Further Reflections on Disentangling Shape and Level Effects in Person-Centered Analyses: An Illustration Exploring the Dimensionality of Psychological Health

Morin and Marsh (2015) proposed a methodological framework to disentangle shape and level effects in latent profile analyses. We discuss limitations of this framework (based on a logic similar to that of higher-order measurement models), and suggest that these limitations are easily solved by a more thorough examination of the variable-centered measurement models underlying profile indicators. This study presents complementary variable- and person-centered approaches aiming to assess the dimensionality of psychometric constructs. Psychometric measures often assess separate conceptually-related facets of global overarching constructs, based on the assumption that these overarching constructs exist as global entities including specificities mapped by the facets. The framework proposed here explicitly models this dimensionality in both variable- and person-centered analyses. To illustrate this revised psychometric framework, we use ratings of psychological health collected from 1,232 teachers, and show how this revised framework provides a clearer picture of teachers’ profiles of psychological health.     

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.     

A Non-arbitrary Method of Identifying and Scaling Latent Variables in SEM and MACS Models

A non-arbitrary method for the identification and scale setting of latent variables in general structural equation modeling is introduced. This particular technique provides identical model fit as traditional methods (e.g., the marker variable method), but it allows one to estimate the latent parameters in a nonarbitrary metric that reflects the metric of the measured indicators. This technique, therefore, is particularly useful for mean and covariance structures (MACS) analyses, where the means of the indicators and latent constructs are of key interest. By introducing this alternative method of identification and scale setting, researchers are provided with an additional tool for conducting MACS analyses that provides a meaningful and nonarbitrary scale for the estimates of the latent variable parameters. Importantly, this tool can be used with single-group single-occasion models as well as with multiple-group models, multiple-occasion models, or both.     

Applying and Interpreting Mixture Distribution Latent State-Trait Models

Latent state-trait (LST) models are commonly applied to determine the extent to which observed variables reflect trait-like versus state-like constructs. Mixture distribution LST (M-LST) models relax the assumption of population homogeneity made in traditional LST models, allowing researchers to identify subpopulations (latent classes) with differing trait- and state-like attributes. Applications of M-LST models are scarce, presumably because of the analysis complexity. We present a step-by-step tutorial for evaluating M-LST models based on an application to mother, father, and teacher reports of children’s inattention (n = 811). In the application, we found three latent classes for mother and father reports and four classes for teacher reports. All reporter solutions contained classes with very low, low, and moderate levels of inattention. The teacher solution also contained a class with high inattention. Comparable mother and father (but not teacher) classes exhibited similar levels of trait and state variance.     

The Effect of Scale Referent on Tests of Mean Structure Parameters

Structured means analysis is a very useful approach for testing hypotheses about population means on latent constructs. In such models, a z test is most commonly used for testing the statistical significance of the relevant parameter estimates or of the differences between parameter estimates, where a z value is computed based on the asymptotic standard error estimate associated with the parameter of interest. In the current article, a series of population analyses demonstrate that the z tests for latent mean structure parameters or, more directly, the standard error estimates upon which those z tests are based are, not invariant to how factors are scaled. As such, circumstances exist in which latent mean inference is compromised solely as a result of scaling decisions. This problem is illustrated in the context of between-subjects (i.e., multisample) latent means models and within-subjects latent means models. Recommendations for practice are also offered.     

Examining the ontological and epistemic assumptions of research on metacognition,self-regulation and self-regulated learning

While research on metacognition, self-regulation and self-regulated learning is quite mature, these studies have been carried out with varying methodologies and with mixed results. This paper explores the ontological and epistemological assumptions of theories, models and methods used to investigate these three constructs to examine the underlying assumptions of all three. Using oft-cited theories and models of the three constructs along with highly cited studies identified in a previous review of these constructs, this paper examined facets of two popular frameworks: Cartesian-split-mechanistic tradition (CSMT) and the relational tradition specifically looking at the role of intra-individual development, the inclusiveness of categories and notions of causality in these theories, models and methods. While the theories and methods contained elements of both traditions, methods to investigate these constructs relied almost exclusively on assumptions from CSMT. Future directions for research include incorporating more studies examining intra-individual change and multiple notions of causality. Future directions for practice include better contextualisation of research results to strengthen the link between theory and practice.     

Measures of self‐reported reading resources,attitudes and activities based on latent variable modeling

In the IEA PIRLS International Report, a number of indices of reading‐related constructs were introduced for the purpose of explaining the variation in reading achievement. These indices, however, raise issues of reliability and validity, due to the way in which they are derived and due to the quality of the data. Targeting these issues, the current study investigates the measurement properties of some of these reading‐related factors by a multivariate latent variable modeling approach. The data is drawn from the PIRLS questionnaires of the fourth graders in six countries. On the basis of a series of confirmatory factor analytic models individual factor scores of these constructs are estimated. The results indicate that the most significant advantage of the suggested approach is that it makes efficient use of the available data to estimate factor scores with higher reliability and validity than the observed index scores.     

