Impact of Artificial Intelligence on the Mental Health Field of Innovation and Entrepreneurship and Empirical Research

Model Assumptions

Logistic regression model is shown in (1) [24-25], namely: (1) logit(p)=log(p1−p)=Xβ

When the sample size is N, then Y=(Y₁,Y₂,…Y_N)‵ let Y be centered (removing the intercept term α), i.e., satisfy ∑i=1NYi=0,β=(β1,β2,⋯,βK)′ as a K -dimensional vector, X=(X1′,X2′,⋯,XN′)′ . Where X_i = (X_i,1,…Xik)′, X unfolds to be the matrix of N × K as shown below. i.e: (2) X=( x1,1x1,2…x1,Kx2,1x2,2…x2,K⋮⋮⋮xN,1xN,2…xN,K )

Let X_i,k be standardized, i.e., satisfy ∑i=1NXi,kN=0 and ∑i=1NXi,k2N=1 .

The assumptions of the logistic regression model are summarized below: (3) Yi∈{0,1},i=1,⋯,N (4) P(Yi=1|Xi)=exp(∑i=1KXi,kβk)1+exp(∑i=1KXi,kβk)

Y₁,…Y_N are independent of each other.

There is no exact or approximate linear relationship between X_i,k,k = 1,⋯K.

Parameter estimation and its nature

According to the model assumption conditions, its distribution is known, so the method of great likelihood estimation can be chosen to estimate the unknown parameters.

Let: (5) pi=P(Yi=1|Xi)=exp(∑i=1Xi,kβk)1+exp(∑i=1KXi,kβk)

Then: (6) P(Yi=0|Xi)=1−pi=11+exp(∑i=1KXi,kβk)

Available: (7) P(Yi|Xi)=piYi(1−pi)1−Yi

And according to the modeling assumption condition Y₁,…,Y_N is independent of each other can be obtained. i.e: (8) P(Y|X)=∏i=1NpiYi(1−pi)1−Yi

The likelihood function can be obtained as shown in the following equation: (9) L(β)=∏i=1N(exp(∑i=1KXi,kβk)1+exp(∑i=1KXi,kβk))Yi(11+exp(∑i=1KXi,kβk))1−Yi,

Taking logarithms yields the log-likelihood function as follows: (10) L(β)=∑i=1N{ Yilog(pi)+(1−Yi)log(1−pi) }=∑i=1N{ YiXi′β−log(1+exp(Xi′β)) }

The likelihood equation can be obtained by taking the first order derivative of β_j,j=1,⋯,K separately and making it 0 as follows: (11) ∂l(β)∂βj=∑i=1N(Yi−exp(Xi′β)1+exp(Xi′β))Xi,j=0,j=1,⋯,K,

Then β^=(β^1,⋯,β^K)′ is the solution of the above system of likelihood equations.

From the above can be obtained from this great likelihood estimate is nonlinear, it is difficult to get direct results, so in the actual operation of the computer often use iterative algorithm to calculate the approximation of the parameter estimate, the estimate to meet the following asymptotic properties, unbiased, validity, normality.

Significance test

In the general linear regression model (9) the residual sum of squares (SSE) is defined as follows: (12) SSE=∑i=1N(Yi−Y^i)2=∑i=1N(Yi−Xi′β^)2

In Logistic regression modeling, the equivalent concept to this is the departure, which comes from the likelihood ratio test between the fitted model and the saturated model. The formula for defining the outlier is shown below: (13) D=−2ln(L(β))

The test of significance for a single variable with the original hypothesis of H₀:β_m=0 is similar to the statistic F defined in the general linear regression process. Defining statistic G in Logistic regression is shown below: (14) G=−2ln(L(β1,⋯,βm−1,βm+1,⋯,βK)L(β1,⋯,βm,⋯,βK))

There are under the condition that the original hypothesis holds: (15) G|H0~χ(1)2

Select 0 < α < 1 and always take α =0.05. If p−value=P(χ(1)2>G)<α holds, the predictor variable corresponding to β_m is said to be significant for the response variable at the 1–α level of significance.

Goodness-of-fit test (20) R2=RSSTSS=1−ESSTSS

R² is the sample coefficient of determination, which, for a given sample, R² reflects the goodness of fit of the regression equation to the sample observations. R² serves as a test of the goodness of fit of the regression equation to the sample values: R²(0≤R² ≤1) the larger, the better the fit between the regression equation and the sample. Conversely, the regression equation is a poor fit to the sample values.

