# Analysis of Influencing Factors of Social Public Management Score Based on Augmented Regression Model

Authors: Zhuo Li
Journal: Advances in Multimedia
 (2022)

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## Abstract

To improve the analysis effect of the factors influencing the score of social public management, this paper combines the enhanced regression model to analyze the factors affecting the score of social public management and constructs a factor analysis model through an intelligent algorithm. Moreover, this paper uses numerical simulation to verify that when the parameters estimated by SEM are linear functions and the relationship between the research variables and auxiliary variables is nonlinear, the estimation effect of SEM estimators is better than that of traditional generalized regression estimators. In addition, this paper proposes a public service channel management model through the measurement and analysis of channel mode public service feature matching, channel type public service feature matching, and channel type and channel mode public service feature matching. Finally, this paper combines the simulation research to verify the effectiveness of the method in this paper.


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## Body

## 1. Introduction

With the development of the times and the progress of the society, the research field and scope of public crisis management are constantly expanding and are increasingly valued by domestic researchers. With the increasing trend of social diversification and value diversification, the fields that can be studied are also more diversified. Moreover, the current information technology is advancing by leaps and bounds, and various civil organizations are flourishing. In particular, after the Wenchuan earthquake in China, all social forces actively participated in the earthquake relief work, which played an important role in the maintenance and reconstruction of the postdisaster order. It can be seen that although the nature and functions of the government make it to play a crucial leading role in the crisis management mechanism and to respond to public crisis events, it is necessary to establish a government-led crisis management mechanism, the government is not omnipotent, and it cannot and does not need to replace everything. In addition, social forces such as nongovernmental organizations, for-profit organizations, and the public, which are important subjects in the crisis management mechanism, also play an important role in responding to public crisis events.The so-called socialization of public management means that when the government implements the management of the social economy, in the field of social management and public services, it changes the traditional practice of the government taking the lead and transfers some government functions to the society or entrusts the agency, etc., in order to achieve the purpose of improving administrative efficiency and saving financial expenditures [1]. The socialization of public management reflects a realistic relationship between government and society. In the process of the formation and development of capitalist society, Western countries have produced general theories of the relationship between government and society, and they have also accumulated a lot of successful experience in dealing with the relationship between government and society. China’s reconstruction of the benign interactive relationship between government and society provides many useful enlightenments [2]. In the era of planned economy, my country has gradually established a governance model of an omnipotent government. The market has been abolished, and the power of the government has penetrated into all areas of urban and rural society and many aspects of individuals, which ultimately leads to the decline of the government’s ability to integrate society and the inefficient operation of administrative organizations. The production enthusiasm of social members is inhibited and other institutional crises [3].Literature [4] believes that cyberspace is a free and independent space that does not require any management or government control. The government’s management of public security in the network society is an interference with freedom. However, the current international practice of managing public security in the network society is completely different from this theory, and the international practice has been supported by many people [5]. The orderly development of the network society requires a certain degree of social autonomy, but the autonomy of social autonomy cannot replace government management, and the management of public security in the network society requires the participation of the government [6]. The healthy development of the network society is inseparable from the government’s control. The autonomy in the network society is a favorable factor for the orderly development of the network society, but social autonomy cannot replace government management. Ultimately, it needs the government to back it up with its coercive power. Those who violate the rules of self-governance and have a serious impact naturally need the coercive power of the government to regulate [7]. The theory that the Internet society is different from the real society and that the Internet excludes government management is untenable. The application of this theory will lead to the disorder of the Internet society, which will ultimately affect the rights of people in the real society. Obligatory relationship. Advocating the theory that public security management in the network society does not require government management will lead to the disorderly development of the network society [8].Literature [9] analyzes the definition of government regulation in economics, law, and political science in detail. He believes that regulation is a general activity that is formulated and implemented by administrative agencies to directly intervene in the market allocation mechanism, and indirectly change the supply and demand decisions of enterprises and consumers. Rules or special behavior. This theory holds that strengthening the management of public security in the network society is an inevitable requirement to safeguard the safety of people’s lives and properties. From the perspective of the basic functions of public security management, the ultimate purpose of this management is to safeguard the safety of people’s lives and properties. From the perspective of contract theory, the basis for the establishment of the government lies in the agreement reached by the people through the contract, the source of the government’s power is also the contract reached by the people, the government’s power originates from the people, and the purpose of its existence and operation is to protect the people. Safety of life and property [10]. Especially in modern society, as the concept of service administration is deeply rooted in the hearts of the people, the government should establish and improve the management mechanism in the process of managing the public security of the network society [11]. At present, many scholars believe that regulation includes economic regulation and social regulation, and the regulation of public security in the network society belongs to the category of social regulation [12]. In order to protect public interests and overcome the network disadvantages of the network society, many foreign countries usually implement the theory of regulation on the public security of the network society. Literature [13] believes that government departments should take the Internet as a part of public management, and the Internet control theory proposes various means and measures for the government to control the Internet, so it can be used as the theoretical basis for public security management in the network society.Literature [14] regards the network society as the same as the real society and assumes that various illegal and criminal activities occur in the network society as in the real society, so it is necessary to formulate relevant laws and regulations for the network society. The current legislation on public security in the network society is mainly reflected in two aspects. First, the current laws tend to focus on cybercrimes involving the computer system itself, while less involving the criminal tools and objects of cybercrime activities. The conviction and sentencing of the Internet society is not perfect, and there is a lack of criminal penalties for property, which makes it impossible to effectively combat illegal and criminal activities in the network society. Second, the Internet is developing at an alarming rate, and the types and models of public security violations in the network society emerge one after another. New problems, the current law has obviously not kept up with the needs of the speed [15].There should be comprehensive legislation on public security in the network society. Many countries have used this theory to establish a set of laws and regulations for the management of public security in the Internet society [16]. The theory of comprehensive legislation on public security in the network society makes people realize the role of legal rules in the management of public security in the network society, but it also ignores the role of relevant law enforcement systems and public governance mechanisms in the management of public security in the network society. The comprehensive legislative theory of social public security management has a certain degree of one-sidedness [17].In order to maintain the orderliness of the Internet cyberspace and protect the interests of online groups and individuals, it is necessary to carry out effective social control over the public security of the Internet society and build a control system with moral control as the main body. Comprehensive and appropriate control of social issues of public security in the network society requires humanistic care in the development of information technology [18]. Literature [19] believes that the Internet has greatly facilitated the production and life of the people and shortened the distance between people, but it has also brought many new problems to people, which have seriously endangered the society. At present, the public security organs are mainly responsible for the management of public security in the network society. However, in order to strengthen the management of public security in the network society, we cannot rely solely on the strength of the public security organs. We should strengthen legislation on the management of public security in the network society, strengthen the guidance of network public opinion, and create a sound social credit system. As the main administrative organ for the comprehensive management of social security, the public security organ plays an important role in the management of the network society. To strengthen the management of the network society, while emphasizing the strengthening of moral control, it is necessary not only to improve the network society management legislation but also to strengthen the moral management of Internet users. On the basis of establishing a sound legal system, his view comprehensively expounds the management of public security in the network society from the perspective of moral control.This paper combines the enhanced regression model to analyze the influencing factors of social public management scores and constructs a factor analysis model through intelligent algorithms to improve the effect of subsequent social public management.


