Selection Between Linear Factor Models and Latent Profile Models Using Conditional Covariances

A method for selecting between K-dimensional linear factor models and (K + 1)-class latent profile models is proposed. In particular, it is shown that the conditional covariances of observed variables are constant under factor models but nonlinear functions of the conditioning variable under latent profile models. The performance of a convenient inferential method suggested by the main result is examined via data simulation and is shown to have acceptable error rate control when deciding between the 2 types of models. The proposed test is illustrated using examples from vocational assessment and developmental psychology.     

Decomposing person and occasion-specific effects: an extension of latent state-trait (LSI) theory to hierarchical LST models

An extension of latent state-trait (LST) theory to hierarchical LST models is presented. In hierarchical LST models, the covariances between 2 or more latent traits are explained by a general 3rd-order factor, and the covariances between latent state residuals pertaining to different traits measured on the same measurement occasion are explained by 2nd-order latent occasion-specific factors. Analogous to recent developments in multitrait-multimethod methodology, all factors are interpreted in relation to factors taken as comparison standards. An empirical example from test anxiety research illustrates how estimates of additive variance components due to general trait, specific trait, occasion, state residual, method, and measurement error can be obtained using confirmatory factor analysis. Advantages and limitations of these models are discussed.     

Factorial validity and measurement invariance of the Revised Physical Self-Perception Profile (PSPP-R) in three countries

The revised physical self-perception profile (PSPP-R) was constructed to measure both perceived competence and importance linked to domains of the physical self. In the present study, we tested the factorial validity of the PSPP-R, using confirmatory factor analytic approach, on samples of university students from three different countries: Sweden, Turkey, and the UK. Multi-sample covariance structure analyses were also used to test the invariance of the PSPP-R across the three national samples. First-order four-factor models, including the latent factors of sport competence, physical conditioning, body attractiveness and physical strength, demonstrated good-fit with the data both for competence and importance factors. Second-order factor models, incorporating the second-order latent domain factor of physical self-worth also exhibited good-fit with the data. Factor patterns and covariances were invariant across samples for both competence and importance scales. Item intercepts were also invariant for the importance scales, whereas partial invariance of intercepts was supported for competence scales. The results are discussed with reference to the validity of the original physical self-perception profile and cross-cultural studies on the physical self.     

Model selection and psychological theory: a discussion of the differences between the Akaike information criterion (AIC) and the Bayesian information criterion (BIC)

This article reviews the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) in model selection and the appraisal of psychological theory. The focus is on latent variable models, given their growing use in theory testing and construction. Theoretical statistical results in regression are discussed, and more important issues are illustrated with novel simulations involving latent variable models including factor analysis, latent profile analysis, and factor mixture models. Asymptotically, the BIC is consistent, in that it will select the true model if, among other assumptions, the true model is among the candidate models considered. The AIC is not consistent under these circumstances. When the true model is not in the candidate model set the AIC is efficient, in that it will asymptotically choose whichever model minimizes the mean squared error of prediction/estimation. The BIC is not efficient under these circumstances. Unlike the BIC, the AIC also has a minimax property, in that it can minimize the maximum possible risk in finite sample sizes. In sum, the AIC and BIC have quite different properties that require different assumptions, and applied researchers and methodologists alike will benefit from improved understanding of the asymptotic and finite-sample behavior of these criteria. The ultimate decision to use the AIC or BIC depends on many factors, including the loss function employed, the study's methodological design, the substantive research question, and the notion of a true model and its applicability to the study at hand.     

纳入式分类分析法在潜在剖面模型的后续多元回归中的应用

纳入式分类分析法能克服传统的分类分析法对后续一元回归模型参数的低估,发挥潜在类别模型的后续分析简化变量间交互作用的功能。本文进一步将纳入式分类分析法拓展至潜在剖面模型后续的多元统计分析中。通过蒙特卡洛模拟实验,比较各种纳入变量的方法思路与后续分析模型在四种常见的多元回归模型中参数估计的表现。结果发现,纳入式分类分析法所需纳入的变量取决于后续分析中与因变量、潜类别变量的关系,且后续分析使用含交互作用的模型更为稳健。     

Connections Between Graphical Gaussian Models and Factor Analysis

Connections between graphical Gaussian models and classical single-factor models are obtained by parameterizing the single-factor model as a graphical Gaussian model. Models are represented by independence graphs, and associations between each manifest variable and the latent factor are measured by factor partial correlations. Power calculations for the single-factor graphical Gaussian model are facilitated by expressing the manifest partial correlations as functions of the factor partial correlations. The power of selecting a graphical Gaussian model with an association structure between manifest variables compatible with a single-factor model is investigated. The results are illustrated using 2 examples: the 1st is a hypothetical factor model with parallel measures. The 2nd uses data from the British Household Panel Survey on job satisfaction.     

