The linear transformation model with frailties for the analysis of item response times

Joint modeling of action sequences and action time in computer-based interactive tasks

Process data refers to data recorded in computer-based assessments that reflect the problem-solving processes of participants and provide greater insight into how they solve problems. Action time, namely the amount of time required to complete a state transition, is also included in such data along with actions. In this study, an action-level joint model of action sequences and action time is proposed, in which the sequential response model (SRM) is used as the measurement model for action sequences, and a new log-normal action time model is proposed as the measurement model for action time. The proposed model can be regarded as an extension of the SRM by incorporating action time within the joint-hierarchical modeling framework and as an extension of the conventional item-level joint models in process data analysis. Results of the empirical and simulation studies demonstrated that the model setup was justified, model parameters could be interpreted, parameter estimates were accurate, and taking into account participants' action time further was beneficial for obtaining a deep understanding of participants' behavioral patterns. Overall, the proposed action-level joint model provides an innovative modeling framework for analyzing process data in computer-based assessments from the latent variable modeling perspective.

An Item Response Theory Model for Incorporating Response Times in Forced-Choice Measures

Forced-choice (FC) measures have been widely used in many personality or attitude tests as an alternative to rating scales, which employ comparative rather than absolute judgments. Several response biases, such as social desirability, response styles, and acquiescence bias, can be reduced effectively. Another type of data linked with comparative judgments is response time (RT), which contains potential information concerning respondents' decision-making process. It would be challenging but exciting to combine RT into FC measures better to reveal respondents' behaviors or preferences in personality measurement. Given this situation, this study aims to propose a new item response theory (IRT) model that incorporates RT into FC measures to improve personality assessment. Simulation studies show that the proposed model can effectively improve the estimation accuracy of personality traits with the ancillary information contained in RT. Also, an application on a real data set reveals that the proposed model estimates similar but different parameter values compared with the conventional Thurstonian IRT model. The RT information can explain these differences.

What Can We Learn from a Semiparametric Factor Analysis of Item Responses and Response Time? An Illustration with the PISA 2015 Data

It is widely believed that a joint factor analysis of item responses and response time (RT) may yield more precise ability scores that are conventionally predicted from responses only. For this purpose, a simple-structure factor model is often preferred as it only requires specifying an additional measurement model for item-level RT while leaving the original item response theory (IRT) model for responses intact. The added speed factor indicated by item-level RT correlates with the ability factor in the IRT model, allowing RT data to carry additional information about respondents' ability. However, parametric simple-structure factor models are often restrictive and fit poorly to empirical data, which prompts under-confidence in the suitablity of a simple factor structure. In the present paper, we analyze the 2015 Programme for International Student Assessment mathematics data using a semiparametric simple-structure model. We conclude that a simple factor structure attains a decent fit after further parametric assumptions in the measurement model are sufficiently relaxed. Furthermore, our semiparametric model implies that the association between latent ability and speed/slowness is strong in the population, but the form of association is nonlinear. It follows that scoring based on the fitted model can substantially improve the precision of ability scores.

Application of Change Point Analysis of Response Time Data to Detect Test Speededness

Computer-based and web-based testing have become increasingly popular in recent years. Their popularity has dramatically expanded the availability of response time data. Compared to the conventional item response data that are often dichotomous or polytomous, response time has the advantage of being continuous and can be collected in an unobstrusive manner. It therefore has great potential to improve many measurement activities. In this paper, we propose a change point analysis (CPA) procedure to detect test speededness using response time data. Specifically, two test statistics based on CPA, the likelihood ratio test and Wald test, are proposed to detect test speededness. A simulation study has been conducted to evaluate the performance of the proposed CPA procedure, as well as the use of asymptotic and empirical critical values. Results indicate that the proposed procedure leads to high power in detecting test speededness, while keeping the false positive rate under control, even when simplistic and liberal critical values are used. Accuracy of the estimation of the actual change point, however, is highly dependent on the true change point. A real data example is also provided to illustrate the utility of the proposed procedure and its contrast to the response-only procedure. Implications of the findings are discussed at the end.

