A Novel Massive Big Data Analysis of Educational Examination Research Using a Linear Mixed-Effects Model

To further solve the problems of storage bottlenecks and excessive calculation time when calculating estimators under two different formats of massive longitudinal data, an examination data analysis and evaluation method based on an improved linear mixed-effects model is proposed in this paper. First, a three-step estimation method is proposed to improve the parameters of the linear-effects model, avoiding the complicated iterative steps of maximum likelihood estimation. Second, we perform spectral clustering based on test data on the basis of defining data attributes and basic evaluation rules. Finally, based on cloud technology, a cross-regional, multiuser educational examination big data analysis and evaluation service platform is developed for evaluating the proposed method. Experimental results have shown that the proposed model can not only effectively improve the efficiency of test data acquisition and storage but also reduce the computational burden and the memory usage, solve the problem of insufficient memory, and increase the calculation speed.


Introduction
Nowadays, the era of big data affects many industries. Among them, the education industry has also improved its educational examinations through the use of big data technology [1]. In traditional educational examinations, teachers have very little understanding of the role of examinations. Teachers believe that examinations can only provide a simple understanding of students' knowledge and skills. However, the results measured by traditional educational examinations have many uncertain factors [2]. In terms of teaching examinations, schools can carry out large-scale networked education examinations and online learning. As long as they are from the perspective of big data, students can participate in online learning activities.
In the process of students learning through the Internet, teachers can accurately grasp the status of students' learning ability to find students' deficiencies and, at the same time, can improve students' nonintellectual factors, such as emotional intelligence, values, learning motivation, and enthusiasm.
Educational examination big data analysis and evaluation is to mine the original test data of students, feedback a large amount of information and laws hidden in the data relationship, and assist the education department, teachers, and students to analyze the reasons for the formation of test results.
e relationship between the test results and the actual ability of students is built to improve the process and methods of education and assessment on this basis. Scientific, accurate, and comprehensive test data analysis and evaluation are of great significance to students' self-diagnosis, teachers' feedback and summation, and educational test policy formulation, which is embodied in [3]: (1) A rational self-diagnosis helps students to understand the strengths and weaknesses of their own learning and improve their sense of self-efficacy and self-psychology (2) Teachers can analyze and summarize test results, link teaching, feedback teaching, and reflect on teaching (3) Educational authorities can adjust education examination policies and improve the forms and methods of examination evaluation through examination evaluation and analysis results (4) rough multidimensional analysis of student test results, the trust and cooperation between the parents and the school can be strengthened, to provide reference for the joint development of a student's individual study and life plan However, the current examination data analysis and evaluation mainly have the following shortcomings [4]: (1) Simplification of the examination data processing (2) Fuzzy analysis of test results (3) Simplification of the test result feedback However, the current simplification of test results can easily lead to the rigidity of the test question system and loss of the vitality of the test questions, which is not conductive to the control of the education authorities. e overall education and teaching situation formulate appropriate education and teaching policies.
With the rapid development of information and network technology, the speed of data growth and change is amazing, showing a trend of data massive quantification [5]. Traditional linear mixed model estimation methods have encountered a series of challenges under massive data, such as storage bottlenecks, computational efficiency, and other problems [6], so it is necessary to explore new algorithms to improve the previous estimation methods of linear mixed effects models. In order to construct the optimal estimation of the coefficients in the linear mixed effects model, [7] proposed a weighted least squares method based on the covariance structure, but the efficiency of this estimation method is closely related to the covariance structure estimation method of longitudinal data. ere are some commonly used covariance structure estimation methods, including maximum likelihood method and limited maximum likelihood method. However, these methods require repeated iterative calculations and optimization steps, which will lead to high calculation time and quantity cost when the amount of data is very large.
To solve such problems, [8] proposed a simple method for estimating variance components when studying random effect variable coefficient models.
is method does not require iterative calculation and can adapt to massive data situations. However, directly using the weighted least squares method in matrix form to estimate model coefficients will encounter storage problems, so the divideand-conquer algorithm has been proposed and has been widely used in the statistical calculation of massive data [9]. e core idea of the divide-and-conquer algorithm is to first decompose a complex problem into several subproblems, find the solutions to these subproblems, and then use a suitable method to combine the results of each subproblem to get the result of the entire problem. e divide-andconquer algorithm proposed by [10] is the most practical method to solve the problem of massive data analysis. Reference [11] combined the least squares method with the divide-and-conquer algorithm to solve the estimation problem of linear regression models under massive data. e dataset is divided into a series of manageable data blocks. en, the least square method is run independently on each data block, and finally, the results of each data block are integrated to obtain the final result. However, previous scholars only used the divide-and-conquer algorithm to solve the estimation problem of simple data models under massive data and have not studied the estimation algorithms of more complex and more widely used linear mixed-effect models under massive data.
Based on the weighted least squares estimation method of linear mixed-effects model coefficients in [12] and the estimation method of variance components and divide-andconquer algorithm in [13], this paper proposes an improved linear mixed-effects model [14]. First, a three-step estimation method for linear mixed model parameters is proposed based on the conventional linear mixed-effects model. In the estimation method, the iterative calculation based on maximum likelihood estimation or limited maximum likelihood estimation is avoided for the requirements of massive data. en, based on the analysis of two different situations of massive data, the rule algorithm calculates the estimator in steps. Experiments show that the algorithm proposed in this paper can not only reduce memory usage and solve storage problems but also shorten computing time and increase computing speed. Aiming at the single, one-sided, and complex characteristics of the educational examination quality evaluation process, as well as the resulting unscientific and nonobjective examination evaluation problems, based on the improved linear mixed effect model, we have developed a large amount of educational examination big data and the application analysis of the proposed method, including the following.
(1) Define test data attributes, including forward attributes and reverse attributes, and establish gradient evaluation rules (2) On the basis of defining data attributes and basic evaluation rules, perform hierarchical filtering of test data based on spectral clustering to identify basic group clusters (3) Based on the gradient evaluation rule, the group cluster is corrected twice to avoid the unscientificity of the single score evaluation mechanism (4) Based on cloud technology, a cross-regional, multiuser educational examination big data analysis and evaluation service platform has been developed 2 Complexity Application results have proved that the platform can effectively improve the efficiency of test data acquisition and storage and, at the same time, provide effective analysis tools for education supervisors and implementation departments.