## 2. Augmented Regression Model

### 2.1. An Extension of the Semiparametric Product Sampling Estimate

The semiparametric model-assisted sampling estimation proposed in this paper first assumes that the parameter part of the model is a linear function, and then multiplies it by an adjustment term to correct it. After that, it is verified that the estimation effect of this estimator is better than that of the GREG estimator by means of numerical simulation. This paper considers that when the parameters of SEM estimation are set to different functional forms, the corresponding estimators will have different estimation effects, that is, when the functional hypothesis of the parameter part can properly describe the relationship between the study variable and the auxiliary variable. At this time, the estimation effect of the SEM estimator will be significantly improved. This section takes the cubic function as an example to briefly introduce the theory and verify its estimation effect through numerical simulation.This paper theoretically introduces the form of the corresponding semiparameter estimator when the parameter part estimated by SEM is a cubic function. The specific derivation steps are as follows:In the first step, this paper establishes a semiparametric hyperpopulation regression model as in the following formula:(1)yk=mxk+εk=mxk,β⋅mxkmxk,β+εk.Among them, the parameter partmxk,β is no longer a simple linear function, but a cubic function, namely,(2)mxk,β=β0+β1xk+β2xk2+β3xk3.The second step assumes that the observed value of the whole unit of the whole finite population can be obtained; then, the parameterβ is obtained by the least square method. The solution based on the finite population is as follows:(3)β˜=XU∑U−1XU′XU∑U−1YU.Among them,XU is the 4×N-dimensional matrix XU=11⋯1x1x2⋯xNx12x22⋯xN2x13x23⋯xN3, and ΣU is the N×N diagonal matrix. However, in the actual sampling survey, the observation value of the population cannot be obtained, so the π estimator of β˜ can be obtained by using the π estimation method according to the observation value of the sample:(4)β^=Xs∑s−1Xs′Xs∑s−1YsAmong them,Xs is an 4×n-dimensional matrix Xs=11⋯1x1x2⋯xnx12x22⋯xn2x13x23⋯xn3,Σs is the n×n diagonal matrix of Σs=σ2π1⋯0⋮⋱⋮0⋯σ2πn,andYs is a n×1-dimensional column matrix Ys=y1,…,yn′.Then, the estimator of the parameter partmxk,β based on the sample unit is as follows:(5)mxk,β^=1,xk,xk2,xk3β^In the same way, the sample estimator of the adjustment item can be obtained according to the solution principle of the adjustment item:(6)r^ks=e1′Xsk′WskXsk−1Xsk′WskVs.Among them, theVs=y1/mx1,β^,…,yn/mxn,β^,n×p+1-dimensional matrix is Xsk=1,xl−xk,…,xl−xkpl∈s and the n×n-dimensional matrix is Wsk=diag1/πlhKxl−xk/hl∈s.The third step is to multiply the linear part obtained above and the sample estimator of the adjustment term, and the sample estimator of the semiparametric functionmxk can be obtained as follows:(7)m^ks=mxk,β^⋅r^ks=1,xk,xk2,xk3β^⋅e1′Xsk′WskXsk−1Xsk′WskVs.The fourth step is to combine the generalized difference estimation formula, that is, bringm^ks into formula (2) to obtain the semiparametric model-assisted regression estimator of the overall total value Y based on the sample s,(8)Y^=∑Um^ks+∑sYk−m^ksπk=∑U1,xk,xk2,xk3β^⋅e1′Xsk′WskXsk−1Xsk′WskVs+∑sYk−1,xk,xk2,xk3β^⋅e1′Xsk′WskXsk−1Xsk′WskVsπk.


### 2.2. Numerical Simulation of SEM Estimator Based on Cubic Function

#### 2.2.1. Comparison with the SEM Estimator Whose Parameter Part Is a Linear Function

This paper uses numerical simulation method to verify. Because the two are mainly aimed at nonlinear functions, the finite population constructed by the quadratic function and the trigonometric function is selected for simulation. Simple random sampling without replacement is still adopted from the finite population ofN = 1000, and 100 units are selected to form the sample s, and 1000 repeated samplings are carried out under each population. When the bandwidth of the adjustment term in the SEM estimation is appropriately chosen, the fitted images under the two finite populations are shown in Figures 1 and 2. The scatter plot is the description of the original function, the green line is the fitting graph when the parameter part estimated by SEM is a linear function, and the red line is the fitting graph when the parameter part estimated by SEM is a cubic function.Figure 1
Overall quadratic function.Figure 2
Overall trigonometric function 2.It can be seen from Figure1 that under the finite population composed of quadratic functions, when the parameter part estimated by SEM is a cubic function, the fitting graph is almost the same as the image of the original function. It can be seen that the fitting effect is better than the fitting effect corresponding to the linear function. Similarly, as can be seen from Figure 2, under the finite population composed of trigonometric function 2, the fitting effect of the parameter part estimated by SEM is a cubic function, which is improved compared with that of the linear function.