The size of the sample coefficient of determination R² is related to the number of explanatory variables in the model, and R² tends to increase when a new explanatory variable is introduced into the model, but an increase in R² due to an increase in the number of explanatory variables does not indicate a better fit. Moreover, given a certain sample size, increasing the number of explanatory variables will increase the number of parameters to be estimated must reduce the degrees of freedom, so an adjustment for R² is also needed. The effect of the number of explanatory variables on the goodness of fit can be removed by dividing the sum of squares of the residuals and the sum of squares of the total deviations by their respective degrees of freedom. To wit: (21) R¯2=1−RSS/(n−k−1)TSS/(n−1)

Using R¯2 to explain the goodness of fit of the regression equation eliminates the dependence of R² on the number of explanatory variables. The relationship between R¯2 and R² is as follows: (22) { R¯2=1−n−1n−k−1(1−R2)R2=1−n−k−1n−1(1−R¯2)

In the actual analysis, the larger the R¯2 or R² of the model, the better the fit, indicating that the explanatory variables in the model have a greater degree of influence on the explained variables as a whole, but it cannot be said that the explanatory variables in the model have a significant degree of influence on the explained variables. In the actual regression analysis, a good regression model should not only fit well, but also consider the reliable estimation of the overall regression coefficients, and the comprehensive consideration of the reliability of the model and the practical significance of the decision coefficients can be appropriately reduced requirements.

Significance test of variables (T-test)

The F-test rejects H₀ and the overall relationship of the equation is significant. However, it does not imply that the effect of all explanatory variables on the explained variables is significant. Therefore, each explanatory variable needs to be tested for significance separately. The t-test is used to determine whether the variable can be retained in the model as an explanatory variable by formulating the hypothesis: H₀:β₀ = β₁ = β₂ = β₀… = β_k = 0, constructing Γ statistic t=β^i/Sρ^i . Assuming that H₀ is valid, constructing statistic t obeys the F-distribution with (n–k–1) degrees of freedom, and given the level of significance α, the critical value t_α/2(n–k–1) can be obtained by looking up the table and calculating to find the value of statistic t, and rejecting or accepting H₀ by |t|>t_α/2(n–k–1) or |t|≤t_α2(n–k–1). Reject H₀, regression coefficients are significant explanatory variables are retained in the model. Accept H₀, regression coefficient is not significant explanatory variables are not retained in the model.

Self-Assessment Scale for Anxiety (SAS)

Anxiety disorders research has been the focus of research on emotional problems. Anxiety disorders are widespread in the population and have a more obvious impact on mental and physical health. The SAS test was conducted for innovation and entrepreneurial students in four institutions in order to understand the current situation of students' anxiety problems related to innovation and entrepreneurship and the factors that affect them.

The SAS test for college students in four universities is shown in Table 1, and the results show that the number of male students surveyed was 893, and the average score for male students was 42.61±10.22. The number of female students surveyed was 927, and the average score for female students was 44.07±9.31. There was no statistically significant difference in the comparison of the overall distributions of SAS scores for male and female students, t=-0.754, P=0.564. It is not possible to assume that the overall distributions of SAS scores are different for male and girls have different overall distributions of SAS scores. Table 1.

Four university college student sas testing

According to the SAS cut-off value of 50 points, ≤50 points is normal and >50 points is an anxiety disorder. The prevalence of anxiety among the respondents is shown in Table 2, and the results show that the number of male students suffering from anxiety disorders is 238, and the number of female students suffering from anxiety disorders is 333, with prevalence rates of 26.65% and 35.92%, respectively. Comparison between gender and the prevalence of anxiety, the test result χ²= 1.524, P= 0.367, the difference is not statistically significant, and it cannot be considered that the prevalence of anxiety disorders is different between genders. Table 2.

The target anxiety rate was investigated

Self-Depression Scale (SDS)

Depression self-assessment scale is a short self-assessment scale, which is convenient to operate, easy to grasp, not affected by age, gender, economic status and other factors, and has a wide range of applications, applicable to normal people of various occupations, cultural classes and ages, or all kinds of mental patients.

The main SDS statistic is the total score, and the sum of the 20 item scores is the rough score (raw score X). The rough score is then converted to standardized score (index score Y), where Y=in (1.25X). In this survey, 1820, college students had a mean total score of (x¯±S) , with a mean score of 49.79±10.94.

The statistics of SDS test for college students in four universities are shown in Table 3. The results show that the number of male students surveyed was 893, and the average score of male students was 49.21±12.36. The number of female students surveyed was 927, and the average score of female students was 50.37±9.52. There was no statistically significant difference in the comparison of the overall distribution of the scores of male students and female students, t=-0.723, P=0.535, which could not be regarded as a difference in the overall distribution of scores of male students and female students. Table 3.