Joint Modeling of Response Accuracy and Time in Between-Item Multidimensional Tests Based on Bi-Factor Model

With the popularity of computer-based testing (CBT), it is easier to collect item response times (RTs) in psychological and educational assessments. RTs can provide an important source of information for respondents and tests. To make full use of RTs, the researchers have invested substantial effort in developing statistical models of RTs. Most of the proposed models posit a unidimensional latent speed to account for RTs in tests. In psychological and educational tests, many tests are multidimensional, either deliberately or inadvertently. There may be general effects in between-item multidimensional tests. However, currently there exists no RT model that considers the general effects to analyze between-item multidimensional test RT data. Also, there is no joint hierarchical model that integrates RT and response accuracy (RA) for evaluating the general effects of between-item multidimensional tests. Therefore, a bi-factor joint hierarchical model using between-item multidimensional test is proposed in this study. The simulation indicated that the Hamiltonian Monte Carlo (HMC) algorithm works well in parameter recovery. Meanwhile, the information criteria showed that the bi-factor hierarchical model (BFHM) is the best fit model. This means that it is necessary to take into consideration the general effects (general latent trait) and the multidimensionality of the RT in between-item multidimensional tests.

Improving the Delivery of Function-Directed Care During Acute Hospitalizations: Methods to Develop and Validate the Functional Assessment in Acute Care Multidimensional Computerized Adaptive Test (FAMCAT)

OBJECTIVE

To (1) develop a patient-reported, multidomain functional assessment tool focused on medically ill patients in acute care settings; (2) characterize the measure's psychometric performance; and (3) establish clinically actionable score strata that link to easily implemented mobility preservation plans.

DESIGN

This article describes the approach that our team pursued to develop and characterize this tool, the Functional Assessment in Acute Care Multidimensional Computer Adaptive Test (FAMCAT). Development involved a multistep process that included (1) expanding and refining existing item banks to optimize their salience for hospitalized patients; (2) administering candidate items to a calibration cohort; (3) estimating multidimensional item response theory models; (4) calibrating the item banks; (5) evaluating potential multidimensional computerized adaptive testing (MCAT) enhancements; (6) parameterizing the MCAT; (7) administering it to patients in a validation cohort; and (8) estimating its predictive and psychometric characteristics.

SETTING

A large (2000-bed) Midwestern Medical Center.

PARTICIPANTS

The overall sample included 4495 adults (2341 in a calibration cohort, 2154 in a validation cohort) who were admitted either to medical services with at least 1 chronic condition or to surgical/medical services if they required readmission after a hospitalization for surgery (N=4495).

INTERVENTION

Not applicable.

MAIN OUTCOME MEASURES

Not applicable.

RESULTS

The FAMCAT is an instrument designed to permit the efficient, precise, low-burden, multidomain functional assessment of hospitalized patients. We tried to optimize the FAMCAT's efficiency and precision, as well as its ability to perform multiple assessments during a hospital stay, by applying cutting edge methods such as the adaptive measure of change (AMC), differential item functioning computerized adaptive testing, and integration of collateral test-taking information, particularly item response times. Evaluation of these candidate methods suggested that all may enhance MCAT performance, but none were integrated into initial MCAT parameterization.

CONCLUSIONS

The FAMCAT has the potential to address a longstanding need for structured, frequent, and accurate functional assessment among patients hospitalized with medical diagnoses and complications of surgery.

Variable Speed Across Dimensions of Ability in the Joint Model for Responses and Response Times

Working speed as a latent variable reflects a respondent's efficiency to apply a specific skill, or a piece of knowledge to solve a problem. In this study, the common assumption of many response time models is relaxed in which respondents work with a constant speed across all test items. It is more likely that respondents work with different speed levels across items, in specific when these items measure different dimensions of ability in a multidimensional test. Multiple speed factors are used to model the speed process by allowing speed to vary across different domains of ability. A joint model for multidimensional abilities and multifactor speed is proposed. Real response time data are analyzed with an exploratory factor analysis as an example to uncover the complex structure of working speed. The feasibility of the proposed model is examined using simulation data. An empirical example with responses and response times is presented to illustrate the proposed model's applicability and rationality.

