Using the Stan Program for Bayesian Item Response Theory

Frequency of missed doses and its effects on the regulation of glucose levels in patients with type 2 diabetes: A retrospective analysis

This study aimed to investigate the association between medication adherence to oral hypoglycemic agents (OHAs) and HbA1c levels in patients with type 2 diabetes mellitus (T2DM) for more than 48 weeks, as well as the factors affecting long-term adherence to OHAs. This retrospective study included 83 patients who had been receiving OHAs for T2DM for ≥48 weeks. Medication adherence values (MAVs) were calculated using the following formula: (total prescription days - prescription days of OHAs brought at admission)/(days from the initiation of OHAs to hospitalization). We assessed the association between HbA1c and MAVs using the Jonckheere-Terpstra test. Furthermore, we examined the association between patient- and medication-related factors and MAVs affecting HbA1c levels. Based on the results, MAVs were categorized as MAV ≤0.86 and MAV >0.86, and factors affecting MAVs were analyzed. Logistic regression analysis revealed that the total number of medications, the number of nonhypoglycemic agents, and a family history of diabetes were independent determinants of MAV ≤0.86 (P < .05). Multiple regression analyses indicated that the number of dosages per day and the timing of OHA administration at lunch were independent determinants of lower MAVs (P < .05). Our findings suggest that poor medication adherence is associated with elevated HbA1c levels in T2DM patients. Independent factors contributing to poor adherence include a lower number of prescribed medications, fewer nonhypoglycemic agents, no family history, a higher daily dosage frequency, and the administration of OHAs at lunch.

A Stan tutorial on Bayesian IRTree models: Conventional models and explanatory extension

IRTree models have been receiving increasing attention. However, to date, there are limited sources that provide a systematic introduction to Bayesian modeling techniques using modern probabilistic programming frameworks for the implementation of IRTree models. To facilitate the research and application of IRTree models, this paper introduces how to perform two families of Bayesian IRTree models (i.e., response tree models and latent tree models) in Stan and how to extend them in an explanatory way. Some suggestions on executing Stan codes and checking convergence are also provided. An empirical study based on the Oxford Achieving Resilience during COVID-19 data was conducted as an example to further illustrate how to apply Bayesian IRTree models to address research questions. Finally, strengths and future directions are discussed.

Robustness of the performance of the optimized hierarchical two-parameter logistic IRT model for small-sample item calibration

Hierarchical Bayesian modeling is beneficial when complex models with many parameters of the same type, such as item response theory (IRT) models, are to be estimated with sparse data. Recently, Koenig et al. (Applied Psychological Measurement, 44, 311-326, 2020) illustrated in an optimized hierarchical Bayesian two-parameter logistic model (OH2PL) how to avoid bias due to unintended shrinkage or degeneracies of the posterior, and how to benefit from this approach in small samples. The generalizability of their findings, however, is limited because they investigated only a single specification of the hyperprior structure. Consequently, in a comprehensive simulation study, we investigated the robustness of the performance of the novel OH2PL in several specifications of their hyperpriors under a broad range of data conditions. We show that the novel OH2PL in the half-Cauchy or Exponential configuration yields unbiased (in terms of bias) model parameter estimates in small samples of N = 50. Moreover, it outperforms (especially in terms of the RMSE of the item discrimination parameters) marginal maximum likelihood (MML) estimation and its nonhierarchical counterpart. This further corroborates the possibility that hierarchical Bayesian IRT models behave differently than general hierarchical Bayesian models. We discuss these results regarding the applicability of complex IRT models in small-scale situations typical in psychological research, and illustrate the extended applicability of the 2PL IRT model with an empirical example.

