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In education and psychology, single-case designs (SCDs) have been used to detect treatment effects using time series data in the presence or absence of intervention. One popular design variant of SCDs is a multiple-baseline design for multiple outcomes, which often collects outcomes with some form of a count. A Poisson model is a natural choice for the count outcome. However, the assumption of the Poisson model that the outcome variable's mean is equal to its variance is often violated in SCDs, as the variance is often larger than the mean (called overdispersion). In addition, when multiple outcomes are from the same participant, it is likely that they are correlated. In this paper, we present a vector Poisson log-normal additive (V-PLN-A) model to deal with (a) change processes (auto- and cross-correlations and data-driven trend) and (b) correlation and overdispersion in multivariate count time series. A multivariate normal distribution was adapted to account for correlation among multiple outcomes as well as possible overdispersion. The V-PLN-A model was applied to an educational intervention study to test treatment effects. Simulation study results showed that parameter recovery of the V-PLN-A model was satisfactory in a large number of timepoints using Bayesian analysis, and that ignoring change processes and overdispersion led to biased estimates of the treatment effects. [ABSTRACT FROM AUTHOR]

Syntactic priming effects have been investigated for several decades in psycholinguistics and the cognitive sciences to understand the cognitive mechanisms that support language production and comprehension. The question of whether speakers prime themselves is central to adjudicating between two theories of syntactic priming, activation-based theories and expectation-based theories. However, there is a lack of a statistical model to investigate the two different theories when nominal repeated measures are obtained from multiple participants and items. This paper presents a Markov mixed-effect multinomial logistic regression model in which there are fixed and random effects for own-category lags and cross-category lags in a multivariate structure and there are category-specific crossed random effects (random person and item effects). The model is illustrated with experimental data that investigates the average and participant-specific deviations in syntactic self-priming effects. Results of the model suggest that evidence of self-priming is consistent with the predictions of activation-based theories. Accuracy of parameter estimates and precision is evaluated via a simulation study using Bayesian analysis. [ABSTRACT FROM AUTHOR]

This paper evaluated multilevel reliability measures in two-level nested designs (e.g., students nested within teachers) within an item response theory framework. A simulation study was implemented to investigate the behavior of the multilevel reliability measures and the uncertainty associated with the measures in various multilevel designs regarding the number of clusters, cluster sizes, and intraclass correlations (ICCs), and in different test lengths, for two parameterizations of multilevel item response models with separate item discriminations or the same item discrimination over levels. Marginal maximum likelihood estimation (MMLE)-multiple imputation and Bayesian analysis were employed to evaluate the accuracy of the multilevel reliability measures and the empirical coverage rates of Monte Carlo (MC) confidence or credible intervals. Considering the accuracy of the multilevel reliability measures and the empirical coverage rate of the intervals, the results lead us to generally recommend MMLE-multiple imputation. In the model with separate item discriminations over levels, marginally acceptable accuracy of the multilevel reliability measures and empirical coverage rate of the MC confidence intervals were found in a limited condition, 200 clusters, 30 cluster size,.2 ICC, and 40 items, in MMLE-multiple imputation. In the model with the same item discrimination over levels, the accuracy of the multilevel reliability measures and the empirical coverage rate of the MC confidence intervals were acceptable in all multilevel designs we considered with 40 items under MMLE-multiple imputation. We discuss these findings and provide guidelines for reporting multilevel reliability measures. [ABSTRACT FROM AUTHOR]

In the current study, we examined the dimensionality of the 16-item Card Sorting subtest of the Delis-Kaplan Executive Functioning System assessment in a sample of 264 native English-speaking children between the ages of 9 and 15 years. We also tested for measurement invariance for these items across age and gender groups using item response theory (IRT). Results of the exploratory factor analysis indicated that a two-factor model that distinguished between verbal and perceptual items provided the best fit to the data. Although the items demonstrated measurement invariance across age groups, measurement invariance was violated for gender groups, with two items demonstrating differential item functioning for males and females. Multigroup analysis using all 16 items indicated that the items were more effective for individuals whose IRT scale scores were relatively high. A single-group explanatory IRT model using 14 non-differential item functioning items showed that for perceptual ability, females scored higher than males and that scores increased with age for both males and females; for verbal ability, the observed increase in scores across age differed for males and females. The implications of these findings are discussed. [ABSTRACT FROM AUTHOR]