Bayesian Analysis of a Quantile Multilevel Item Response Theory Model

Multilevel item response theory (MLIRT) models are used widely in educational and psychological research. This type of modeling has two or more levels, including an item response theory model as the measurement part and a linear-regression model as the structural part, the aim being to investigate the relation between explanatory variables and latent variables. However, the linear-regression structural model focuses on the relation between explanatory variables and latent variables, which is only from the perspective of the average tendency. When we need to explore the relationship between variables at various locations along the response distribution, quantile regression is more appropriate. To this end, a quantile-regression-type structural model named as the quantile MLIRT (Q-MLIRT) model is introduced under the MLIRT framework. The parameters of the proposed model are estimated using the Gibbs sampling algorithm, and comparison with the original (i.e., linear-regression-type) MLIRT model is conducted via a simulation study. The results show that the parameters of the Q-MLIRT model could be recovered well under different quantiles. Finally, a subset of data from PISA 2018 is analyzed to illustrate the application of the proposed model.

Modeling Responses and Response Times in Tests With the Hierarchical Model and the Three-Parameter Lognormal Distribution

The hierarchical model of van der Linden is the most popular model for responses and response times in tests. It is composed of two separate submodels-one for the responses and one for the response times-that are joined at a higher level. The submodel for the response times is based on the lognormal distribution. The lognormal distribution is a skew distribution with a support from zero to infinity. Such a support is unrealistic as the solution process demands a minimal processing time that sets a response time threshold. Ignoring this response time threshold misspecifies the model and threatens the validity of model-based inferences. In this article, the response time model of van der Linden is replaced by a model that is based on the three-parameter lognormal distribution. The three-parameter lognormal distribution extends the lognormal distribution by an additional location parameter that bounds the support away from zero. Two different approaches to model fitting are proposed and evaluated with regard to parameter recovery in a simulation study. The extended model is applied to two data sets. In both data sets, the extension improves the fit of the hierarchical model.

Marginalized maximum a posteriori estimation for the four-parameter logistic model under a mixture modelling framework

The four-parameter logistic model (4PLM) has recently attracted much interest in various applications. Motivated by recent studies that re-express the four-parameter model as a mixture model with two levels of latent variables, this paper develops a new expectation-maximization (EM) algorithm for marginalized maximum a posteriori estimation of the 4PLM parameters. The mixture modelling framework of the 4PLM not only makes the proposed EM algorithm easier to implement in practice, but also provides a natural connection with popular cognitive diagnosis models. Simulation studies were conducted to show the good performance of the proposed estimation method and to investigate the impact of the additional upper asymptote parameter on the estimation of other parameters. Moreover, a real data set was analysed using the 4PLM to show its improved performance over the three-parameter logistic model.

Cognitive Diagnostic Models for Random Guessing Behaviors

Many test-takers do not carefully answer every test question; instead they sometimes quickly answer without thoughtful consideration (rapid guessing, RG). Researchers have not modeled RG when assessing student learning with cognitive diagnostic models (CDMs) to personalize feedback on a set of fine-grained skills (or attributes). Therefore, this study proposes to enhance cognitive diagnosis by modeling RG via an advanced CDM with item response and response time. This study tests the parameter recovery of this new CDM with a series of simulations via Markov chain Monte Carlo methods in JAGS. Also, this study tests the degree to which the standard and proposed CDMs fit the student response data for the Programme for International Student Assessment (PISA) 2015 computer-based mathematics test. This new CDM outperformed the simpler CDM that ignored RG; the new CDM showed less bias and greater precision for both item and person estimates, and greater classification accuracy of test results. Meanwhile, the empirical study showed different levels of student RG across test items and confirmed the findings in the simulations.

