Agriculture is the main body in the traditional rural economy[1]. Rural economy and agricultural economy are often used interchangeably as equivalent concepts. With the continuous expansion of the rural economic field, traditional agriculture can no longer cover the connotation and extension of the rural economy. The rural economy covers agriculture in a broad sense and the secondary and tertiary industries that occur in rural areas. Therefore, the agricultural economic growth can be measured by the agricultural output value and the non-agricultural income of the rural part-timers [2]. Rural economic growth is affected by factors such as rural industrial structure, human capital, rural culture, and policies that benefit farmers and the intermediate inputs of agricultural production. Most of the related studies do not make a strict distinction between rural economic growth and agricultural economic growth. These studies lack relatively systematic econometric empirical studies on the influencing factors of rural economic growth. Therefore, this paper intends to construct a variable system that affects rural economic growth based on relevant research. We used a binary discrete choice model to perform regression analysis on the survey sample. The article analyzes the influence of each variable and explores the countermeasures to develop the rural economy.

Because the ordinal dependent variable is not continuous, the latent variable method is usually used to estimate the model. Respondents’ selection of ordinal variables implies a selection of an interval of continuous net utility values. We assume that ^{*} is an unobservable continuous latent variable [3]. We have a total of

If ^{*} ∈ [_{d− 1}, _{d}_{0} = −∞, _{1} = 0, _{D}_{2} …, _{D}_{+1}) is also a parameter to be estimated. Bayesian methods treat both parameters and latent variables as random variables. The hierarchical model structure is just right for the MCMC method [4]. Therefore, this paper chooses the Bayesian method to estimate the model. First, analyze an ordinary ordinal regression:

Assuming that the latent variable ^{*} is known to obtain ^{2} | ^{*}) = ^{2} | ^{*}, ^{*}, ^{*} and other parameters [5]. The second-level models of the hierarchical model are all ordinary continuous variable models. This paper assumes that the one-layer model error obeys a normal distribution (Probit model). First, assuming that ^{*} is known, the likelihood probability is:

^{*}, _{1} = ^{*} − _{1}],
_{n}

First set the prior distribution of parameters belonging to layer one only. The conjugate prior distribution of the normal mean when the variance is known is also normal, so we set the prior distribution of

We guarantee that the error covariance matrix is positive definite.

Since layer 2 provides some useful information about _{0j} and _{1j}, the prior distribution can be obtained using this information. Since the errors of the two models are not independent of each other, we need to combine them to estimate [6]. First analyze the
_{0} and _{1} contain constant terms. The prior distribution of parameter

Among them, _{2} =

Then we set the prior distribution of each model parameter of layer 2 in turn. In this paper, the setting of the prior distribution of

Due to the problem of model identification, we need to fix _{0,0} = 1. This will result in Σ not obeying a known distribution [7]. Suppose there are _{1}, _{2}, L, _{Q}_{G} Represents the variance-covariance matrix of _{11}) _{G} − ^{′} / σ_{11}), let Φ = Σ_{G} − ^{′}_{11}, then:

Then the parameter to be estimated becomes

The prior distribution setting principle of each parameter of layer two can be consistent with that of layer one. Then there are:

Knowing the Bayesian method, there is the following relation

Then the joint posterior distribution of each parameter of layer 1 is:

Then the fully conditional posterior distribution of each parameter can be calculated one by one:

The fully conditional posterior distribution of ^{*} = (^{′}^{−1}.

Equation (18) uses an informative prior distribution. We need to set the parameters in the prior distribution reasonably. If you set ^{−1} = _{k}^{10}. Assuming that the mean of ^{*} is exactly the least-squares estimate of _{β} = (^{−1}. The kernel of the conditional posterior distribution of

The prior distribution of

Which is:

Where

Among them,

It can be seen that the conditional posterior distribution of

Finally, this paper obtains the conditional posterior distribution of ^{*} and ^{*} obeys the multivariate truncated normal distribution according to the corresponding relationship as follows:

Where
_{y*}, Σ):

Where Σ = (^{′} ^{−1}, ^{*}.