SDS test statistics of four college students

According to the SDS cut-off value of 50 points, ≤50 points is normal and >50 points is anxiety disorder. The prevalence of depression among the respondents is shown in Table 4, the number of male students suffering from depressive disorders is 392, and the number of female students suffering from depressive disorders is 432, the prevalence rate is 43.90% and 46.60% respectively. Comparison of gender and depression prevalence rate, test results χ²= 0.082, P= 0.895, the difference is not statistically significant, can not be regarded as different gender depression disorder prevalence rate is different. Table 4.

The rate of depression in the survey was reported

Symptom self-assessment scale (SCL-90)

The detection rate of SCL-90 psychological problems in the four universities is shown in Table 5, and according to the level of α=0.05, the detection rate of psychological problems in the SCL-90 Symptom Self-Rating Scale is not statistically significant among different institutions, P=0.351, and it can be assumed that there is no difference in the rate of incidence of the SCL-90 Symptom Self-Rating Scale among different institutions with the SCL-90 Symptom Self-Rating Scale. Table 5.

Regression analysis of the use behavior of artificial intelligence technology on emotions

Modeling: (23) Y=W0+W1X1+W2X2+…+W7X7

Model 1: Used to test the influence effect between the control variables and each dependent variable.

Model 2: Introducing the frequency of use of artificial intelligence technology, controlling other variables, and exploring the influence effect between it and each variable.

Model 3: Introducing the use function of artificial intelligence technology, controlling other variables, and exploring the influence effect between it and each variable.

Where, Y is the dependent variable mood. W₀ is the intercept, which indicates the average value taken by the dependent variable Y when both the independent and control variables are zero. X is the independent variables, which are X₁ for gender, X₂ for age, X₃ for academic status, X₄ for education level, X₅ for type of residence, X₆ for frequency of AI technology use, and X₇ for function of AI technology use. W_1–7 is the regression coefficient. Model 1, Model 2, and Model 3 were built with emotion as the dependent variable, and control variables, frequency of use of AI technology, and function of use of AI technology in that order, respectively.

The results of the regression analysis of the use behavior and emotion of artificial intelligence technology are shown in Table 6, and the R₂ value of model 3 is 0.171, indicating that the model is well constructed. Table 6.

Intelligent technology USES behavior and emotional regression analysis results

According to the R₂ value of the model, it can be seen that the R₂ value of the model increased by 3.6% after adding the frequency of use of AI technology and the function of use, which can indicate that model 3 has more explanatory power for social emotions. Overall, age and type of residence always significantly and negatively affect social sentiment, and after controlling for the effects of demographic variables, the frequency of use of AI technology and the function of use still significantly and positively affect the social sentiment of innovative entrepreneurs.

Regression analysis of the use behavior of artificial intelligence technology on cognition

The regression analysis of the use behavior of artificial intelligence technology on cognition is shown in Table 7. In the same way as the previous method, a regression model was established for analysis using cognition as the independent variable. The model is significant and there is no covariance problem, the R₂ value of model 3 is 0.251, and the model is well constructed. Table 7.

Artificial intelligence usage behavior for cognitive regression analysis

Regression analysis of the use behavior of artificial intelligence technology on values

Table 8 depicts the regression analysis of the use behavior of artificial intelligence technology on values. Table 8.

The use of artificial intelligence is a regression analysis of values

In the same way as above, the regression model is constructed using social values as the independent variable for analysis. The model is significant and there is no covariance problem, the R₂ value is 0.247, the model is well constructed.

Regression analysis of the use behavior of AI technology on behavioral intention

The regression analysis of the use behavior of AI technology on behavioral intention is shown in Table 9. In the same way as above, a regression model was established for analysis with behavioral intention as the independent variable. The model is significant and there is no covariance problem, the R₂ value is 0.234, and the model is well constructed. Table 9.

The use of artificial intelligence is a regression analysis of behavioral intent

Based on the R² value of the model, it can be seen that the R² value of model 3 increased by 3.6% after the addition of the independent variables, which can indicate that model 3 has more explanatory power for behavioral intention. Gender and marital status do not have a significant impact on the model. Age always has a significant negative effect on behavioral intention, i.e., the older the age, the more negative the behavioral intention. Education level always has a significant positive effect on behavioral intention, i.e. the higher the education level, the more positive the behavioral intention.

In this chapter, the research hypotheses H1 and H2 were verified through regression analysis. And the research hypotheses H1 and H2 were further verified after controlling the effects of relevant variables by establishing a multiple linear regression model for regression analysis. It can be seen that the motivation to use AI technology significantly and positively affects user behavior. And both the frequency of use and the function of use in the use behavior significantly and positively affect social emotions, social cognition, values, and behavioral intentions. Therefore, the research in this paper fully confirms that the use of AI technology reinforces usage behavior through motivation. And the frequency of use and the intensity of use function of AI technology will have a significant positive impact on the psychological health of innovative entrepreneurs.