Linear Mixed-Effects Model and Its Estimation Method.
Consider the linear mixed effects model of longitudinal data: Here, the unknown parameter β is a p × 1 dimensional fixed effect vector, b i is a q × 1 dimensional random effect vector, and X ij and Z ij , respectively, represent the covariates related to it. Assume that the random effects b i ⇔N(0, ), and the model error is ε ij ⇔N(0, σ 2 ). Both satisfy the condition of independent and identical distribution, and b i and ε ij are independent of each other.
To avoid iterative calculation, a three-step estimation method is proposed to estimate the variance components and fixed effects of the linear mixed-effects model, respectively. e consistency and asymptotic normality of the estimates can be obtained by using the proof steps similar to those in [15]. erefore, this paper only considered the estimation algorithm. First, we use the least square method to make a preliminary estimate of the coefficients. Let en, (1) can be reexpressed as follows: e least squares estimation of the model coefficients is directly obtained by (2). en, a preliminary estimation can also be obtained by the following equation: Second, the variance component is estimated. We use the principle of [15] to estimate the variance component σ 2 , . Let erefore, the estimated value of random effect b i can be obtained by using the least square method According to the estimation procedure in [15], further considering the influence of the estimated value of the coefficient β 0 , the estimation of the variance can be constructed similarly: where N � n i�1 n i , q is the dimension of b i , and p is the dimension of β. Next, the is estimated according to the definition of By directly calculating the first and second moments of each item, it can be proved that the order of the last two items in (6) is O p (n (1/2) ), so it can be ignored compared with the other items. us, So, we can obtain Finally, calculate the weighted least squares estimate of β From (6) and (8), the following is obtained: According to the weighted least squares estimation method of [13], we can obtain Or we also can use the calculation of the sample summation equation (12) in [13]: (1) e amount of individual data is larger, but the amount of data in the group is smaller, (2) e amount of individual data is smaller, but the amount of data in the group is larger.
At this time, storage bottlenecks and computational inefficiencies will be encountered, and the previously mentioned estimation methods are no longer applicable. erefore, in these two scenarios, the divide-and-conquer algorithm is used to adjust the three-step estimation method proposed previously.

