A cross-time point cognitive diagnosis method considering students' influencing factors

Abstract

The present invention discloses a cross-time point cognitive diagnosis method that considers student influencing factors, belonging to the field of educational assessment technology, comprising: obtaining student answer data at several time points, fitting the student answer data at each time point respectively; assigning each student to a potential knowledge mastery state based on the fitting results, and calculating the classification error probability; constructing a potential transfer cognitive diagnosis model, optimizing the potential transfer cognitive diagnosis model based on the classification error probability, obtaining an estimated initial state probability and an estimated transfer probability based on the optimized potential transfer cognitive diagnosis model; and performing cross-time point cognitive diagnosis on students based on the estimated initial state probability and the estimated transfer probability. The present invention can effectively analyze the impact of covariates on students' initial state, as well as the changing pattern of potential knowledge mastery state at different time points.

Description

Technical Field

[0001] The present invention belongs to the technical field of educational assessment, and in particular relates to a cross-time point cognitive diagnosis method that takes student influencing factors into consideration. Background Art

[0002] While many different types of cognitive diagnostic models (CDMs) have been developed, most methods and applications focus on a single point in time, categorizing students' knowledge attributes. However, in some contexts, such as tracking student learning progress or studying changes before and after a specific event (such as an intervention), relying solely on a single-point model is insufficient. In these cases, longitudinal or pre- and post-test models are needed to examine changes in students' underlying knowledge status across multiple time points.

[0003] Furthermore, current research has paid little attention to the integration of covariates with the CDM. Covariates can be correlated factors that influence student learning. Educational researchers often also want to understand how these covariates influence students' underlying knowledge and their role in predicting student learning progress.

[0004] In existing studies, most methods use a one-step or three-step approach to estimate CDM:

[0005] The one-step approach simultaneously estimates the CDM (measurement model) and the regression model (structural model). For example, logistic regression is used in DINA and higher-order DINA models to estimate how covariates affect the probability of mastering each attribute. While this approach provides relatively precise results, it lacks model flexibility because any change to any component requires refitting the entire model.

[0006] In contrast, the three-step approach is more flexible. It divides model construction into three stages, allowing researchers to independently adjust different parts of the model and correct for potential errors in student classification, thereby improving the accuracy of the analysis.

[0007] Current research on covariates remains limited. Existing methods primarily focus on the relationship between covariates and the potential knowledge mastery state at a single point in time, but few explore how covariates influence the evolution of a student's potential knowledge mastery state. For example, one study proposed a high-order hidden Markov model incorporating covariates to track changes in student knowledge mastery and analyze the impact of covariates on the transition to potential knowledge mastery state. However, this approach also uses a one-step approach, resulting in limited flexibility. Furthermore, the model does not consider the impact of covariates on the initial state. Summary of the Invention

[0008] In order to solve the above technical problems, the present invention proposes a cross-time point cognitive diagnosis method that takes into account student influencing factors to solve the problems existing in the above-mentioned existing technologies.

[0009] To achieve the above objectives, the present invention provides a cross-time point cognitive diagnosis method that takes into account student influencing factors, comprising:

[0010] Obtain student answer data at several time points, and perform fitting on the student answer data at each time point;

[0011] Assign each student to a potential knowledge mastery status based on the fitting results and calculate the probability of classification error;

[0012] constructing a potential transfer cognitive diagnosis model, optimizing the potential transfer cognitive diagnosis model based on the classification error probability, and obtaining an estimated initial state probability and an estimated transfer probability based on the optimized potential transfer cognitive diagnosis model;

[0013] Conduct cognitive diagnosis of students across time points based on estimated initial state probabilities and estimated transition probabilities.

[0014] Optionally, the process of obtaining student answer data at several time points and fitting the student answer data at each time point includes:

[0015] Analyze the question content and assessment objectives, obtain the relationship between the question and each cognitive attribute, and construct a Q matrix based on the relationship between the question and each cognitive attribute;

[0016] Obtain covariates and student answer data at several time points; based on the Q matrix, perform G-DINA model fitting on the covariates and student answer data at several time points to obtain the probability of each student mastering each cognitive attribute at each time point.

[0017] Optionally, the process of assigning each student to a potential knowledge mastery state includes:

[0018] The posterior probability of each student on each cognitive attribute is calculated based on the mastery probability of each student on each cognitive attribute at each time point, and each student is assigned to a potential knowledge mastery status.