#### 2.2.2. Comparison with Local Polynomial Estimators

The semiparametric estimator proposed in this paper is compared with the numerical simulation results of the traditional GREG estimator. It is concluded that when the parameters are properly selected, when the auxiliary variables and the research variables do not satisfy a strict linear relationship, the effect of SEM estimation is significantly better than that of GREG estimation. Both SEM estimation and local polynomial estimation in this paper are proposed to make up for the shortcomings of traditional generalized regression estimation. Therefore, it is mainly applicable when auxiliary variables and study variables cannot satisfy the preconditions for generalized regression estimation (i.e., strictly linear relationship). Moreover, this paper mainly considers the quadratic function and trigonometric function 1 used in the numerical simulation for simulation comparison.Then, we construct a simulated population, according toyik=mixk+εk, k=1,…,N. Among them, x∈0,1, the auxiliary variable xk takes a uniform value in the interval [0,1], and the error term is εk∼iid.N0,σ2 . Moreover, this paper adopts simple random sampling without replacement from the finite population of N = 1000, selects 100 units to form the sample s, and conducts 1000 repeated samplings under each finite population. The series p of the local polynomial estimation of the adjustment term in the semiparametric model is 1, the series of the nonparametric local polynomial estimation is also 1, and the kernel function K⋅ is Gaussian kernel. The fitting effects of the above three estimators under the above two finite populations are shown in Figures 3 and 4. Among them, the scatter plot is the finite population composed of the original function, and the red line is the fitting graph when the parameter part estimated by SEM is a linear function. The green line is the fitting graph corresponding to the local polynomial estimation, and the yellow line is the fitting graph when the parameter part estimated by the SEM is a cubic function.Figure 3
Finite population composed of quadratic functions.Figure 4
Finite population formed by trigonometric function 2.It can be seen from Figure3 that under the finite population composed of quadratic functions, the fitting graph when the parameter part estimated by SEM is a linear function almost completely coincides with the fitting graph estimated by the local polynomial. The overall trend is consistent with the original function, but there is a certain deviation. However, when the parameter part of the SEM estimation is a cubic function, the corresponding fitting graph can more accurately describe the characteristics and trends of the original function, and the fitting effect is more accurate than that of the local polynomial estimation. In Figure 4, it can be seen that when the parameter part of the SEM estimation is a linear function, the fitting effect is roughly the same as that of the local polynomial estimation. However, when the parameter part estimated by SEM is a cubic function, the fitting graph is more in line with the overall trend of the original function, and the fitting effect is obviously better than the fitting effect of the former two. Therefore, it can be seen from the above fitting graph that when the parameter part of SEM estimation is a linear function, the fitting effect of the SEM estimation method proposed in this paper is similar to that of the local polynomial estimation. However, when the parameter part is a cubic function, the fitting effect of the SEM estimation proposed in this paper is significantly better than that of the local polynomial estimation.When the parameter part of the SEM estimation is a cubic function, it is under the finite population composed of the quadratic function and the trigonometric function 2. Compared with the local polynomial estimator, the relative mean square error of both is less than 0.3. It can be seen from this that the mean square error of SEM estimation is significantly smaller than that of local polynomial estimation. The relative design deviation of the SEM estimation when the parameter part is a cubic function is slightly smaller than the RB value of the local polynomial estimator.Therefore, we can know that compared with the local polynomial estimator widely used in the world, the SEM estimator proposed in this paper has a slightly lower estimation accuracy than the local polynomial estimator when the parameter part is a linear function. However, when the parameter part is a cubic function, the estimation accuracy of the SEM estimation is much higher than that of the local polynomial estimator.From the above numerical simulations, we can draw the following conclusions:(1)
Compared with the traditional generalized regression estimation, when there is no linear relationship between the research variables and auxiliary variables, the estimation effect of the SEM estimator is generally better than that of the GREG estimator.(2)
Compared with the local polynomial estimator, there are the following two conclusions:(a)
When the parameter part of the SEM estimation is assumed to be correct or the model is assumed to be incorrect but within a reasonable range, the estimation effect of the SEM estimation is better than the local polynomial estimation.(b)
When the parameter part of the SEM estimation is obviously wrong, the adjusted estimation effect will be reduced.


### 2.3. Enhanced Regression Semiparametric Product Estimation

Drawing on the theoretical method of generalized regression estimation in the first-order unit sampling model group, this section mainly discusses how to use auxiliary information to establish a model group in the case of typical first-order unit sampling such as simple random sampling, stratified sampling, and unequal probability sampling. Furthermore, a semiparametric model-assisted sampling estimation with higher estimation accuracy is obtained. This subsection mainly deduces the case where the parameter part estimated by SEM is a linear function. When the parameter part estimated by SEM is set as a cubic function or other appropriate parameter form, the same model extension can also be done.


