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.     

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.     

Extending latent class solutions to other variables

A procedure is derived for estimating the latent parameters of items not initially included in a latent class solution, on the assumption that the relations between those additional items and the original ones are accounted for by the same latent structure. A chi-square test is proposed for evaluating the relatedness of the additional items to the latent structure. The extension is generalized to associate continuous outside variables with the original solution, and this is accompanied by the suggestion that a simple analysis of variance be used to assess the results. Finally, this latent structure extension is compared with the Dwyer extension of factor analysis.I am grateful to J. J. Mellinger for clarifying discussions of the statistical portions of this paper.Opinions expressed herein are the author's, not the Army's.     

A general framework for using latent class analysis to test hierarchical and nonhierarchical learning models

Several articles in the past fifteen years have suggested various models for analyzing dichotomous test or questionnaire items which were constructed to reflect an assumed underlying structure. This paper shows that many models are special cases of latent class analysis. A currently available computer program for latent class analysis allows parameter estimates and goodness-of-fit tests not only for the models suggested by previous authors, but also for many models which they could not test with the more specialized computer programs they developed. Several examples are given of the variety of models which may be generated and tested. In addition, a general framework for conceptualizing all such models is given. This framework should be useful for generating models and for comparing various models.     

A note on the derivation of the general latent class model

A general formulation of the latent structure principle is suggested, from which it is possible to derive Lazarsfeld's accounting equations in their most general form. The basic equations of Gibson's latent profile model can thence be derived in a single step.     

Taxometric analysis as a general strategy for distinguishing categorical from dimensional latent structure

Statistical analyses investigating latent structure can be divided into those that estimate structural model parameters and those that detect the structural model type. The most basic distinction among structure types is between categorical (discrete) and dimensional (continuous) models. It is a common, and potentially misleading, practice to apply some method for estimating a latent structural model such as factor analysis without first verifying that the latent structure type assumed by that method applies to the data. The taxometric method was developed specifically to distinguish between dimensional and 2-class models. This study evaluated the taxometric method as a means of identifying categorical structures in general. We assessed the ability of the taxometric method to distinguish between dimensional (1-class) and categorical (2-5 classes) latent structures and to estimate the number of classes in categorical datasets. Based on 50,000 Monte Carlo datasets (10,000 per structure type), and using the comparison curve fit index averaged across 3 taxometric procedures (Mean Above Minus Below A Cut, Maximum Covariance, and Latent Mode Factor Analysis) as the criterion for latent structure, the taxometric method was found superior to finite mixture modeling for distinguishing between dimensional and categorical models. A multistep iterative process of applying taxometric procedures to the data often failed to identify the number of classes in the categorical datasets accurately, however. It is concluded that the taxometric method may be an effective approach to distinguishing between dimensional and categorical structure but that other latent modeling procedures may be more effective for specifying the model.     

Estimating latent correlations between repeated testings

A model for longitudinal latent structure analysis is proposed. We assume that test scores for a given mental or attitudinal test are observed for the same individuals at two different points in time. The purpose of the analysis is to fit a model that combines the values of the latent variable at the two time points in a two-dimensional latent density. The correlation coefficient between the two values of the latent variable can then be estimated. The theory and methods are illustrated by a Danish dataset concerning psychic vulnerability.     

多阶段混合增长模型的影响因素：距离与形态

通过模拟研究, 考察潜类别距离和发展形态等因素对多阶段混合增长模型的模型选择和参数估计的影响：(1)潜类别距离越大, 模型选择和分类效果越好。(2)混合模型的选择, 应以一定样本量(至少200)为前提, 首先考虑BIC选出正确的分类模型, 再通过熵值、ARI等选择分类确定性较高的模型。(3)多阶段的发展形态对正确模型的选择和分类的确定性均有一定程度影响。(4)潜类别距离和样本量越大, 参数估计精度越高。(5)在判断分类准确性的指标中, ARI的选择更偏向于真实的模型。     

