The latent Markov model (LMM) has been increasingly used to analyze log data from computer-interactive assessments. An important consideration in applying the LMM to assessment data is measurement effects of items. In educational and psychological assessment, items exhibit distinct psychometric qualities and induce systematic variance to assessment outcome data. The current development in LMM, however, assumes that items have uniform effects and do not contribute to the variance of measurement outcomes. In this study, we propose a refinement of LMM that relaxes the measurement invariance constraint and examine empirical performance of the new framework through numerical experimentation. We modify the LMM for noninvariant measurements and refine the inferential scheme to accommodate the event-specific measurement effects. Numerical experiments are conducted to validate the proposed inference methods and evaluate the performance of the new framework. Results suggest that the proposed inferential scheme performs adequately well in retrieving the model parameters and state profiles. The new LMM framework demonstrated reliable and stable performance in modeling latent processes while appropriately accounting for items’ measurement effects. Compared with the traditional scheme, the refined framework demonstrated greater relevance to real assessment data and yielded more robust inference results when the model was ill-specified. The findings from the empirical evaluations suggest that the new framework has potential for serving large-scale assessment data that exhibit distinct measurement effects.

Process data, in particular, log data collected from a computerized test, documents the sequence of actions performed by an examinee in pursuit of solving a problem, affording an opportunity to understand test-taking behavioral patterns that account for demographic group differences in key outcomes of interest, for instance, final score on a cognitive item. Addressing this aim, this article proposes a latent class mediation analysis procedure. Using continuous process features extracted from action sequence data as indicators, latent classes underlying the test-taking behavior are identified in a latent class mediation model, where an examinee’s nominal latent class membership enters as the mediator between the observed grouping and outcome variables. A headlong search algorithm for selecting the subset of process features that maximizes the total indirect effect of the latent class mediator is implemented. The proposed procedure is validated with a series of simulations. An application to a large-scale assessment highlights how the proposed method can be used to explain performance gaps between students with learning disability and their typically developing peers on the National Assessment of Educational Progress (NAEP) math assessment.

Protocol analysis, in the form of concurrent verbal ‘thinking aloud’ reports, is a method of collecting and analyzing data about cognitive processes. This approach can help economists in evaluating competing theories of behavior and in categorizing heterogeneity of thinking patterns. As a proof of concept, I tested this method in the context of a guessing game. I found that concurrent think aloud protocols can inform us about individual’s thought processes without affecting decisions. The method allowed me to identify game theoretic thinking and heterogeneous approaches to unravelling the guessing game. The think aloud protocol is inexpensive and scalable, and it is a useful tool for identifying empirical regularities regarding decision processes.

Problem solving has been recognized as a central skill that today’s students need to thrive and shape their world. As a result, the measurement of problem-solving competency has received much attention in education in recent years. A popular tool for the measurement of problem solving is simulated interactive tasks, which require students to uncover some of the information needed to solve the problem through interactions with a computer-simulated environment. A computer log file records a student’s problem-solving process in details, including his/her actions and the time stamps of these actions. It thus provides rich information for the measurement of students’ problem-solving competency. On the other hand, extracting useful information from log files is a challenging task, due to its complex data structure. In this paper, we show how log file process data can be viewed as a marked point process, based on which we propose a continuous-time dynamic choice model. The proposed model can serve as a measurement model for scaling students along the latent traits of problem-solving competency and action speed, based on data from one or multiple tasks. A real data example is given based on data from Program for International Student Assessment 2012.

Accurate assessment of a student’s ability is the key task of a test. Assessments based on final responses are the standard. As the infrastructure advances, substantially more information is observed. One of such instances is the process data that is collected by computer-based interactive items and contain a student’s detailed interactive processes. In this paper, we show both theoretically and with simulated and empirical data that appropriately including such information in the assessment will substantially improve relevant assessment precision.

