Mediation Analysis in a Latent Growth Curve Modeling Framework

This article presents several longitudinal mediation models in the framework of latent growth curve modeling and provides a detailed account of how such models can be constructed. Logical and statistical challenges that might arise when such analyses are conducted are also discussed. Specifically, we discuss how the initial status (intercept) and change (slope) of the putative mediator variable can be appropriately included in the causal chain between the independent and dependent variables in longitudinal mediation models. We further address whether the slope of the dependent variable should be controlled for the dependent variable's intercept to improve the conceptual relevance of the mediation models. The models proposed are illustrated by analyzing a longitudinal data set. We conclude that for certain research questions in developmental science, a multiple mediation model where the dependent variable's slope is controlled for its intercept can be considered an adequate analytical model. However, such models also show several limitations.     

Using Fixed Thresholds with Grouped Data in Structural Equation Modeling

Valuable methods have been developed for incorporating ordinal variables into structural equation models using a latent response variable formulation. However, some model parameters, such as the means and variances of latent factors, can be quite difficult to interpret because the latent response variables have an arbitrary metric. This limitation can be particularly problematic in growth models, where the means and variances of the latent growth parameters typically have important substantive meaning when continuous measures are used. However, these methods are often applied to grouped data, where the ordered categories actually represent an interval-level variable that has been measured on an ordinal scale for convenience. The method illustrated in this article shows how category threshold values can be incorporated into the model so that interpretation is more meaningful, with particular emphasis given to the application of this technique with latent growth models.     

How Often Is the Misfit of Item Response Theory Models Practically Significant?

Standard 3.9 of the Standards for Educational and Psychological Testing ( 1999 ) demands evidence of model fit when item response theory (IRT) models are employed to data from tests. Hambleton and Han ( 2005 ) and Sinharay ( 2005 ) recommended the assessment of practical significance of misfit of IRT models, but few examples of such assessment can be found in the literature concerning IRT model fit. In this article, practical significance of misfit of IRT models was assessed using data from several tests that employ IRT models to report scores. The IRT model did not fit any data set considered in this article. However, the extent of practical significance of misfit varied over the data sets.     

The Weird World,and Equally Weird Measurement Models: Reactive Indicators and the Validity Revolution

Researchers using structural equation modeling (SEM) aspire to learn about the world by seeking models with causal specifications that match the causal forces extant in the world. This quest for a model matching existing worldly causal forces constitutes an ontology that orients, or perhaps reorients, thinking about measurement validity. This article illustrates several ways the seemingly innocuous quest for structural equation models that mirror “the world beyond” confronts entrenched notions of measurement validity. The article begins by considering simple measurement models and ends by “discovering” a new class of indicators called reactive indicators. Reactive indicators act as both the cause and effect of an underlying latent variable. The identifiability of a simple model containing a reactive indicator is proven and a research example illustrating the use of a reactive indicator is provided. However, the real challenge is to understand how an indicator can be both a cause and effect of the latent it measures. The understanding does not come from complying with the traditional rules for reliability and validity, but from focusing on the quest to make the structural equation model match the structuring of the worldly forces we seek to understand. Valid measurement in the context of a weirdly structured world requires an equally weird structural equation model.     

On Fitting Nonlinear Latent Curve Models to Multiple Variables Measured Longitudinally

This article shows how nonlinear latent curve models may be fitted for simultaneous analysis of multiple variables measured longitudinally using Mx statistical software. Longitudinal studies often involve observation of several variables across time with interest in the associations between change characteristics of different variables measured within individuals. Other applications involve repeated measures for distinguishable individuals nested within small groups, such as families, with interest in the associations between change characteristics in variables for individuals within groups. This article shows how Mx can be used to carry out analysis of multiple variables measured over time where at least one variable is described by a function that includes one or more parameters that enter the model nonlinearly. An example is provided.     

Modeling Unmeasured Third Variables in Longitudinal Studies

This article discusses techniques to account for unmeasured third variables in longitudinal designs. As an extension of the synchronous common factor (SCF) model, which is the basis of the cross-lagged panel correlation technique, a series of less restrictive synchronous common factor (LRSCF) models are introduced. LRSCF models can be tested by using structural equation modeling. Although both SCF and LRSCF models rest on a 2-wave design, the SCF model requires only 2 variables measured at each wave, whereas LRSCF models require 3 variables. This enables several restrictions of the SCF model to be relaxed. Among others, a particular advantage is that the strength of lagged relations among the variables can be estimated. It is recommended that LRSCF models be applied routinely whenever possible third variables might have been omitted.     