e Amount of Individual Data Is Large, and the Amount of Data in the Group Is
n,n i i�1,j�1 be the entire dataset. According to the divide-and-conquer algorithm, the dataset D is divided into K subsets D 1 , D 2 , . . . , D K . e number of samples in each subset m � n/K, and the data contained in each subset is X kij , Z kij , Y kij , where 1 ≤ j ≤ n ki , 1 ≤ i ≤ m, 1 ≤ k ≤ K, and the data contained in each subset cannot exceed the processing capacity of a single machine. First, we have calculated a preliminary estimate. Remember and ε k are similarly defined, and T are well-defined according to the previously mentioned theory. en, the data model corresponding to the k-th subset can be written as e least square estimation for each subdataset directly according to the divide-and-conquer algorithm, integrate the results of each subset, save each group of X T k X k , β 0k , and finally obtain preliminary estimates: Second, we use the divide-and-conquer algorithm to estimate the variance component. Remember that erefore, we can obtain From the previous section, we can see that (16), the data to be calculated and saved cor- Finally, a weighted estimate of the model coefficient β is calculated. According to the calculation equations (15) and (16) of the variance component, the covariance matrix of the k-th subdata model is estimated as V k � Z k Z T k + σ 2 I n i ×m . Using the weighted least squares method to estimate that k X k , β k is retained, and the integrated result of each subset to get:

e Amount of Individual Data Is Small, and the Amount of Data in the Group Is
Large. First, we have applied the divide-and-conquer algorithm to each individual. Let . . , D iK , and the number of samples in each subset is m i � n i /K. e data contained in each subset are X ikj , Y ikj , and Z ikj , where 1 ≤ j ≤ m i , 1 ≤ k ≤ K, 1 ≤ i ≤ n, and the data contained in each subset cannot exceed the processing capacity of a single machine. First, we have calculated a preliminary estimate. Remember are similarly defined, and the data model corresponding to the k-th subset of the i-th individual is For each dataset of each individual, direct least squares According to the divide-and-conquer algorithm, we have integrated the results of each individual and each subset, saved each group of X T ik X ik , β 0ik , and finally obtained a preliminary estimate: Second, use the divide-and-conquer algorithm to estimate the variance component. Remember the definition of Complexity erefore, we can obtain It can be seen from Section 2.1 that e weighting is applied to each subset of each individual, and the least squares estimates are It can be seen that the data is retained for each subset of each individual:

Data Attributes.
e continuous score attribute of the test data is defined by combining the test data mining theme, characteristics of the tested students, gradient evaluation rules, and secondary calibration target [16]. Take the objective question type as an example: a multiple-choice question has four answers, one of which is the correct answer. However, from the perspective of the proposition, the other three options are not added casually without basis, and there are some wrong options that are "close" to the correct answer. e reason why students choose the wrong option is not that they do not know anything about this knowledge, but just because they are inadequate or careless and are deceived by the confusing options. In the traditional examination evaluation process, this feature is not accurate for the reflection.
On the contrary, there are individual options that do not have any connection with the knowledge point, and selecting this option can basically judge that the students have no knowledge of this point. Obviously, these two types of subjects are different, so examination analysis and evaluation should treat them differently and conduct targeted guidance and treatment. In addition, for different test objectives, the ability to examine students should not be solely based on test scores. Some assessment objectives hope to get students' comprehensive ability assessment, including practical ability, specialty, interest, and so on. erefore, in the proposition of the test questions, for different question types, possible different answers, and different test objectives, the positive and negative multidimensional attributes of the test data are defined, and the multidimensional attribute model of the test data is established [17]. e data model is shown in Figure 1, except the score attribute. e fact attribute is set at the same time to reflect the factual mastery of the test knowledge points of the examinee and provide a data basis for the secondary calibration.
According to the definition of the data model, examination evaluation is also divided into two categories: regular evaluation rules and correction rules. e regular evaluation rules only include the test scores of a certain test. e correction rules include the gradient evaluation of the candidates' wrong answers, usual results, test results, special hobbies, family background, parents' occupations, and so on. Gradient evaluation of wrong answers can be used to find a special group of students whose answers are wrong due to special reasons. e usual scores are used to evaluate the students' usual learning status. Test scores are a direct evaluation of a certain stage of learning. Special hobbies are important for comprehensive evaluation of students. According to the basis, family background and parent occupation are an important factor in investigating students' specialties and partial subjects. At the same time, the relationship between different family backgrounds and parent occupations and students' academic performance can be analyzed [18].
On taking objective questions as an example, among the four options, the only correct answer scores 100, and the confusing answer set to examine a certain knowledge point can be defined as a score of 50 to 70 according to the degree of relevance between it and the correct answer. e score is 0 for options that are completely unrelated to changing the topic and investigating knowledge points. In addition, we set up a statistical rule. If a student chooses the wrong option in a certain subject examination, there are more options that are highly related to the knowledge points examined, and then the score weight of the wrong option can be increased. On the contrary, if there are more choices of wrong options with a low degree of relevance, the score weight should be appropriately reduced. e correction rules can objectively reflect the participants' understanding of the knowledge points tested. Fact evaluation rules can discover special Complexity 5 subject groups, such as "careless mistakes," "nothing at all," and "random selection," and provide targeted guidance and treatment to them. To achieve this goal, this paper first performs hierarchical filtering based on spectral clustering on the test data [19] and then performs secondary correction on each data cluster that is hierarchically filtered.

