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Despite the growing interest in incorporating response time data into item response models, there has been a lack of research investigating how the effect of speed on the probability of a correct response varies across different groups (e.g., experimental conditions) for various items (i.e., differential response time item analysis). Furthermore, previous research has shown a complex relationship between response time and accuracy, necessitating a functional analysis to understand the patterns that manifest from this relationship. In this study, response time data are incorporated into an item response model for two purposes: (a) to examine how individuals' speed within an experimental condition affects their response accuracy on an item, and (b) to detect the differences in individuals' speed between conditions in the presence of within‐condition effects. For these two purposes, by‐variable smooth functions are employed to model differential and functional response time effects by experimental condition for each item. This model is illustrated using an empirical data set to describe the effect of individuals' speed on their reading comprehension ability in two experimental conditions of reading medium (paper vs. digital) by item. A simulation study showed that the recovery of parameters and by‐variable smooth functions of response time was satisfactory, and that the type I error rate and power of the test for the by‐variable smooth function of response time were acceptable in conditions similar to the empirical data set. In addition, the proposed method correctly identified the range of response time where between‐condition differences in the effect of response time on the probability of a correct response were accurate. [ABSTRACT FROM AUTHOR]

Popular statistical software provides the Bayesian information criterion (BIC) for multi‐level models or linear mixed models. However, it has been observed that the combination of statistical literature and software documentation has led to discrepancies in the formulas of the BIC and uncertainties as to the proper use of the BIC in selecting a multi‐level model with respect to level‐specific fixed and random effects. These discrepancies and uncertainties result from different specifications of sample size in the BIC's penalty term for multi‐level models. In this study, we derive the BIC's penalty term for level‐specific fixed‐ and random‐effect selection in a two‐level nested design. In this new version of BIC, called BICE1, this penalty term is decomposed into two parts if the random‐effect variance–covariance matrix has full rank: (a) a term with the log of average sample size per cluster and (b) the total number of parameters times the log of the total number of clusters. Furthermore, we derive the new version of BIC, called BICE2, in the presence of redundant random effects. We show that the derived formulae, BICE1 and BICE2, adhere to empirical values via numerical demonstration and that BICE (E indicating either E1 or E2) is the best global selection criterion, as it performs at least as well as BIC with the total sample size and BIC with the number of clusters across various multi‐level conditions through a simulation study. In addition, the use of BICE1 is illustrated with a textbook example dataset. [ABSTRACT FROM AUTHOR]

Marginal maximum likelihood estimation (MMLE) is commonly used for item response theory item parameter estimation. However, sufficiently large sample sizes are not always possible when studying rare populations. In this paper, empirical Bayes and hierarchical Bayes are presented as alternatives to MMLE in small sample sizes, using auxiliary item information to estimate the item parameters of a graded response model with higher accuracy. Empirical Bayes and hierarchical Bayes methods are compared with MMLE to determine under what conditions these Bayes methods can outperform MMLE, and to determine if hierarchical Bayes can act as an acceptable alternative to MMLE in conditions where MMLE is unable to converge. In addition, empirical Bayes and hierarchical Bayes methods are compared to show how hierarchical Bayes can result in estimates of posterior variance with greater accuracy than empirical Bayes by acknowledging the uncertainty of item parameter estimates. The proposed methods were evaluated via a simulation study. Simulation results showed that hierarchical Bayes methods can be acceptable alternatives to MMLE under various testing conditions, and we provide a guideline to indicate which methods would be recommended in different research situations. R functions are provided to implement these proposed methods. [ABSTRACT FROM AUTHOR]