#### 2.3.1. The Derivation Process of the Estimator

In the first step, the algorithm assumes that the samples is drawn from the finite population U according to a certain-order unit sampling design method, and assumes that the sampling frame or some external information can be used to divide the population into Q subpopulations in the sampling estimation stage, and denote it as U1,…Uq,…UQ. At the same time, the part of the sample s that falls into the subpopulation Uq is denoted as sq=s∩Uq. Then, it is assumed that there are auxiliary variables related to the research variables in each subpopulation Uq, denoted as xqk, where q=1,…,Q.In the second step, according to the modeling idea of formula (1), the algorithm establishes the corresponding model in each subpopulation Uq. The auxiliary regression model looks like this:(9)yk=mxqk+εqk=βq0+βq1xqkmxqkβq0+βq1xqk+εqk.Among them,k∈Uq,Eεqk=0,Vεqk=σq2<∞, and when k≠l, covεqk,εql=0 is satisfied. The algorithm uses the sample data yk,xqk in each subpopulation Uq to estimate the above model corresponding to each subpopulation. The estimation of the parameter part is as follows:(10)B^q=∑k∈sqxqk−x˜sqyk−y˜sq/πk∑k∈sqxqk−x˜sq2/πk,A^q=y˜sq−B^x˜sq.Among them,s˜sq=∑l∈sqxql/πl/N^,y˜sq=∑l∈sqyl/πl/N^q,andN^q=∑l∈sq1/πl. From this, the estimator of the linear part of the subpopulation model can be obtained as follows:(11)mxqk,β^q∗=A^q+B^qxqkThe estimate for the adjustment term is as follows:(12)r^ksp=e1′Xspk′WspkXspk−1Xspk′WspkVsp.Among them, theVsq=y1/mxq1,β^q∗,…,yn/mxqn,β^q∗,n×p+1-dimensional matrix is Xsqk=1,xql−xqk,…,xql−xqkplΘq, and the n×n-dimensional matrix is Wsqk=diag1/πlhKxql−xqk/hl∈sq.In the third step, the algorithm multiplies the linear part obtained above and the sample estimator of the adjustment term, and the sample estimator of the semiparametric functionmxqk in the subpopulation Uq can be obtained as follows:(13)m^ksq=mxqk,β^q∗⋅r^ksq.In the fourth step, the overall total valueYq of the subpopulation Uq can be obtained. The semiparametric model-assisted regression estimator based on sample sq is as follows:(14)Y^q,SEM=∑sqyk−A^q+B^qxqkr^ksqπk+A^q∑Uqr^ksq+B^q∑Uqxqkr^ksq.The fifth step is to add the estimates of the total value of each subpopulation to get the total value(15)Y^SEM=∑q=1QY^q,SEM.


#### 2.3.2. Types of Model Groups

In the actual investigation and research, the above theoretical methods mainly include two cases under the first-order sampling. The first is separate regression estimation under the condition of stratified sampling, namely, prior stratification. The basic condition of this method is that sufficient auxiliary information is needed. The second is post hoc stratified regression estimation under the conditions of unequal probability sampling and simple random sampling. Because there is a lot of auxiliary information required for prior stratification, which cannot be obtained in most investigations, or requires a great deal of time or expense, the method of ex post stratification can be used at this time. The above two situations are described as follows:First, we assume that the auxiliary variablex∈0,2 and the auxiliary variable xk take uniform values in the interval [0, 2]. When xk∈0,1, there is a linear relationship between the study variable and the auxiliary variable. When xk∈1,2, the relationship between the two is a quadratic function, the error term is εk∼iid.N0,σ2,σ=0.1, and the simulated population is constructed according to yk=mxk+εk.Secondly, it is assumed that the finite population can be divided into model groups according to auxiliary variables, and the overall unit ofxk∈0,1 is divided into model group 1, and the rest are model group 2.


## 2.1. An Extension of the Semiparametric Product Sampling Estimate

The semiparametric model-assisted sampling estimation proposed in this paper first assumes that the parameter part of the model is a linear function, and then multiplies it by an adjustment term to correct it. After that, it is verified that the estimation effect of this estimator is better than that of the GREG estimator by means of numerical simulation. This paper considers that when the parameters of SEM estimation are set to different functional forms, the corresponding estimators will have different estimation effects, that is, when the functional hypothesis of the parameter part can properly describe the relationship between the study variable and the auxiliary variable. At this time, the estimation effect of the SEM estimator will be significantly improved. This section takes the cubic function as an example to briefly introduce the theory and verify its estimation effect through numerical simulation.This paper theoretically introduces the form of the corresponding semiparameter estimator when the parameter part estimated by SEM is a cubic function. The specific derivation steps are as follows:In the first step, this paper establishes a semiparametric hyperpopulation regression model as in the following formula:(1)yk=mxk+εk=mxk,β⋅mxkmxk,β+εk.Among them, the parameter partmxk,β is no longer a simple linear function, but a cubic function, namely,(2)mxk,β=β0+β1xk+β2xk2+β3xk3.The second step assumes that the observed value of the whole unit of the whole finite population can be obtained; then, the parameterβ is obtained by the least square method. The solution based on the finite population is as follows:(3)β˜=XU∑U−1XU′XU∑U−1YU.Among them,XU is the 4×N-dimensional matrix XU=11⋯1x1x2⋯xNx12x22⋯xN2x13x23⋯xN3, and ΣU is the N×N diagonal matrix. However, in the actual sampling survey, the observation value of the population cannot be obtained, so the π estimator of β˜ can be obtained by using the π estimation method according to the observation value of the sample:(4)β^=Xs∑s−1Xs′Xs∑s−1YsAmong them,Xs is an 4×n-dimensional matrix Xs=11⋯1x1x2⋯xnx12x22⋯xn2x13x23⋯xn3,Σs is the n×n diagonal matrix of Σs=σ2π1⋯0⋮⋱⋮0⋯σ2πn,andYs is a n×1-dimensional column matrix Ys=y1,…,yn′.Then, the estimator of the parameter partmxk,β based on the sample unit is as follows:(5)mxk,β^=1,xk,xk2,xk3β^In the same way, the sample estimator of the adjustment item can be obtained according to the solution principle of the adjustment item:(6)r^ks=e1′Xsk′WskXsk−1Xsk′WskVs.Among them, theVs=y1/mx1,β^,…,yn/mxn,β^,n×p+1-dimensional matrix is Xsk=1,xl−xk,…,xl−xkpl∈s and the n×n-dimensional matrix is Wsk=diag1/πlhKxl−xk/hl∈s.The third step is to multiply the linear part obtained above and the sample estimator of the adjustment term, and the sample estimator of the semiparametric functionmxk can be obtained as follows:(7)m^ks=mxk,β^⋅r^ks=1,xk,xk2,xk3β^⋅e1′Xsk′WskXsk−1Xsk′WskVs.The fourth step is to combine the generalized difference estimation formula, that is, bringm^ks into formula (2) to obtain the semiparametric model-assisted regression estimator of the overall total value Y based on the sample s,(8)Y^=∑Um^ks+∑sYk−m^ksπk=∑U1,xk,xk2,xk3β^⋅e1′Xsk′WskXsk−1Xsk′WskVs+∑sYk−1,xk,xk2,xk3β^⋅e1′Xsk′WskXsk−1Xsk′WskVsπk.