Dynamic Response Strategies: Accounting for Response Process Heterogeneity in IRTree Decision Nodes

It is essential to control self-reported trait measurements for response style effects to ensure a valid interpretation of estimates. Traditional psychometric models facilitating such control consider item responses as the result of two kinds of response processes-based on the substantive trait, or based on response styles-and they assume that both of these processes have a constant influence across the items of a questionnaire. However, this homogeneity over items is not always given, for instance, if the respondents' motivation declines throughout the questionnaire so that heuristic responding driven by response styles may gradually take over from cognitively effortful trait-based responding. The present study proposes two dynamic IRTree models, which account for systematic continuous changes and additional random fluctuations of response strategies, by defining item position-dependent trait and response style effects. Simulation analyses demonstrate that the proposed models accurately capture dynamic trajectories of response processes, as well as reliably detect the absence of dynamics, that is, identify constant response strategies. The continuous version of the dynamic model formalizes the underlying response strategies in a parsimonious way and is highly suitable as a cognitive model for investigating response strategy changes over items. The extended model with random fluctuations of strategies can adapt more closely to the item-specific effects of different response processes and thus is a well-fitting model with high flexibility. By using an empirical data set, the benefits of the proposed dynamic approaches over traditional IRTree models are illustrated under realistic conditions.

Comparison between pystan and numpyro in Bayesian item response theory: evaluation of agreement of estimated latent parameters and sampling performance

Purpose

The purpose of this study is to compare two libraries dedicated to the Markov chain Monte Carlo method: pystan and numpyro. In the comparison, we mainly focused on the agreement of estimated latent parameters and the performance of sampling using the Markov chain Monte Carlo method in Bayesian item response theory (IRT).

Materials and methods

Bayesian 1PL-IRT and 2PL-IRT were implemented with pystan and numpyro. Then, the Bayesian 1PL-IRT and 2PL-IRT were applied to two types of medical data obtained from a published article. The same prior distributions of latent parameters were used in both pystan and numpyro. Estimation results of latent parameters of 1PL-IRT and 2PL-IRT were compared between pystan and numpyro. Additionally, the computational cost of the Markov chain Monte Carlo method was compared between the two libraries. To evaluate the computational cost of IRT models, simulation data were generated from the medical data and numpyro.

Results

For all the combinations of IRT types (1PL-IRT or 2PL-IRT) and medical data types, the mean and standard deviation of the estimated latent parameters were in good agreement between pystan and numpyro. In most cases, the sampling time using the Markov chain Monte Carlo method was shorter in numpyro than that in pystan. When the large-sized simulation data were used, numpyro with a graphics processing unit was useful for reducing the sampling time.

Conclusion

Numpyro and pystan were useful for applying the Bayesian 1PL-IRT and 2PL-IRT. Our results show that the two libraries yielded similar estimation result and that regarding to sampling time, the fastest libraries differed based on the dataset size.

A Bayesian many-facet Rasch model with Markov modeling for rater severity drift

Fair performance assessment requires consideration of the effects of rater severity on scoring. The many-facet Rasch model (MFRM), an item response theory model that incorporates rater severity parameters, has been widely used for this purpose. Although a typical MFRM assumes that rater severity does not change during the rating process, in actuality rater severity is known to change over time, a phenomenon called rater severity drift. To investigate this drift, several extensions of the MFRM have been proposed that incorporate time-specific rater severity parameters. However, these previous models estimate the severity parameters under the assumption of temporal independence. This introduces inefficiency into the parameter estimation because severities between adjacent time points tend to have temporal dependency in practice. To resolve this problem, we propose a Bayesian extension of the MFRM that incorporates time dependency for the rater severity parameters, based on a Markov modeling approach. The proposed model can improve the estimation accuracy of the time-specific rater severity parameters, resulting in improved estimation accuracy for the other rater parameters and for model fitting. We demonstrate the effectiveness of the proposed model through simulation experiments and application to actual data.