基于潜在类别分析的6~15岁儿童平衡秤任务认知规则探索

本研究使用自编平衡秤测验测试468名6~15岁儿童,通过潜在类别分析对认知规则进行分类。结果发现,被试使用了规则Ⅰ、规则Ⅰ'、规则Ⅱ、补偿规则、规则Ⅳ、距离优势规则等六种规则;6~9岁儿童主要使用规则Ⅰ;10~13岁儿童主要使用补偿规则;14岁以上儿童主要使用规则Ⅳ;13岁到14岁之间,使用规则Ⅳ的儿童数量呈跳跃式增加。与规则评估技术相比,潜在类别分析用于认知规则研究具有明显优势,最后对运用此方法的前提假设与局限进行了讨论。     

Generalized latent trait models

In this paper we discuss a general model framework within which manifest variables with different distributions in the exponential family can be analyzed with a latent trait model. A unified maximum likelihood method for estimating the parameters of the generalized latent trait model will be presented. We discuss in addition the scoring of individuals on the latent dimensions. The general framework presented allows, not only the analysis of manifest variables all of one type but also the simultaneous analysis of a collection of variables with different distributions. The approach used analyzes the data as they are by making assumptions about the distribution of the manifest variables directly.     

Factor analysis with (mixed) observed and latent variables in the exponential family

We develop a general approach to factor analysis that involves observed and latent variables that are assumed to be distributed in the exponential family. This gives rise to a number of factor models not considered previously and enables the study of latent variables in an integrated methodological framework, rather than as a collection of seemingly unrelated special cases. The framework accommodates a great variety of different measurement scales and accommodates cases where different latent variables have different distributions. The models are estimated with the method of simulated likelihood, which allows for higher dimensional factor solutions to be estimated than heretofore. The models are illustrated on synthetic data. We investigate their performance when the distribution of the latent variables is mis-specified and when part of the observations are missing. We study the properties of the simulation estimators relative to maximum likelihood estimation with numerical integration. We provide an empirical application to the analysis of attitudes.     

The Personal Disturbance Scale (sAD): normative data and latent structure in a large non-clinical sample

The Personal Disturbance Scale [sAD; Bedford & Foulds (1978) Delusions–Symptoms–States Inventory State of Anxiety and Depression. Windsor: NFER-Nelson] is widely used in diverse settings and yet there are unresolved issues concerning its psychometric properties and normative data for the English speaking version are limited. The sAD was administered to a large sample of the general adult population (N=758). Demographic variables (gender, age, years of education and occupational status) had only very modest influences on sAD scores. Tables are presented for conversion of raw scores on the Anxiety, Depression and Total scales to percentiles. The sAD scales possessed adequate convergent and discriminant validity, as demonstrated by their pattern of correlations with two other measures of depression and anxiety (the DASS and the HADS). Ten competing models of the latent structure of the sAD were derived from theoretical and empirical sources. These models were evaluated using confirmatory factor analysis. The best fitting model (CFI=0.96) had a tripartite structure, and consisted of a general factor of psychological distress/negative affectivity (all items loaded on this factor) plus orthogonal specific factors of anxiety and depression. Correlated errors specified according to previous empirical findings were permitted. The theoretical and practical implications of this latent structure are discussed.     

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.     

Structural modeling and psychometrika: An historical perspective on growth and achievements

The field of linear structural equation modeling with continuous variables is reviewed. Trends in psychometric theory and data analysis across the five decades of publication ofPsychometrika are discussed, especially the clarification of concepts of population and sample, explication of the parametric structure of models, delineation of concepts of exploratory and confirmatory data analysis, expansion of statistical theory in psychometrics, estimation via optimization of an explicit objective function, and implementation of general function minimization methods. Developments in the ideas of factor analysis, latent variables, as well as structural and causal modeling are noted. Some major conceptual achievements involving general covariance structure representations, multiple population models, and moment structures are reviewed. The major statistical achievements of normal theory generalized least squares estimation, elliptical and distribution-free estimation, and higher-moment estimation are discussed. Computer programs that implement some of the theoretical developments are described.This review was supported in part by USPHS grants DA00017 and DA01070.     

