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The purpose of this study was to examine the effects of different data conditions on item parameter recovery and classification accuracy of three dichotomous mixture item response theory (IRT) models: the Mix1PL, Mix2PL, and Mix3PL. Manipulated factors in the simulation included the sample size (11 different sample sizes from 100 to 5000), test length (10, 30, and 50), number of classes (2 and 3), the degree of latent class separation (normal/no separation, small, medium, and large), and class sizes (equal vs. nonequal). Effects were assessed using root mean square error (RMSE) and classification accuracy percentage computed between true parameters and estimated parameters. The results of this simulation study showed that more precise estimates of item parameters were obtained with larger sample sizes and longer test lengths. Recovery of item parameters decreased as the number of classes increased with the decrease in sample size. Recovery of classification accuracy for the conditions with two-class solutions was also better than that of three-class solutions. Results of both item parameter estimates and classification accuracy differed by model type. More complex models and models with larger class separations produced less accurate results. The effect of the mixture proportions also differentially affected RMSE and classification accuracy results. Groups of equal size produced more precise item parameter estimates, but the reverse was the case for classification accuracy results. Results suggested that dichotomous mixture IRT models required more than 2,000 examinees to be able to obtain stable results as even shorter tests required such large sample sizes for more precise estimates. This number increased as the number of latent classes, the degree of separation, and model complexity increased. 

Response Process Validity (RPV) reflects the degree to which items are interpreted as intended by item developers. In this study, teacher responses to constructed response (CR) items to assess pedagogical content knowledge (PCK) of middle school mathematics teachers were evaluated to determine what types of teacher responses signaled weak RPV. We analyzed 38 CR pilot items on proportional reasoning across up to 13 middle school mathematics teachers per item. By coding teacher responses and using think-alouds, we found teachers' responses deemed indicative of low item RPV often had one of the following characteristics: vague answers, unanticipated assumptions, a focus on unintended topics, and paraphrasing. To develop a diverse pool of items with strong RPV, we suggest it is helpful to be aware of these symptoms, use them to consider how to improve items, and then revise and retest items accordingly. 

Selected response items and constructed response (CR) items are often found in the same test. Conventional psychometric models for these two types of items typically focus on using the scores for correctness of the responses. Recent research suggests, however, that more information may be available from the CR items than just scores for correctness. In this study, we describe an approach in which a statistical topic model along with a diagnostic classification model (DCM) was applied to a mixed item format formative test of English and Language Arts. The DCM was used to estimate students’ mastery status of reading skills. These mastery statuses were then included in a topic model as covariates to predict students’ use of each of the latent topics in their written answers to a CR item. This approach enabled investigation of the effects of mastery status of reading skills on writing patterns. Results indicated that one of the skills, Integration of Knowledge and Ideas, helped detect and explain students’ writing patterns with respect to students’ use of individual topics. 

Results of a comprehensive simulation study are reported investigating the effects of sample size, test length, number of attributes and base rate of mastery on item parameter recovery and classification accuracy of four DCMs (i.e., C-RUM, DINA, DINO, and LCDMREDUCED). Effects were evaluated using bias and RMSE computed between true (i.e., generating) parameters and estimated parameters. Effects of simulated factors on attribute assignment were also evaluated using the percentage of classification accuracy. More precise estimates of item parameters were obtained with larger sample size and longer test length. Recovery of item parameters decreased as the number of attributes increased from three to five but base rate of mastery had a varying effect on the item recovery. Item parameter and classification accuracy were higher for DINA and DINO models. 

The purpose of this poster is to report on findings from our development efforts. In prior papers, we have reflected on some of the challenges in writing items to measure teachers’ specialized content knowledge (e.g., Orrill et al, 2015). In this paper, we reflect on our analysis of think-aloud interviews to identify what we have learned about the development of PCK items for proportional reasoning.