[0019] Optionally, the formula for calculating the probability of classification error is as follows:

[0020]

[0021] Among them, Y represents the answer data of each student at each time point, T represents the number of time points, N represents the total number of students, and s t Indicates the potential knowledge mastery status of students at a certain point in time, L trepresents the student’s potential knowledge mastery status at a certain point in time, r t Represents the estimated potential knowledge mastery state, W t Represents the estimated potential knowledge mastery status of a student at a certain point in time.

[0022] Optionally, the potential transfer cognitive diagnostic model is:

[0023]

[0024] Among them, P(Y t |L t =s t ) is the potential knowledge mastery state corresponding to the t-th time point, P(L1=s1|Z1) is the initial state probability, P(L t =s t |L t-1 =s t-1 ,Z t ) is the transition probability; Y represents the answer data of each student at each time point, s t Indicates the potential knowledge mastery status of students at a certain point in time, L t represents the student's potential knowledge mastery status at a certain point in time, T represents the number of time points, t represents the time point, Z represents the covariate, and S represents the number of potential knowledge mastery states.

[0025] Optionally, the objective function of the potential transfer cognitive diagnosis model is a log-likelihood function, which is expressed as follows:

[0026]

[0027] Where N is the total number of students, Y i represents the answer data of student i, Z i represents the covariate of student i.

[0028] Optionally, the process of optimizing the potential transfer cognitive diagnosis model based on the classification error probability includes:

[0029] A correction weight is calculated based on the classification error probability and the estimated potential knowledge mastery state, and the objective function is corrected using the correction weight to obtain an optimized potential transfer cognitive diagnosis model.

[0030] Optionally, based on the classification error probability, the estimated initial state probability and the estimated transition probability are obtained by maximizing the corresponding log-likelihood function of the optimized potential transfer cognitive diagnosis model; regression modeling is performed based on the covariates and the estimated transition probability to achieve cognitive diagnosis of students across time points.

[0031] Compared with the prior art, the present invention has the following advantages and technical effects:

[0032] The present invention discloses a cross-time point cognitive diagnosis method that takes student influencing factors into consideration. First, student answer data at several time points are obtained, and the student answer data at each time point are fitted respectively; then, each student is assigned to a potential knowledge mastery state based on the fitting result, and the classification error probability is calculated; then, a potential transfer cognitive diagnosis model is constructed, and the potential transfer cognitive diagnosis model is optimized based on the classification error probability. Based on the optimized potential transfer cognitive diagnosis model, an estimated initial state probability and an estimated transfer probability are obtained; finally, a cross-time point cognitive diagnosis of students is performed based on the estimated initial state probability and the estimated transfer probability.

[0033] This method accurately estimates the classification of latent knowledge mastery status in multi-time point data analysis, analyzes the relationship between covariates and latent knowledge mastery status in a step-by-step manner, and effectively controls classification errors. This correction process makes the model more robust in practical applications, especially in situations where the quality of questions or sample size is low, providing more reliable estimates and demonstrating significant advantages over uncorrected methods in multiple scenarios.

[0034] This method can be easily adapted to data spanning multiple time points. This is because the measurement and structural components of the method are estimated independently, and the number of items and attributes only affects the computational complexity of the measurement model. This design enables the method to run efficiently within existing software, providing technical support for large-scale and complex cognitive diagnostic analyses. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] The accompanying drawings, which constitute part of this application, are intended to provide a further understanding of this application. The exemplary embodiments and descriptions of this application are intended to explain this application and do not constitute an improper limitation on this application. In the accompanying drawings:

[0036] Figure 1 Schematic diagram of a method flow in an embodiment of the present invention;

[0037] Figure 2 Schematic diagram of the fitting process of an embodiment of the present invention;

[0038] Figure 3 Schematic diagram of the process of assigning students to potential knowledge mastery states at each time point and calculating classification error probability in an embodiment of the present invention;

[0039] Figure 4 Schematic diagram of the result generation process of an embodiment of the present invention. DETAILED DESCRIPTION

[0040] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments in this application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0041] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0042] Example 1

[0043] In order to more flexibly introduce covariates into longitudinal CDM, this paper designs a cross-time point cognitive diagnosis method based on the G-DINA model framework that considers students' influencing factors, such as Figure 1 Shown, including:

[0044] Obtain student answer data at several time points, and perform fitting on the student answer data at each time point;

[0045] In some specific implementations, the process of obtaining student answer data at several time points and fitting the student answer data at each time point includes:

[0046] Analyze the question content and assessment objectives, obtain the relationship between the question and each cognitive attribute, and construct a Q matrix based on the relationship between the question and each cognitive attribute;

[0047] Obtain covariates and student answer data at several time points; based on the Q matrix, perform G-DINA model fitting on the covariates and student answer data at several time points to obtain the probability of each student mastering each cognitive attribute at each time point.