Exploration and analysis of a generalized one-parameter item response model with flexible link functions

This paper primarily analyzes the one-parameter generalized logistic (1PGlogit) model, which is a generalized model containing other one-parameter item response theory (IRT) models. The essence of the 1PGlogit model is the introduction of a generalized link function that includes the probit, logit, and complementary log-log functions. By transforming different parameters, the 1PGlogit model can flexibly adjust the speed at which the item characteristic curve (ICC) approaches the upper and lower asymptote, breaking the previous constraints in one-parameter IRT models where the ICC curves were either all symmetric or all asymmetric. This allows for a more flexible way to fit data and achieve better fitting performance. We present three simulation studies, specifically designed to validate the accuracy of parameter estimation for a variety of one-parameter IRT models using the Stan program, illustrate the advantages of the 1PGlogit model over other one-parameter IRT models from a model fitting perspective, and demonstrate the effective fit of the 1PGlogit model with the three-parameter logistic (3PL) and four-parameter logistic (4PL) models. Finally, we demonstrate the good fitting performance of the 1PGlogit model through an analysis of real data.

Estimating the Multidimensional Generalized Graded Unfolding Model with Covariates Using a Bayesian Approach

Noncognitive constructs are commonly assessed in educational and organizational research. They are often measured by summing scores across items, which implicitly assumes a dominance item response process. However, research has shown that the unfolding response process may better characterize how people respond to noncognitive items. The Generalized Graded Unfolding Model (GGUM) representing the unfolding response process has therefore become increasingly popular. However, the current implementation of the GGUM is limited to unidimensional cases, while most noncognitive constructs are multidimensional. Fitting a unidimensional GGUM separately for each dimension and ignoring the multidimensional nature of noncognitive data may result in suboptimal parameter estimation. Recently, an R package bmggum was developed that enables the estimation of the Multidimensional Generalized Graded Unfolding Model (MGGUM) with covariates using a Bayesian algorithm. However, no simulation evidence is available to support the accuracy of the Bayesian algorithm implemented in bmggum. In this research, two simulation studies were conducted to examine the performance of bmggum. Results showed that bmggum can estimate MGGUM parameters accurately, and that multidimensional estimation and incorporating relevant covariates into the estimation process improved estimation accuracy. The effectiveness of two Bayesian model selection indices, WAIC and LOO, were also investigated and found to be satisfactory for model selection. Empirical data were used to demonstrate the use of bmggum and its performance was compared with three other GGUM software programs: GGUM2004, GGUM, and mirt.

Bayesian multidimensional nominal response model for observer study of radiologists

PURPOSE

This study proposes a Bayesian multidimensional nominal response model (MD-NRM) to statistically analyze the nominal response of multiclass classifications.

MATERIALS AND METHODS

First, for MD-NRM, we extended the conventional nominal response model to achieve stable convergence of the Bayesian nominal response model and utilized multidimensional ability parameters. We then applied MD-NRM to a 3-class classification problem, where radiologists visually evaluated chest X-ray images and selected their diagnosis from one of the three classes. The classification problem consisted of 150 cases, and each of the six radiologists selected their diagnosis based on a visual evaluation of the images. Consequently, 900 (= 150 × 6) nominal responses were obtained. In MD-NRM, we assumed that the responses were determined by the softmax function, the ability of radiologists, and the difficulty of images. In addition, we assumed that the multidimensional ability of one radiologist were represented by a 3 × 3 matrix. The latent parameters of the MD-NRM (ability parameters of radiologists and difficulty parameters of images) were estimated from the 900 responses. To implement Bayesian MD-NRM and estimate the latent parameters, a probabilistic programming language (Stan, version 2.21.0) was used.

RESULTS

For all parameters, the Rhat values were less than 1.10. This indicates that the latent parameters of the MD-NRM converged successfully.

CONCLUSION

The results show that it is possible to estimate the latent parameters (ability and difficulty parameters) of the MD-NRM using Stan. Our code for the implementation of the MD-NRM is available as open source.

