Research on quality evaluation of innovation and entrepreneurship education for college students based on random forest algorithm and logistic regression model

Overview of the random forest algorithm

RF is a supervised algorithm that absorbs training samples and then input (X) into each sample to get the one output result (Y), through a mapping (f: X ⟶Y). Once the mapping is established by the model, predictions (Y’) for any unknown sample (X’) can be obtained. RF can be used for both classification and regression problems. The fundamental unit of RF is the Decision Tree (DT) and it works by integrating bagging with a random subspace. This combination helps the RF to improve its prediction accuracy.

The RF classifier integrates the decision of individual DTs d₁(x), d₂(x), …,d_n(x) till sufficient accuracy is reached. This process is shown in Fig. 5 (Onesmus, 2020). The results of the individual trees are combined through majority voting technique to give the result (Fawagreh, Gaber & Elyan, 2014). Two important phases in modelling RF are:

• Randomized training data: Bootstrapping method is employed in RF where the data samples are randomly picked by each DT.

• Randomized features: At each partitioning point of the individual DTs, the RF algorithm selects subset of features in random fashion without any replacement. K number of features will be selected, and then various indicators of the data will change under the K splits so as to choose the best split each time. This process will be continued till desired accuracy is reached.

The partitioning at each tree depends on two main metrics namely the entropy and information gain. The entropy of the sampled data T is found using Eq. (1). (1)${\displaystyle \text{Entropy}\left(\mathrm{T}\right)=-\sum _{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{P}}_{\mathrm{i}}log2{\mathrm{P}}_{\mathrm{i}}.}$

The term P_i signifies the quantity of data samples belonging to a particular category i that contributes to the total samples. For every feature (A) the data will be sampled into k splits. The information entropy and gain will proceed according to Eqs. (2) and (3). (2)${\displaystyle \text{Information Entropy}=-\sum _{\mathrm{j}=1}^{\mathrm{k}}\frac{\left|{\mathrm{T}}_{\mathrm{j}}\right|}{\left|\mathrm{T}\right|}\text{Entropy}\left(\mathrm{T}\right)}$ (3)${\displaystyle \text{Information gain}=\text{Entropy(T)}-\text{Information Entropy}.}$

The variance or Mean Square Error is a measure that quantifies the best fit of the RF tree. It estimates the deviation of the estimated value from its actual value (Meyners & Hasted, 2022) and its expression is given in Eq. (4). (4)${\displaystyle \mathrm{MSE}=\frac{1}{n}\sum _{i=1}^n{\left(y_{i-}\mu \right)}^2.}$

The term y_i is the label of the n number of instances used for the construction of trees. The value μ represents the mean of the y_i for all the n instances considered in the study.

Overview of logistic regression

The logit or LR is a statistical model used for classification problems which estimates the likelihood of an event based on the independent variables (Niu, 2020). The result of LR is probability bounded within [0,1] and the transformation is obtained by the odds: ratio of success probability to the failure probability. Equation (5) depicts the Logit function. (5)${\displaystyle \mathrm{Log}\left[\frac{\mathrm{Y}}{\left(1-\mathrm{Y}\right)}\right]={\mathrm{b}}_0+{\mathrm{b}}_1{\mathrm{X}}_1+\dots +{\mathrm{b}}_{\mathrm{n}}{\mathrm{X}}_{\mathrm{n}}.}$

The response variable (Y) is measured as the sigmoid function that estimates the values between [0-1]. The beta parameters are coefficients learned by the model using maximum likelihood estimation and are multiplied with the indicator or explanatory variables (X). The algorithm is run iteratively to find the best estimate. After obtaining the optimal coefficient the conditional probabilities for each record is determined and logged. The aggregation of this logged value will be the prediction or the response variable using the method of Goodness of fit.

Proposed model to assess the quality of Innovation and Entrepreneurship in college students

The research on evaluating the quality of I&E education based on the questionnaire collected from college students is done based on the model given in Fig. 6. This model integrated two ML algorithms namely RF and LR as discussed earlier. This hybrid model analysis the explanatory variables under five different genres namely Curriculum Design, Training and skill set enrichment, Resources, Talent acquisition by teachers and Entrepreneurial environment. Each of the topics is individually fit using RF algorithm to predict the Quality Index (QI). Each of the QI from QI_1 to QI_5 represents the quantitative value of the topic. The RF algorithm is an ensemble model that integrates individual decision trees till sufficient GI, Information gain and entropy is reached. This index is the quantitative metric that gauges the performance of the I&E of the colleges. To complete the research the QIs are fit using the Logit model to give the classification of the that is the final outcome. Table 3 lists the explanatory variables considered for the research.

The estimation of individual QIs are given in Eqs. (6) to (10). (6)${\displaystyle QI\text{\_}1=\text{Mean}\left(f\text{\_}IDT\left(X1,X2,X3,X4,X5\right)\right)}$ (7)${\displaystyle QI\text{\_}2=\text{Mean}\left(f\text{\_}IDT\left(X6,X7\right)\right)}$ (8)${\displaystyle QI\text{\_}3=\text{Mean}\left(f\text{\_}IDT\left(X8,X9,X10\right)\right)}$ (9)${\displaystyle QI\text{\_}4=\text{Mean}\left(f\text{\_}IDT\left(X11,X12,X13,X14,X15\right)\right)}$ (10)${\displaystyle QI\text{\_}5=\text{Mean}\left(f\text{\_}IST\left(X16,X17\right)\right).}$

The proposed method uses predictive RF technique that averages the estimations of Individual Decision Trees (IDT) that are constructed in the implementation. Thus, it is evident from the Eqs. (6)–(10) that each RF explores the data space of the questionnaire independent of each other, to estimate the QI. Internally, the individual RFs namely RF_1, RF_2, RF_3, RF_4 and RF_5 were constructed using the information and entropy gain as discussed in the previous section. Constructing the trees based on these metrics will help the trees to assign higher adaptive weights to the instances or variables that holds greater significance. The models will be trained iteratively till better MSE is achieving, which is a direct implication of the error component between actual and predicted value.

The proposed novel hybrid model finally deploys LR or logit model that combines the statistically powerful linear regression and squeezes the estimated Y value into two classes. This result will be the comprehensive and holistic TQE that is the quality assessment outcome using the explanatory variables considered in this study. The estimation of TQE is given in Eqs. (11) and (12). (11)${\displaystyle \mathrm{Y}={\mathrm{b}}_0+{\mathrm{b}}_1{\mathrm{QI}}_1+{\mathrm{b}}_2{\mathrm{QI}}_2+{\mathrm{b}}_3{\mathrm{QI}}_3+{\mathrm{b}}_4{\mathrm{QI}}_4+{\mathrm{b}}_5{\mathrm{QI}}_5}$ (12)${\displaystyle \mathrm{TQE}=\frac{1}{1+{\mathrm{e}}^{-\mathrm{Y}}}.}$

The coefficients b₀, b₁, b₂, b₃, b₄ and b₅ are computed adaptively by the login algorithm by training over the presented instances of the study. The proposed novel hybrid model is is motivated to achieve the following three major goals:

1. Prediction of the quality of I&E in education using the hybrid model constructed using RF and LR.

2. Assessment of individual topic of interest by constructing the QI using the RF algorithm.

3. Ranking the HEI’s performance in various topics as mentioned in Table 3.