Exploring examinees' responses to constructed response items with a supervised topic model.

Textual data are increasingly common in test data as many assessments include constructed response (CR) items as indicators of participants' understanding. The development of techniques based on natural language processing has made it possible for researchers to rapidly analyse large sets of textual data. One family of statistical techniques for this purpose are probabilistic topic models. Topic modelling is a technique for detecting the latent topic structure in a collection of documents and has been widely used to analyse texts in a variety of areas. The detected topics can reveal primary themes in the documents, and the relative use of topics can be useful in investigating the variability of the documents. Supervised latent Dirichlet allocation (SLDA) is a popular topic model in that family that jointly models textual data and paired responses such as could occur with participants' textual answers to CR items and their rubric-based scores. SLDA has an assumption of a homogeneous relationship between textual data and paired responses across all documents. This approach, while useful for some purposes, may not be satisfied for situations in which a population has subgroups that have different relationships. In this study, we introduce a new supervised topic model that incorporates finite-mixture modelling into the SLDA. This new model can detect latent groups of participants that have different relationships between their textual responses and associated scores. The model is illustrated with an example from an analysis of a set of textual responses and paired scores from a middle grades assessment of science inquiry knowledge. A simulation study is presented to investigate the performance of the proposed model under practical testing conditions.

Reliability for Tests With Items Having Different Numbers of Ordered Categories.

This study describes a structural equation modeling (SEM) approach to reliability for tests with items having different numbers of ordered categories. A simulation study is provided to compare the performance of this reliability coefficient, coefficient alpha and population reliability for tests having items with different numbers of ordered categories, a one-factor and a bifactor structures, and different skewness distributions of test scores. Results indicated that the proposed reliability coefficient was close to the population reliability in most conditions. An empirical example was used to illustrate the performance of the different coefficients for a test of items with two or three ordered categories.

Visuospatial Working Memory Mediates the Relationship Between Executive Functioning and Spatial Ability.

This study investigates the relationships among EF, VSWM, VWM, and spatial ability (mental rotation) at the construct level through testing a series of mediation models. A second objective of the study is to investigate whether the mediation relationship changes depending on the secondary demand of the tests used to measure EF. Covariates age and gender were controlled for in theses analyses. The results showed that when the Tower test, an EF test with a spatial secondary demand, was used to represent EF, VSWM significantly mediated the relationship between EF and mental rotation. However, when the composite inhibition and switching scores from the Color-Interference Test, an EF test with a verbal secondary demand, was used to represent EF, VSWM no longer significantly mediated the relationship between EF and mental rotation. This pattern of findings suggests that the test effect is real. Therefore, a grain of salt should be taken when interpreting prior findings concerning the relationship between EF and VSWM, when EF was measured using a variety of instruments, some of which have a spatial secondary demand, whereas others do not. Regarding VWM as a mediator, it was not found to be significantly mediating the relationship between EF and mental rotation, regardless of whether the Tower test or the Color-Interference Test was used to measure EF. A third objective of the study is to investigate the relative importance of EF, VSWM, and VWM in predicting mental rotation via dominance analysis. The results showed that VSWM is more important than VWM in explaining individual differences in mental rotation; the Tower test is more important than the Color-Interference Test in explaining individual differences in mental rotation. These findings again suggest that cautions need to be taken when interpreting prior findings that showed EF is highly involved in spatial ability, as test effect is real and may at least be partially be responsible for the linkage between the two constructs.

Cognitive and adaptive correlates of an ADOS-derived joint attention composite.

Joint attention skills have been shown to predict language outcomes in children with autism spectrum disorder (ASD). Less is known about the relationship between joint attention (JA) abilities in children with ASD and cognitive and adaptive abilities. In the current study, a subset of items from the Autism Diagnostic Observation Schedule (ADOS), designed to quantify JA abilities, were used to investigate social attention among an unusually large cross-sectional sample of children with ASD (n = 1061). An examination of the association between JA and a range of functional correlates (cognitive and adaptive) revealed JA was significantly related to verbal (VIQ) and non-verbal (NVIQ) cognitive ability as well as all domains of adaptive functioning (socialization, communication, and daily living skills). Additional analyses examined the degree to which the relation between adaptive abilities (socialization, communication, and daily living skills) and JA was maintained after taking into account the potentially mediating role of verbal and nonverbal cognitive ability. Results revealed that VIQ fully mediated the relation between JA and adaptive functioning, whereas the relation between these adaptive variables and JA was only partially mediated by NVIQ. Moderation analyses were also conducted to examine how verbal and non-verbal cognitive ability and gender impacted the relation between JA and adaptive functioning. In line with research showing a relation between language and JA, this indicates that while JA is significantly related to functional outcomes, this appears to be mediated specifically through a verbal cognitive pathway.

Bayesian Inference for Growth Mixture Models with Latent Class Dependent Missing Data.

Growth mixture models (GMMs) with nonignorable missing data have drawn increasing attention in research communities but have not been fully studied. The goal of this article is to propose and to evaluate a Bayesian method to estimate the GMMs with latent class dependent missing data. An extended GMM is first presented in which class probabilities depend on some observed explanatory variables and data missingness depends on both the explanatory variables and a latent class variable. A full Bayesian method is then proposed to estimate the model. Through the data augmentation method, conditional posterior distributions for all model parameters and missing data are obtained. A Gibbs sampling procedure is then used to generate Markov chains of model parameters for statistical inference. The application of the model and the method is first demonstrated through the analysis of mathematical ability growth data from the National Longitudinal Survey of Youth 1997 (Bureau of Labor Statistics, U.S. Department of Labor, 1997). A simulation study considering 3 main factors (the sample size, the class probability, and the missing data mechanism) is then conducted and the results show that the proposed Bayesian estimation approach performs very well under the studied conditions. Finally, some implications of this study, including the misspecified missingness mechanism, the sample size, the sensitivity of the model, the number of latent classes, the model comparison, and the future directions of the approach, are discussed.

Acoustical diffraction tomography in a finite form based on the Rytov transform.

A new reconstruction algorithm in a finite form based on the Rytov transform is presented for acoustical diffraction tomography. Applying the Rytov transform to the governing differential wave equation necessarily introduces the so-called generalized scattering. Our analysis shows that the generalized scattered wave is asymptotically equivalent to the physically scattered wave, and also satisfies the Sommerfeld radiation condition in the far field. Using the method of formal parameter expansion, we further find that all other terms in the expansion of the object function vanish except the first- and second-order ones, and thus reach a finite form solution to the diffraction tomography. Our computer simulation confirms the effectiveness of the algorithm in the case of the scattering objects with cylindrical symmetry, also shows its limitations when it applies to the strong scattering.