Information processing systems, information processing methods, and programs

Abstract

The purpose is to appropriately estimate the ability level of test-takers across different subjects. [Solution] The system includes an acquisition unit 120 that acquires first answer information indicating the user's answer to a first problem among multiple problems in a first subject among multiple subjects, and an estimation unit 130 that estimates a first ability estimate indicating the user's ability to answer the first subject and a second ability estimate indicating the user's ability to answer a second subject different from the first subject, using a predetermined statistical method. The estimation unit 130 estimates, using the predetermined statistical method, a third ability estimate, which is the ability characteristic of the user to correctly answer the questions in the first subject, and a fourth ability estimate, which is the ability characteristic of the user to correctly answer the questions in the second subject, at the time the user has answered the second of several questions in the second subject.

Description

Technical Field

[0001] The present disclosure relates to an information processing system, an information processing method, and a program.

Background Art

[0002] Generally, as a test for measuring the ability of a test taker, a computerized adaptive testing (CAT) based on item response theory (IRT) is known. And an ability measurement device for measuring the ability of a test taker in an adaptive test using item response theory is disclosed (see, for example, Patent Document 1).

Prior Art Documents

Patent Documents

[0003]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0004] For example, in an adaptive test based on item response theory, an item optimal for estimating the ability value of a test taker is selected as the next item to be presented. And in an adaptive test, for example, the ability value of a test taker is estimated by repeatedly presenting items selected based on the answers of the test taker from a plurality of items (questions) accumulated in an item pool. In an adaptive test, an item optimal for estimating a certain ability value is often optimal when estimating a certain range of ability values, and there may arise a problem that the items optimal for estimating the ability value are frequently presented.

[0005] Therefore, the ability measurement device described in Patent Document 1 determines the selection probability of each of a plurality of items based on the ability value of the examinee estimated using item response theory. The ability measurement device solves the problem that a specific item is frequently output by selecting and presenting the items to be presented from the plurality of items based on the determined selection probability.

[0006] By the way, although the questions presented to the examinee are questions of a certain subject, they may require the academic ability of other subjects, and there are few questions that purely evaluate a certain subject. That is, when evaluating the academic ability of an examinee with a low correct answer rate in a certain subject by simply evaluating the estimated value of the said subject low, it may result in an inappropriate evaluation. That is, when evaluating the academic ability of an examinee using only a single subject like a conventional adaptive test, there arises a problem that the academic ability of the examinee cannot be appropriately evaluated. <>

[0007] That is, although the ability measurement device described in Patent Document 1 can evaluate the academic ability of an examinee for each single subject, since it cannot estimate the academic ability using the evaluation results of other subjects across subjects, there arises a problem that the academic ability of the examinee cannot be appropriately evaluated.

[0008] Therefore, the present disclosure aims to appropriately estimate the academic ability of an examinee across subjects.

Means for Solving the Problem

[0009] An information processing system according to one aspect of this disclosure includes: an acquisition unit that acquires first answer information indicating the content of a user's answer to a first problem among a plurality of problems in a first subject among a plurality of subjects; first correct / incorrect information indicating the correctness of the answer to the first problem identified based on the first answer information; a first discriminative power indicating the degree to which the respondent's ability to answer the problem in the first subject affects the answer result to the first problem in the first subject; and an information processing system according to one aspect of the plurality of subjects that is different from the first subject among the plurality of subjects The system includes an estimation unit that estimates, using a predetermined statistical method, a first ability estimate indicating the user's ability to answer the first subject and a second ability estimate indicating the user's ability to answer the second subject, based on a second discriminative power indicating the degree to which the ability to answer the second subject's questions influences the answer to the first question in the first subject, and a first difficulty level relating to the first question, wherein the acquisition unit estimates the first ability estimate and the second ability estimate After estimation, the estimation unit obtains second answer information indicating the user's answer to the second of several questions in the second subject among the multiple subjects, and the estimation unit obtains the first correct / incorrect information, the first discriminative power, the second discriminative power, the first difficulty level, second correct / incorrect information indicating the correctness of the answer to the second question identified based on the second answer information, and the degree to which the respondent's ability to answer the questions in the first subject influences the answer result to the second question in the second subject. Based on the discriminative power of 3, a fourth discriminative power indicating the degree to which the respondent's ability to answer the questions of the second subject influences the answer result for the second questions of the second subject, and a second difficulty level for the second questions, a third ability estimate, which is the ability characteristic of the user to correctly answer the questions of the first subject, and a fourth ability estimate, which is the ability characteristic of the user to correctly answer the questions of the second subject, are estimated using the predetermined statistical method at the time the second questions are answered.

[0010] An information processing method according to one aspect of this disclosure includes: a computer obtaining first answer information indicating the user's answer to a first problem among a plurality of problems in a first subject among a plurality of subjects; first correct / incorrect information indicating the correctness of the answer to the first problem identified based on the first answer information; first discriminative power indicating the degree to which the respondent's ability to answer the problem in the first subject influences the answer result to the first problem in the first subject; and the respondent's ability to answer the first problem among a plurality of subjects Based on a second discriminative power indicating the degree to which the ability to answer questions in a second subject different from the subject affects the answer result to the first question in the first subject, and a first difficulty level for the first question, a first ability estimate indicating the user's ability to answer questions in the first subject at the time the first question was answered, and a second ability estimate indicating the user's ability to answer questions in the second subject, are estimated using a predetermined statistical method, and the first ability estimate and the second ability estimate are estimated. Subsequently, obtaining second answer information indicating the user's answer to the second of multiple questions in the second subject among the multiple subjects; first correct / incorrect information; first discriminative power; second discriminative power; first difficulty level; second correct / incorrect information indicating the correctness of the answer to the second question identified based on the second answer information; third discriminative power indicating the degree to which the respondent's ability to answer the questions in the first subject influences the answer result to the second question in the second subject; and respondent Based on a fourth discriminative power indicating the degree to which the ability to answer the second subject's questions in the second subject influences the answer to the second subject's questions, and a second difficulty level related to the second subject, the system estimates a third ability value, which is the user's ability characteristic to correctly answer the first subject's questions, and a fourth ability value, which is the user's ability characteristic to correctly answer the second subject's questions, using the predetermined statistical method.

