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.     

An Introduction to Network Psychometrics: Relating Ising Network Models to Item Response Theory Models

In recent years, network models have been proposed as an alternative representation of psychometric constructs such as depression. In such models, the covariance between observables (e.g., symptoms like depressed mood, feelings of worthlessness, and guilt) is explained in terms of a pattern of causal interactions between these observables, which contrasts with classical interpretations in which the observables are conceptualized as the effects of a reflective latent variable. However, few investigations have been directed at the question how these different models relate to each other. To shed light on this issue, the current paper explores the relation between one of the most important network models—the Ising model from physics—and one of the most important latent variable models—the Item Response Theory (IRT) model from psychometrics. The Ising model describes the interaction between states of particles that are connected in a network, whereas the IRT model describes the probability distribution associated with item responses in a psychometric test as a function of a latent variable. Despite the divergent backgrounds of the models, we show a broad equivalence between them and also illustrate several opportunities that arise from this connection.     

The structure of the Hospital Anxiety and Depression Scale: Theoretical and methodological considerations

The Hospital Anxiety and Depression Scale (HADS; Zigmond - Snaith, 1983) is widely used; however, its factor structure is unclear, with studies reporting differing unidimensional, two-factor and three-factor models. We aimed to address some key theoretical and methodological issues contributing to inconsistencies in HADS structures across samples. We reviewed existing HADS models and compared their fit using confirmatory factor analysis (CFA). We also investigated methodological effects by comparing factor structures derived from Rasch and Principal Components Analysis (PCA) methods, as well as effects of a negative wording factor. An Australian community-dwelling sample consisting of 189 females and 158 males aged 17–86 (M = 35.73, SD = 17.41) completed the 14-item HADS. The Rasch Analysis, PCA and CFA all supported the original two-factor structure. Although some three-factor models had good fit, they had unacceptable reliability. In the CFA, a hierarchical bifactor model with a general distress factor and uncorrelated depression and anxiety subscales produced the best fit, but the general factor was not unidimensional. The addition of a negative wording factor improved model fit. These findings highlight the effects of differing methodologies in producing inconsistent HADS factor structures across studies. Further replication of model fit across samples and refinement of the HADS items is warranted.     

Bifactor and item response theory analyses of interviewer report scales of cognitive impairment in schizophrenia

A psychometric analysis of 2 interview-based measures of cognitive deficits was conducted: the 21-item Clinical Global Impression of Cognition in Schizophrenia (CGI-CogS; Ventura et al., 2008), and the 20-item Schizophrenia Cognition Rating Scale (SCoRS; Keefe et al., 2006), which were administered on 2 occasions to a sample of people with schizophrenia. Traditional psychometrics, bifactor analysis, and item response theory methods were used to explore item functioning and dimensionality and to compare instruments. Despite containing similar item content, responses to the CGI-CogS demonstrated superior psychometric properties (e.g., higher item intercorrelations, better spread of ratings across response categories) relative to the SCoRS. The authors argue that these differences arise mainly from the differential use of prompts and how the items are phrased and scored. Bifactor analysis demonstrated that although both measures capture a broad range of cognitive functioning (e.g., working memory, social cognition), the common variance on each is overwhelmingly explained by a single general factor. Item response theory analyses of the combined pool of 41 items showed that measurement precision is peaked in the mild to moderate range of cognitive impairment. Finally, simulated adaptive testing revealed that only about 10 to 12 items are necessary to achieve latent trait level estimates with reasonably small standard errors for most individuals. This suggests that these interview-based measures of cognitive deficits could be shortened without loss of measurement precision.     

Psychometric analysis of the Empathy Quotient (EQ)

This study assessed the dimensionality of the Empathy Quotient (EQ) using two statistical approaches: Rasch and Confirmatory Factor Analysis (CFA). Participants included N = 658 with an autism spectrum condition diagnosis (ASC), N = 1375 family members of this group, and N = 3344 typical controls. Data were applied to the Rasch model (Rating Scale) using WINSTEPS. The Rasch model explained 83% of the variance. Reliability estimates were greater than .90. Analysis of differential item functioning (DIF) demonstrated item invariance between the sexes. Principal Components Analysis (PCA) of the residual factor showed separation into Agree and Disagree response subgroups. CFA suggested that 26-item model with response factors had the best fit statistics (RMSEA.05, CFI .93). A shorter 15-item three-factor model had an omega (ω) of .779, suggesting a hierarchical factor of empathy underlies these sub-factors. The EQ is an appropriate measure of the construct of empathy and can be measured along a single dimension.     

A Psychometric Network Perspective on the Validity and Validation of Personality Trait Questionnaires

This article reviews the causal implications of latent variable and psychometric network models for the validation of personality trait questionnaires. These models imply different data generating mechanisms that have important consequences for the validity and validation of questionnaires. From this review, we formalize a framework for assessing the evidence for the validity of questionnaires from the psychometric network perspective. We focus specifically on the structural phase of validation, where items are assessed for redundancy, dimensionality, and internal structure. In this discussion, we underline the importance of identifying unique personality components (i.e. an item or set of items that share a unique common cause) and representing the breadth of each trait's domain in personality networks. After, we argue that psychometric network models have measures that are statistically equivalent to factor models but we suggest that their substantive interpretations differ. Finally, we provide a novel measure of structural consistency, which provides complementary information to internal consistency measures. We close with future directions for how external validation can be executed using psychometric network models. © 2020 European Association of Personality Psychology     

Personality and conditioning: Factors of classical CR acquisition and extinction and their relationship to personality types

Anumber of psychophysiological, cognitive and personality measures, and classical appetitive and aversive SR acquisition and extinction rates were taken from a sample of 25 male undergraduate volunteers. Principal Components Analysis of the data revealed general acquisition and extinction factors which were indexed by the psychophysiological variables. Regression analyses showed additionally that Eysenck’s E-I dimension predicts both acquisition and extinction rates, and that imagery may be an important mediational variable in CR acquisition.     