If you know _{−d}, you can get the interval of _{−d}, _{+d}]. At the same time, we can find the maximum
^{*}. We strictly control the increasing relationship of _{d}

If the fully conditional posterior distribution of the parameters obeys a known type of posterior distribution, then we can use Gibbs sampling for iterative sampling. However, the conditional posterior distributions of

Step 1 Given _{(0)}, _{(0)}, _{(0)}, _{(0)}, we draw

Step 2 Given
_{(0)}, _{(0)}, _{(0)},, we sample _{(1)} from a uniform distribution as in (30).

Step 3 Given
_{(0)}, _{(0)}, we draw _{(1)} from the multivariate normal distribution _{β}_{β}).

Step 4 Given
_{(1)}, _{(0)}, we draw _{(1)}, from distribution

Step 5 Given
_{(1)}, _{(1)}, _{0(0)}, _{1(0)}, _{(0)}, Φ_{(0)}, we draw _{(1)} from the multivariate normal distribution _{δ} _{δ}_{δ}).

Step 6 Given _{(1)}, _{0(0)}, _{1(0)}, _{(0)}, Φ_{(0)}, we draw _{1} from the multivariate normal distribution _{α}_{α}].

Step 7 Given _{(1)}, _{1}, _{1(0)}, _{(0)}, Φ_{(0)}, we draw _{0(1)} from distribution _{0}|) using the M-H method.

Step 8 Given _{(1)}, _{1}, _{0(1)}, _{(0)}, Φ_{(0)}, we draw _{1(1)} from distribution _{1}|) using the M-H method.

Step 9 Given _{(1)}, _{1}, _{0(1)}, _{1(1)}, Φ_{(0)}, we sample _{(1)} from the normal distribution as in (25).

Step 10 Given _{(1)}, _{1}, _{0(1)}, _{1(1)}, _{(1)}, we sample Φ_{(1)}, from the distribution as in (26).

Then continue to iterate until the Markov chain of each parameter converges.

We sample the following process for

Let _{t}^{*} of parameters from some proposed distribution ^{*}| _{t}^{*}− _{t}

We randomly sample from the uniform distribution

Calculate the probability of acceptance. We prevent the denominator from approaching 0. The log determinant is easier to compute. So we make the acceptance probability as:

Judgment if _{t}^{*}_{t}_{+ 1}, ^{*}

This paper also adopts the standard normal distribution generally used in the research, that is, the candidate value generation process is ^{*}_{t}

Because a fixed ^{*}

The article studies the demographic variables of respondents’ income _{1}, age _{2}, gender _{3}, education level _{4}, and non-agricultural skills _{5}. Investigate the input characteristic variables of the per capita agricultural machinery and equipment _{6} and the per capita arable land area _{7}. It also includes soft environmental variables such as rural public culture _{8}, agricultural direct subsidy _{9}, and other agricultural-friendly policies _{10}. Each variable is assigned according to the discrete variable processing method.

We use the Probit function module in SPSS13.0 for analysis. By default, the system analyzes the frequency table when each variable takes different values. Specify the frequency variable here. We chose to transform with the inverse of the cumulative standard normal distribution function [12]. At this point, we are required to calculate the observed value, expected value, residual, and probability of each independent variable with different value levels. In this way, the goodness of fit and parameter estimation of the Probit equation are obtained. In the Pearson goodness-of-fit test, the chi-square value, degrees of freedom, and model value were 96.988, 119, and 0.999, respectively. This indicates that the goodness of fit of the model is good.

Table 1 shows the optimal parameter estimates after 20 iterations. At this point, we obtain the binary Pro-plus discrete choice model as:

