Abstract Most of the existing classification accuracy indices of attribute patterns lose effectiveness when the response data is absent in diagnostic testing. To handle this issue, this article proposes new indices to predict the correct classification rate of a diagnostic test before administering the test under the deterministic noise input “and” gate (DINA) model. The new indices include an item‐level expected classification accuracy (ECA) for attributes and a test‐level ECA for attributes and attribute patterns, and both of them are calculated based solely on the known item parameters and Q‐matrix. Theoretical analysis showed that the item‐level ECA could be regarded as a measure of correct classification rates of attributes contributed by an item. This article also illustrates how to apply the item‐level ECA for attributes to estimate the correct classification rate of attributes patterns at the test level. Simulation results showed that two test‐level ECA indices, ECA_I_W (an index based on the independence assumption and the weighted sum of the item‐level ECAs) and ECA_C_M (an index based on Gaussian Copula function that incorporates the dependence structure of the events of attribute classification and the simple average of the item‐level ECAs), could make an accurate prediction for correct classification rates of attribute patterns.

Abstract Allowing item review in computerized adaptive testing (CAT) is getting more attention in the educational measurement field as more and more testing programs adopt CAT. The research literature has shown that allowing item review in an educational test could result in more accurate estimates of examinees’ abilities. The practice of item review in CAT, however, is hindered by the potential danger of test‐manipulation strategies. To provide review opportunities to examinees while minimizing the effect of test‐manipulation strategies, researchers have proposed different algorithms to implement CAT with restricted revision options. In this article, we propose and evaluate a new method that implements CAT without any restriction on item review. In particular, we evaluate the new method in terms of the accuracy on ability estimates and the robustness against test‐manipulation strategies. This study shows that the newly proposed method is promising in a win‐win situation: examinees have full freedom to review and change answers, and the impacts of test‐manipulation strategies are undermined.

Abstract Person reliability parameters (PRPs) model temporary changes in individuals’ attribute level perceptions when responding to self‐report items (higher levels of PRPs represent less fluctuation). PRPs could be useful in measuring careless responding and traitedness. However, it is unclear how well current procedures for estimating PRPs can recover parameter estimates. This study assesses these procedures in terms of mean error (ME), average absolute difference (AAD), and reliability using simulated data with known values. Several prior distributions for PRPs were compared across a number of conditions. Overall, our results revealed little differences between using the χ or lognormal distributions as priors for estimated PRPs. Both distributions produced estimates with reasonable levels of ME; however, the AAD of the estimates was high. AAD did improve slightly as the number of items increased, suggesting that increasing the number of items would ameliorate this problem. Similarly, a larger number of items were necessary to produce reasonable levels of reliability. Based on our results, several conclusions are drawn and implications for future research are discussed.

Abstract This study investigates the effect of multidimensionality on extraction of latent classes in mixture Rasch models. In this study, two‐dimensional data were generated under varying conditions. The two‐dimensional data sets were analyzed with one‐ to five‐class mixture Rasch models. Results of the simulation study indicate the mixture Rasch model tended to extract more latent classes than the number of dimensions simulated, particularly when the multidimensional structure of the data was more complex. In addition, the number of extracted latent classes decreased as the dimensions were more highly correlated regardless of multidimensional structure. An analysis of the empirical multidimensional data also shows that the number of latent classes extracted by the mixture Rasch model is larger than the number of dimensions measured by the test.

Abstract The goal of this study is to model pauses extracted from writing keystroke logs as a way of characterizing the processes students use in essay composition. Low‐level timing data were modeled, the interkey interval and its subtype, the intraword duration, thought to reflect processes associated with keyboarding skills and composition fluency. Heavy‐tailed probability distributions (lognormal and stable distributions) were fit to individual students' data. Both density functions fit reasonably well, and estimated parameters were found to be robust across prompts designed to assess student proficiency for the same writing purpose. In addition, estimated parameters for both density functions were statistically significantly associated with human essay scores after accounting for total time spent writing the essay, a result consistent with cognitive theory on the role of low‐level processes in writing.

Abstract Both the statistical and interpretational shortcomings of the three‐parameter logistic (3PL) model in accommodating guessing effects on multiple‐choice items are well documented. We consider the use of a residual heteroscedasticity (RH) model as an alternative, and compare its performance to the 3PL with real test data sets and through simulation analyses. Our results suggest advantages to the RH approach, including closer fit to real data, more interpretable parameter estimates, and greater psychological plausibility.

Abstract Person‐fit assessment (PFA) is concerned with uncovering atypical test performance as reflected in the pattern of scores on individual items on a test. Existing person‐fit statistics (PFSs) include both parametric and nonparametric statistics. Comparison of PFSs has been a popular research topic in PFA, but almost all comparisons have employed simulated data. This article suggests an approach for comparing the performance of parametric and nonparametric PFSs using real data. This article then shows that there is no clear winner between , a popular parametric PFS, and , a popular nonparametric statistic, in a comparison using the suggested approach. This finding is contradictory to the common finding shown by Karabatsos, Dimitrov and Smith, and Tendeiro and Meijer that is more powerful than several parametric PFSs including and .

Abstract Competence data from low‐stakes educational large‐scale assessment studies allow for evaluating relationships between competencies and other variables. The impact of item‐level nonresponse has not been investigated with regard to statistics that determine the size of these relationships (e.g., correlations, regression coefficients). Classical approaches such as ignoring missing values or treating them as incorrect are currently applied in many large‐scale studies, while recent model‐based approaches that can account for nonignorable nonresponse have been developed. Estimates of item and person parameters have been demonstrated to be biased for classical approaches when missing data are missing not at random (MNAR). In our study, we focus on parameter estimates of the structural model (i.e., the true regression coefficient when regressing competence on an explanatory variable), simulating data according to various missing data mechanisms. We found that model‐based approaches and ignoring missing values performed well in retrieving regression coefficients even when we induced missing data that were MNAR. Treating missing values as incorrect responses can lead to substantial bias. We demonstrate the validity of our approach empirically and discuss the relevance of our results.

Abstract In this article we present a general approach not relying on item response theory models (non‐IRT) to detect differential item functioning (DIF) in dichotomous items with presence of guessing. The proposed nonlinear regression (NLR) procedure for DIF detection is an extension of method based on logistic regression. As a non‐IRT approach, NLR can be seen as a proxy of detection based on the three‐parameter IRT model which is a standard tool in the study field. Hence, NLR fills a logical gap in DIF detection methodology and as such is important for educational purposes. Moreover, the advantages of the NLR procedure as well as comparison to other commonly used methods are demonstrated in a simulation study. A real data analysis is offered to demonstrate practical use of the method.