[0011] A program according to one aspect of this disclosure provides a computer with: first answer information indicating the user's answer to a first problem among a plurality of problems in a first subject among a plurality of subjects; first correct / incorrect information indicating the correctness of the answer to the first problem identified based on the first answer information; first discriminative power indicating the degree to which the respondent's ability to answer the problems in the first subject influences the answer result to the first problem in the first subject; and the respondent's ability to answer the problems in the first subject among a plurality of subjects Based on a second discriminative power indicating the degree to which the ability to answer questions in a second subject different from the subject affects the answer result to the first question in the first subject, and a first difficulty level for the first question, a first ability estimate indicating the user's ability to answer questions in the first subject at the time the first question was answered, and a second ability estimate indicating the user's ability to answer questions in the second subject, are estimated using a predetermined statistical method, and after the first ability estimate and the second ability estimate are estimated... , obtaining second answer information indicating the user's answer to a second problem among multiple problems in the second subject among the multiple subjects, the first correct / incorrect information, the first discriminative power, the second discriminative power, the first difficulty level, second correct / incorrect information indicating the correctness of the answer to the second problem identified based on the second answer information, a third discriminative power indicating the degree to which the respondent's ability to answer the problems in the first subject influences the answer result to the second problem in the second subject, and to the respondent Based on a fourth discriminative power indicating the degree to which the ability to answer the second subject's questions influences the answer to the second subject's questions, and a second difficulty level related to the second subject, the system estimates a third ability value, which is the user's ability characteristic for correctly answering the first subject's questions, and a fourth ability value, which is the user's ability characteristic for correctly answering the second subject's questions, using the predetermined statistical method. [Effects of the Invention]

[0012] According to this disclosure, it is possible to appropriately estimate the academic ability of test takers across subjects. [Brief explanation of the drawing]

[0013] [Figure 1] This is a diagram showing an example of a learning system configuration. [Figure 2] This is a flowchart showing the processing steps of the learning system. [Figure 3] This is screen T10, where the problem is displayed. [Figure 4] Screen T20 displays estimated ability values ​​for each of the multiple subjects, which are updated when a problem is answered. [Figure 5] This figure shows an example of a hardware configuration. [Modes for carrying out the invention]

[0014] Preferred embodiments of this disclosure will be described below with reference to the accompanying drawings. The embodiments described below are merely examples of specific actions taken to implement this disclosure and are not intended to restrict the scope of this disclosure. Furthermore, to facilitate understanding of the explanation, the same reference numerals are used for identical components in the drawings whenever possible, and redundant explanations may be omitted.

[0015] ===Overview of Learning System 100=== Referring to Figure 1, we will now describe the overview of the learning system 100. Figure 1 is a diagram showing an example of the configuration of the learning system 100.

[0016] Learning System 100 is a system that executes adaptive tests capable of evaluating learners' abilities across subjects. In Learning System 100, for example, a test-taker's abilities in multiple subjects are estimated across subjects based on factors (hereinafter referred to as "discriminative power") that can evaluate the academic ability of multiple subjects, including the given subject, and the difficulty level of a given subject's questions (for example, "items" in item response theory).

[0017] An adaptive test is a test that estimates a test-taker's ability score by repeatedly presenting questions selected based on the test-taker's answers from a database of multiple questions. The questions presented in an adaptive test may include, for example, questions where the test-taker chooses one answer from multiple options, or questions requiring written answers. For convenience, in the following explanation, an adaptive test will be described as a question where the test-taker chooses one answer from multiple options. In an adaptive test, the test-taker's ability score is calculated based on Bayesian estimation, using information indicating the correctness of the test-taker's answers (hereinafter referred to as "correct / incorrect information"). In the following explanation, the ability score, which quantifies academic ability calculated based on Bayesian estimation, will be called the "ability estimate." Note that the ability estimate can be any numerical value determined by the adaptive test, and may be called, for example, academic ability or latent trait.

[0018] A problem database is, for example, a database that stores a large number of questions to be given to test-takers for the purpose of conducting adaptive tests. Each question in the problem pool is associated with, for example, the discriminatory ability required for multiple subjects and its difficulty level.

[0019] Discriminative ability refers to the degree to which a test-taker's ability to answer questions in a given subject influences the outcome of their answer to those questions. In other words, discriminative ability is an indicator of how well a test-taker can distinguish between those with low problem-solving ability and those with high problem-solving ability. Specifically, discriminative ability will be high if, for example, a test-taker with high ability to solve arithmetic problems has a high probability of getting that arithmetic problem right. Conversely, discriminative ability will be low if, for example, a test-taker with high ability to solve arithmetic problems has a low probability of getting that arithmetic problem right.

[0020] In this way, for example, each of the multiple problems is assigned a discriminatory ability corresponding to each of the multiple subjects. Specifically, for example, each of the multiple problems is associated with a discriminatory ability corresponding to science (hereinafter referred to as "science discriminatory ability"), a discriminatory ability corresponding to arithmetic (hereinafter referred to as "arithmetic discriminatory ability"), and a discriminatory ability corresponding to Japanese language (hereinafter referred to as "Japanese language discriminatory ability"). In other words, even if it is a science problem, for example, the problem includes not only elements that require the ability to solve science problems, but also elements that require the ability to solve Japanese language problems and arithmetic problems. For the sake of explanation, in the following explanation, we will assume, as an example, that each of the multiple problems is assigned a science discriminatory ability, an arithmetic discriminatory ability, and a Japanese language discriminatory ability.

[0021] Difficulty level is an indicator that shows the level of difficulty required to correctly answer a question, for example, by determining the degree of ability and characteristics needed.

[0022] As mentioned above, questions in one subject (for example, science) sometimes comprehensively assess the academic abilities required in other subjects (for example, Japanese language or mathematics). The learning system 100 has a function to grasp not only the academic abilities required in a particular subject, but also the academic abilities required in other subjects, in order to understand the level of achievement in that subject.

[0023] Furthermore, the learning system 100 does not evaluate the learner's abilities separately for each subject, but rather evaluates the learner's abilities across subjects by reflecting the evaluation results of other subjects for each subject. In other words, when a student solves a science problem and then a math problem, the learning system 100 uses the history of the answers to the science problem that was already solved to calculate the estimated ability value for each subject of the test-taker. The learning system 100 then simultaneously calculates estimated ability values ​​for multiple subjects (for example, science, Japanese language, and math) when a student solves problems in a predetermined subject.

[0024] Specifically, the learning system 100 calculates an estimated ability value for each of the multiple subjects using a predetermined statistical method, based on item characteristics such as discriminative ability and difficulty level in the questions for each of the multiple subjects, and the test taker's correct / incorrect answer information for the questions for each of the multiple subjects.