Probit model regression coefficients, standard deviation estimates

Regression Coe£ | Standard Error | Coeff./S.E | |
---|---|---|---|

Intercept | 1.398 | 0.815 | 1.593 |

X1 | 1.814 | 0.777 | 3.78 |

X2 | 0.071 | 0.181 | 0.338 |

X3 | 0.351 | 0.397 | 0.885 |

X4 | 0.139 | 0.435 | 0.337 |

X5 | −0.039 | 0.707 | −0.055 |

X6 | 0.35 | 0.743 | 0.388 |

X7 | 0.355 | 0.778 | 0.533 |

X8 | −0.387 | 0.385 | −1.008 |

X9 | 0.577 | 0.417 | 1.385 |

X10 | 0.571 | 0.354 | 1.585 |

The constant term in the binary Probit discrete choice model is 1.298. This indicates that the rural economy has an initial growth momentum without other variables. Among the respective variables, the coefficient of concurrent employment is the largest (1.841), followed by the coefficients of direct agricultural subsidies and other policies that benefit farmers, and the coefficients of non-agricultural skills and rural public culture are negative [13]. The binary Probit discrete choice model can obtain the observed value, expected value, residual, and probability of each independent variable at different value levels (Table 2).

Parameter estimation of the logistic regression equation

B | SE | Wald | DF | Sig | Exp(B) | 95%CI for EXP(B) | ||
---|---|---|---|---|---|---|---|---|

Lower | Lower | |||||||

−1414 | 1152 | 1508 | 1 | 218 | 0.243 | |||

X1 | 5333 | 1712 | 10848 | 1 | 1 | 207087 | 8783 | 48778 |

X2 | 3837 | 3 | 0.278 | |||||

X2 | −1280 | 1075 | 1418 | 1 | 234 | 0.278 | 0.034 | 2287 |

X2 | 0755 | 1073 | 505 | 1 | 477 | 2128 | 0.275 | 17084 |

X2 | −1573 | 1382 | 1287 | 1 | 255 | 0.207 | 0014 | 3110 |

X 3 | 881 | 785 | 1288 | 1 | 257 | 2437 | 523 | 11352 |

X 4 | −0347 | 841 | 171 | 1 | 778 | 707 | 137 | 3772 |

X 5 | −0801 | 1375 | 0.435 | 1 | 508 | 0.407 | 0028 | 5800 |

X 6 | 1133 | 1070 | 1121 | 1 | 280 | 3105 | 381 | 25285 |

X7 | 178 | 1112 | 23 | 1 | 880 | 1183 | 0.134 | 10457 |

X8 | −0805 | 707 | 2232 | 1 | 135 | 0.405 | 0.123 | 1327 |

X9 | 1537 | 825 | 3474 | 1 | 72 | 4753 | 824 | 23433 |

X10 | 0.775 | 573 | 1844 | 1 | 175 | 2148 | 0712 | 7478 |

This paper uses Probit and Logistic binary discrete choice models to analyze the survey samples. The results show that the degree of part-time job is the decisive factor of rural economic growth. The impact of human capital and agricultural production and management methods is not significant. Therefore, we must continue accelerating the transformation and upgrading of the rural economy from traditional agriculture with a single structure to three industries. Spare no effort to promote the process of agricultural industrialization. While encouraging farmers to “go out,” farmers are trained by strengthening rural education. Migrant workers are encouraged to return to their hometowns to optimize rural human capital to start businesses. By consolidating and improving the land contract responsibility system and circulation mechanism, we can mobilize farmers’ enthusiasm for production and improve the efficiency of land resource allocation. We will continue to increase capital investment in “Sannong” while integrating capital channels, optimizing the structure of expenditures, and improving the supervision mechanism. This will improve the efficiency of the use of funds.

#### Parameter estimation of the logistic regression equation

B | SE | Wald | DF | Sig | Exp(B) | 95%CI for EXP(B) | ||
---|---|---|---|---|---|---|---|---|