Hierarchical Filtering Based on Spectral Clustering.
Clustering is the process of distinguishing and classifying things according to certain rules and requirements. In this process, there is no prior knowledge about classification, and only the similarity between things is used as the criterion for classification. Compared with traditional clustering algorithms, spectral clustering has the advantage of being able to cluster on sample spaces of arbitrary shapes and converging to the global optimal solution. e spectral clustering algorithm can be briefly described as follows: given a dataset . . , n is the set of vertices, and E � e ij is the edge connecting the vertices (v i , v j ). Each node v i in the graph G is related to x i in the dataset X. A similarity criterion is used to construct the similarity matrix W between the vertices of the graph G, W ∈ R n×n . For two objects x i and x j , the similarity s is defined . e algorithm inputs the similarity matrix W of the graph G and the number of clusters k and outputs the clustering results of x 1 , x 2 , . . . , x n . e hierarchical filtering algorithm based on spectral clustering adds the distance matrix of the answer data object based on the characteristics of the test answer data object based on the spectral clustering and obtains a spectral clustering algorithm suitable for answering data analysis [20]. Assuming that the questionnaire data object x of the study has p test points, expressed as (x 1 , x 2 , . . . , x p ), the distance d(u, v) between the two questionnaire data objects u and v can be defined as follows: According to the distance between the questionnaire data objects, the similarity s(u, v) between the questionnaire data objects u and v of two subjects can be defined as follows: S(u, v) � exp(− d(u, v)/2σ 2 ), normally, σ � 1. e hierarchical filtering and analysis algorithm of spectral clustering algorithm for answering data includes the following steps.
(1) Read into the exam database record.
e set of answer data objects is represented as X � x 1 , x 2 , . . . , x n , x i ∈ R P . Among them, x i is the answer information of the i-th subject, and P is the number of questions. We have calculated the distance matrix A of the subject's answer sheet data object.  (2) Calculate the similarity matrix W of the subject's answer data object. e order of the matrix W is the same as the order of the matrix A. (3) Calculate the extended adjacency matrix L.
According to the similarity matrix W, a diagonal matrix is established, denoted as D � (d ij ) n×n , d ii � n j�1 w ij , and the matrix is defined as L � D − 1/2 WD − 1/2 . (4) Calculate the eigenvalues and eigenvectors of the matrix L, select the first k eigenvectors u 1 , u 2 , . . . , u k , construct a matrix U ∈ R n×k with the eigenvectors u 1 , u 2 , . . . , u k as the columns, and compare the matrix each line of U is unitized. (5) Let y i ∈ R k (i � 1, 2, . . . , n) be the vector corresponding to the i-th row of the matrix U. Using the k-means algorithm, cluster the vector . . . , n. According to the correspondence between x i and x j , the clustering results of the row vector y i of the matrix U in step (5) are used to determine the results of the points x 1 , x 2 , . . . , x n in the clustering.