A Mixture Group Bifactor Model for Binary Responses

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.     

Exploratory analyses to improve model fit: Errors due to misspecification and a strategy to reduce their occurrence

Two Lagrange multiplier (LM) methods may be used in specification searches for adding parameters to models: one based on univariate LM tests and respecification of the model (LM‐respecified method) and the other based on a partitioning of multivariate LM tests (LM‐incremental method). These methods may result in extraneous parameters being included in models due to either sampling error or the model being misspecified. A 2‐stage specification search may be used to reduce errors due to misspecification. In the 1st stage, parameters are added to models based on LM tests to maximize fit. Second, parameters added in the 1st stage are deleted if they are no longer necessary to maintain model fit. Illustrations are presented to demonstrate that errors due to misspecification occur with the LM‐respecified method and are even more likely with the LM‐incremental approach. These illustrations also show how the deletion stage can help eliminate some of these errors.     

Dynamic Modeling for Development and Education: From Concepts to Numbers

The general aim of the article is to teach the reader how to transform conceptual models of change, development, and learning into mathematical expressions and how to use these equations to build dynamic models by means of the widely used spreadsheet program Excel. The explanation is supported by a number of Excel files, which the reader can download at www.paulvangeert.nl/articles_appendices.htm . The article begins with a discussion of how to define variables in the context of modeling and the difference with the context of measurement. It proceeds with a simple dynamic model to give the reader a general idea, and continues with an explanation of the extended logistic model, which can be conceived of as a building block of more complex growth models pertaining to learning and development. The final section discusses the building of a concrete developmental model, answering the question of why girls like pink.     

Communities of development: A new model for R&;D work

This article provides the reader with insight into what research and development (R&D) work specifically entails. The various stages in development processes are described from the research question and analyses that have current practice as the point of departure to consolidation and new practice based on the testing of concrete teaching programs. This article also illuminates the “R” in R&D work. A thorough review is given of how the development processes can be explored by having a meta-perspective on concrete practice. A number of models have been developed to visualize development and research. We introduce our own R&D model in the article which is a very accessible way of presenting the various processes within the stages and levels of R&D work. The article ends by pointing out the importance that focused research questions have for R&D work and how the model can be a tool for researchers cooperating with teachers in communities of development.     

Models and Strategies for Factor Mixture Analysis: An Example Concerning the Structure Underlying Psychological Disorders

The factor mixture model (FMM) uses a hybrid of both categorical and continuous latent variables. The FMM is a good model for the underlying structure of psychopathology because the use of both categorical and continuous latent variables allows the structure to be simultaneously categorical and dimensional. This is useful because both diagnostic class membership and the range of severity within and across diagnostic classes can be modeled concurrently. Although the conceptualization of the FMM has been explained in the literature, the use of the FMM is still not prevalent. One reason is that there is little research about how such models should be applied in practice and, once a well-fitting model is obtained, how it should be interpreted. In this article, the FMM is explored by studying a real data example on conduct disorder. By exploring this example, this article aims to explain the different formulations of the FMM, the various steps in building a FMM, and how to decide between an FMM and alternative models.     

在线考试：机遇与挑战

在线考试是一种通过网络来实现的计算机考试。本文就这种考试的特点、模式、应用范围,以及它在美国的应用情况和给中国带来的机遇和挑战等问题进行了初步探讨。     

Chronicling innovative learning in primary classrooms: conceptualizing a theatrical pedagogy to successfully engage young children learning science

This article reports on an innovative pedagogical approach devised to re-envigorate primary (elementary) teachers’ practice in the United Kingdom for older children. Learning science in elementary schools for 8–11 year olds (Key Stage 2 in England) has been constrained for several decades while teachers prepared them for national tests. The recent demise of these high stakes assessments (for the 11 year olds) has opened up creative space to enable re-development of the ways that science is taught and learnt. This article describes how an innovative approach to teaching science to more mature primary children can be developed through the application of theatrical techniques. Dramatizing science can offer a more lively, none traditional way to learn, that can appeal to and involve all children in a science classroom. In this study, 17 teachers from 12 Staffordshire schools experimented with these new pedagogical approaches to explore how they might enhance their practice and augment their children’s learning. Reflective journal extracts, field notes, informal discussions, interviews and classroom observations indicated how successfully the thespian techniques were applied. Findings indicate that dramatizing science learning through various means that encourage social interaction, improvisation and reflection on historical narratives appears to not only engage and motivate learners but also aid them in grasping more challenging conceptual and procedural ideas.     