Recent years have witnessed the emergence of measurement models for analyzing action sequences in computer-based problem-solving interactive tasks. The cutting-edge psychometrics process models require pre-specification of the effectiveness of state transitions often simplifying them into dichotomous indicators. However, the dichotomous effectiveness becomes impractical when dealing with complex tasks that involve multiple optimal paths and numerous state transitions. Building on the concept of problem-solving, we introduce polytomous indicators to assess the effectiveness of problem states $d_s$\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$d_{s}$$\end{document} and state-to-state transitions ${\mathrm{\Delta }d}_{\mathrm{s}\to {\mathrm{s}}^{\prime }}$\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\mathrm {\Delta }d}_{\mathrm {s\rightarrow s'}}$$\end{document}. The three-step evaluation method for these two types of indicators is proposed and illustrated across two real problem-solving tasks. We further present a novel psychometrics process model, the sequential response model with polytomous effectiveness indicators (SRM-PEI), which is tailored to encompass a broader range of problem-solving tasks. Monte Carlo simulations indicated that SRM-PEI performed well in the estimation of latent ability and transition tendency parameters across different conditions. Empirical studies conducted on two real tasks supported the better fit of SRM-PEI over previous models such as SRM and SRMM, providing rational and interpretable estimates of latent abilities and transition tendencies through effectiveness indicators. The paper concludes by outlining potential avenues for the further application and enhancement of polytomous effectiveness indicators and SRM-PEI.

Process data, which are temporally ordered sequences of categorical observations, are of recent interest due to its increasing abundance and the desire to extract useful information. A process is a collection of time-stamped events of different types, recording how an individual behaves in a given time period. The process data are too complex in terms of size and irregularity for the classical psychometric models to be directly applicable and, consequently, new ways for modeling and analysis are desired. We introduce herein a latent theme dictionary model for processes that identifies co-occurrent event patterns and individuals with similar behavioral patterns. Theoretical properties are established under certain regularity conditions for the likelihood-based estimation and inference. A nonparametric Bayes algorithm using the Markov Chain Monte Carlo method is proposed for computation. Simulation studies show that the proposed approach performs well in a range of situations. The proposed method is applied to an item in the 2012 Programme for International Student Assessment with interpretable findings.

Process data refer to data recorded in computer-based assessments (CBAs) that reflect respondents’ problem-solving processes and provide greater insight into how respondents solve problems, in addition to how well they solve them. Using the rich information contained in process data, this study proposed an item expansion method to analyze action-level process data from the perspective of diagnostic classification in order to comprehensively understand respondents’ problem-solving competence. The proposed method cannot only estimate respondents’ problem-solving ability along a continuum, but also classify respondents according to their problem-solving skills. To illustrate the application and advantages of the proposed method, a Programme for International Student Assessment (PISA) problem-solving item was used. The results indicated that (a) the estimated latent classes provided more detailed diagnoses of respondents’ problem-solving skills than the observed score categories; (b) although only one item was used, the estimated higher-order latent ability reflected the respondents’ problem-solving ability more accurately than the unidimensional latent ability estimated from the outcome data; and (c) interactions among problem-solving skills followed the conjunctive condensation rule, which indicated that the specific action sequence appeared only when a respondent mastered all required problem solving skills. In conclusion, the proposed diagnostic classification approach is feasible and promising analyzing process data.

The data storage capacities of modern process automation systems have grown rapidly. Nowadays, the systems are able to frequently carry out even hundreds of measurements in parallel and store them in databases. However, these data are still rarely used in the analysis of processes. In this article, preparation of the raw data for further analysis is considered using feature extraction from signals by piecewise linear modeling. Prior to modeling, a preprocessing phase that removes some artifacts from the data is suggested. Because optimal models are computationally infeasible, fast heuristic algorithms must be utilized. Outlines for the optimal and some fast heuristic algorithms with modifications required by the preprocessing are given. In order to illustrate utilization of the features, a process diagnostics framework is presented. Among a large number of signals, the procedure finds the ones that best explain the observed short-term fluctuations in one signal. In the experiments, the piecewise linear modeling algorithms are compared using a massive data set from an operational paper machine. The use of piecewise linear representations in the analysis of changes in one real process measurement signal is demonstrated.