Quadratic Correction Algorithm Based on Improved
Linear Effect Model. e hierarchical filtering based on spectral clustering is the first classification process for the subjects. In the classification process, only the test score information of the subjects is used. However, in some specific selection processes, only scores used to measure the ability of the examinee appeared to be insufficiently scientific and cannot truly reflect the overall ability of the examinee and the special group caused by special circumstances during the examination process. erefore, on the basis of the first hierarchical filtering of test scores, the clustering results are corrected twice [21]. Take a single-choice objective multiple-choice question as an example. Suppose a test question has four answers A, B, C, and D. Among them, A is the correct answer with a score of x; B is a strongly related answer with a score of k 1 x; C is a weakly related answer with a score of k 2 x; D is an irrelevant answer with a score of k 3 x. k 1 x > k 2 x > k 3 x and the value interval is [0, 1). Suppose the number of exam questions is N, and the number of questions answered by a certain student is M, where M ≤ N. e number of wrong questions with weights k 1 , k 2 , and k 3 in the wrong answers are M 1 , M 2 , and M 3 , respectively, and M 1 + M 2 + M 3 � M. en, the final correction score X of the participant is recorded as follows: Similarly, for multiple-choice questions, suppose there are six options A, B, C, D, E, and F for a question, and the number of correct answers for the question with an incorrect answer is N * , 1 ≤ N * ≤ 6. e number of correct answer options selected by the participant is M * , 0 ≤ M * ≤ N * . e number of wrong answer options selected by the participant is K * , 0 ≤ K * ≤ 6 − N * . en, the participant gives the right answer. e final score Y of this multiple choice question is defined as follows: Based on the previously mentioned description, a new correction and measurement can be made on the actual ability of the participant based on the classification of the basic test scores. e second correction algorithm is described as follows. archical filtering and secondary correction, each subject has two scores: real score and corrected score. Each subject is in its own cluster. is will analyze the test examinee and the ability of subject and teacher to provide a more accurate basis for judgment.

Example Analysis of Improved Linear Mixed-Effects
Model. In order to compare the estimation algorithm in this paper with the maximum likelihood method [12], verify the advantages of the algorithm in this paper in terms of calculation time, and test the feasibility of the algorithm at the same time, the Matlab software is used for numerical simulation and experiment. e experiment was performed on a hardware platform of Intel i7 9700K CPU with 16 GB memories machine, running on the Windows 10 operating system. Suppose the linear mixed-effects model of longitudinal data is as follows: In the equation, we consider two sample scenarios under massive data.
Scenario (1): the number of individuals is large, but the amount of data in the group is small. Two samples are considered as follows: (1) n � 10000, n i � 10, and the total sample size is 100, 000 Complexity 7 (2) n � 100000, n i � 10, and the total sample size is 1000, 000 Scenario (2): there are a limited number of individuals, but the amount of data in the group is large. e sample is n � 10 and n i � 10000. In addition, the parameter N(0, 1), and X ij1 , X ij2 , X ij3 , X ij4 , X ij5 are independent of each other. Z ij � (Z ij1 , Z ij2 ) T , Z ij1 , and Z ij2 are all independently and identically distributed in N(0, 2);  (1). In the two sample cases of scenario (1), the maximum likelihood method [12] and the algorithm in this paper are used to estimate the model coefficients and variance components, respectively, and the calculation time and estimation accuracy used by the two methods are compared.