Bridging Models of Biometric and Psychometric Assessment: A Three-Way Joint Modeling Approach of Item Responses, Response Times, and Gaze Fixation Counts

Recently, joint models of item response data and response times have been proposed to better assess and understand test takers' learning processes. This article demonstrates how biometric information such as gaze fixation counts obtained from an eye-tracking machine can be integrated into the measurement model. The proposed joint modeling framework accommodates the relations among a test taker's latent ability, working speed and test engagement level via a person-side variance-covariance structure, while simultaneously permitting the modeling of item difficulty, time-intensity, and the engagement intensity through an item-side variance-covariance structure. A Bayesian estimation scheme is used to fit the proposed model to data. Posterior predictive model checking based on three discrepancy measures corresponding to various model components are introduced to assess model-data fit. Findings from a Monte Carlo simulation and results from analyzing experimental data demonstrate the utility of the model.

Bayesian Item Response Theory Models With Flexible Generalized Logit Links

In educational and psychological research, the logit and probit links are often used to fit the binary item response data. The appropriateness and importance of the choice of links within the item response theory (IRT) framework has not been investigated yet. In this paper, we present a family of IRT models with generalized logit links, which include the traditional logistic and normal ogive models as special cases. This family of models are flexible enough not only to adjust the item characteristic curve tail probability by two shape parameters but also to allow us to fit the same link or different links to different items within the IRT model framework. In addition, the proposed models are implemented in the Stan software to sample from the posterior distributions. Using readily available Stan outputs, the four Bayesian model selection criteria are computed for guiding the choice of the links within the IRT model framework. Extensive simulation studies are conducted to examine the empirical performance of the proposed models and the model fittings in terms of "in-sample" and "out-of-sample" predictions based on the deviance. Finally, a detailed analysis of the real reading assessment data is carried out to illustrate the proposed methodology.

Regularized Bayesian calibration and scoring of the WD-FAB IRT model improves predictive performance over marginal maximum likelihood

Item response theory (IRT) is the statistical paradigm underlying a dominant family of generative probabilistic models for test responses, used to quantify traits in individuals relative to target populations. The graded response model (GRM) is a particular IRT model that is used for ordered polytomous test responses. Both the development and the application of the GRM and other IRT models require statistical decisions. For formulating these models (calibration), one needs to decide on methodologies for item selection, inference, and regularization. For applying these models (test scoring), one needs to make similar decisions, often prioritizing computational tractability and/or interpretability. In many applications, such as in the Work Disability Functional Assessment Battery (WD-FAB), tractability implies approximating an individual's score distribution using estimates of mean and variance, and obtaining that score conditional on only point estimates of the calibrated model. In this manuscript, we evaluate the calibration and scoring of models under this common use-case using Bayesian cross-validation. Applied to the WD-FAB responses collected for the National Institutes of Health, we assess the predictive power of implementations of the GRM based on their ability to yield, on validation sets of respondents, ability estimates that are most predictive of patterns of item responses. Our main finding indicates that regularized Bayesian calibration of the GRM outperforms the regularization-free empirical Bayesian procedure of marginal maximum likelihood. We also motivate the use of compactly supported priors in test scoring.

Evaluating Stan’s Variational Bayes Algorithm for Estimating Multidimensional IRT Models

Bayesian estimation of multidimensional item response theory (IRT) models in large data sets may come with impractical computational burdens when general-purpose Markov chain Monte Carlo (MCMC) samplers are employed. Variational Bayes (VB)—a method for approximating the posterior distribution—poses a potential remedy. Stan’s general-purpose VB algorithms have drastically improved the accessibility of VB methods for a wide psychometric audience. Using marginal maximum likelihood (MML) and MCMC as benchmarks, the present simulation study investigates the utility of Stan’s built-in VB function for estimating multidimensional IRT models with between-item dimensionality. VB yielded a marked speed-up in comparison to MCMC, but did not generally outperform MML in terms of run time. VB estimates were trustworthy only for item difficulties, while bias in item discriminations depended on the model’s dimensionality. Under realistic conditions of non-zero correlations between dimensions, VB correlation estimates were subject to severe bias. The practical relevance of performance differences is illustrated with data from PISA 2018. We conclude that in its current form, Stan’s built-in VB algorithm does not pose a viable alternative for estimating multidimensional IRT models.