[0025] For example, when the learning system 100 solves a problem in the first subject (for example, science), it calculates ability estimates for each of the multiple subjects (for example, ability estimates for science, Japanese language, and mathematics) based on the correctness information indicating whether the answer to the problem in that subject is correct or incorrect, the discriminative power corresponding to each of the multiple subjects in that problem (for example, science discriminative power, Japanese language discriminative power, and mathematics discriminative power), and the difficulty level of the problem. Then, when the learning system 100 solves a problem in the second subject (for example, mathematics) following the first subject, it calculates ability estimates (for example, ability estimates for science, Japanese language, and mathematics) using a predetermined statistical method based on the correctness information, discriminative power, and difficulty level of each problem in the first subject (for example, science) and the correctness information, discriminative power, and difficulty level of the problems in the second subject.

[0026] As a result, the learning system 100 can assess the examinee's abilities across multiple subjects, thereby reducing the number of questions required to evaluate the examinee's abilities and enabling a more accurate assessment of their capabilities.

[0027] Furthermore, in learning system 100, the method used to calculate an estimated ability value when solving a problem in a single subject is, for example, a method based on item response theory. Therefore, in the following explanation, some aspects of item response theory may be omitted.

[0028] In item response theory, a linear relationship is assumed where the higher a respondent's ability to solve a problem, the higher the probability of answering the problem correctly. Item response theory then estimates the respondent's problem-solving ability and the problem's evaluation characteristics by applying a statistical model, defined by a function of the respondent's ability characteristics, the problem's difficulty, and the problem's discriminative power, to actual data. In other words, if the evaluation characteristics of a problem are known, item response theory allows for the statistical estimation of the test-taker's ability characteristics from the correct / incorrect answers to multiple sets of problems.

[0029] The learning system 100 may be, for example, a cloud computer, a server computer, a personal computer (e.g., a desktop, laptop, tablet, etc.), a media computer platform (e.g., a cable, satellite set-top box, digital video recorder), a handheld computer device (e.g., a PDA, email client, etc.), or other types of computers or communication platforms. At least a portion of the processing in the learning system 100 may be implemented by one or more computers (not limited to, but for example, a cloud computing system consisting of one or more computers).

[0030] Furthermore, the terminal devices 200 and 300 described later may be, for example, smartphones, mobile phones (feature phones), personal computers (e.g., desktops, laptops, tablets, etc.), media computer platforms (e.g., cable, satellite set-top boxes, digital video recorders), handheld computer devices (e.g., PDAs (Personal Digital Assistants), email clients, etc.), wearable devices (glasses-type devices, watch-type devices, etc.), other types of computers, or communication platforms.

[0031] ===Configuration of Learning System 100=== Referring to Figure 1, the configuration of the learning system 100 will be described.

[0032] The learning system 100 includes, for example, a storage unit 110, an acquisition unit 120, an estimation unit 130, and a display processing unit 140.

[0033] The memory unit 110 stores various types of information, such as the problem database D111. The problem database D111 stores, for example, a problem ID that can identify problems registered as candidates for questions, the problem itself, its discriminative power, difficulty level, correct / incorrect information indicating whether the examinee's answer is correct or incorrect, statistical information, and various other information necessary for processing by the estimation unit 130. The statistical information includes, for example, information estimated by the estimation unit 130, which will be described later. In this way, the problem database D111 stores problems of a wide range of difficulty levels, from high to low difficulty, and each problem is associated with a discriminative power.

[0034] The acquisition unit 120 is a functional unit that acquires various types of information, for example, it acquires answer information indicating the content of the answers to predetermined questions from the examinee's terminal device (not shown). The learning system 100 determines whether the answers are correct or incorrect based on the answer information and stores the answer information and the correct / incorrect information in the storage unit 110.

[0035] The estimation unit 130 is a functional unit that estimates the ability values ​​of each of the test taker's multiple subjects. Rather than calculating an ability value for a single subject, the estimation unit 130 estimates ability values ​​across multiple subjects using past performance history.

[0036] Specifically, the process in the estimation unit 130 that calculates the ability estimates for each of multiple subjects when the examinee solves the first problem (hereinafter referred to as "the first problem") of the first subject (hereinafter referred to as "the first subject") is called the "first estimation process." Also, the process in the estimation unit 130 that presents an unpresented problem (hereinafter referred to as "the second problem") of the first subject after the first problem has been solved is called the "first question presentation process."

[0037] Furthermore, in the estimation unit 130, the process of presenting the first question of the second subject (hereinafter referred to as the "second subject," for example, arithmetic) after the examinee has solved the second question of the first subject (hereinafter referred to as the "third question") is called the "second question presentation process." Also, in the estimation unit 130, the process of calculating the ability estimates for each of the multiple subjects when the third question is solved is called the "second estimation process."

[0038] The following describes the "first estimation process," "first question generation process," "second question generation process," and "second estimation process" performed by the estimation unit 130. First, the parameters used in each process will be explained.

[0039] In equation (1), the discriminant power is "a ij Let i be the problem number (i=1,2,3...) and j be the subject (j=1,2,3...). Specifically, a 11 For example, this shows the science discriminative ability of the first problem (i=1) in science (j=1), and a 12 For example, this shows the Japanese language discrimination ability in the first problem (i=1) of the Japanese language test (j=2), and a 13 This shows, for example, the arithmetic discriminative power of the first problem (i=1) in arithmetic (j=3).

[0040] In equation (1), the difficulty level is "b i Let i be the problem number (i=1,2,3...).

[0041] In equation (1), the estimated value of the examinee's ability in subject j is given by "θ". j ”, and θ=(θ1,θ2,...θ j Let θ1 be an estimate of science ability, θ2 be an estimate of Japanese language ability, and θ3 be an estimate of arithmetic ability.

[0042] The multivariate normal distribution is denoted as "Multinormal," and in equation (1), let θ ~ Multinormal(μ,ρ). In equation (1), for example, let μ = (0,0,0,···0).

[0043] In Equation (1), the threshold value for determining the end of the question set for subject j is set to "c j ".

[0044] Let the matrix of the mutual correlations between the ability parameters be "ρ", and let the correlation coefficient between the ability value of subject m and the ability value of subject n be r m × n .

[0045] Let the correct / incorrect information of the examinee for question i be "u i ", and for example, when u i is a correct answer, it is set to "1", and when it is an incorrect answer, it is set to "0".