[0048] Specifically, the fitting process is as follows Figure 2 Shown, including:

[0049] 1) Invite experts in the field of education to conduct an in-depth analysis of the test items to clarify which cognitive attributes each item tests. By analyzing the item content and assessment objectives, the experts determine the relationship between the items and each cognitive attribute, thereby constructing a Q matrix. The Q matrix is ​​a binary matrix in which rows represent each item and columns represent cognitive attributes. A "1" or "0" indicates whether a question touches on a particular attribute.

[0050] 2) Collect and organize student response data at multiple time points. This data describes whether students answered the test correctly or not, and can cover multiple cognitive attributes such as information literacy, communication and collaboration, and problem-solving. Rows in this data represent each student's correct answer, and columns represent each question. Also, consider covariates (such as gender and socioeconomic status) and analyze the collected student response data and covariates to explore the relationship between covariates and student skill mastery.

[0051] 3) Using the determined Q matrix, the G-DINA model is fitted to the response data at each time point to obtain the students' mastery of cognitive attributes at different time points and capture the degree of change in their mastery of each cognitive attribute.

[0052] Assign each student to a potential knowledge mastery status based on the fitting results and calculate the probability of classification error;

[0053] Specifically, such as Figure 3 As shown, the above process includes:

[0054] 1) Based on the student response data at each time point, the posterior probability (e.g., expected posterior probability, EAP) of each student on each cognitive attribute is calculated. Based on the posterior probability, whether the student has mastered a specific cognitive attribute is determined and classified into discrete potential knowledge mastery states.

[0055] 2) Calculate the classification error probability (CEP) to assess the accuracy of the student's classification. CEP measures the student's classification error rate at each potential knowledge mastery state. The probability of classification errors is calculated by comparing the student's answer data with the prediction results of the fitted model.

[0056] 3) Calculate correction weights based on the CEP to further adjust the classification results of each potential knowledge mastery state. The determination of correction weights ensures that the model predicts the potential knowledge mastery state more accurately and makes the results more interpretable.

[0057] In some embodiments, the process of assigning each student to a potential knowledge mastery state includes:

[0058] The posterior probability of each student on each cognitive attribute is calculated based on the mastery probability of each student on each cognitive attribute at each time point, and each student is assigned to a potential knowledge mastery status.

[0059] In some embodiments, the formula for calculating the probability of classification error is as follows:

[0060]

[0061] Among them, Y represents the answer data of each student at each time point, T represents the number of time points, N represents the total number of students, and s t Indicates the potential knowledge mastery status of students at a certain point in time, L t represents the student’s potential knowledge mastery status at a certain point in time, r t Represents the estimated potential knowledge mastery state, W t Represents the estimated potential knowledge mastery status of a student at a certain point in time.

[0062] The probability of classification error is a 2 K ×2 K matrix, which contains the states assigned to the potential knowledge mastery states r t The actual potential knowledge mastery state t The rows represent the true potential knowledge mastery status and the columns represent the estimated potential knowledge mastery status.

[0063] constructing a potential transfer cognitive diagnosis model, optimizing the potential transfer cognitive diagnosis model based on the classification error probability, and obtaining an estimated initial state probability and an estimated transfer probability based on the optimized potential transfer cognitive diagnosis model;

[0064] In some embodiments, the potential transfer cognitive diagnostic model is:

[0065]

[0066] Among them, P(Y t |L t =s t ) is the potential knowledge mastery state corresponding to the t-th time point, P(L1=s1|Z1) is the initial state probability, P(L t =s t |L t-1 =s t-1 ,Z t ) is the transition probability; Y represents the answer data of each student at each time point, s t Indicates the potential knowledge mastery status of students at a certain point in time, L t It represents the potential knowledge mastery status of students at a certain point in time. T represents the number of time points, t represents the time point, Z represents the covariate, and S represents the number of potential knowledge mastery states.

[0067] In some embodiments, the objective function of the potential transfer cognitive diagnostic model is a log-likelihood function, which is expressed as follows:

[0068]

[0069] Where N is the total number of students, Yi represents the answer data of student i, Z i represents the covariate of student i.