Categorizing and combining theories of cognitive development and learning

The present paper considers the centrality of meta-theoretical belief systems (MTBSs) for theories of cognitive development and learning. It is argued that MTBSs guide and constrain the construction of theoretical models and developmental mechanisms. Moreover, it is shown how MTBSs can be effectively used to categorize theories and to address the issue of whether theories of cognitive development and learning can be coherently combined to form larger, more comprehensive theories. The paper proceeds by first defining the nature of theories and then defining eight major MTBSs: nativism, empiricism, constructivism, structuralism, functionalism, behaviorism, neobehaviorism, and cognitivism. Following this exposition, it is shown how MTBSs underlie model construction. Next, the issue of whether theories can be combined is discussed in terms of the logical compatibility of their underlying MTBSs. Then, two contemporary theories which combine constructs from several different theoretical perspectives are described to illustrate how theories can be combined coherently. Finally, implications are drawn.     

Using structural equation models with latent variables to study student growth and development

Calls for accountability, coupled with a desire to improve teaching and learning, have prompted many colleges and universities to consider ways of assessing the effects of postsecondary education on student growth and development. Despite widespread support for the concept of assessing student change, relatively few institutions have implemented this type of assessment, in part because of a concern about the best method of measuring change. This article describes the use of structural equation models with latent variables to assess the effects of education on change. Advantages of using structural equation models with latent variables include error-free measurement of change, direct tests of the assumptions underlying change research, along with the power and flexibility of maximum likelihood estimation. An analysis of data on freshman-to-senior gains provides evidence of the advantages of latent variable structural equation modeling and also suggests that the group differences identified by traditional analysis of variance and covariance techniques may be an artifact of measurement error.     

A Bayesian Approach for Analyzing Hierarchical Data With Missing Outcomes Through Structural Equation Models

Structural equation models are widely appreciated in behavioral, social, and psychological research to model relations between latent constructs and manifest variables, and to control for measurement errors. Most applications of structural equation models are based on fully observed data that are independently distributed. However, hierarchical data with a correlated structure are common in behavioral research, and very often, missing data are encountered. In this article, we propose a 2-level structural equation model for analyzing hierarchical data with missing entries, and describe a Bayesian approach for estimation and model comparison. We show how to use WinBUGS software to get the solution conveniently. The proposed methodologies are illustrated through a simulation study, and a real application in relation to organizational and management research concerning the study of the interrelationships of the latent constructs about job satisfaction, job responsibility, and life satisfaction for citizens in 43 countries.     

Exploratory Structural Equation Modeling

This article examines the problem of specification error in 2 models for categorical latent variables; the latent class model and the latent Markov model. Specification error in the latent class model focuses on the impact of incorrectly specifying the number of latent classes of the categorical latent variable on measures of model adequacy as well as sample reallocation to latent classes. The results show that the clarity of remaining latent classes, as measured by the entropy statistic depends on the number of observations in the omitted latent class—but this statistic is not reliable. Specification error in the latent Markov model focuses on the transition probabilities when a longitudinal Guttman process is incorrectly specified. The findings show that specifying a longitudinal Guttman process that is not true in the population impacts other transition probabilities through the covariance matrix of the logit parameters used to calculate those probabilities.     

Performance of Nonrecursive Latent Variable Models under Misspecification

A problem central to structural equation modeling is measurement model specification error and its propagation into the structural part of nonrecursive latent variable models. Full-information estimation techniques such as maximum likelihood are consistent when the model is correctly specified and the sample size large enough; however, any misspecification within the model can affect parameter estimates in other parts of the model. The goals of this study included comparing the bias, efficiency, and accuracy of hypothesis tests in nonrecursive latent variable models with indirect and direct feedback loops. We compare the performance of maximum likelihood, two-stage least-squares and Bayesian estimators in nonrecursive latent variable models with indirect and direct feedback loops under various degrees of misspecification in small to moderate sample size conditions.     

Self-report measures of the home learning environment in large scale research: Measurement properties and associations with key developmental outcomes

Favourable home learning environments (HLEs) support children’s literacy, numeracy and social development. In large-scale research, HLE is typically measured by self-report survey, but there is little consistency between studies and many different items and latent constructs are observed. Little is known about the stability of these items and constructs over time when used in either longitudinal research or studies with children with a wide range of ages. A review of the literature shows commonalities and differences between approaches in research on HLE. When we tested the psychometric properties of a short-form measure of HLE with a Rasch item-response-model using longitudinal data from over 1600 Australian families, there was support for two dimensions of HLE—formal and informal learning frequency. We found that this measure was stable over the transitional period from pre-K to school as well as between gender and family language background. There were small but significant associations between the HLE measures and cognitive and behavioural developmental outcomes. We recommend that other measures of HLE could be similarly validated to assess their suitability for use in longitudinal research on learning environments. Recommendations are made for the future development of measures of broader constructs of the HLE.     