Simulation Results and Analysis of Scenario
(1) Estimate Accuracy and Calculation Efficiency. e mean square error (MSE) is used to measure the deviation between the simulated estimated value and the true value, and the estimation accuracy is analyzed. A smaller MSE value causes the higher estimation accuracy. e calculation equation of the mean square error is as follows: In (29), m is the number of simulations, x real is the true value of the parameter, and x obs,k is the estimated value of the parameter obtained from the k-th simulation. e calculation time and the mean square error values under the two sample sizes in scenario (1) are obtained by simulation as shown in Table 1.
It can be seen from Table 1 that the MSE values of the model parameters estimated by the maximum likelihood method and the algorithm in this paper are both small, indicating that the parameter estimation effect is better and the estimation accuracy is higher. In addition, compared with the maximum likelihood method, the proposed algorithm can increase the operating efficiency by four times while almost not reducing the estimation accuracy, indicating that the algorithm can greatly reduce the calculation time and increase the calculation speed.
To study the relationship between the calculation time and the number of subdataset blocks and illustrate the necessity of using the divide-and-conquer algorithm for block calculation, the data under the two sample sizes are divided into different dataset block numbers, and the estimated parameters are recorded. e relationship between the calculation time of sample (1) and sample (2) and the number of dataset blocks is shown in Figure 2. e data generated in the figure is the time used by the sample summation method.
It can be seen from Figure 2 that when K � 1, the weighted least square equation (11) is directly used to estimate the model coefficients. At this time, it will exceed the memory and cannot be calculated. Under samples (1) and (2), that is, when K takes 10000 and 100,000, respectively, use the sample sum equation (12) to estimate the model coefficients. K takes other values in the table, according to the algorithm calculated in this article. When K slowly increases, the time used gradually decreases. Taking an appropriate value of K, such as 2000 and 20000 in the samples (1) and (2), respectively, the calculation time is minimized compared with the sample sum method. e running speed can be increased by more than 20%. is is because when K increases, the number of samples allocated to each dataset block is reduced at the same time, so the amount of calculation time is also reduced. At the same time, in the case of limited and fixed stand-alone processing capacity, a certain level of data is suitable. e best calculation speed can be achieved under the number of single machines. In practice, the amount of data is larger, usually reaching millions or even tens of millions, and the effect of the algorithm in this paper will be better at this time. In summary, the algorithm in this paper can reduce memory overhead and calculation time and increase calculation speed. (2). In scenario (2), the relationship between the calculation time used by the algorithm in this paper and the number of dataset blocks is shown in Figure 3. e data generated in the figure is the time used by the sample summation method. When K � 1, use the sample summation equation (12) to calculate the coefficient. When K takes other values calculated by this algorithm, it can be seen that the change trend of time with the number of data blocks is similar to scenario (1), and when K � 200, t � 1.38s, the calculation time reaches the minimum. At the same time, the maximum likelihood method is used to calculate the model parameters of the scenario (2). e time used is 2269.71 s, which proves the efficiency of the algorithm in this paper again.

Simulation Results and Analysis of Scenario
Select the data of the year-end gross domestic product (GDP), industrial output, and total retail sales of consumer goods. For the selected data, we fixed asset investment and urban residents' savings at the year-end balance of 285 prefecture-level across the country from 2006 to 2010. Take the regional gross product (Y) as the response variable and the gross industrial output value (X 1 ) and the total retail sales of consumer goods (X 2 ) as covariates of fixed effects. Considering the fixed asset investment (Z 1 ) and the yearend balance of urban and rural residents' savings (Z 2 ), such factors will also affect the regional GDP. erefore, these two factors are taken as part of the random effect, and a linear mixed effect model is established: 8 Complexity Bringing the data into (30) shows that the data structure at this time conforms to the scenario (1), so the estimation algorithm in the scenario (1) is used to estimate the parameters. e specific results are shown in Table 2.
It can be seen from Table 2 that the coefficients of the gross industrial output value and the total retail sales of consumer goods are both positive, indicating that these two factors positively affect the regional gross product and the model built is effective. erefore, to increase the regional GDP, we must strive to increase the level of industrial production, increase the total retail sales of consumer goods, increase people's income, improve the consumption environment, stabilize the price level, and solve medical, health, and employment issues.

Architecture of Mass Education Examination Big Data
System. In order to verify the efficiency and accuracy of the hierarchical filtering and secondary correction strategy for test big data analysis, a cloud computing-based education test big data analysis and evaluation service platform was developed. e overall construction of the platform includes a centre, two-level applications, and three layers of subsystems. e overall architecture of this system is shown in Figure 4.  (1).   Complexity e platform mainly includes three layers: infrastructure layer, public support base layer, and application service layer. e functional modules are shown in Figure 5. e infrastructure layer mainly includes cloud infrastructure and system software. Its main function is to complete the distributed cloud storage of educational examination data. e hadoop distributed file system (HDFS) system based on cloud technology is mainly used for the organization and management of the file system; the public basic support layer is the evaluation analysis system, and the main components of the data warehouse include the data warehouse part [22] and secondary data processing tools. e data warehouse part mainly includes the realization of basic functions of data collection, data exchange, data mining, and evaluation engine. In units of schools and subjects, the public support application part includes the test question bank, data cleaning, test paper generation, historical information analysis, subject analysis engine, and so on. e application service layer is the user-oriented service module of the platform, which mainly includes basic examination data query, online marking comprehensive service system, evaluation analysis and management subsystem, and test question bank application system. e educational examination data analysis and evaluation cloud platform built by this project directly interacts with users through these services, and such platform is therefore the most user-oriented part.