随机截距因子分析模型在控制条目表述效应中的应用

本研究用中文修订版罗森博格自尊量表(RSES-R)考察随机截距因子分析模型在控制条目表述效应时的表现。用RSES-R和过分宣称问卷组成的量表调查621名中学生。结果表明,随机截距模型在建模时,拟合指数良好、因子方差与负荷合理,自尊因子分与RSES-R总分有极高相关,表明该模型能有效分离RSES-R得分的特质与表述效应。分离的表述效应因子分与受测者的自我提升水平具有显著但较弱的相关,表明表述效应与自受测者的社会赞许性有共同的成分。     

A checklist for testing measurement invariance

The analysis of measurement invariance of latent constructs is important in research across groups, or across time. By establishing whether factor loadings, intercepts and residual variances are equivalent in a factor model that measures a latent concept, we can assure that comparisons that are made on the latent variable are valid across groups or time. Establishing measurement invariance involves running a set of increasingly constrained structural equation models, and testing whether differences between these models are significant. This paper provides a step-by-step guide to analysing measurement invariance.     

Robustness of normal theory methods in the analysis of linear latent variate models

The structure of the covariance matrix of sample covariances under the class of linear latent variate models is derived using properties of cumulants. This is employed to provide a general framework for robustness of statistical inference in the analysis of covariance structures arising from linear latent variate models. Conditions for normal theory estimators and test statistics to retain each of their usual asymptotic properties under non-normality of latent variates are given. Factor analysis, LISREL and other models are discussed as examples.     

Temperament in adults--reliability, stability, and factor structure of the EAS Temperament Survey

We assessed the factor structure and psychometric properties of the Emotionality, Activity, and Sociability (EAS) Temperament Survey (Buss & Plomin, 1984) for adults using a longitudinal sample of adult women. The stability estimates of the EAS instrument were assessed over a period of 3 years. The results indicated an acceptable fit for the basic theoretical EAS model, implying that the scale is functioning satisfactory. However, the results also suggest that the measure could be improved. Across time, latent stability factors explained within-scale covariances. Both latent stability factors and time-specific factors accounted for cross-sectional covariances between subscales. Additional research is warranted to guide the further development of the EAS model.     

Confirmatory Measurement Model Comparisons Using Latent Means

Confirmatory factor analysis (CFA) is often used to verify measurement models derived from classical test theory: the parallel, tau-equivalent, and congeneric test models. In this application, CFA is traditionally applied to the observed covariance or correlation matrix, ignoring the observed mean structure. But CFA is easily extended to allow nonzero observed and latent means. The use of CFA with nonzero latent means in testing six measurement models derived from classical test theory is discussed. Three of these models have not been addressed previously in the context of CFA. The implications of the six models for observed mean and covariance structures are fully described. Three examples of the use of CFA in testing these models are presented. Some advantages and limitations in using CFA with nonzero latent means to verify classical measurement models are discussed.     

Measurement equivalence/invariance of the abusive supervision measure across workers from Taiwan and the United States

Growing international research interest in negative-leadership behaviors prompts the need to examine whether measures of ineffective leadership developed in the United States are equivalent across countries outside the United States. B. J. Tepper's (2000) abusive supervision measure has been used widely inside and outside the United States and merits research attention on its construct equivalence across different cultural settings. The authors conducted a series of multigroup confirmatory factor analyses to investigate the measurement equivalence of this measure across Taiwan (N = 256) and the United States (N = 389). Configural invariance was established, suggesting that both U.S. and Taiwanese samples perceive abusive supervision as a single-factor concept. Furthermore, the establishment of partial metric invariance and partial scalar invariance suggests that the abusive supervision measure is applicable to crosscultural comparisons in latent means, construct variance, construct covariances, and unstandardized path coefficients with the caution that workers from different cultures calibrate their responses differently when answering some items.     

Heterogeneous factor analysis models: A bayesian approach

Multilevel factor analysis models are widely used in the social sciences to account for heterogeneity in mean structures. In this paper we extend previous work on multilevel models to account for general forms of heterogeneity in confirmatory factor analysis models. We specify various models of mean and covariance heterogeneity in confirmatory factor analysis and develop Markov Chain Monte Carlo (MCMC) procedures to perform Bayesian inference, model checking, and model comparison.We test our methodology using synthetic data and data from a consumption emotion study. The results from synthetic data show that our Bayesian model perform well in recovering the true parameters and selecting the appropriate model. More importantly, the results clearly illustrate the consequences of ignoring heterogeneity. Specifically, we find that ignoring heterogeneity can lead to sign reversals of the factor covariances, inflation of factor variances and underappreciation of uncertainty in parameter estimates. The results from the emotion study show that subjects vary both in means and covariances. Thus traditional psychometric methods cannot fully capture the heterogeneity in our data.     