Book Review of Using Multivariate Statistics by Barbara G. Tabachnick and Linda S. Fidell

In applications of structural equation modeling, it is often desirable to obtain measures of uncertainty for special functions of model parameters. This article provides a didactic discussion of how a method widely used in applied statistics can be employed for approximate standard error and confidence interval evaluation of such functions. The described approach is illustrated with data from a cognitive intervention study, in which it is used to estimate time-invariant reliability in multiwave, multiple indicator models.     

BTEC课业教学本土化的实践探索

深化能力本位教学是目前高职高专的一项重要课题。本文全面阐述了英国BTEC课程模式,并对在本土课程中成功引进、借鉴和运用BTEC课业方法进行了分析总结,提出了BTEC课业教学本土化所必须面对的一些关键问题。     

Modeling Latent Growth Curves With Incomplete Data Using Different Types of Structural Equation Modeling and Multilevel Software

This article offers different examples of how to fit latent growth curve (LGC) models to longitudinal data using a variety of different software programs (i.e., LISREL, Mx, Mplus, AMOS, SAS). The article shows how the same model can be fitted using both structural equation modeling and multilevel software, with nearly identical results, even in the case of models of latent growth fitted to incomplete data. The general purpose of this article is to provide a demonstration that integrates programming features from different software. The most immediate goal is to help researchers implement these LGC models as a useful way to test hypotheses of growth.     

IRT Approaches to Modeling Scores on Mixed-Format Tests

This article considers psychometric properties of composite raw scores and transformed scale scores on mixed-format tests that consist of a mixture of multiple-choice and free-response items. Test scores on several mixed-format tests are evaluated with respect to conditional and overall standard errors of measurement, score reliability, and classification consistency and accuracy under three item response theory (IRT) frameworks: unidimensional IRT (UIRT), simple structure multidimensional IRT (SS-MIRT), and bifactor multidimensional IRT (BF-MIRT) models. Illustrative examples are presented using data from three mixed-format exams with various levels of format effects. In general, the two MIRT models produced similar results, while the UIRT model resulted in consistently lower estimates of reliability and classification consistency/accuracy indices compared to the MIRT models.     

“Ye Shall Be As Gods Knowing Good and Evil”: Using the Bible to Teach Conflict

Theology courses can offer perspective on a multitude of other disciplines. The course described in this article is one model of how theology and other courses might be integrated to provide a theological perspective on a topic. For our purposes, biblical studies and conflict were combined. The model, however, may serve as impetus and inspiration for other disciplines to provide an opportunity for integrated learning. This article describes how the case study method was used with biblical studies to explore another discipline, conflict and negotiation.     

A Specification Error Test That Uses Instrumental Variables to Detect Latent Quadratic and Latent Interaction Effects

The relations between the latent variables in structural equation models are typically assumed to be linear in form. This article aims to explain how a specification error test using instrumental variables (IVs) can be employed to detect unmodeled interactions between latent variables or quadratic effects of latent variables. An empirical example is presented, and the results of a simulation study are reported to evaluate the sensitivity and specificity of the test and compare it with the commonly employed chi-square model test. The results show that the proposed test can identify most unmodeled latent interactions or latent quadratic effects in moderate to large samples. Furthermore, its power is higher when the number of indicators used to define the latent variables is large. Altogether, this article shows how the IV-based test can be applied to structural equation models and that it is a valuable tool for researchers using structural equation models.     

Bias-Adjusted Three-Step Latent Markov Modeling With Covariates

Latent Markov models with covariates can be estimated via 1-step maximum likelihood. However, this 1-step approach has various disadvantages, such as that the inclusion of covariates in the model might alter the formation of the latent states and that parameter estimation could become infeasible with large numbers of time points, responses, and covariates. This is why researchers typically prefer performing the analysis in a stepwise manner; that is, they first construct the measurement model, then obtain the latent state classifications, and subsequently study the relationship between covariates and latent state memberships. However, such a stepwise approach yields downward-biased estimates of the covariate effects on initial state and transition probabilities. This article, shows how to overcome this problem using a generalization of the bias-corrected 3-step estimation method proposed for latent class analysis (Asparouhov & Muthén, 2014; Bolck, Croon, & Hagenaars, 2004; Vermunt, 2010). We give a formal derivation of the generalization to latent Markov models and discuss how it can be used with many time points by incorporating it into a Baum–Welch type of expectation-maximization algorithm. We evaluate the method through a simulation study and illustrate it using an application on household financial portfolio change. Our study shows that the proposed correction method yields unbiased parameter estimates and accurate standard errors, except for situations with very poorly separated classes and a small sample.