[0046] In Equation (1), let the probability of answering question i correctly be "p i ".

[0047] Let the Bernoulli distribution be denoted as "Bernoulli", and for example, u i ~Bernoulli(p i ).

[0048] In Equation (2), let the estimated value of the probability of answering question k, which is an unasked question of a predetermined subject, correctly be "q k ".

[0049] In Equation (3), let the probability of answering question k, which is an unasked question of a predetermined subject, correctly be "p k ".

[0050] Next, the "first estimation process" will be described.

[0051] The estimation unit 130 tentatively sets the ability estimation value, which is an unknown parameter of the examinee for the first subject (for example, science). When the examinee first solves a question, the ability estimation value is tentatively left blank.

[0052] The estimation unit 130 acquires the correct / incorrect information indicating the correct / incorrect answer of question i (here i = 1) by the examinee. The estimation unit 130, for example, uses the correct / incorrect information (0 or 1) of question i, the discrimination power a ij of question i, the difficulty level b i of question i, and the ability estimation value θj Under the following model equation (1), the posterior distribution of the unknown parameter, the ability estimate, is estimated using the MCMC (Markov Chain Monte Carlo method).

[0053]

number

[0054] The estimation unit 130 generates MCMC samples randomly based on the values ​​of the MCMC samples at the current step (here, the parameters when i=1, j=1) according to model equation (1), and successively calculates ability estimates that become the posterior distribution (probability density function). Then, the estimation unit 130 calculates the average estimated value θ of the ability estimates for subject j. j Calculate the mean estimated value θ. j ' represents, for example, the mean of the posterior distribution of ability estimates.

[0055] In other words, the estimation unit 130 estimates ability estimates for each of the multiple subjects (e.g., science, Japanese language, and mathematics) based on the discriminative ability of each of the multiple subjects for the first question (e.g., science discriminative ability, Japanese language discriminative ability, and mathematics discriminative ability) and the difficulty level of the first question, using model equation (1). For example, the ability estimate for science is the average estimate θ1' above, the ability estimate for Japanese language is the average estimate θ2' above, and the ability estimate for mathematics is the average estimate θ3' above.

[0056] Then, the estimation unit 130 calculates the estimation error SE(θ) of the estimated ability value for subject j. j Calculate the estimated error SE(θ). j ') is, for example, the standard deviation of the posterior distribution of multiple ability estimates (hereinafter referred to as "the first standard deviation h1").

[0057] The estimation unit 130 uses the first standard deviation h1 and the threshold c j The comparison is made. The estimation unit 130 determines that the first standard deviation h1 is a threshold c jIf the value is greater than this, it is determined that the accuracy of the estimated ability is low. In this case, the estimation unit 130 executes the first question-presentation process, which is the process of presenting the second question in the first subject.

[0058] Next, I will explain the "first question processing method."

[0059] Based on model equations (1), (2), and (3), the estimation unit 130 calculates the expected posterior variance (EPV) among the unasked questions k of the first subject stored in the question database D111. k The problem that results in the smallest value will be identified from problem database D111 and presented as a question.

[0060]

number

number

[0061] Specifically, the estimation unit 130 calculates the probability q of correctly answering the unasked question k in the first subject, according to model equation (2). k We estimate this.

[0062] Next, the estimation unit 130 calculates the estimation error SE of the ability estimate for the first subject (j=1) (hereinafter referred to as the "first re-execution ability estimate") in the case where the unasked question k is answered correctly. ksu (θ j Calculate the estimated error SE. ksu (θ j ') is, for example, the standard deviation of the posterior distribution of the first re-execution capability estimate.

[0063] Specifically, the estimation unit 130 applies model equation (1) to all the questions i that have been answered (in this case, the first question), and applies model equation (3) to the unanswered questions k in the first subject to generate MCMC samples using random numbers, and successively calculates the first re-execution capability estimates which are the posterior distributions. Then, the estimation unit 130 calculates the average estimate θ of the first re-execution capability estimates for subject j. jCalculate the mean estimated value θ. j ' is, for example, the mean of the posterior distribution of the first re-execution capability estimate.

[0064] Based on the posterior distribution of the estimated first re-execution ability estimates, the estimation error SE of the ability estimates for each unasked problem in the first subject is calculated by the estimation unit 130. ksu Calculate (θ1').

[0065] Next, the estimation unit 130 calculates the estimation error SE of the ability estimate for the first subject (j=1) in the case where the answer to problem k is incorrect. kfail (θ j Calculate the estimated error SE. kfail (θ j ') is, for example, the standard deviation of the posterior distribution of the ability estimates.

[0066] Specifically, the estimation unit 130 applies model equation (1) to all the questions i that have been answered (in this case, the first question), and applies model equation (3) to the questions k that have not yet been asked in the first subject, generating MCMC samples using random numbers, and successively calculating the first re-execution capability estimates which are the posterior distributions.

[0067] The estimation unit 130 calculates the estimation error SE of the first re-execution ability estimate in the first subject based on the posterior distribution of the estimated first re-execution ability estimate. kfail Calculate (θ1').

[0068] Then, the estimation unit 130 calculates the expected posterior variance (EPV) of the first subject based on equation (4). k Identify the second question, which will be the one that minimizes [the specified value].

[0069]

number

[0070] Next, I will explain the "second question processing method."

[0071] The estimation unit 130, using model equation (1), generates MCMC samples randomly based on the values ​​of the MCMC samples at the current step (here, the parameters when i=2 and j=1) when the second problem is answered, and successively calculates ability estimates that become the posterior distribution (probability density function). Then, the estimation unit 130 calculates the average estimated value θ of the ability estimates for subject j (here, j=1). j Calculate '.

[0072] Furthermore, similar to the first estimation process, the estimation unit 130 calculates the estimation error SE(θ) of the estimated ability value for subject j. j Calculate the estimated error SE(θ). j ') is, for example, the standard deviation of the posterior distribution of multiple ability estimates (hereinafter referred to as "the second standard deviation h²").

[0073] The estimation unit 130 uses the second standard deviation h2 and the threshold c j The estimation unit 130 compares the second standard deviation h2 with the threshold c. j The accuracy of the estimated ability value is determined to be high in the following cases. In this case, the estimation unit 130 finishes the first subject and identifies unknown problems for the second subject from the problem database D111 as follows.

[0074] Based on model equations (1), (2), and (3), the estimation unit 130 calculates the expected posterior variance (EPV) for the unassigned questions k of the second subject in the question database D111. k Identify the problem that results in the smallest value from problem database D111.