多项式加工树模型次序约束的量化分析及其应用

多项式加工树（MPT）模型是一种认知测量模型,能够对潜在认知过程进行测量和检验。已有研究探讨了二链MPT模型次序约束的重新参数化问题,本研究探讨了MPT模型次序约束的量化分析方法并从二链推广到多链,同时归纳出MPT模型参数向量内和参数向量间两参数次序约束量化分析的结论。数据分析结果表明该方法不仅在MPT模型框架下验证了潜在参数次序关系,而且给出了约束的量化指标,为潜在认知测量提供更有意义的解释。     

Three multivariate models: Factor analysis,latent structure analysis,and latent profile analysis

The factor analysis model and Lazarsfeld's latent structure scheme for analyzing dichotomous attributes are derived to show how the latter model avoids three knotty problems in factor analysis: communality estimation, rotation, and curvilinearity. Then the latent structure model is generalized into latent profile analysis for the study of interrelations among quantitative measures. Four latent profile examples are presented and discussed in terms of their limitations and the problems of latent metric and dimensionality thereby raised. The possibility of treating higher order empirical relations in a manner paralleling their various uses in the latent structure model is indicated.The latter model is anticipated in an earlier paper by Green [12].The major portion of this paper was completed at the Center for Advanced Study in the Behavioral Sciences. The opinions expressed are those of the author and are not to be construed as reflecting official Department of the Army policy.     

Adult age differences in multiple cognitive functions: differentiation, dedifferentiation, or process-specific change?

Adult age differences in covariance structures of latent variables of vocabulary, list recall, speed, working memory, and text recall, were analyzed to test hypotheses of structural changes with age. There were baseline data from 613 men and women aged 30-97, data from a second wave of testing from 322 people, and complete longitudinal data from 289 people. There were age differences in the size but not configuration of factor loadings cross-sectionally but not longitudinally. There were no changes in factor standard deviations or covariances. Findings did not support models of dedifferentiation with age.     

Robustness of Parameter Estimation to Assumptions of Normality in the Multidimensional Graded Response Model

A central assumption that is implicit in estimating item parameters in item response theory (IRT) models is the normality of the latent trait distribution, whereas a similar assumption made in categorical confirmatory factor analysis (CCFA) models is the multivariate normality of the latent response variables. Violation of the normality assumption can lead to biased parameter estimates. Although previous studies have focused primarily on unidimensional IRT models, this study extended the literature by considering a multidimensional IRT model for polytomous responses, namely the multidimensional graded response model. Moreover, this study is one of few studies that specifically compared the performance of full-information maximum likelihood (FIML) estimation versus robust weighted least squares (WLS) estimation when the normality assumption is violated. The research also manipulated the number of nonnormal latent trait dimensions. Results showed that FIML consistently outperformed WLS when there were one or multiple skewed latent trait distributions. More interestingly, the bias of the discrimination parameters was non-ignorable only when the corresponding factor was skewed. Having other skewed factors did not further exacerbate the bias, whereas biases of boundary parameters increased as more nonnormal factors were added. The item parameter standard errors recovered well with both estimation algorithms regardless of the number of nonnormal dimensions.     

Indeterminacy Problems in the Lisrel Model

The latent variables and errors of the Lisrel model are indeterminate even when the parameters of the model are perfectly identified. The reason for the indeterminacy is that the Lisrel model gives a solution in terms of estimation of latent variables by means of observed variables. The indeterminacy is relevant also in practice; the minimum correlation between equivalent latent variables, is often negative in empirical examples. The degree of indeterminacy of the latent variables depends on the data. The average minimum correlation is a linear combination of the eigenvalues of the correlation matrix of solutions and it is always included in weak bounds which depend on the same eigenvalues.     

Useful scientific theories are useful: A reply to Rouder, Pratte, and Morey (2010)

In a recognition memory experiment, Mickes, Wixted, and Wais (2007) reported that distributional statistics computed from ratings made using a 20-point confidence scale (which showed that the standard deviation of the ratings made to lures was approximately 0.80 times that of the targets) essentially matched the distributional statistics estimated indirectly by fitting a Gaussian signal-detection model to the receiver-operating characteristic (ROC). We argued that the parallel results serve to increase confidence in the Gaussian unequal-variance model of recognition memory. Rouder, Pratte, and Morey (2010) argue that the results are instead uninformative. In their view, parametric models of latent memory strength are not empirically distinguishable. As such, they argue, our conclusions are arbitrary, and parametric ROC analysis should be abandoned. In an attempt to demonstrate the inherent untestability of parametric models, they describe a non-Gaussian equal-variance model that purportedly accounts for our findings just as well as the Gaussian unequal-variance model does. However, we show that their new model—despite being contrived after the fact and in full view of the to-be-explained data—does not account for the results as well as the unequal-variance Gaussian model does. This outcome manifestly demonstrates that parametric models are, in fact, testable. Moreover, the results differentially favor the Gaussian account over the probit model and over several other reasonable distributional forms (such as the Weibull and the lognormal).