[0070] In some embodiments, the process of optimizing the potential transfer cognitive diagnostic model based on the classification error probability includes:

[0071] A correction weight is calculated based on the classification error probability and the estimated potential knowledge mastery state, and the objective function is corrected using the correction weight to obtain an optimized potential transfer cognitive diagnosis model.

[0072] Specifically, in order to correct the classification error, the sample-level correction weight of student i is calculated based on the CEP matrix and the student's estimated potential knowledge mastery state. The sample-level correction weight of student i is expressed as:

[0073]

[0074] This example estimates the parameters of the structural model by maximizing the corresponding log-likelihood, which can be done using the uncorrected and corrected three-step method. In the third step of the corrected three-step method, the correction weights are used. The objective function after correction is:

[0075]

[0076] in, is the potential knowledge mastery state s of student i t In the uncorrected three-step method, the latent state r directly estimated by the G-DINA model is used. it (i.e. expected posterior probability EAP) rather than correction weights

[0077] Conduct cognitive diagnosis of students across time points based on estimated initial state probabilities and estimated transition probabilities.

[0078] In some specific embodiments, based on the classification error probability, the estimated initial state probability and the estimated transition probability are obtained by maximizing the corresponding log-likelihood function of the optimized potential transfer cognitive diagnosis model; regression modeling is performed based on covariates and the estimated transition probability to achieve cognitive diagnosis of students across time points.

[0079] Specifically, the known CEP is used to estimate the potential transition CDM and calculate the regression coefficients between the initial state probability and the transition probability. Figure 4 As shown, the description is as follows:

[0080] The calculated classification error probability is introduced into the latent transfer cognitive diagnosis model, and the parameters of the structural model are estimated by maximizing the corresponding log-likelihood function.

[0081] Estimating Initial State Probabilities: Using student response data at the first time point, we estimate initial state probabilities based on each student's potential knowledge mastery distribution. To enhance the model's explanatory power, we incorporate covariates (such as gender and socioeconomic status) into the estimation process, allowing for a more comprehensive analysis of their impact on students' initial knowledge mastery. Initial state probabilities describe students' mastery of various cognitive attributes at the first time point, reflecting their knowledge and skill levels at the starting point of their learning.

[0082] Estimating transition probabilities: Based on the distribution of students' potential knowledge mastery states at multiple time points, the transition probability of their potential knowledge mastery states from one time point to the next is calculated, and covariates are introduced to analyze the impact of these factors on the change in potential knowledge mastery states. Combining covariates with state transition probabilities for regression modeling can assess the role of these covariates in the transition process of potential knowledge mastery states. For example, it is possible to analyze whether gender significantly affects the state change of "communication and collaboration" skills, or whether socioeconomic status affects the transition probability of "information literacy" from "not mastered" to "mastered". This transition probability analysis not only quantifies the change pattern of students' knowledge mastery in different periods, but also reveals their learning progress and development trends between consecutive time points.

[0083] Generated results: The results generated based on the model can help teachers and relevant educators gain an in-depth understanding of each student's learning characteristics and development trends at different stages, analyze the specific effects of different influencing factors on students' learning outcomes at different time points, accurately identify students' learning needs at different stages, and design scientific and effective personalized learning plans.

[0084] The G-DINA model is a general cognitive diagnostic model used to analyze student test responses and infer mastery of specific cognitive attributes. The model uses a Q matrix to identify the attribute combinations required for each question and models the responses as the relationship between these attribute combinations and the student's mastery pattern. The G-DINA model employs a flexible framework that can represent both main and interaction effects between attributes, thus encompassing a variety of cognitive diagnostic models, such as the DINA and DINO models.

[0085] Compared to traditional, simple models, the G-DINA model's advantages lie in its high degree of freedom and its ability to describe complex answering behaviors. By allowing interactions between attributes, the model can capture more nuanced cognitive information, such as how multiple attributes synergistically influence student performance. The G-DINA model is widely used in educational assessment and intelligent learning systems, helping to provide students with more personalized feedback and learning suggestions.

[0086] The Latent Transfer Model (LTM), also known as the Latent or Hidden Markov Model, is a longitudinal extension of the Latent Class Model (LCM). It can not only analyze a student's potential knowledge state at a given point in time, but also describe how these states change over time.

[0087] In LTM, measurement models are used to analyze students' performance at each time point and predict their potential knowledge mastery status. Structural models are used to describe the distribution of these potential knowledge mastery statuses and how students transition between different time points.