## 2.2. Numerical Simulation of SEM Estimator Based on Cubic Function

### 2.2.1. Comparison with the SEM Estimator Whose Parameter Part Is a Linear Function

This paper uses numerical simulation method to verify. Because the two are mainly aimed at nonlinear functions, the finite population constructed by the quadratic function and the trigonometric function is selected for simulation. Simple random sampling without replacement is still adopted from the finite population ofN = 1000, and 100 units are selected to form the sample s, and 1000 repeated samplings are carried out under each population. When the bandwidth of the adjustment term in the SEM estimation is appropriately chosen, the fitted images under the two finite populations are shown in Figures 1 and 2. The scatter plot is the description of the original function, the green line is the fitting graph when the parameter part estimated by SEM is a linear function, and the red line is the fitting graph when the parameter part estimated by SEM is a cubic function.Figure 1
Overall quadratic function.Figure 2
Overall trigonometric function 2.It can be seen from Figure1 that under the finite population composed of quadratic functions, when the parameter part estimated by SEM is a cubic function, the fitting graph is almost the same as the image of the original function. It can be seen that the fitting effect is better than the fitting effect corresponding to the linear function. Similarly, as can be seen from Figure 2, under the finite population composed of trigonometric function 2, the fitting effect of the parameter part estimated by SEM is a cubic function, which is improved compared with that of the linear function.


### 2.2.2. Comparison with Local Polynomial Estimators

The semiparametric estimator proposed in this paper is compared with the numerical simulation results of the traditional GREG estimator. It is concluded that when the parameters are properly selected, when the auxiliary variables and the research variables do not satisfy a strict linear relationship, the effect of SEM estimation is significantly better than that of GREG estimation. Both SEM estimation and local polynomial estimation in this paper are proposed to make up for the shortcomings of traditional generalized regression estimation. Therefore, it is mainly applicable when auxiliary variables and study variables cannot satisfy the preconditions for generalized regression estimation (i.e., strictly linear relationship). Moreover, this paper mainly considers the quadratic function and trigonometric function 1 used in the numerical simulation for simulation comparison.Then, we construct a simulated population, according toyik=mixk+εk, k=1,…,N. Among them, x∈0,1, the auxiliary variable xk takes a uniform value in the interval [0,1], and the error term is εk∼iid.N0,σ2 . Moreover, this paper adopts simple random sampling without replacement from the finite population of N = 1000, selects 100 units to form the sample s, and conducts 1000 repeated samplings under each finite population. The series p of the local polynomial estimation of the adjustment term in the semiparametric model is 1, the series of the nonparametric local polynomial estimation is also 1, and the kernel function K⋅ is Gaussian kernel. The fitting effects of the above three estimators under the above two finite populations are shown in Figures 3 and 4. Among them, the scatter plot is the finite population composed of the original function, and the red line is the fitting graph when the parameter part estimated by SEM is a linear function. The green line is the fitting graph corresponding to the local polynomial estimation, and the yellow line is the fitting graph when the parameter part estimated by the SEM is a cubic function.Figure 3
Finite population composed of quadratic functions.Figure 4
Finite population formed by trigonometric function 2.It can be seen from Figure3 that under the finite population composed of quadratic functions, the fitting graph when the parameter part estimated by SEM is a linear function almost completely coincides with the fitting graph estimated by the local polynomial. The overall trend is consistent with the original function, but there is a certain deviation. However, when the parameter part of the SEM estimation is a cubic function, the corresponding fitting graph can more accurately describe the characteristics and trends of the original function, and the fitting effect is more accurate than that of the local polynomial estimation. In Figure 4, it can be seen that when the parameter part of the SEM estimation is a linear function, the fitting effect is roughly the same as that of the local polynomial estimation. However, when the parameter part estimated by SEM is a cubic function, the fitting graph is more in line with the overall trend of the original function, and the fitting effect is obviously better than the fitting effect of the former two. Therefore, it can be seen from the above fitting graph that when the parameter part of SEM estimation is a linear function, the fitting effect of the SEM estimation method proposed in this paper is similar to that of the local polynomial estimation. However, when the parameter part is a cubic function, the fitting effect of the SEM estimation proposed in this paper is significantly better than that of the local polynomial estimation.When the parameter part of the SEM estimation is a cubic function, it is under the finite population composed of the quadratic function and the trigonometric function 2. Compared with the local polynomial estimator, the relative mean square error of both is less than 0.3. It can be seen from this that the mean square error of SEM estimation is significantly smaller than that of local polynomial estimation. The relative design deviation of the SEM estimation when the parameter part is a cubic function is slightly smaller than the RB value of the local polynomial estimator.Therefore, we can know that compared with the local polynomial estimator widely used in the world, the SEM estimator proposed in this paper has a slightly lower estimation accuracy than the local polynomial estimator when the parameter part is a linear function. However, when the parameter part is a cubic function, the estimation accuracy of the SEM estimation is much higher than that of the local polynomial estimator.From the above numerical simulations, we can draw the following conclusions:(1)
Compared with the traditional generalized regression estimation, when there is no linear relationship between the research variables and auxiliary variables, the estimation effect of the SEM estimator is generally better than that of the GREG estimator.(2)
Compared with the local polynomial estimator, there are the following two conclusions:(a)
When the parameter part of the SEM estimation is assumed to be correct or the model is assumed to be incorrect but within a reasonable range, the estimation effect of the SEM estimation is better than the local polynomial estimation.(b)
When the parameter part of the SEM estimation is obviously wrong, the adjusted estimation effect will be reduced.