The purpose of the current study is to examine the performance of four information criteria (Akaike's information criterion [AIC], corrected AIC [AICC] Bayesian information criterion [BIC], sample-size adjusted BIC [SABIC]) for detecting the correct number of latent classes in the mixture Rasch model through simulations. The simulation study manipulated various class-distinction features (percentages of class-variant items, magnitudes, and patterns of item difficulty differences) and mixing proportions, assuming that a mixture Rasch model with two latent classes was the true model. Unlike previous studies that showed BIC's superiority to other indices, our findings from this study suggested that the four information criteria had differential performance depending on the percentage of class-variant items and the magnitude and pattern of item difficulty differences under a two-class structure. Furthermore, the present study revealed that AICC and SABIC generally performed as good as or better than their counterparts, AIC and BIC, respectively, for the class-class structure with a sample of 3,000. [ABSTRACT FROM PUBLISHER]

Utilizing a longitudinal item response model, this study investigated the effect of item parameter drift (IPD) on item parameters and person scores via a Monte Carlo study. Item parameter recovery was investigated for various IPD patterns in terms of bias and root mean-square error (RMSE), and percentage of time the 95% confidence interval covered the true parameter. The simulation results suggest that item parameters were not recovered well when IPD was ignored, especially if there was a larger number of IPD conditions. In addition, coverage was not accurate in all IPD conditions when IPD is ignored. Also, the results suggest that the accuracy of person scores (measured by bias) is potentially problematic when the larger number of IPD items is ignored. However, the overall accuracy (measured by RMSE) and coverage were unexpectedly acceptable in the presence of IPD as defined in this study. [ABSTRACT FROM PUBLISHER]

This study explores reader, word, and learning activity characteristics related to vocabulary learning for 202 fifth and sixth graders (N = 118 and 84, respectively) learning 16 words. Three measures of word knowledge were used: multiple-choice definition knowledge, self-report of meaning knowledge, and production of morphologically related words. Results indicate that significant vocabulary learning occurred on each measure and that certain words were easier to learn for certain types of readers. Controlling for other predictors in the model, reader characteristics like morphological awareness, reading comprehension, and language background were significant predictors of vocabulary learning, but not word reading fluency. Also, word characteristics like morphological family size and opaqueness were significant predictors of word difficulty but not number of morphemes or frequency of the word or root-word or affix. Controlling for other predictors in the model, morphological learning activities supported vocabulary learning for all 3 aspects of word knowledge. Implications for theory and instruction are discussed. [ABSTRACT FROM AUTHOR]

The presence of nuisance dimensionality is a potential threat to the accuracy of results for tests calibrated using a measurement model such as a factor analytic model or an item response theory model. This article describes a mixture group bifactor model to account for the nuisance dimensionality due to a testlet structure as well as the dimensionality due to differences in patterns of responses. The model can be used for testing whether or not an item functions differently across latent groups in addition to investigating the differential effect of local dependency among items within a testlet. An example is presented comparing test speededness results from a conventional factor mixture model, which ignores the testlet structure, with results from the mixture group bifactor model. Results suggested the 2 models treated the data somewhat differently. Analysis of the item response patterns indicated that the 2-class mixture bifactor model tended to categorize omissions as indicating speededness. With the mixture group bifactor model, more local dependency was present in the speeded than in the nonspeeded class. Evidence from a simulation study indicated the Bayesian estimation method used in this study for the mixture group bifactor model can successfully recover generated model parameters for 1- to 3-group models for tests containing testlets. [ABSTRACT FROM PUBLISHER]

Markov chain Monte Carlo (MCMC) algorithms have been shown to be useful for estimation of complex item response theory (IRT) models. Although an MCMC algorithm can be very useful, it also requires care in use and interpretation of results. In particular, MCMC algorithms generally make extensive use of priors on model parameters. In this paper, MCMC estimation is illustrated using a simple mixture IRT model, a mixture Rasch model (MRM), to demonstrate how the algorithm operates and how results may be affected by some commonly used priors. Priors on the probabilities of mixtures, label switching, model selection, metric anchoring, and implementation of the MCMC algorithm using WinBUGS are described, and their effects illustrated on parameter recovery in practical testing situations. In addition, an example is presented in which an MRM is fitted to a set of educational test data using the MCMC algorithm and a comparison is illustrated with results from three existing maximum likelihood estimation methods. [ABSTRACT FROM AUTHOR]