[0088] By combining the cognitive diagnostic model (CDM) with LTM, we can study how students' knowledge mastery changes at different time points. In addition, by introducing covariates (such as students' gender, family background, and other influencing factors) into the LTM, we can further identify key characteristics that influence the classification of students' potential knowledge mastery status and its transformation patterns over time.

[0089] This method is sufficiently versatile to handle both time constants and time-varying covariates, broadening its applicability. This allows for more comprehensive capture of the dynamic changes in students' underlying knowledge mastery and cognitive characteristics when applied in areas such as educational assessment, learning process tracking, and personalized learning path optimization, thereby providing education authorities with more accurate assessment tools. In practical applications, such precise cognitive diagnostic models will contribute to more efficient allocation of educational resources, improve educational quality, and reduce resource waste caused by assessment errors, thus having significant social and economic benefits.

[0090] The present invention can model the effects of covariates at the attribute level and the overall feature level. That is, it can not only analyze the impact of a specific attribute, but also analyze the effect of covariates on the initial state and transition probability as a whole, providing users with a scientific basis for personalized analysis and comprehensive interpretation of multi-dimensional data.

[0091] The above are merely preferred embodiments of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in this application should be included in the scope of protection of the present application. Therefore, the scope of protection of the present application should be based on the scope of protection of the claims.

Claims

1. A cross-time point cognitive diagnosis method that considers student influencing factors, characterized by: The following steps are involved: Obtain student answer data at several time points, and perform fitting on the student answer data at each time point; Assign each student to a potential knowledge mastery status based on the fitting results and calculate the probability of classification error; constructing a potential transfer cognitive diagnosis model, optimizing the potential transfer cognitive diagnosis model based on the classification error probability, and obtaining an estimated initial state probability and an estimated transfer probability based on the optimized potential transfer cognitive diagnosis model; Conduct cognitive diagnosis of students across time points based on estimated initial state probabilities and estimated transition probabilities; The formula for calculating the probability of classification error is as follows: Among them, Y represents the answer data of each student at each time point, T represents the number of time points, N represents the total number of students, and s t Indicates the potential knowledge mastery status of students at a certain point in time, L t represents the student’s potential knowledge mastery status at a certain point in time, r t Represents the estimated potential knowledge mastery state, W t =r t The value of the student's estimated potential knowledge mastery state at time point t is r t ; The potential transfer cognitive diagnostic model is: Among them, P(Y t |L t =s t ) is the potential knowledge mastery state corresponding to the t-th time point, P(L1=s1|Z1) is the initial state probability, P(L t =s t |L t-1 =s t-1 ,Z t ) is the transition probability; Y represents the answer data of each student at each time point, t represents the time point, Z represents the covariate, and S represents the number of potential knowledge mastery states.

2. The cross-time point cognitive diagnosis method considering student influencing factors according to claim 1 is characterized in that: The process of obtaining student answer data at several time points and fitting the student answer data at each time point includes: Analyze the question content and assessment objectives, obtain the relationship between the question and each cognitive attribute, and construct a Q matrix based on the relationship between the question and each cognitive attribute; Obtain covariates and student answer data at several time points; based on the Q matrix, perform G-DINA model fitting on the covariates and student answer data at several time points to obtain the probability of each student mastering each cognitive attribute at each time point.

3. The cross-time point cognitive diagnosis method considering student influencing factors according to claim 2 is characterized in that: The process of assigning each student to a potential knowledge mastery state involves: The posterior probability of each student on each cognitive attribute is calculated based on the mastery probability of each student on each cognitive attribute at each time point, and each student is assigned to a potential knowledge mastery status.

4. The cross-time point cognitive diagnosis method considering student influencing factors according to claim 1 is characterized in that: The objective function of the potential transfer cognitive diagnosis model is the log-likelihood function, which is expressed as follows: Where Y i represents the answer data of student i, Z i represents the covariate of student i.

5. The cross-time point cognitive diagnosis method considering student influencing factors according to claim 4 is characterized in that: The process of optimizing the potential transfer cognitive diagnosis model based on the classification error probability includes: A correction weight is calculated based on the classification error probability and the estimated potential knowledge mastery state, and the objective function is corrected using the correction weight to obtain an optimized potential transfer cognitive diagnosis model.

6. The cross-time point cognitive diagnosis method considering student influencing factors according to claim 5 is characterized in that: Based on the classification error probability, obtaining an estimated initial state probability and an estimated transition probability by maximizing the corresponding log-likelihood function of the optimized latent transfer cognitive diagnosis model; Regression modeling is performed based on covariates and estimated transition probabilities to achieve cognitive diagnosis of students across time points.

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