## 2.2.1. Comparison with the SEM Estimator Whose Parameter Part Is a Linear Function

This paper uses numerical simulation method to verify. Because the two are mainly aimed at nonlinear functions, the finite population constructed by the quadratic function and the trigonometric function is selected for simulation. Simple random sampling without replacement is still adopted from the finite population ofN = 1000, and 100 units are selected to form the sample s, and 1000 repeated samplings are carried out under each population. When the bandwidth of the adjustment term in the SEM estimation is appropriately chosen, the fitted images under the two finite populations are shown in Figures 1 and 2. The scatter plot is the description of the original function, the green line is the fitting graph when the parameter part estimated by SEM is a linear function, and the red line is the fitting graph when the parameter part estimated by SEM is a cubic function.Figure 1
Overall quadratic function.Figure 2
Overall trigonometric function 2.It can be seen from Figure1 that under the finite population composed of quadratic functions, when the parameter part estimated by SEM is a cubic function, the fitting graph is almost the same as the image of the original function. It can be seen that the fitting effect is better than the fitting effect corresponding to the linear function. Similarly, as can be seen from Figure 2, under the finite population composed of trigonometric function 2, the fitting effect of the parameter part estimated by SEM is a cubic function, which is improved compared with that of the linear function.


## 2.2.2. Comparison with Local Polynomial Estimators

The semiparametric estimator proposed in this paper is compared with the numerical simulation results of the traditional GREG estimator. It is concluded that when the parameters are properly selected, when the auxiliary variables and the research variables do not satisfy a strict linear relationship, the effect of SEM estimation is significantly better than that of GREG estimation. Both SEM estimation and local polynomial estimation in this paper are proposed to make up for the shortcomings of traditional generalized regression estimation. Therefore, it is mainly applicable when auxiliary variables and study variables cannot satisfy the preconditions for generalized regression estimation (i.e., strictly linear relationship). Moreover, this paper mainly considers the quadratic function and trigonometric function 1 used in the numerical simulation for simulation comparison.Then, we construct a simulated population, according toyik=mixk+εk, k=1,…,N. Among them, x∈0,1, the auxiliary variable xk takes a uniform value in the interval [0,1], and the error term is εk∼iid.N0,σ2 . Moreover, this paper adopts simple random sampling without replacement from the finite population of N = 1000, selects 100 units to form the sample s, and conducts 1000 repeated samplings under each finite population. The series p of the local polynomial estimation of the adjustment term in the semiparametric model is 1, the series of the nonparametric local polynomial estimation is also 1, and the kernel function K⋅ is Gaussian kernel. The fitting effects of the above three estimators under the above two finite populations are shown in Figures 3 and 4. Among them, the scatter plot is the finite population composed of the original function, and the red line is the fitting graph when the parameter part estimated by SEM is a linear function. The green line is the fitting graph corresponding to the local polynomial estimation, and the yellow line is the fitting graph when the parameter part estimated by the SEM is a cubic function.Figure 3
Finite population composed of quadratic functions.Figure 4
Finite population formed by trigonometric function 2.It can be seen from Figure3 that under the finite population composed of quadratic functions, the fitting graph when the parameter part estimated by SEM is a linear function almost completely coincides with the fitting graph estimated by the local polynomial. The overall trend is consistent with the original function, but there is a certain deviation. However, when the parameter part of the SEM estimation is a cubic function, the corresponding fitting graph can more accurately describe the characteristics and trends of the original function, and the fitting effect is more accurate than that of the local polynomial estimation. In Figure 4, it can be seen that when the parameter part of the SEM estimation is a linear function, the fitting effect is roughly the same as that of the local polynomial estimation. However, when the parameter part estimated by SEM is a cubic function, the fitting graph is more in line with the overall trend of the original function, and the fitting effect is obviously better than the fitting effect of the former two. Therefore, it can be seen from the above fitting graph that when the parameter part of SEM estimation is a linear function, the fitting effect of the SEM estimation method proposed in this paper is similar to that of the local polynomial estimation. However, when the parameter part is a cubic function, the fitting effect of the SEM estimation proposed in this paper is significantly better than that of the local polynomial estimation.When the parameter part of the SEM estimation is a cubic function, it is under the finite population composed of the quadratic function and the trigonometric function 2. Compared with the local polynomial estimator, the relative mean square error of both is less than 0.3. It can be seen from this that the mean square error of SEM estimation is significantly smaller than that of local polynomial estimation. The relative design deviation of the SEM estimation when the parameter part is a cubic function is slightly smaller than the RB value of the local polynomial estimator.Therefore, we can know that compared with the local polynomial estimator widely used in the world, the SEM estimator proposed in this paper has a slightly lower estimation accuracy than the local polynomial estimator when the parameter part is a linear function. However, when the parameter part is a cubic function, the estimation accuracy of the SEM estimation is much higher than that of the local polynomial estimator.From the above numerical simulations, we can draw the following conclusions:(1)
Compared with the traditional generalized regression estimation, when there is no linear relationship between the research variables and auxiliary variables, the estimation effect of the SEM estimator is generally better than that of the GREG estimator.(2)
Compared with the local polynomial estimator, there are the following two conclusions:(a)
When the parameter part of the SEM estimation is assumed to be correct or the model is assumed to be incorrect but within a reasonable range, the estimation effect of the SEM estimation is better than the local polynomial estimation.(b)
When the parameter part of the SEM estimation is obviously wrong, the adjusted estimation effect will be reduced.