A cluster randomized controlled trial (C‐RCT) is common in educational intervention studies. Multilevel modelling (MLM) is a dominant analytic method to evaluate treatment effects in a C‐RCT. In most MLM applications intended to detect an interaction effect, a single interaction effect (called a conflated effect) is considered instead of level‐specific interaction effects in a multilevel design (called unconflated multilevel interaction effects), and the linear interaction effect is modelled. In this paper we present a generalized additive mixed model (GAMM) that allows an unconflated multilevel interaction to be estimated without assuming a prespecified form of the interaction. R code is provided to estimate the model parameters using maximum likelihood estimation and to visualize the nonlinear treatment‐by‐covariate interaction. The usefulness of the model is illustrated using instructional intervention data from a C‐RCT. Results of simulation studies showed that the GAMM outperformed an alternative approach to recover an unconflated logistic multilevel interaction. In addition, the parameter recovery of the GAMM was relatively satisfactory in multilevel designs found in educational intervention studies, except when the number of clusters, cluster sizes, and intraclass correlations were small. When modelling a linear multilevel treatment‐by‐covariate interaction in the presence of a nonlinear effect, biased estimates (such as overestimated standard errors and overestimated random effect variances) and incorrect predictions of the unconflated multilevel interaction were found. [ABSTRACT FROM AUTHOR]

Eye-tracking has emerged as a popular method for empirical studies of cognitive processes across multiple substantive research areas. Eye-tracking systems are capable of automatically generating fixation-location data over time at high temporal resolution. Often, the researcher obtains a binary measure of whether or not, at each point in time, the participant is fixating on a critical interest area or object in the real world or in a computerized display. Eye-tracking data are characterized by spatial-temporal correlations and random variability, driven by multiple fine-grained observations taken over small time intervals (e.g., every 10 ms). Ignoring these data complexities leads to biased inferences for the covariates of interest such as experimental condition effects. This article presents a novel application of a generalized additive logistic regression model for intensive binary time series eye-tracking data from a between- and within-subjects experimental design. The model is formulated as a generalized additive mixed model (GAMM) and implemented in the mgcv R package. The generalized additive logistic regression model was illustrated using an empirical data set aimed at understanding the accommodation of regional accents in spoken language processing. Accuracy of parameter estimates and the importance of modeling the spatial-temporal correlations in detecting the experimental condition effects were shown in conditions similar to our empirical data set via a simulation study. [ABSTRACT FROM AUTHOR]

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]

Explanatory item response models (EIRMs) have been applied to investigate the effects of person covariates, item covariates, and their interactions in the fields of reading education and psycholinguistics. In practice, it is often assumed that the relationships between the covariates and the logit transformation of item response probability are linear. However, this linearity assumption obscures the differential effects of covariates over their range in the presence of nonlinearity. Therefore, this paper presents exploratory plots that describe the potential nonlinear effects of person and item covariates on binary outcome variables. This paper also illustrates the use of EIRMs with smooth functions to model these nonlinear effects. The smooth functions examined in this study include univariate smooths of continuous person or item covariates, tensor product smooths of continuous person and item covariates, and by‐variable smooths between a continuous person covariate and a binary item covariate. Parameter estimation was performed using the mgcv R package through the maximum penalized likelihood estimation method. In the empirical study, we identified a nonlinear effect of the person‐by‐item covariate interaction and discussed its practical implications. Furthermore, the parameter recovery and the model comparison method and hypothesis testing procedures presented were evaluated via simulation studies under the same conditions observed in the empirical study. [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]

Eye-tracking has emerged as a popular method for empirical studies of cognitive processes across multiple substantive research areas. Eye-tracking systems are capable of automatically generating fixation-location data over time at high temporal resolution. Often, the researcher obtains a binary measure of whether or not, at each point in time, the participant is fixating on a critical interest area or object in the real world or in a computerized display. Eye-tracking data are characterized by spatial-temporal correlations and random variability, driven by multiple fine-grained observations taken over small time intervals (e.g., every 10 ms). Ignoring these data complexities leads to biased inferences for the covariates of interest such as experimental condition effects. This article presents a novel application of a generalized additive logistic regression model for intensive binary time series eye-tracking data from a between- and within-subjects experimental design. The model is formulated as a generalized additive mixed model (GAMM) and implemented in the mgcv R package. The generalized additive logistic regression model was illustrated using an empirical data set aimed at understanding the accommodation of regional accents in spoken language processing. Accuracy of parameter estimates and the importance of modeling the spatial-temporal correlations in detecting the experimental condition effects were shown in conditions similar to our empirical data set via a simulation study. (PsycInfo Database Record (c) 2022 APA, all rights reserved).