Fitting direct covariance structures by the MSTRUCT modeling language of the CALIS procedure

This paper demonstrates the usefulness and flexibility of the general structural equation modelling (SEM) approach to fitting direct covariance patterns or structures (as opposed to fitting implied covariance structures from functional relationships among variables). In particular, the MSTRUCT modelling language (or syntax) of the CALIS procedure (SAS/STAT version 9.22 or later: SAS Institute, 2010) is used to illustrate the SEM approach. The MSTRUCT modelling language supports a direct covariance pattern specification of each covariance element. It also supports the input of additional independent and dependent parameters. Model tests, fit statistics, estimates, and their standard errors are then produced under the general SEM framework. By using numerical and computational examples, the following tests of basic covariance patterns are illustrated: sphericity, compound symmetry, and multiple‐group covariance patterns. Specification and testing of two complex correlation structures, the circumplex pattern and the composite direct product models with or without composite errors and scales, are also illustrated by the MSTRUCT syntax. It is concluded that the SEM approach offers a general and flexible modelling of direct covariance and correlation patterns. In conjunction with the use of SAS macros, the MSTRUCT syntax provides an easy‐to‐use interface for specifying and fitting complex covariance and correlation structures, even when the number of variables or parameters becomes large.     

A general proof of consistency of heuristic classification for cognitive diagnosis models

The Asymptotic Classification Theory of Cognitive Diagnosis (Chiu et al., 2009, Psychometrika, 74, 633–665) determined the conditions that cognitive diagnosis models must satisfy so that the correct assignment of examinees to proficiency classes is guaranteed when non‐parametric classification methods are used. These conditions have only been proven for the Deterministic Input Noisy Output AND gate model. For other cognitive diagnosis models, no theoretical legitimization exists for using non‐parametric classification techniques for assigning examinees to proficiency classes. The specific statistical properties of different cognitive diagnosis models require tailored proofs of the conditions of the Asymptotic Classification Theory of Cognitive Diagnosis for each individual model – a tedious undertaking in light of the numerous models presented in the literature. In this paper a different way is presented to address this task. The unified mathematical framework of general cognitive diagnosis models is used as a theoretical basis for a general proof that under mild regularity conditions any cognitive diagnosis model is covered by the Asymptotic Classification Theory of Cognitive Diagnosis.     

Looking ahead from age 6 to 13: A deeper insight into the development of planning ability

Planning ability gradually increases throughout childhood. However, it remains unknown whether this is attributable to global factors such as an increased ability and willingness to inhibit premature, impulsive responding, or due to the availability of specific planning operations, such as being able to mentally plan ahead more steps (‘search depth’) or to derive a clear temporal order of goals by the task layout (‘goal hierarchy’). Here, we studied the development of planning ability with respect to these global and problem‐specific aspects (search depth and goal hierarchy) of performance in 178 children from 6 to 13 years using the Tower of London task. As expected, global performance gradually developed with age. In accordance, planning durations increasingly reflected global problem demands with longer pre‐planning in harder problems. Furthermore, specific planning parameters revealed that children were increasingly capable of mentally searching ahead more steps. In contrast, the ability to derive a goal hierarchy did not show age‐related changes. While the global development of planning performance and adaptive planning durations were proposed to primarily reflect enhanced self‐monitoring, the specific increase in search depth across childhood that most likely proceeds until young adult age represents more directly planning‐related processes. Thus, development of planning ability is supported by multiple contributions.     

A Comparison of Taped-Problem Interventions to Increase Math Fact Fluency: Does the Length of Time Delay Affect Student Learning Rates?

An alternating treatments design with a control condition was used to evaluate and compare the effects of two taped-problem interventions on addition fact fluency. Both taped-problem interventions were identical with the exception of the time delay between the auditory cue of the problem and the answer. One condition used a 2-s delay and the other condition used no delay. Results showed that both taped-problem conditions showed growth in student digits correct per minute scores and that the no-delay condition was slightly more efficient as the taped-problem no-delay procedure took approximately 33% less time. Discussion focuses on using comparative intervention designs to detect nuances in procedures to improve our understanding of math fact interventions that result in the highest learning rates.