Lower | Lower | |||||||

−1414 | 1152 | 1508 | 1 | 218 | 0.243 | |||

X1 | 5333 | 1712 | 10848 | 1 | 1 | 207087 | 8783 | 48778 |

X2 | 3837 | 3 | 0.278 | |||||

X2 | −1280 | 1075 | 1418 | 1 | 234 | 0.278 | 0.034 | 2287 |

X2 | 0755 | 1073 | 505 | 1 | 477 | 2128 | 0.275 | 17084 |

X2 | −1573 | 1382 | 1287 | 1 | 255 | 0.207 | 0014 | 3110 |

X 3 | 881 | 785 | 1288 | 1 | 257 | 2437 | 523 | 11352 |

X 4 | −0347 | 841 | 171 | 1 | 778 | 707 | 137 | 3772 |

X 5 | −0801 | 1375 | 0.435 | 1 | 508 | 0.407 | 0028 | 5800 |

X 6 | 1133 | 1070 | 1121 | 1 | 280 | 3105 | 381 | 25285 |

X7 | 178 | 1112 | 23 | 1 | 880 | 1183 | 0.134 | 10457 |

X8 | −0805 | 707 | 2232 | 1 | 135 | 0.405 | 0.123 | 1327 |

X9 | 1537 | 825 | 3474 | 1 | 72 | 4753 | 824 | 23433 |

X10 | 0.775 | 573 | 1844 | 1 | 175 | 2148 | 0712 | 7478 |

#### Probit model regression coefficients, standard deviation estimates

Regression Coe£ | Standard Error | Coeff./S.E | |
---|---|---|---|

Intercept | 1.398 | 0.815 | 1.593 |

X1 | 1.814 | 0.777 | 3.78 |

X2 | 0.071 | 0.181 | 0.338 |

X3 | 0.351 | 0.397 | 0.885 |

X4 | 0.139 | 0.435 | 0.337 |

X5 | −0.039 | 0.707 | −0.055 |

X6 | 0.35 | 0.743 | 0.388 |

X7 | 0.355 | 0.778 | 0.533 |

X8 | −0.387 | 0.385 | −1.008 |

X9 | 0.577 | 0.417 | 1.385 |

X10 | 0.571 | 0.354 | 1.585 |

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Equation to Solve the Bending Performance Test of Corroded Reinforced Concrete Beams under Prestressed Fatigue Load Animation VR scene mosaic modeling based on generalized Laplacian equation Radial Basis Function Neural Network in Vibration Control of Civil Engineering Structure Optimal Model Combination of Cross-border E-commerce Platform Operation Based on Fractional Differential Equations The influence of accounting computer information processing technology on enterprise internal control under panel data simultaneous equation Research on Stability of Time-delay Force Feedback Teleoperation System Based on Scattering Matrix BIM Building HVAC Energy Saving Technology Based on Fractional Differential Equation Construction of comprehensive evaluation index system of water-saving irrigation project integrating penman Montei the quation Human Resource Management Model of Large Companies Based on Mathematical Statistics Equations Data Forecasting of Air-Conditioning Load in Large Shopping Malls Based on Multiple Nonlinear Regression Analysis of technical statistical indexes of college tennis players under the win-lose regression function equation Automatic extraction and discrimination of vocal main melody based on quadratic wave equation Analysis of wireless English multimedia communication based on spatial state model equation Optimization of Linear Algebra Core Function Framework on Multicore Processors Optimisation of Modelling of Finite Element Differential Equations with Modern Art Design Theory Mathematical function data model analysis and synthesis system based on short-term human movement Human gait modelling and tracking based on motion functionalisation The Control Relationship Between the Enterprise's Electrical Equipment and Mechanical Equipment Based on Graph Theory Financial Accounting Measurement Model Based on Numerical Analysis of Rigid Normal Differential Equation and Rigid Functional Equation Mathematical Modeling and Forecasting of Economic Variables Based on Linear Regression Statistics Nonlinear Differential Equations in Cross-border E-commerce Controlling Return Rate Differential equation model of financial market stability based on Internet big data 3D Mathematical Modeling Technology in Visualized Aerobics Dance Rehearsal System Children’s cognitive function and mental health based on finite element nonlinear mathematical model Fractional Differential Equations in Electronic Information Models BIM Engineering Management Oriented to Curve Equation Model Leakage control of urban water supply network and mathematical analysis and location of leakage points based on machine learning Analysis of higher education management strategy based on entropy and dissipative structure theory Prediction of corporate financial distress based on digital signal processing and multiple regression analysis Mathematical Method to Construct the Linear Programming of Football Training Multimedia sensor image detection based on constrained underdetermined equation The Size of Children's Strollers of Different Ages Based on Ergonomic Mathematics Design Application of Numerical Computation of Partial Differential Equations in Interactive Design of Virtual Reality Media Stiffness Calculation of Gear Hydraulic System Based on the Modeling of Nonlinear Dynamics Differential Equations in the Progressive Method Knowledge Analysis of Charged Particle Motion in Uniform Electromagnetic Field Based on Maxwell Equation Relationship Between