Schizotypy, taxometrics, and disconfirming theories in soft science: Comment on

Among the most consistently replicated findings in literature addressing the latent structure of psychopathology is evidence for a discrete latent class of individuals who are vulnerable to schizophrenia (schizotypes). Rawlings, Williams, Haslam, and Claridge (2008) challenge these findings by subjecting schizotypy scale scores to taxometric analysis, using a data simulation technique to accommodate variable skew. The authors conclude that schizotypy reflects a latent dimension, and that evidence for discrete latent structure from previous studies is likely an artifact of skewed variables. In this comment, we discuss (a) the philosophical implications of disconfirming well replicated findings in soft science with a single study, (b) important considerations when defining the schizotypy construct, (c) intricacies in executing and interpreting a taxometric analysis, and (d) problems with drawing strong conclusions from null results. Considerable evidence suggests that schizotypy is a discrete latent class, a conclusion that is unlikely the result of skewed variables.     

Investigating the Factor Structure of the Kessler Psychological Distress Scale in Community and Clinical Samples of the Australian Population

The Kessler 10 Psychological Distress Scale (K10) is a brief dimensional scale designed to measure and monitor trends of psychological distress. Recently the scale has been utilised by general practitioners and clinicians to screen for common mental disorders and measure treatment outcomes. Despite the K10 demonstrating a sound one dimensional structure in the general population, the scale??s structure has yet to be comprehensively tested in clinical samples. The current study aimed to use confirmatory factor analysis to test three theoretical structure models of the K10 and one model for the K6 (a six item variant) in a sample from a tertiary referral clinic for mood and anxiety disorders and compare those results with a population sample from the Australian National Survey of Mental Health and Wellbeing. The results demonstrated that a two factor model with correlated latent factors representing depression and anxiety fit the clinical sample the best whilst a one factor model with correlated errors between several items fit the population sample the best. The results are discussed further in relation to scoring and interpreting the Kessler scales.     

项目间多维测验作答时间数据分析：潜在特质速度间效应建模

随着计算机测验使用的普及化,被试在心理与教育测验上的作答反应时的获取也越发便利。为了充分利用项目反应时信息,单维与多维的反应时模型相继被提出。然后,在项目间多维反应时数据中,潜在特质速度之间可能存在共同关系（比如,层阶关系）,此时现有的反应时模型并不能适用。基于此,本研究提出了高阶对数正态反应时模型与双因子对数正态反应时模型。在模拟研究中,高阶对数正态反应时模型与双因子对数正态反应时模型的各参数都能被准确估计。在瑞文标准推理测验的三组测验项目的反应时数据中,双因子对数正态反应时模型表现出更为优秀的拟合效果,同时基于多个统计量说明了局部与全局潜在特质速度同时存在的必要性。因此,在项目间多维测验反应时数据分析中,非常有必要考虑多维潜在特质速度之间的共同效应。     

The Development of Latent Dimensions of Psychopathology across Early Childhood: Stability of Dimensions and Moderators of Change

Recent research has described the structure of psychopathology as including one general and multiple specific factors, and this structure has been found in samples across development. However, little work has examined whether this structure is consistent across time, particularly in young children, within the same sample. Further, few studies have examined factors that influence the magnitude of the stability of latent dimensions of psychopathology. In the present study, we examine these issues in a community sample of 545 children assessed at ages 3 and 6. In addition, we explored child temperament, parental history of psychopathology, and parenting behaviors as potential moderators of the longitudinal stability of latent dimensions of psychopathology. We found that the same bifactor model structure identified at age 3 provided an adequate fit to the data at age 6. Further, our model revealed significant homotypic stability of the general, internalizing, and externalizing specific factors. We also found evidence of differentiation of psychopathology over time with the general factor at age 3 predicting the externalizing factor at age 6. However, we failed to identify moderators of the longitudinal associations between psychopathology latent factors. Overall, our results bolster support for the bifactor structure of psychopathology, particularly in early childhood.