A mixture model for responses and response times with a higher-order ability structure to detect rapid guessing behaviour

Many educational and psychological assessments focus on multidimensional latent traits that often have a hierarchical structure to provide both overall-level information and fine-grained diagnostic information. A test will usually have either separate time limits for each subtest or an overall time limit for administrative convenience and test fairness. In order to complete the items within the allocated time, examinees frequently adopt different test-taking behaviours during the test, such as solution behaviour and rapid guessing behaviour. In this paper we propose a new mixture model for responses and response times with a hierarchical ability structure, which incorporates auxiliary information from other subtests and the correlation structure of the abilities to detect rapid guessing behaviour. A Markov chain Monte Carlo method is proposed for model estimation. Simulation studies reveal that all model parameters could be recovered well, and the parameter estimates had smaller absolute bias and mean squared error than the mixture unidimensional item response theory (UIRT) model. Moreover, the true positive rate of detecting rapid guessing behaviour is also higher than when using the mixture UIRT model separately for each subscale, whereas the false detection rate is much lower than the mixture UIRT model. The deviance information criterion and the logarithm of the pseudo-marginal likelihood are employed to evaluate the model fit. Finally, a real data analysis is presented to demonstrate the practical value of the proposed model.

A Speed-Accuracy Tradeoff Hierarchical Model Based on Cognitive Experiment

Most tests are administered within an allocated time. Due to the time limit, examinees might have different trade-offs on different items. In educational testing, the traditional hierarchical model cannot adequately account for the tradeoffs between response time and accuracy. Because of this, some joint models were developed as an extension of the traditional hierarchical model based on covariance. However, they cannot directly reflect the dynamic relationship between response time and accuracy. In contrast, response moderation models took the residual response time as the independent variable of the response model. Nevertheless, the models enlarge the time effect. Alternatively, the speed-accuracy tradeoff (SAT) model is superior to other experimental models in the SAT experiment. Therefore, this paper incorporates the SAT model with the traditional hierarchical model to establish a SAT hierarchical model. The results demonstrated that the Bayesian Markov chain Monte Carlo (MCMC) algorithm performed well in the SAT hierarchical model of parameters by using simulation. Finally, the deviance information criterion (DIC) more preferred the SAT hierarchical model than other models in empirical data. This means that it is indispensable to add the effect of response time on accuracy, but likewise should limit the effect on the empirical data.

Modeling Differences Between Response Times of Correct and Incorrect Responses

While standard joint models for response time and accuracy commonly assume the relationship between response time and accuracy to be fully explained by the latent variables of the model, this assumption of conditional independence is often violated in practice. If such violations are present, taking these residual dependencies between response time and accuracy into account may both improve the fit of the model to the data and improve our understanding of the response processes that led to the observed responses. In this paper, we propose a framework for the joint modeling of response time and accuracy data that allows for differences in the processes leading to correct and incorrect responses. Extensions of the standard hierarchical model (van der Linden in Psychometrika 72:287-308, 2007. https://doi.org/10.1007/s11336-006-1478-z ) are considered that allow some or all item parameters in the measurement model of speed to differ depending on whether a correct or an incorrect response was obtained. The framework also allows one to consider models that include two speed latent variables, which explain the patterns observed in the responses times of correct and of incorrect responses, respectively. Model selection procedures are proposed and evaluated based on a simulation study, and a simulation study investigating parameter recovery is presented. An application of the modeling framework to empirical data from international large-scale assessment is considered to illustrate the relevance of modeling possible differences between the processes leading to correct and incorrect responses.

Using Response Times as Collateral Information About Latent Traits in Psychological Tests

Abstract. In psychological tests, the time needed to respond to the items provides collateral information about the latent traits of the test takers. This, however, requires a measurement model that incorporates the response times in addition to the responses. Such a measurement model is usually based on a full specification of the response time distribution. In the present article, we suggest a novel modeling approach that requires fewer assumptions. In the approach, the responses are modeled with a unidimensional two-parameter logistic model. The single response times are summed to the scale-specific total testing time which is then related to the latent trait of the two-parameter logistic model via a smooth adaptive Gaussian mixture (SAGM) model. The approach can be justified against the background of the bivariate generalized linear item response theory modeling framework ( Molenaar, Tuerlinckx, & van der Maas, 2015a ). Its utility is investigated in two simulation studies and an empirical example.