Analysis of Massive Education Examination Big Data
Results.
e system can perform statistical analysis for a certain course in a certain class or perform statistical analysis on a certain course in a certain area. In addition, it can also perform statistical analysis on all students within a certain range for a certain topic [23]. Taking a second-grade political and English test in a certain area as an example, the original scores and the second-corrected scores of the subjects are calculated, respectively. e statistical results are shown in Figures 6 and 7.
It can be seen from Figures 6 and 7 that the subjects are basically divided into three categories: the first category has a score of 35 to 65, the second category has a score of 65 to 90, and the third category has a score of 90 or more. At the same time, it can be seen that, after the second correction, the scores of all students have improved compared with the original scores, but the increase in the first and third categories is significantly smaller than the second category. e reason for the small increase in the first category is that this group usually has a poor academic performance. erefore, during the examination process, the wrong questions are basically of the type that is not understood, so the correction range is small. e reason for the small increase in the third category is that the performance of this group is already very high, and the room for correction has been severely compressed. e second type of improvement is relatively large because this group of students is in the middle class, and there is a large room for improvement. Teachers should pay special attention and guidance to the problems that lead to mistakes.

Massive Education Examination Big Data Analysis
Report.
e cloud computing-based education examination big data analysis and evaluation service system currently serves 13 provinces and more than 100 cities across the country. e examination data acquisition, storage, and evaluation analysis business accounts for 40% of the national academic examination and analysis evaluation business market. e system supports multiple types of report formats and provides relevant analysis reports for different groups of people through various parameters.
ere are three reports mainly included as follows: e student user report mainly shows the performance of the students in the exam. It analyzes the students from the overall situation of the students and the individual subjects, points out their strengths and weaknesses, and gives targeted improvement opinions [24]. An example of a student report is shown in Figure 8(a).
(2) Institutional Report. e institutions here cover the school and the school's competent department. e institutional user report mainly displays the overall examination conditions of the institution's students in the examination. e institution is statistically analyzed from the overall situation of the students and the individual subjects of the students. ere are various indicators that are used to study the  strengths and weaknesses of the institution. Institutional reports are divided into test overview report, institutional subject report, subquestion answering report, institutional knowledge comparison, and student knowledge comparison. An example of an agency report is shown in Figure 8(b).
(3) Teacher Report. e teacher's report is mainly based on the establishment of a one-to-many multidimensional mapping relationship of knowledge points, knowledge sections, cognitive levels, and ability fields [13]. e score of each dimension item is the main statistical indicator. As a sample group of     different candidates, grades or classes point out the weak links in teaching and play a role in guidance, inspiration, and feedback for teachers' follow-up teaching. An example of the analysis report is shown in Figure 8(c).

Conclusions
With the rapid development of the big data era nowadays, many applications derived from big data have also been used in educational examinations. is paper proposes a threestep estimation algorithm, so that complex statistical models can also be applied to massive data. Numerical simulation shows that the algorithm can greatly reduce the calculation time, improve the calculation efficiency, and solve the problem of insufficient computer memory under massive data. On applying the improved linear mixed-effects model to the massive educational examination big data, this paper carries out the corresponding platform architecture and experiments: (1) define the test data attributes; (2) based on the definition of data attributes and basic evaluation rules, the group cluster data is corrected twice based on the gradient evaluation rules to avoid single score evaluation; (3) the cloud-based services technology research and development is a cross-regional, multiuser educational examination big data analysis and evaluation cloud platform. Future works will concentrate on how to reduce the relationships between different massive big data on educational examination and pay more attention to improving the analyzed performance and efficiency.

Data Availability
e raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.