[0075] Specifically, the estimation unit 130 calculates the probability q of correctly answering the unasked question k in the second subject using model equation (2). k We estimate this.

[0076] Next, the estimation unit 130 calculates the estimation error SE of the ability estimate for the second subject (j=2) in the case where problem k is answered correctly (hereinafter referred to as the "second re-execution ability estimate"). ksu (θ j Calculate ').

[0077] Specifically, the estimation unit 130 applies model equation (1) to all the questions i that have been answered (in this case, Question 1 and Question 2), and applies model equation (3) to the questions k that have not yet been asked in the second subject, generating MCMC samples using random numbers, and successively calculating a second re-execution capability estimate that is the posterior distribution.

[0078] Based on the posterior distribution of the estimated second re-execution ability estimates, the estimation error SE of the ability estimates for each unasked question in the second subject is calculated by the estimation unit 130. ksu Calculate (θ2').

[0079] Next, the estimation unit 130 calculates the estimation error SE of the second re-execution ability estimate for the second subject (j=2) in the case where the answer to problem k is incorrect. kfail (θ j Calculate the estimated error SE. kfail (θ j ') is, for example, the standard deviation of the posterior distribution of the ability estimates.

[0080] Specifically, the estimation unit 130 applies model equation (1) to all the questions i that have been answered (in this case, the first and second questions), and applies model equation (3) to the unanswered questions k in the second subject to generate MCMC samples using random numbers, and successively calculates a second re-execution capability estimate that is the posterior distribution.

[0081] The estimation unit 130 calculates the estimation error SE of the ability estimate in the second subject based on the posterior distribution of the estimated second re-execution ability estimate. kfail Calculate (θ2').

[0082] Then, the estimation unit 130 calculates the expected posterior variance (EPV) of the first subject based on equation (4). k Identify the third question to be presented at the beginning of the second subject that minimizes [the specified value].

[0083] Next, we will explain the "second estimation process."

[0084] The estimation unit 130 obtains correct / incorrect information indicating whether the examinee answered question i (in this case, question 3 (i=3)) correctly or incorrectly. Similar to the first estimation process, the estimation unit 130 obtains correct / incorrect information (0 or 1) for question i and the discriminative power a of question i. ij And the difficulty level of problem i is b i And, the ability estimate θ j We estimate these using the following model equation (1).

[0085] The estimation unit 130 generates MCMC samples randomly based on the values ​​of the MCMC samples for the current step (here, the parameters for the case where i=3 and j=2) according to model equation (1), and successively calculates ability estimates that become the posterior distribution (probability density function). Then, the estimation unit 130 calculates the average estimated value θ of the ability estimates for each of the multiple subjects j. j Calculate the mean estimated value θ. j '' is, for example, the mean of the posterior distribution of ability estimates.

[0086] In other words, the estimation unit 130 estimates ability estimates for each of the multiple subjects (e.g., science, Japanese language, and mathematics) based on the correct / incorrect information for the first and second questions in the first subject, the discriminatory powers for each of the multiple subjects (e.g., science discriminatory power, Japanese language discriminatory power, and mathematics discriminatory power) for each of the first and second questions in the first subject, the difficulty levels of the first and second questions, the correct / incorrect information for the third question in the second subject, the discriminatory powers for each of the multiple subjects (e.g., science discriminatory power, Japanese language discriminatory power, and mathematics discriminatory power) for the third question, which is the first question in the second subject, and the difficulty level of the third question. For example, the ability estimate for science is the average estimate θ1'' above, the ability estimate for Japanese language is the average estimate θ2'' above, and the ability estimate for mathematics is the average estimate θ3'' above.

[0087] As a result, the learning system 100 can evaluate the test-taker's abilities by considering not only the characteristics of items and correct / incorrect information in the subject being solved, but also the characteristics of items and correct / incorrect information in subjects solved in the past. Therefore, it can evaluate the test-taker's abilities more appropriately with fewer questions.

[0088] The display processing unit 140 generates information for displaying various screens on the display unit of the examinee's terminal device 200. The various screens will be described later.

[0089] ===Processing Procedure=== The processing procedure of the learning system 100 will be explained with reference to Figures 2 to 4. Figure 2 is a flowchart of the processing procedure of the learning system 100. Figure 3 is screen T10 on which the questions are displayed. Figure 4 is screen T20 on which the ability estimates for each of the multiple subjects, which are updated when the questions are answered, are displayed.

[0090] The following explains, as an example, how to calculate estimated ability scores for science, Japanese language, and mathematics. Furthermore, the following describes the process of solving two science problems followed by the first mathematics problem. Note that the process of presenting a mathematics problem after a Japanese language problem is the same as the process of outputting a Japanese language problem after a science problem, so its explanation is omitted.

[0091] In step S100, the learning system 100 obtains the examinee's identification information from the examinee's terminal device 200.

[0092] In step S101, the learning system 100 displays the first science question on the display unit of the examinee's terminal device 200.

[0093] As shown in Figure 3, the screen T10 displayed on the display unit of the terminal device 200 includes a question display area T11 and an answer selection area T12. When the terminal device 200 receives an operation input from the examinee in the answer selection area T12, it transmits the answer information to the learning system 100.

[0094] In step S102, the learning system 100 obtains the examinee's answer information for the first science question from the terminal device 200. Based on the answer information, the learning system 100 determines whether the answer is correct or incorrect and stores the answer information and the correct / incorrect information in the storage unit 110.

[0095] In step S103, the learning system 100 uses a predetermined statistical method to estimate the abilities in science, Japanese language, and mathematics / Japanese language (the average estimated value θ mentioned above) based on the correctness information of the first science question, the science discrimination ability, Japanese language discrimination ability, and mathematics / Japanese language discrimination ability of the first question, and the difficulty level. j We estimate ').

[0096] In step S104, the learning system 100 displays the estimated ability value on the display unit of the administrator's terminal device 300.

[0097] As shown in Figure 4, the screen T20 displayed on the administrator's terminal device 300 includes a column area T21 for displaying the estimated science ability, a column area T22 for displaying the estimated Japanese language ability, and a column area T23 for displaying the estimated mathematics ability. That is, each time the examinee solves a problem, the screen T20 displays the estimated science, Japanese language, and mathematics ability values ​​(average estimated value θ) estimated by the estimation unit 130. j The symbol ') is displayed. This allows administrators to properly assess the abilities of test takers.

