unbalanced data sets that are not evenly distributed. Although the data set used was a balanced one, the success of the hybrid models created has also been evaluated based on other metrics. The precision value is very important, especially when the cost of a false positive is high. Here, if the prediction model marks the companies that should be approved as a rejection instead of acceptance, the company will fail the audit. High precision is an important criterion for us when selecting a model in this case. Hybrid models, which are None-XGB, Ada-KNN, Ada-GBM, Ada-SVM, and CART-KNN, have 94.84%, 94.44%, 94.22%, 92.49%, and 92.22% the highest top 5 predicted precision scores, respectively. It is therefore reasonable to assume that the hybrid model predictions are superior to the other classical methods considered. Hybrid models, which are None-KNN, RF-MLP, None-SVM, None-MLP, and GBM-RF, have 75.44%, 82.71%, 83.45%, 84.61%, and 85.12% the lowest predicted precision scores, respectively. This means that the predictive value of hybrid models can be increased or decreased.

The execution of standard ML algorithms was go along with a benchmarking process that was identify by the data structure and domain context of bankruptcy and audit risk prediction. In this setting, hybrid models, especially those associating AdaBoost and CART techniques, yield the most reliable and comprehensive predictive performance for ongoing business evaluations, as demonstrated by the aggregated results for accuracy, recall, and F1 score. Both Ada-RF and Ada-GBM reveal the highest accuracy while maintaining strong recall and F1 values. This experimental result proposes that boosting rises both the overall predictive power of the model and its ability to detect distressed firms. Tree-based models such as None–XGB and None–RF perform well, but hybrid SVM, KNN, and some combinations of MLP are less successful, have lower accuracy and precision, and have difficulty handling noisy or heterogeneous financial patterns. Overall, these experimentalresults demonstrate that auditors should be cautious when interpreting outputs from margin- or distance-based classifiers and place greater emphasis on signals detected by augmented and tree-structured models, especially those indicating liquidity deterioration, enhanced leverage, and weak cash flow. Hybrid tree enhancement configurations are valuable analytical tools in audit planning, particularly when mitigating the risk of false negative audits by identifying financial distress at an early stage is crucial. Their superior performance supports their use.

The purpose of including multiple models in this study is not only to compare metrics but also to develop a methodological framework and improve interpretation. A variety of hybrid and classical algorithms are designed to test when and why hybridization improves or reduces performance in ongoing business forecasting. When we interpret the experimantal results, ensemble-based combinations such as RF–Ada, RF–RF yield consistent gains because they combine variance reduction (bagging) with bias correction (boosting) and they grap non- linear interactions among liquidity, solvency, and turnover ratios. On the otherhand, SVM-based hybrids frequently underperform due to kernel redundancy and sensitivity to scaling, which demonstrates that hybridization does not always guarantee better performance.

These observations contribute valuable insights for auditors and financial-prediction researcher: prediction framework depends on the suitable learner and feature-selection model rather than on algorithm count. Therefore, this comparisons explains the mechanistic origins of performance differences and offers a reproducible framework for assessing hybrid ML systems in other financial-auditing contexts.

The results go beyond just doing experiments by explaining why different models work better. For example, models that combine feature reweighting and ensemble aggregation can capture the multidimensional structure of financial distress indicators, but distance-based or purely linear classifiers are limited in their ability to detect non-linear interdependencies. This domain-based framework prioritizes the contribution to interpretability rather than model comparison. This contributes to both auditing theory and ML model design.