Longitudinal association between an overall diet quality index and latent profiles of cardiovascular risk factors: results from a population based 13-year follow up cohort study

BACKGROUND

Cardiovascular diseases (CVDs) are associated with an unhealthy lifestyle, including poor diet. Indices reflecting the overall quality of diets are more effective than single food or nutrient-based approaches in clarifying the diet disease relationship. The present study aims to use latent variable modeling to examine the longitudinal joint relationships between the latent profiles of CVDs risk factors and the diet quality index (DQI).

METHODS

A total of 4390 Iranian adults aged 35 and older within the framework of the Isfahan Cohort Study were included in the current secondary analysis. DQI focused on food groups, including fast foods, sweets, vegetables, fruits, fats, and proteins, based on a validated food frequency questionnaire. The score of DQI has a range between 0 (indicating healthy and high diet quality) and 2 (indicating unhealthy and low diet quality). Blood pressure (BP), anthropometric measurements, blood glucose, serum lipids, and high-sensitivity C-Reactive Protein (hs-CRP) were measured according to standard protocols in 2001, 2007, and 2013 to evaluate the profiles of CVDs risk factors. A Bayesian Multidimensional Graded Responses Linear Mixed Model was used for data analysis.

RESULTS

At baseline, the participants' mean ± standard deviation age was 50.09 ± 11.21, and 49.5% of them were male. Three latent profiles of CVDs risk factors were derived: (1) Fit Pre-Metabolic Syndrome (FPMS) profile characterized by normal anthropometric indices and some impaired metabolic risk factors; (2) DysLipoproteinemia Central Obese (DLCO) profile with abdominal obesity and impaired low-density lipoprotein cholesterol as well as other normal risk factors; (3) Impaired Laboratory Inflammatory State (ILIS) profile with impaired high-density lipoprotein cholesterol and hs-CRP and other normal risk factors. In general, higher scores of the extracted latent profiles indicated more impaired function in the related risk factors. After controlling for various potential fixed and time-varying confounding variables, a significant positive longitudinal association was found between FPMS, DLCO, and ILIS profiles and DQI (β (95% CrI): 0.26 (0.03,0.51), 0.14 (0.01,0.27), and 0.24 (0.11,0.38), respectively), demonstrating that lower overall diet quality was associated with more impaired function of the related risk factors.

CONCLUSIONS

More adherence to a healthy quality diet is associated with lower levels of all emerging latent profiles of CVDs risk factors. Increasing the knowledge of the community about the importance of the quality of consumed foods may help to prevent CVDs. It is recommended that further investigations, particularly interventional studies, be conducted to confirm our results.

Bayesian Statistical Model of Item Response Theory in Observer Studies of Radiologists

RATIONALE AND OBJECTIVES

The purpose of this study was to validate a Bayesian statistical model of item response theory (IRT). IRT was used to evaluate a new modality (temporal subtraction, TS) in observer studies of radiologists, compared with a conventional modality (computed tomography).

MATERIALS AND METHODS

From previously published papers, we obtained two datasets of clinical observer studies of radiologists. Those studies used a multi-reader and multi-case paradigm to evaluate radiologists' detection abilities, primarily to determine if TS could enhance the detectability of bone metastasis or brain infarctions. We applied IRT to these studies' datasets using Stan software. Before applying IRT, the radiologists' responses were recorded as binaries for each case (1 = correct, 0 = incorrect). Effect of TS on detectability was evaluated by using our IRT model and calculating the 95% credible interval of the effect.

RESULTS

The mean, median, and 95% credible interval of the effect of TS were 0.913, 0.885, and 0.243-1.745 for the bone metastasis detection, and 2.524, 2.50, and 1.827-3.310, for the brain infarction detection. For both detection studies, the 95% credible intervals of the effect of TS did not include zero, indicating that TS significantly improved diagnostic ability.

CONCLUSION

Judgments based on the present study results were compatible with the two previous studies. Our study results demonstrated that the Bayesian statistical model of IRT could judge a new modality's usefulness.