[0098] For example, when the learning system 100 obtains the examinee's answer information to the first question in science, it displays the examinee's estimated abilities in science, Japanese language, and mathematics, relating them to the first question, which is "Question 1" in the "Science" subject column in Figure 4.

[0099] In step S105, after obtaining the answer information for the first question, the learning system 100 estimates the proficiency estimate for the science subject j by the estimation error SE(θ). j Calculate the first standard deviation h1, which is ).

[0100] In step S106, the learning system 100 compares the first standard deviation h1 with a threshold.

[0101] If the first standard deviation h1 is determined to be greater than the threshold (step S106: NO), the learning system 100 determines that the accuracy of the ability estimate is low, increments the problem, and repeats the process from step S101.

[0102] In other words, in this case, the learning system 100 executes the first question presentation process described above and displays the second science question on the display unit of the examinee's terminal device 200. The learning system 100 obtains the answer information for the second question. Then, based on the correct / incorrect information for the first science question, the science discrimination ability, Japanese language discrimination ability, and arithmetic discrimination ability for the first question, and the difficulty level, and the correct / incorrect information for the second science question, the science discrimination ability, Japanese language discrimination ability, and arithmetic discrimination ability for the second question, and the difficulty level, the learning system 100 uses a predetermined statistical method to estimate the ability values ​​for science, Japanese language, and arithmetic respectively (the average estimated value θ described above). j The learning system 100 estimates the ability estimates. The learning system 100 then relates the estimated ability estimates to the second question, "Question 2," in the subject column "Science" in Figure 4, and displays the estimated ability values ​​for each of the test takers in science, Japanese language, and mathematics. Then, in step S106, the learning system 100 again compares the second standard deviation h2 of the estimated ability estimates with a threshold. In this way, the learning system 100 presents the test taker with science questions and has the test taker answer them until the accuracy of the ability estimates meets a predetermined condition.

[0103] If the first standard deviation h1 is determined to be below the threshold (step S106: YES), the learning system 100 determines that the accuracy of the ability estimate is high and proceeds to step S107, which is the process of outputting a question for the next subject, Japanese language.

[0104] In step S107, the learning system 100 moves on to the next subject, Japanese language.

[0105] In step S108, the learning system 100 performs the second question-presentation process described above to identify the first Japanese language question from the unpresented Japanese language questions stored in the question database D111. The third question, which is the first Japanese language question, is displayed on the display unit of the examinee's terminal device 200.

[0106] In step S109, the learning system 100 obtains the examinee's answer information for the third question from the terminal device 200. Based on the answer information, the learning system 100 determines whether the answer is correct or incorrect and stores the answer information and the correct / incorrect information in the storage unit 110.

[0107] In step S110, the learning system 100 uses a predetermined statistical method to estimate the abilities in science, Japanese language, and mathematics (the average estimated value θ mentioned above) based on the correct / incorrect information of the third question, the science discrimination ability, Japanese language discrimination ability, and mathematics discrimination ability of the first question, and the difficulty level. j We estimate ´´).

[0108] In step S111, the learning system 100 displays the estimated ability values ​​on the display unit of the administrator's terminal device 300. Specifically, when the learning system 100 obtains the examinee's answer information for the third question, which is the first question in the Japanese language section, it displays the examinee's estimated ability values ​​in science, Japanese language, and mathematics, in relation to the third question, which is "Question 1" in the subject column "Japanese Language" in Figure 4.

[0109] In step S112, after obtaining the answer information for the third question, the learning system 100 estimates the proficiency estimate for the subject j of arithmetic by the error SE(θ). j The standard deviation is calculated. Then, the learning system 100 compares this standard deviation with a threshold.

[0110] If the system determines that the standard deviation is greater than the threshold (step S112: NO), the learning system 100 determines that the accuracy of the ability estimate is low, increments the problem, and repeats the process from step S108. If the system determines that the standard deviation is less than or equal to the threshold (step S112: YES), the learning system 100 determines that the accuracy of the ability estimate is high, and proceeds to output a problem for the next subject, arithmetic. The subsequent processing is the same as the processing from step S107, so the explanation is omitted.

[0111] As a result, the learning system 100 can assess the examinee's abilities across multiple subjects, thereby reducing the number of questions required to evaluate the examinee's abilities and enabling a more accurate assessment of their capabilities.

[0112] Furthermore, in learning system 100, item characteristics and the estimated ability values ​​of test takers are separated, so each test taker's estimated ability value is not affected by the items. In other words, learning system 100 makes it possible to compare ability estimates between different tests, provided they measure the same ability. Therefore, using learning system 100, it becomes possible to compare scores from tests administered multiple times a year, and to capture changes in each test taker's ability.

[0113] ===Hardware Configuration=== The hardware configuration of the learning system 100 will be described with reference to Figure 5. Figure 5 is a diagram showing an example of the hardware configuration.

[0114] As shown in Figure 5, the computer 1000 includes a processor 1001, a memory 1002, a storage device 1003, an input I / F unit 1004, a data I / F unit 1005, a communication I / F unit 1006, and a display device 1007.

[0115] The processor 1001 is a control unit that controls various processes in the computer 1000 by executing programs stored in the memory 1002.

[0116] Memory 1002 is a storage medium such as RAM (Random Access Memory). Memory 1002 temporarily stores the program code of the program executed by the processor 1001, as well as data required during program execution.

[0117] The storage device 1003 is a non-volatile storage medium such as a hard disk drive (HDD) or flash memory. The storage device 1003 stores the operating system and various programs for realizing the above configurations.

[0118] The input interface unit 1004 is a device for receiving input from the user. Specific examples of the input interface unit 1004 include keyboards, mice, touch panels, various sensors, and wearable devices. The input interface unit 1004 may be connected to the computer 1000 via an interface such as USB (Universal Serial Bus).

[0119] The data I / F unit 1005 is a device for inputting data from outside the computer 1000. Specific examples of the data I / F unit 1005 include drive devices for reading data stored on various storage media. The data I / F unit 1005 may also be located outside the computer 1000. In that case, the data I / F unit 1005 would be connected to the computer 1000 via an interface such as USB.

[0120] The communication interface unit 1006 is a device for performing data communication via the Internet N with external devices of the computer 1000, either via wired or wireless connection. The communication interface unit 1006 may also be located outside the computer 1000. In that case, the communication interface unit 1006 is connected to the computer 1000 via an interface such as USB.