## 2.3. Enhanced Regression Semiparametric Product Estimation

Drawing on the theoretical method of generalized regression estimation in the first-order unit sampling model group, this section mainly discusses how to use auxiliary information to establish a model group in the case of typical first-order unit sampling such as simple random sampling, stratified sampling, and unequal probability sampling. Furthermore, a semiparametric model-assisted sampling estimation with higher estimation accuracy is obtained. This subsection mainly deduces the case where the parameter part estimated by SEM is a linear function. When the parameter part estimated by SEM is set as a cubic function or other appropriate parameter form, the same model extension can also be done.


### 2.3.1. The Derivation Process of the Estimator

In the first step, the algorithm assumes that the samples is drawn from the finite population U according to a certain-order unit sampling design method, and assumes that the sampling frame or some external information can be used to divide the population into Q subpopulations in the sampling estimation stage, and denote it as U1,…Uq,…UQ. At the same time, the part of the sample s that falls into the subpopulation Uq is denoted as sq=s∩Uq. Then, it is assumed that there are auxiliary variables related to the research variables in each subpopulation Uq, denoted as xqk, where q=1,…,Q.In the second step, according to the modeling idea of formula (1), the algorithm establishes the corresponding model in each subpopulation Uq. The auxiliary regression model looks like this:(9)yk=mxqk+εqk=βq0+βq1xqkmxqkβq0+βq1xqk+εqk.Among them,k∈Uq,Eεqk=0,Vεqk=σq2<∞, and when k≠l, covεqk,εql=0 is satisfied. The algorithm uses the sample data yk,xqk in each subpopulation Uq to estimate the above model corresponding to each subpopulation. The estimation of the parameter part is as follows:(10)B^q=∑k∈sqxqk−x˜sqyk−y˜sq/πk∑k∈sqxqk−x˜sq2/πk,A^q=y˜sq−B^x˜sq.Among them,s˜sq=∑l∈sqxql/πl/N^,y˜sq=∑l∈sqyl/πl/N^q,andN^q=∑l∈sq1/πl. From this, the estimator of the linear part of the subpopulation model can be obtained as follows:(11)mxqk,β^q∗=A^q+B^qxqkThe estimate for the adjustment term is as follows:(12)r^ksp=e1′Xspk′WspkXspk−1Xspk′WspkVsp.Among them, theVsq=y1/mxq1,β^q∗,…,yn/mxqn,β^q∗,n×p+1-dimensional matrix is Xsqk=1,xql−xqk,…,xql−xqkplΘq, and the n×n-dimensional matrix is Wsqk=diag1/πlhKxql−xqk/hl∈sq.In the third step, the algorithm multiplies the linear part obtained above and the sample estimator of the adjustment term, and the sample estimator of the semiparametric functionmxqk in the subpopulation Uq can be obtained as follows:(13)m^ksq=mxqk,β^q∗⋅r^ksq.In the fourth step, the overall total valueYq of the subpopulation Uq can be obtained. The semiparametric model-assisted regression estimator based on sample sq is as follows:(14)Y^q,SEM=∑sqyk−A^q+B^qxqkr^ksqπk+A^q∑Uqr^ksq+B^q∑Uqxqkr^ksq.The fifth step is to add the estimates of the total value of each subpopulation to get the total value(15)Y^SEM=∑q=1QY^q,SEM.


### 2.3.2. Types of Model Groups

In the actual investigation and research, the above theoretical methods mainly include two cases under the first-order sampling. The first is separate regression estimation under the condition of stratified sampling, namely, prior stratification. The basic condition of this method is that sufficient auxiliary information is needed. The second is post hoc stratified regression estimation under the conditions of unequal probability sampling and simple random sampling. Because there is a lot of auxiliary information required for prior stratification, which cannot be obtained in most investigations, or requires a great deal of time or expense, the method of ex post stratification can be used at this time. The above two situations are described as follows:First, we assume that the auxiliary variablex∈0,2 and the auxiliary variable xk take uniform values in the interval [0, 2]. When xk∈0,1, there is a linear relationship between the study variable and the auxiliary variable. When xk∈1,2, the relationship between the two is a quadratic function, the error term is εk∼iid.N0,σ2,σ=0.1, and the simulated population is constructed according to yk=mxk+εk.Secondly, it is assumed that the finite population can be divided into model groups according to auxiliary variables, and the overall unit ofxk∈0,1 is divided into model group 1, and the rest are model group 2.