Modeling Response Time and Responses in Multidimensional Health Measurement

This study explored calibrating a large item bank for use in multidimensional health measurement with computerized adaptive testing, using both item responses and response time (RT) information. The Activity Measure for Post-Acute Care is a patient-reported outcomes measure comprised of three correlated scales (Applied Cognition, Daily Activities, and Mobility). All items from each scale are Likert type, so that a respondent chooses a response from an ordered set of four response options. The most appropriate item response theory model for analyzing and scoring these items is the multidimensional graded response model (MGRM). During the field testing of the items, an interviewer read each item to a patient and recorded, on a tablet computer, the patient's responses and the software recorded RTs. Due to the large item bank with over 300 items, data collection was conducted in four batches with a common set of anchor items to link the scale. van der Linden's (2007) hierarchical modeling framework was adopted. Several models, with or without interviewer as a covariate and with or without interaction between interviewer and items, were compared for each batch of data. It was found that the model with the interaction between interviewer and item, when the interaction effect was constrained to be proportional, fit the data best. Therefore, the final hierarchical model with a lognormal model for RT and the MGRM for response data was fitted to all batches of data via a concurrent calibration. Evaluation of parameter estimates revealed that (1) adding response time information did not affect the item parameter estimates and their standard errors significantly; (2) adding response time information helped reduce the standard error of patients' multidimensional latent trait estimates, but adding interviewer as a covariate did not result in further improvement. Implications of the findings for follow up adaptive test delivery design are discussed.

An Overview of Models for Response Times and Processes in Cognitive Tests

Response times (RTs) are a natural kind of data to investigate cognitive processes underlying cognitive test performance. We give an overview of modeling approaches and of findings obtained with these approaches. Four types of models are discussed: response time models (RT as the sole dependent variable), joint models (RT together with other variables as dependent variable), local dependency models (with remaining dependencies between RT and accuracy), and response time as covariate models (RT as independent variable). The evidence from these approaches is often not very informative about the specific kind of processes (other than problem solving, information accumulation, and rapid guessing), but the findings do suggest dual processing: automated processing (e.g., knowledge retrieval) vs. controlled processing (e.g., sequential reasoning steps), and alternative explanations for the same results exist. While it seems well-possible to differentiate rapid guessing from normal problem solving (which can be based on automated or controlled processing), further decompositions of response times are rarely made, although possible based on some of model approaches.

A semi-parametric within-subject mixture approach to the analyses of responses and response times

In item response theory, modelling the item response times in addition to the item responses may improve the detection of possible between- and within-subject differences in the process that resulted in the responses. For instance, if respondents rely on rapid guessing on some items but not on all, the joint distribution of the responses and response times will be a multivariate within-subject mixture distribution. Suitable parametric methods to detect these within-subject differences have been proposed. In these approaches, a distribution needs to be assumed for the within-class response times. In this paper, it is demonstrated that these parametric within-subject approaches may produce false positives and biased parameter estimates if the assumption concerning the response time distribution is violated. A semi-parametric approach is proposed which resorts to categorized response times. This approach is shown to hardly produce false positives and parameter bias. In addition, the semi-parametric approach results in approximately the same power as the parametric approach.

Cognitive diagnosis modelling incorporating item response times

To provide more refined diagnostic feedback with collateral information in item response times (RTs), this study proposed joint modelling of attributes and response speed using item responses and RTs simultaneously for cognitive diagnosis. For illustration, an extended deterministic input, noisy 'and' gate (DINA) model was proposed for joint modelling of responses and RTs. Model parameter estimation was explored using the Bayesian Markov chain Monte Carlo (MCMC) method. The PISA 2012 computer-based mathematics data were analysed first. These real data estimates were treated as true values in a subsequent simulation study. A follow-up simulation study with ideal testing conditions was conducted as well to further evaluate model parameter recovery. The results indicated that model parameters could be well recovered using the MCMC approach. Further, incorporating RTs into the DINA model would improve attribute and profile correct classification rates and result in more accurate and precise estimation of the model parameters.