Analysing Standard Progressive Matrices (SPM-LS) with Bayesian Item Response Models

Raven's Standard Progressive Matrices (SPM) test and related matrix-based tests are widely applied measures of cognitive ability. Using Bayesian Item Response Theory (IRT) models, I reanalyzed data of an SPM short form proposed by Myszkowski and Storme (2018) and, at the same time, illustrate the application of these models. Results indicate that a three-parameter logistic (3PL) model is sufficient to describe participants dichotomous responses (correct vs. incorrect) while persons' ability parameters are quite robust across IRT models of varying complexity. These conclusions are in line with the original results of Myszkowski and Storme (2018). Using Bayesian as opposed to frequentist IRT models offered advantages in the estimation of more complex (i.e., 3-4PL) IRT models and provided more sensible and robust uncertainty estimates.

A Comparison of Monte Carlo Methods for Computing Marginal Likelihoods of Item Response Theory Models

Nowadays, Bayesian methods are routinely used for estimating parameters of item response theory (IRT) models. However, the marginal likelihoods are still rarely used for comparing IRT models due to their complexity and a relatively high dimension of the model parameters. In this paper, we review Monte Carlo (MC) methods developed in the literature in recent years and provide a detailed development of how these methods are applied to the IRT models. In particular, we focus on the "best possible" implementation of these MC methods for the IRT models. These MC methods are used to compute the marginal likelihoods under the one-parameter IRT model with the logistic link (1PL model) and the two-parameter logistic IRT model (2PL model) for a real English Examination dataset. We further use the widely applicable information criterion (WAIC) and deviance information criterion (DIC) to compare the 1PL model and the 2PL model. The 2PL model is favored by all of these three Bayesian model comparison criteria for the English Examination data.

Modeling Dependence Structures for Response Times in a Bayesian Framework

A multivariate generalization of the log-normal model for response times is proposed within an innovative Bayesian modeling framework. A novel Bayesian Covariance Structure Model (BCSM) is proposed, where the inclusion of random-effect variables is avoided, while their implied dependencies are modeled directly through an additive covariance structure. This makes it possible to jointly model complex dependencies due to for instance the test format (e.g., testlets, complex constructs), time limits, or features of digitally based assessments. A class of conjugate priors is proposed for the random-effect variance parameters in the BCSM framework. They give support to testing the presence of random effects, reduce boundary effects by allowing non-positive (co)variance parameters, and support accurate estimation even for very small true variance parameters. The conjugate priors under the BCSM lead to efficient posterior computation. Bayes factors and the Bayesian Information Criterion are discussed for the purpose of model selection in the new framework. In two simulation studies, a satisfying performance of the MCMC algorithm and of the Bayes factor is shown. In comparison with parameter expansion through a half-Cauchy prior, estimates of variance parameters close to zero show no bias and undercoverage of credible intervals is avoided. An empirical example showcases the utility of the BCSM for response times to test the influence of item presentation formats on the test performance of students in a Latin square experimental design.

How Do Test Takers Interact With Simulation-Based Tasks? A Response-Time Perspective

Many traditional educational assessments use multiple-choice items and constructed-response items to measure fundamental skills. Virtual performance assessments, such as game- or simulation-based assessments, are designed recently in the field of educational measurement to measure more integrated skills through the test takers' interactive behaviors within an assessment in a virtual environment. This paper presents a systematic timing study based on data collected from a simulation-based task designed recently at Educational Testing Service. The study is intended to understand the response times in complex simulation-based tasks so as to shed light on possible ways of leveraging response time information in designing, assembling, and scoring of simulation-based tasks. To achieve this objective, a series of five analyses were conducted to first understand the statistical properties of the timing data, and then investigate the relationship between the timing patterns and the test takers' performance on the items/task, demographics, motivation level, personality, and test-taking behaviors through use of different statistical approaches. We found that the five analyses complemented each other and revealed different useful timing aspects of this test-taker sample's behavioral features in the simulation-based task. The findings were also compared with notable existing results in the literature related to timing data.