[0121] The display device 1007 is a device for displaying various types of information. Specific examples of the display device 1007 include liquid crystal displays, organic EL (Electro-Luminescence) displays, and displays for wearable devices. The display device 1007 may be located outside the computer 1000. In that case, the display device 1007 is connected to the computer 1000, for example, via a display cable. Furthermore, if a touch panel is used as the input I / F unit 1004, the display device 1007 can be integrated with the input I / F unit 1004.

[0122] ===Summary=== <1> The learning system 100 includes an acquisition unit 120 that acquires first answer information indicating the user's answer to the first of several questions in a first subject (e.g., science) among several subjects, first correct / incorrect information indicating the correctness of the answer to the first question identified based on the first answer information, first discriminative power (e.g., science discriminative power) indicating the degree to which the respondent's ability to answer questions in the first subject influences the answer result to the first question in the first subject, and a second subject different from the first subject among several subjects ( The system includes an estimation unit 130 that estimates, using a predetermined statistical method (e.g., MCMC method), a first ability estimate (e.g., science ability estimate) and a second ability estimate (e.g., arithmetic ability estimate) that indicates the user's ability to answer the first problem in the first subject at the time the first problem is answered, based on a second discriminative ability (e.g., arithmetic discriminative ability) that indicates the degree to which the ability to answer the first problem in the first subject influences the answer result in the first problem in the first subject, and a first difficulty level related to the first problem, and an estimation unit 130 that estimates, using a predetermined statistical method (e.g., MCMC method), a first ability estimate (e.g., science ability estimate) that indicates the user's ability to answer the second subject at the time the first problem is answered, and an acquisition unit 120 that acquires the first ability After the ability estimate and the second ability estimate are estimated, the estimation unit 130 obtains second answer information indicating the user's answer to the second problem (e.g., the third problem) among multiple problems in the second subject (e.g., mathematics) among multiple subjects, and the estimation unit 130 obtains second answer information indicating the correctness of the answer to the second problem identified based on the first correct / incorrect information, the first discriminative ability (e.g., science discriminative ability), the second discriminative ability (e.g., mathematics discriminative ability), the first difficulty level, and the second correct / incorrect information indicating the correctness of the answer to the second problem identified based on the second answer information, and the ability of the respondent to answer the problem in the first subject to answer the second problem in the second subject. Based on a third discriminative ability (e.g., science discriminative ability) indicating the degree to which it influences the answer result, a fourth discriminative ability (e.g., arithmetic discriminative ability) indicating the degree to which the respondent's ability to answer the second subject's questions influences the answer result for the second question in the second subject, and a second difficulty level related to the second question, a third ability estimate, which is the ability characteristic of the user to correctly answer the first subject's questions, and a fourth ability estimate, which is the ability characteristic of the user to correctly answer the second subject's questions, are estimated using a predetermined statistical method at the time the second question is answered.As a result, the learning system 100 can assess the examinee's abilities across multiple subjects, thereby reducing the number of questions required to evaluate the examinee's abilities and enabling a more accurate assessment of their capabilities.

[0123] <2> In the learning system 100, the estimation unit 130 estimates the first ability estimate and the second ability estimate, and then uses a predetermined statistical method to estimate the first standard deviation (e.g., the first standard deviation h1) of the multiple ability estimates, which is the posterior distribution of the first ability estimate that indicates the user's ability to answer questions in the first subject (e.g., science). Based on the comparison result between the first standard deviation and a threshold, the unit determines whether or not to output the second problem of the second subject (e.g., arithmetic) to the user. As a result, the learning system 100 can move on to the next subject when it has been able to estimate the ability estimate with high accuracy, making it possible to estimate the ability estimate more appropriately with fewer problems.

[0124] <3> If the estimation unit 130 in the learning system 100 determines that the first standard deviation is greater than or equal to a threshold, it estimates a posterior distribution, which is the user's ability to answer each of the multiple unasked questions in the first subject, using a predetermined statistical method. This estimation unit 130 then outputs to the user the question that has the smallest standard deviation among the multiple first re-execution ability estimates for each of the multiple first re-execution ability estimates, which are the user's ability to answer each of the multiple unasked questions in the first subject. The estimation unit 130 in the learning system 100 determines that the first standard deviation is greater than or equal to a threshold. This allows the learning system 100 to present test takers with questions that allow for a highly accurate estimation of their abilities, thereby enabling a more appropriate estimation of ability values ​​with fewer questions.

[0125] <4> If the estimation unit 130 in the learning system 100 determines that the first standard deviation is smaller than a threshold, it outputs the second question (for example, the third question) of the second subject to the user. This allows the learning system 100 to move on to the next subject when it determines that it has been able to estimate the ability with high accuracy in a given subject, thereby enabling more appropriate estimation of ability values.

[0126] <5> If the estimation unit 130 in the learning system 100 determines that the first standard deviation is smaller than a threshold, it estimates a posterior distribution, which is the user's ability to answer each of the multiple unasked questions in the second subject, using a predetermined statistical method. Based on the first correct / incorrect information, the first discriminative power (e.g., science discriminative power), the second discriminative power (e.g., arithmetic discriminative power), the first difficulty level, the discriminative powers (e.g., science discriminative power and arithmetic discriminative power) that indicate the degree to which the responder's ability to answer each of the multiple unasked questions in the second subject influences the answer result for each of the multiple unasked questions in the second subject, and the difficulty level of each of the multiple unasked questions, the estimation unit 130 in the learning system 100 estimates a multiple second re-execution ability, which is the user's ability to answer each of the multiple unasked questions in the second subject, using a predetermined statistical method, and outputs to the user the question that shows the smallest standard deviation among the multiple second re-execution ability estimates for each of the multiple second re-execution ability estimates for each of the multiple unasked questions in the second subject. This allows the learning system 100 to present test takers with questions that allow for a highly accurate estimation of their abilities, thereby enabling a more appropriate estimation of ability values ​​with fewer questions.

[0127] The embodiments described above are provided to facilitate understanding of this disclosure and are not intended to limit it. The elements of the embodiments, as well as their arrangement, materials, conditions, shapes, and sizes, are not limited to those exemplified and can be modified as appropriate. Furthermore, configurations shown in different embodiments can be partially substituted or combined. [Explanation of Symbols]

[0128] 100...Learning system, 110...Memory unit, 120...Acquisition unit, 130...Estimation unit, 140...Display processing unit, 200...Terminal device, 300...Terminal device.