Joint Testlet Cognitive Diagnosis Modeling for Paired Local Item Dependence in Response Times and Response Accuracy

In joint models for item response times (RTs) and response accuracy (RA), local item dependence is composed of local RA dependence and local RT dependence. The two components are usually caused by the same common stimulus and emerge as pairs. Thus, the violation of local item independence in the joint models is called paired local item dependence. To address the issue of paired local item dependence while applying the joint cognitive diagnosis models (CDMs), this study proposed a joint testlet cognitive diagnosis modeling approach. The proposed approach is an extension of Zhan et al. (2017) and it incorporates two types of random testlet effect parameters (one for RA and the other for RTs) to account for paired local item dependence. The model parameters were estimated using the full Bayesian Markov chain Monte Carlo (MCMC) method. The 2015 PISA computer-based mathematics data were analyzed to demonstrate the application of the proposed model. Further, a brief simulation study was conducted to demonstrate the acceptable parameter recovery and the consequence of ignoring paired local item dependence.

A Two-Stage Approach to Differentiating Normal and Aberrant Behavior in Computer Based Testing

Statistical methods for identifying aberrances on psychological and educational tests are pivotal to detect flaws in the design of a test or irregular behavior of test takers. Two approaches have been taken in the past to address the challenge of aberrant behavior detection, which are (1) modeling aberrant behavior via mixture modeling methods, and (2) flagging aberrant behavior via residual based outlier detection methods. In this paper, we propose a two-stage method that is conceived of as a combination of both approaches. In the first stage, a mixture hierarchical model is fitted to the response and response time data to distinguish normal and aberrant behaviors using Markov chain Monte Carlo (MCMC) algorithm. In the second stage, a further distinction between rapid guessing and cheating behavior is made at a person level using a Bayesian residual index. Simulation results show that the two-stage method yields accurate item and person parameter estimates, as well as high true detection rate and low false detection rate, under different manipulated conditions mimicking NAEP parameters. A real data example is given in the end to illustrate the potential application of the proposed method.

A heteroscedastic generalized linear model with a non-normal speed factor for responses and response times

In generalized linear modelling of responses and response times, the observed response time variables are commonly transformed to make their distribution approximately normal. A normal distribution for the transformed response times is desirable as it justifies the linearity and homoscedasticity assumptions in the underlying linear model. Past research has, however, shown that the transformed response times are not always normal. Models have been developed to accommodate this violation. In the present study, we propose a modelling approach for responses and response times to test and model non-normality in the transformed response times. Most importantly, we distinguish between non-normality due to heteroscedastic residual variances, and non-normality due to a skewed speed factor. In a simulation study, we establish parameter recovery and the power to separate both effects. In addition, we apply the model to a real data set.

Hidden Markov Item Response Theory Models for Responses and Response Times

Current approaches to model responses and response times to psychometric tests solely focus on between-subject differences in speed and ability. Within subjects, speed and ability are assumed to be constants. Violations of this assumption are generally absorbed in the residual of the model. As a result, within-subject departures from the between-subject speed and ability level remain undetected. These departures may be of interest to the researcher as they reflect differences in the response processes adopted on the items of a test. In this article, we propose a dynamic approach for responses and response times based on hidden Markov modeling to account for within-subject differences in responses and response times. A simulation study is conducted to demonstrate acceptable parameter recovery and acceptable performance of various fit indices in distinguishing between different models. In addition, both a confirmatory and an exploratory application are presented to demonstrate the practical value of the modeling approach.

A Mixture Proportional Hazards Model With Random Effects for Response Times in Tests

In this article, a new model for test response times is proposed that combines latent class analysis and the proportional hazards model with random effects in a similar vein as the mixture factor model. The model assumes the existence of different latent classes. In each latent class, the response times are distributed according to a class-specific proportional hazards model. The class-specific proportional hazards models relate the response times of each subject to his or her work pace, which is considered as a random effect. The latent class extension of the proportional hazards model allows for differences in response strategies between subjects. The differences can be captured in the hazard functions, which trace the progress individuals make over time when working on an item. The model can be calibrated with marginal maximum likelihood estimation. The fit of the model can either be assessed with information criteria or with a test of model fit. In a simulation study, the performance of the proposed approaches to model calibration and model evaluation is investigated. Finally, the model is used for a real data set.