Changes in the relation of self-efficacy beliefs and behaviors across development

Many social science theories that examine the connection between beliefs and behaviors assume that belief constructs will predict behaviors similarly across development. Converging research implies that this assumption may not be tenable across all ages or all belief constructs. Thus, to test this implication, the relation between behavior and beliefs about the self was examined in 2 independent data sets with 2 different constructs: aggression and achievement. The respondents were 6-18 years of age and predominately Caucasian. Results using quasi-simplex structural equation models suggest that self-beliefs become more strongly related to behavior as children grow older independent of the reliability of the measures used. Possible limitations in the use of self-report methodology with young children are discussed.     

Specifying and Interpreting Latent State–Trait Models With Autoregression: An Illustration

Latent state–trait models are valuable tools for representing the longitudinal stability and variability of individuals’ relative standing on a construct (e.g., a behavior or psychological process). Specifically, state–trait models partition construct variance into time-varying and time-invariant components, enabling one to examine the relations between these components and other variables. Such partitioning of construct variance has a number of valuable applications including the improvement of risk-outcome research. The trait–state–occasion (TSO) model and latent state–trait model with autoregression (LST–AR) are ideal for use with constructs with relative stability that decreases with increasing durations, but relative stability that does not decrease to 0 even over long durations. Despite the fact that this pattern of relative stability expression is observed for a wide variety of constructs, there are relatively few applications of the TSO and LST–AR models. Thus, this article describes the TSO and LST–AR models and illustrates application of these models.     

Hierarchical Regression Without Phantom Factors

In a recent note in the Teacher's Corner of this journal, de Jong (1999) proposed a method for computing hierarchical or fixed-order regressions in the context of latent variables. The essence of this approach is to decompose the predictor variables in the regression into orthogonal components based on a Cholesky decomposition and to regress the dependent variable on these orthogonal components. The components may be conceived of as phantom factors that do not have their own indicators. Because the idea of sequential entry of predictors in a latent variable regression framework seems generally to be unknown, the approach was developed by de Jong for latent variable regressions. However, it equally can be used for observed variable regression or path models. In this article we show that the phantom factors are unnecessary to achieve the objectives of a hierarchical regression. We give a direct approach that is equivalent to de Jong's approach.     

内隐社会认知:从测验方法到作用机制

人类的大多数认知活动都发生意识觉察或意识控制之外。部分内隐加工会影响社会知觉、判断和行为。基于大量的内隐测量程序被开发、应用,以及更多使用内隐测量程序研究社会认知的报告的事实,内隐社会认知的最近15年可以被称为"测量时代(Age of Measurement)"。内隐测量的内容、结果与外显测量的既有区别也有联系,在关于社会认知的内容、加工过程及预测行为等方面各有优势。今后内隐测量的研究方向是探索内隐测量背手的心理机制,以及内隐测量到的心理构念影响行为的过程。     

Conducting Confirmatory Latent Class Analysis Using Mplus

Latent class analysis (LCA) is an increasingly popular tool that researchers can use to identify latent groups in the population underlying a sample of responses to categorical observed variables. LCA is most commonly used in an exploratory fashion whereby no parameters are specified a priori. Although this exploratory approach is reasonable when very little prior research has been conducted in the area under study, it can be very limiting when much is already known about the variables and population. Confirmatory latent class analysis (CLCA) provides researchers with a tool for modeling and testing specific hypotheses about response patterns in the observed variables. CLCA is based on placing specific constraints on the parameters to reflect these hypotheses. The popular and easy-to-use latent variable modeling software package Mplus can be used to conduct a variety of CLCA types using these parameter constraints. This article focuses on the basic principles underlying the use of CLCA, and the Mplus programming code necessary for carrying it out.     

Phonological Awareness and Rapid Automatized Naming Predicting Early Development in Reading and Spelling: Results from a Cross-Linguistic Longitudinal Study

In this study, the relationship between latent constructs of phonological awareness (PA) and rapid automatized naming (RAN) were investigated and related to later measures of reading and spelling in children learning to read in different alphabetic writing systems (i.e., Norwegian/Swedish vs. English). 750 U.S./Australian children and 230 Scandinavian children were followed longitudinally between kindergarten and 2nd grade. PA and RAN were measured in kindergarten and Grade 1, while word recognition, phonological decoding, and spelling were measured in kindergarten, Grade 1, and Grade 2. In general, high stability was observed for the various reading and spelling measures, such that little additional variance was left open for PA and RAN. However, results demonstrated that RAN was more related to reading than spelling across orthographies, with the opposite pattern shown for PA. In addition, tests of measurement invariance show that the factor loadings of each observed indicator on the latent PA factor was the same across U.S./Australia and Scandinavia. Similar findings were obtained for RAN. In general, tests of structural invariance show that models of early literacy development are highly transferable across languages.