Claims

1. An acquisition unit that acquires first answer information indicating the user's answer to the first of several questions in the first of several subjects, An estimation unit estimates, using a predetermined statistical method, a first ability estimate indicating the user's ability to answer the first problem at the time the first problem was answered, and a second ability estimate indicating the user's ability to answer the second problem at the time the first problem was answered, based on: first correct / incorrect information indicating the correctness of the answer to the first problem identified based on the first answer information; first discriminative power indicating the degree to which the answerer's ability to answer the first problem in the first subject affects the answer result for the first problem in the first subject; second discriminative power indicating the degree to which the answerer's ability to answer the second problem in the first subject affects the answer result for the first problem in the first subject; and a first difficulty level relating to the first problem. Equipped with, After the first ability estimate and the second ability estimate have been estimated, the acquisition unit acquires second answer information indicating the user's answer to the second of the multiple questions in the second subject among the multiple subjects, The estimation unit estimates, based on the first correct / incorrect information, the first discriminative power, the second discriminative power, the first difficulty level, the second correct / incorrect information indicating the correctness of the answer to the second problem identified based on the second answer information, the third discriminative power indicating the degree to which the respondent's ability to answer the first subject problem influences the answer result to the second subject problem, the fourth discriminative power indicating the degree to which the respondent's ability to answer the second subject problem influences the answer result to the second subject problem, and the second difficulty level related to the second problem, a third ability estimate, which is the user's ability characteristic to correctly answer the first subject problem, and a fourth ability estimate, which is the user's ability characteristic to correctly answer the second subject problem, at the time the second problem is answered, using the predetermined statistical method. Information processing system.

2. The estimation unit, After the first ability estimate and the second ability estimate are estimated, the first standard deviation of a plurality of ability estimates, which is a posterior distribution of the first ability estimate that indicates the user's ability to answer the first subject, is estimated using the predetermined statistical method. Based on the comparison result between the first standard deviation and the threshold, it is determined whether or not to output the second problem of the second subject to the user. The information processing system according to claim 1.

3. If the estimation unit determines that the first standard deviation is greater than or equal to the threshold, it estimates a plurality of first re-execution ability estimates, which are posterior distributions representing the user's ability to answer each of the multiple unasked questions in the first subject, using the predetermined statistical method, based on the first correct / incorrect information, the first discriminative power, the second discriminative power, the first difficulty level, the discriminative power indicating the degree to which the respondent's ability to answer each of the multiple unasked questions in the first subject influences the answer result for each of the multiple unasked questions in the first subject, and the difficulty level for each of the multiple unasked questions in the first subject. For each of the multiple unassigned questions in the first subject, the question that shows the smallest standard deviation among the multiple first re-execution ability estimates is output to the user. The information processing system according to claim 2.

4. If the estimation unit determines that the first standard deviation is smaller than the threshold, it outputs the second problem of the second subject to the user. The information processing system according to claim 3.

5. The estimation unit, If the first standard deviation is determined to be smaller than the threshold, a plurality of second re-execution ability estimates, which are posterior distributions representing the user's ability to answer each of the multiple unasked questions in the second subject, are estimated using the predetermined statistical method, based on the first correct / incorrect information, the first discriminative power, the second discriminative power, the first difficulty level, the discriminative power indicating the degree to which the respondent's ability to answer each of the multiple unasked questions in the second subject influences the answer result for each of the multiple unasked questions in the second subject, and the difficulty level for each of the multiple unasked questions. For each of the multiple unassigned questions in the second subject, the question that shows the smallest standard deviation among the multiple second re-execution ability estimates is output to the user. The information processing system according to claim 3.

6. Computers Obtaining first answer information that shows the user's answer to the first of several questions in the first of several subjects, Based on the first answer information, a first correct / incorrect information indicating the correctness of the answer to the first problem, a first discriminative power indicating the degree to which the respondent's ability to answer the first subject's questions influences the answer result for the first subject, a second discriminative power indicating the degree to which the respondent's ability to answer questions in a second subject different from the first subject influences the answer result for the first subject, and a first difficulty level related to the first problem, a first ability estimate indicating the user's ability to answer the first subject, and a second ability estimate indicating the user's ability to answer the second subject, are estimated using a predetermined statistical method. After the first and second ability estimates are estimated, second answer information is obtained that shows the user's answer to the second of several questions in the second subject among the several subjects. Based on the first correct / incorrect information, the first discriminative power, the second discriminative power, the first difficulty level, the second correct / incorrect information indicating the correctness of the answer to the second problem identified based on the second answer information, the third discriminative power indicating the degree to which the respondent's ability to answer the first subject problem influences the answer result to the second subject problem, the fourth discriminative power indicating the degree to which the respondent's ability to answer the second subject problem influences the answer result to the second subject problem, and the second difficulty level related to the second problem, the third ability estimate, which is the ability characteristic of the user to correctly answer the first subject problem, and the fourth ability estimate, which is the ability characteristic of the user to correctly answer the second subject problem, are estimated using the predetermined statistical method at the time the second problem is answered. An information processing method that performs the following.

7. On the computer, Obtaining first answer information that shows the user's answer to the first of several questions in the first of several subjects, Based on the first answer information, a first correct / incorrect information indicating the correctness of the answer to the first problem, a first discriminative power indicating the degree to which the respondent's ability to answer the first subject's questions influences the answer result for the first subject, a second discriminative power indicating the degree to which the respondent's ability to answer questions in a second subject different from the first subject influences the answer result for the first subject, and a first difficulty level related to the first problem, a first ability estimate indicating the user's ability to answer the first subject, and a second ability estimate indicating the user's ability to answer the second subject, are estimated using a predetermined statistical method. After the first and second ability estimates are estimated, second answer information is obtained that shows the user's answer to the second of several questions in the second subject among the several subjects. Based on the first correct / incorrect information, the first discriminative power, the second discriminative power, the first difficulty level, the second correct / incorrect information indicating the correctness of the answer to the second problem identified based on the second answer information, the third discriminative power indicating the degree to which the respondent's ability to answer the first subject problem influences the answer result to the second subject problem, the fourth discriminative power indicating the degree to which the respondent's ability to answer the second subject problem influences the answer result to the second subject problem, and the second difficulty level related to the second problem, the third ability estimate, which is the ability characteristic of the user to correctly answer the first subject problem, and the fourth ability estimate, which is the ability characteristic of the user to correctly answer the second subject problem, are estimated using the predetermined statistical method at the time the second problem is answered. A program that executes the command.

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