A mixture hierarchical model for response times and response accuracy

In real testing, examinees may manifest different types of test-taking behaviours. In this paper we focus on two types that appear to be among the more frequently occurring behaviours – solution behaviour and rapid guessing behaviour. Rapid guessing usually happens in high-stakes tests when there is insufficient time, and in low-stakes tests when there is lack of effort. These two qualitatively different test-taking behaviours, if ignored, will lead to violation of the local independence assumption and, as a result, yield biased item/person parameter estimation. We propose a mixture hierarchical model to account for differences among item responses and response time patterns arising from these two behaviours. The model is also able to identify the specific behaviour an examinee engages in when answering an item. A Monte Carlo expectation maximization algorithm is proposed for model calibration. A simulation study shows that the new model yields more accurate item and person parameter estimates than a non-mixture model when the data indeed come from two types of behaviour. The model also fits real, high-stakes test data better than a non-mixture model, and therefore the new model can better identify the underlying test-taking behaviour an examinee engages in on a certain item.

Psychometrics behind Computerized Adaptive Testing

The paper provides a survey of 18 years' progress that my colleagues, students (both former and current) and I made in a prominent research area in Psychometrics-Computerized Adaptive Testing (CAT). We start with a historical review of the establishment of a large sample foundation for CAT. It is worth noting that the asymptotic results were derived under the framework of Martingale Theory, a very theoretical perspective of Probability Theory, which may seem unrelated to educational and psychological testing. In addition, we address a number of issues that emerged from large scale implementation and show that how theoretical works can be helpful to solve the problems. Finally, we propose that CAT technology can be very useful to support individualized instruction on a mass scale. We show that even paper and pencil based tests can be made adaptive to support classroom teaching.

A Bivariate Generalized Linear Item Response Theory Modeling Framework to the Analysis of Responses and Response Times

A generalized linear modeling framework to the analysis of responses and response times is outlined. In this framework, referred to as bivariate generalized linear item response theory (B-GLIRT), separate generalized linear measurement models are specified for the responses and the response times that are subsequently linked by cross-relations. The cross-relations can take various forms. Here, we focus on cross-relations with a linear or interaction term for ability tests, and cross-relations with a curvilinear term for personality tests. In addition, we discuss how popular existing models from the psychometric literature are special cases in the B-GLIRT framework depending on restrictions in the cross-relation. This allows us to compare existing models conceptually and empirically. We discuss various extensions of the traditional models motivated by practical problems. We also illustrate the applicability of our approach using various real data examples, including data on personality and cognitive ability.

Semi-parametric proportional hazards models with crossed random effects for psychometric response times

The semi-parametric proportional hazards model with crossed random effects has two important characteristics: it avoids explicit specification of the response time distribution by using semi-parametric models, and it captures heterogeneity that is due to subjects and items. The proposed model has a proportionality parameter for the speed of each test taker, for the time intensity of each item, and for subject or item characteristics of interest. It is shown how all these parameters can be estimated by Markov chain Monte Carlo methods (Gibbs sampling). The performance of the estimation procedure is assessed with simulations and the model is further illustrated with the analysis of response times from a visual recognition task.

The Joint Multivariate Modeling of Multiple Mixed Response Sources: Relating Student Performances with Feedback Behavior

The present study concerns a Dutch computer-based assessment, which includes an assessment process about information literacy and a feedback process for students. The assessment is concerned with the measurement of skills in information literacy and the feedback process with item-based support to improve student learning. To analyze students' feedback behavior (i.e. feedback use and attention time), test performance, and speed of working, a multivariate hierarchical latent variable model is proposed. The model can handle multivariate mixed responses from multiple sources related to different processes and comprehends multiple measurement components for responses and response times. A flexible within-subject latent variable structure is defined to explore multiple individual latent characteristics related to students' test performance and feedback behavior. Main results of the computer-based assessment showed that feedback-information pages were less visited by well-performing students when they relate to easy items. Students' attention paid to feedback was positively related to working speed but not to the propensity to use feedback.