Enterprise Talent Management and Performance Based on the Structural Equation Model Method Term structure of economic management rate based on parameter analysis of estimation model of ordinary differential equation Influence analysis of piano music immersion virtual reality cooperation based on mapping equation Chinese painting and calligraphy image recognition technology based on pseudo linear directional diffusion equation Label big data compression in Internet of things based on piecewise linear regression Animation character recognition and character intelligence analysis based on semantic ontology and Poisson equation Design of language assisted learning model and online learning system under the background of artificial intelligence Application of machine learning in stock selection Comparative analysis of CR of ideological and political education in different regions based on improved fuzzy clustering Action of Aut( G ) on the set of maximal subgroups ofp -groupsThe internal mechanism of corporate social responsibility fulfillment affecting debt risk in China: analysis of intermediary transmission effect based on degree of debt concentration and product market competitive advantage Study on transmission characteristics in three kinds of deformed finlines based on edge-based finite element method Asymptotic stability problem of predator–prey system with linear diffusion Research on loyalty prediction of e-commerce customer based on data mining Algebraic Equations in Educational Model of College Physical Education Course Education Professional English Translation Corpus Under the Binomial Theorem Coefficient Geometric Tolerance Control Method for Precision Machinery Based on Image Modeling and Novel Saturation Function Retrieval and Characteristic Analysis of Multimedia Tester Based on Bragg Equation Semiparametric Spatial Econometric Analysis of Household Consumption Based on Ordinary Linear Regression Model Video adaptive watermark embedding and detection algorithm based on phase function equation English Learning Motivation of College Students Based on probability Distribution Scientific Model of Vocational Education Teaching Method in Differential Nonlinearity Research on mobile Awareness service and data privacy Protection based on Linear Equations computing protocol Vocal Music Teaching Model Based on Finite Element Differential Mathematical Equations Research on threat assessment problems of island air defence system based on the leader-follower model Studying a matching method combining distance proximity and buffer constraints The trend and influence of media information Propagation based on nonlinear Differential equation Research on the construction of early warning model of customer churn on e-commerce platform Study on inefficient land use determination method for cities and towns from a city examination perspective A sentiment analysis method based on bidirectional long short-term memory networks Evaluation of ecosystem health in Futian mangrove wetland based on the PSR-AHP model A study of local smoothness-informed convolutional neural network models for image inpainting Towards more efficient control of the ironmaking blast furnace: modelling gaseous reduction of iron ores in H _{2}-N_{2}atmosphereAlgorithm of overfitting avoidance in CNN based on maximum pooled and weight decay Mathematical Calculus Modeling in Improving the Teaching Performance of Shot Put Application of Nonlinear Differential Equation in Electric Automation Control System Higher Mathematics Teaching Curriculum Model Based on Lagrangian Mathematical Model Decisions of competing supply chain with altruistic retailer under risk aversion Optimization of Color Matching Technology in Cultural Industry by Fractional Differential Equations The Marketing of Cross-border E-commerce Enterprises in Foreign Trade Based on the Statistics of Mathematical Probability Theory Application of Linear Partial Differential Equation Theory in Guiding Football Scientific Training The Evolution Model of Regional Tourism Economic Development Difference Based on Spatial Variation Function System Model of Shipping Enterprise Safety Culture Based on Dynamic Calculation Matrix Model The Inner Relationship between Students' Psychological Factors and Physical Exercise Based on Structural Equation Model (SEM) Analysis and Research on Influencing Factors of Ideological and Political Education Teaching Effectiveness Based on Linear Equation Fractional Differential Equations in Sports Training in Universities Examination and Countermeasures of Network Education in Colleges and Universities Based on Ordinary Differential Equation Model Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model Chinese-English Contrastive Translation System Based on Lagrangian Search Mathematical Algorithm Model