## 2.3.1. The Derivation Process of the Estimator

In the first step, the algorithm assumes that the samples is drawn from the finite population U according to a certain-order unit sampling design method, and assumes that the sampling frame or some external information can be used to divide the population into Q subpopulations in the sampling estimation stage, and denote it as U1,…Uq,…UQ. At the same time, the part of the sample s that falls into the subpopulation Uq is denoted as sq=s∩Uq. Then, it is assumed that there are auxiliary variables related to the research variables in each subpopulation Uq, denoted as xqk, where q=1,…,Q.In the second step, according to the modeling idea of formula (1), the algorithm establishes the corresponding model in each subpopulation Uq. The auxiliary regression model looks like this:(9)yk=mxqk+εqk=βq0+βq1xqkmxqkβq0+βq1xqk+εqk.Among them,k∈Uq,Eεqk=0,Vεqk=σq2<∞, and when k≠l, covεqk,εql=0 is satisfied. The algorithm uses the sample data yk,xqk in each subpopulation Uq to estimate the above model corresponding to each subpopulation. The estimation of the parameter part is as follows:(10)B^q=∑k∈sqxqk−x˜sqyk−y˜sq/πk∑k∈sqxqk−x˜sq2/πk,A^q=y˜sq−B^x˜sq.Among them,s˜sq=∑l∈sqxql/πl/N^,y˜sq=∑l∈sqyl/πl/N^q,andN^q=∑l∈sq1/πl. From this, the estimator of the linear part of the subpopulation model can be obtained as follows:(11)mxqk,β^q∗=A^q+B^qxqkThe estimate for the adjustment term is as follows:(12)r^ksp=e1′Xspk′WspkXspk−1Xspk′WspkVsp.Among them, theVsq=y1/mxq1,β^q∗,…,yn/mxqn,β^q∗,n×p+1-dimensional matrix is Xsqk=1,xql−xqk,…,xql−xqkplΘq, and the n×n-dimensional matrix is Wsqk=diag1/πlhKxql−xqk/hl∈sq.In the third step, the algorithm multiplies the linear part obtained above and the sample estimator of the adjustment term, and the sample estimator of the semiparametric functionmxqk in the subpopulation Uq can be obtained as follows:(13)m^ksq=mxqk,β^q∗⋅r^ksq.In the fourth step, the overall total valueYq of the subpopulation Uq can be obtained. The semiparametric model-assisted regression estimator based on sample sq is as follows:(14)Y^q,SEM=∑sqyk−A^q+B^qxqkr^ksqπk+A^q∑Uqr^ksq+B^q∑Uqxqkr^ksq.The fifth step is to add the estimates of the total value of each subpopulation to get the total value(15)Y^SEM=∑q=1QY^q,SEM.


## 2.3.2. Types of Model Groups

In the actual investigation and research, the above theoretical methods mainly include two cases under the first-order sampling. The first is separate regression estimation under the condition of stratified sampling, namely, prior stratification. The basic condition of this method is that sufficient auxiliary information is needed. The second is post hoc stratified regression estimation under the conditions of unequal probability sampling and simple random sampling. Because there is a lot of auxiliary information required for prior stratification, which cannot be obtained in most investigations, or requires a great deal of time or expense, the method of ex post stratification can be used at this time. The above two situations are described as follows:First, we assume that the auxiliary variablex∈0,2 and the auxiliary variable xk take uniform values in the interval [0, 2]. When xk∈0,1, there is a linear relationship between the study variable and the auxiliary variable. When xk∈1,2, the relationship between the two is a quadratic function, the error term is εk∼iid.N0,σ2,σ=0.1, and the simulated population is constructed according to yk=mxk+εk.Secondly, it is assumed that the finite population can be divided into model groups according to auxiliary variables, and the overall unit ofxk∈0,1 is divided into model group 1, and the rest are model group 2.


## 3. Analysis of Influencing Factors of Social Public Management Score

The most direct manifestation of the complex social reality is the increasing ungovernability of society. The so-called ungovernability does not mean that the society has really fallen into a state of complete disorder, but a state of “chaos”; that is, it has the dual characteristics of chaos and order at the same time. The simple logic of “disorder-control-order” is still unworkable for public governance in view of complex social reality, and it will only form a vicious circle of “disorder-control-disorder,” as shown in Figure5. Instead, we should recognize the “chaotic” state of social complexity and social reality, and on this basis, we should carry out the social construction of public governance.Figure 5
Traditional ways of solving social problems.The pluralism of social management innovation seems to provide a whole set of solutions to the problem, that is, to achieve the goal of “good governance” by repeatedly emphasizing “participation, dialogue, co-governance, multi-agent consultation, and cooperation.” The pluralism of social management innovation presupposes a definite social macro-governance framework for complex social governance, and it is a governance framework built in a patchwork manner. However, it lacks a microscopic interaction basis, so there are inherent deficiencies. Specifically, the pluralism of social management innovation follows the logic shown in Figure6.Figure 6
The logic of governance theory.Through the measurement and analysis of channel mode public service feature matching, channel type public service feature matching, and channel type and channel mode public service feature matching, this paper proposes a public service channel management model, as shown in Figure7.Figure 7
Public service channel management model based on service feature matching degree.This paper proposes a life cycle model for public safety data (Figure8(a)). Starting from public safety data, the model fully considers the differences of participants in data activities in public safety governance and forms a cyclic process including five main stages of data planning, data collection, data processing, data preservation, and data use.Figure 8
Public safety data management. (a) Life cycle model of public safety data. (b) 3D model of public safety data management based on life cycle.
(a)(b)Since risk management, emergency management, and crisis management also have the characteristics of their life cycle stages, it is possible to embed the data life cycle into public security governance activities and make it possible for data activities to respond to the data needs of public security governance activities at different stages. Based on this, a three-dimensional model of public safety data management based on life cycle is constructed (Figure8(b)). The model combines the life cycle of public safety data with the life cycle of public safety governance content, helping to refine data requirements under different management content and contexts. Furthermore, data management activities can be adapted to public security governance activities and business management activities within different organizations, so as to achieve effective data management that is in line with public security governance practices.On the basis of the above research, the application of the enhanced regression method in this paper in the social public management score is analyzed, and its clustering effect is counted. The results are shown in Figure9.Figure 9
Clustering effect of enhanced regression method in social public management score.Through the above research, we can see that the analysis model of social public management score influencing factors based on the enhanced regression model proposed in this paper has a certain effect.


## 4. Conclusion

Public crisis events are extremely harmful to society, difficult to control, and urgent. Moreover, it is extremely destructive, has a wide impact, and has great uncertainty, which makes the cost of coping very high and requires high professional skills and organizational systems. At the same time, its social harm determines that responding to public crises has public and charitable significance, and has strong social significance. This paper combines the enhanced regression model to analyze the influencing factors of social public management scores, and constructs the factor analysis model through intelligent algorithms. Through the measurement and analysis of the public service feature matching of channel mode, channel type public service feature matching, and the matching of channel type and channel mode public service feature, this paper proposes a public service channel management model. The research results show that the analysis model of social public management score influencing factors based on the enhanced regression model proposed in this paper has a certain effect.



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*Source: 3012627-2022-07-08.xml*