Preventive chemotherapy reverses covert, lymphatic-associated tissue change in young people with lymphatic filariasis in Myanmar

OBJECTIVES

This longitudinal comparative study investigated the effect of preventive chemotherapy (PC) on covert tissue changes associated with lymphatic filariasis (LF) among young people living in an LF-endemic area in Myanmar.

METHODS

Tissue compressibility and extracellular free fluid in the lower limbs of people aged 10-21 years were measured using indurometry and bioimpedance spectroscopy (BIS). Baseline measures were taken in October 2014, annual mass drug administration (MDA) of PC was delivered in December, and in March 2015 further PC was offered to LF-positive cases who had missed MDA. Follow-up measures were taken in February and June 2015.

RESULTS

A total of 50 antigen-positive cases and 46 antigen-negative controls were included. Self-reported PC consumption was 60.1% during 2014 MDA and 66.2% overall. At second follow-up, 24 of 34 cases and 27 of 43 controls had consumed PC. Significant and clinically relevant between-group differences at baseline were not found post-PC. Bayesian linear mixed models showed a significant change in indurometer scores at both calves for antigen-positive cases who consumed any PC (dominant calf: -0.30 [95% CI -0.52, -0.07], P < 0.05 and non-dominant calf: -0.35 [95% CI -0.58, -0.12], P < 0.01). Changes in antigen-negative participants or those not consuming PC were not significant.

CONCLUSION

This study is the first attempt to use simple field-friendly tools to track fluid and tissue changes after treatment of asymptomatic people infected with LF. Results suggested that PC alone is sufficient to reverse covert lymphatic disturbance. Longer follow-up of larger cohorts is required to confirm these improvements and whether they persist over time. These findings should prompt increased efforts to overcome low PC coverage, which misses many infected young people, particularly males, who are unaware of their infection status, unmotivated to take PC and at risk of developing lymphoedema. Indurometry and BIS should be considered in assessment of lymphatic filariasis-related lymphedema.

A Short Note on Obtaining Point Estimates of the IRT Ability Parameter With MCMC Estimation in Mplus: How Many Plausible Values Are Needed?

Plausible values can be used to either estimate population-level statistics or compute point estimates of latent variables. While it is well known that five plausible values are usually sufficient for accurate estimation of population-level statistics in large-scale surveys, the minimum number of plausible values needed to obtain accurate latent variable point estimates is unclear. This is especially relevant when an item response theory (IRT) model is estimated with MCMC (Markov chain Monte Carlo) methods in Mplus and point estimates of the IRT ability parameter are of interest, as Mplus only estimates the posterior distribution of each ability parameter. In order to obtain point estimates of the ability parameter, a number of plausible values can be drawn from the posterior distribution of each individual ability parameter and their mean (the posterior mean ability estimate) can be used as an individual ability point estimate. In this note, we conducted a simulation study to investigate how many plausible values were needed to obtain accurate posterior mean ability estimates. The results indicate that 20 is the minimum number of plausible values required to obtain point estimates of the IRT ability parameter that are comparable to marginal maximum likelihood estimation(MMLE)/expected a posteriori (EAP) estimates. A real dataset was used to demonstrate the comparison between MMLE/EAP point estimates and posterior mean ability estimates based on different number of plausible values.

Diagnostic Classification Models for Ordinal Item Responses

The purpose of this study is to develop and evaluate two diagnostic classification models (DCMs) for scoring ordinal item data. We first applied the proposed models to an operational dataset and compared their performance to an epitome of current polytomous DCMs in which the ordered data structure is ignored. Findings suggest that the much more parsimonious models that we proposed performed similarly to the current polytomous DCMs and offered useful item-level information in addition to option-level information. We then performed a small simulation study using the applied study condition and demonstrated that the proposed models can provide unbiased parameter estimates and correctly classify individuals. In practice, the proposed models can accommodate much smaller sample sizes than current polytomous DCMs and thus prove useful in many small-scale testing scenarios.