The BPQ: a scale for the assessment of borderline personality based on DSM-IV criteria

The aim of the study was to develop a self-report measure that assesses borderline personality traits as defined by DSM-IV criteria, including separate subscales for each criterion. A sample of normal subjects from community colleges in the midwestern region of the United States was used to develop the scale. The psychometric properties of the scale were examined using an additional United States sample and student samples from England and Australia. The scale was compared with existing measures of borderline and schizotypal personality. Evidence for the internal consistency and convergent and divergent validity of the new scale is presented. The results of several analyses of variance comparing males and females in the three national groups are reported. A Principal Components Analysis of the subscales suggested either a single factor or two correlated factors. Oblique rotation yielded a structure that distinguished identity/interpersonal and impulsivity borderline personality traits. It is concluded that the new scale provides a useful tool for clinicians and researchers interested in screening for borderline personality traits in both general and clinical populations. Suggestions for further research are indicated.     

A note on McDonald's generalization of principal components analysis

It is shown that McDonald's generalization of classical Principal Components Analysis to groups of variables maximally channels the total variance of the original variables through the groups of variables acting as groups. A useful equation is obtained for determining the vectors of correlations of theL2 components with the original variables. A calculation example is given.     

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.     

PROGRESS IN PSYCHOMETRICS: CAN INDUSTRIAL AND ORGANIZATIONAL PSYCHOLOGY CATCH UP?

Murphy and DeShon (2000) show that interrater correlations do not provide reasonable estimates of the reliability of job performance ratings, and suggest that better estimates can be obtained by applying the methods of generalizability theory. Schmidt, Viswesvaran, and Ones (2000) criticize our suggestions as radical, and argue that: (a) the reliability of ratings should be evaluated using the parallel test model rather than the more general and more realistic generalizability model, (b) reliability and validity are distinct concepts that should not be confused, and (c) measurement models have little to do with substantive models of the processes that generate scores on a test or measure. All three of these ideas were once part of the psychometric mainstream, but progress in psychometrics over the last 3 decades has moved the field well beyond these assumptions and approaches. Modern psychometric theory calls for close linkages between measurement models and substantive models of the phenomena being measured.     

Psychometrics in Psychological Research: Role Model or Partner in Science?

This is a reaction to Borsboom's (2006) discussion paper on the issue that psychology takes so little notice of the modern developments in psychometrics, in particular, latent variable methods. Contrary to Borsboom, it is argued that latent variables are summaries of interesting data properties, that construct validation should involve studying nomological networks, that psychological research slowly but definitely will incorporate latent variable methods, and that the role of psychometrics in psychology is that of partner, not role model. Requests for reprints should be sent to Klaas Sijtsma, Department of Methodology and Statistics, FSW, Tilburg University, PO Box 90153, 5000 LE, Tilburg, The Netherlands.     

EP Component Identification and Measurement by Principal Components-Analysis

Between the acquisition of Evoked Potential (EP) data and their interpretation lies a major problem: What to measure? An approach to this kind of problem is outlined here in terms of Principal Components Analysis (PCA). An important second theme is that experimental manipulation is important to functional interpretation. It would be desirable to have a system of EP measurement with the following characteristics: (1) represent the data in a concise, parsimonous way; (2) determine EP components from the data without assuming in advance any particular waveforms for the components; (3) extract components which are independent of each other; (4) measure the amounts (contributions) of various components in observed EPs; (5) use measures that have greater reliability than measures at any single time point or peak; and (6) identify and measure conponents that overlap in time. PCA has these desirable characteristics. Simulations are illustrated. PCA′s beauty also has some warts that are discussed. In addition to discussing the usual two-mode model of PCA, an extension of PCA to a three-mode model is described that provides separate parameters for (1) waveforms over time, (2) coefficients for spatial distribution, and (3) scores telling the amount of each component in each EP. PCA is compared with more traditional approaches. Some biophysical considerations are briefly discussed. Choices to be made in applying PCA are considered. Other issues include misallocation of variance, overlapping components, validation, and latency changes.     

Dimensional analyses of taxonic data

Principal component analysis (PCA) and common factor analysis are often used to model latent data structures. Typically, such analyses assume a single population whose correlation or covariance matrix is modelled. However, data may sometimes be unwittingly sampled from mixed populations containing a taxon (nonarbitrary subpopulation) and its complement class. One derives relations between values of PCA parameters within subpopulations and their values in the mixed population. These results are then extended to factor analysis in mixed populations. As relationships between subpopulation and mixed-population principal components and factors sensitively depend on within-subpopulation structures and between-subpopulation differences, naive interpretation of PCA or factor analytic findings can potentially mislead. Several analyses, better suited to the dimensional analysis of admixture data structures, are presented and compared.     

Analyzing Longitudinal Item Response Data via the Pairwise Fitting Method

Multidimensional item response theory (MIRT) models can be applied to longitudinal educational surveys where a group of individuals are administered different tests over time with some common items. However, computational problems typically arise as the dimension of the latent variables increases. This is especially true when the latent variable distribution cannot be integrated out analytically, as with MIRT models for binary data. In this article, based on the pseudolikelihood theory, we propose a pairwise modeling strategy to estimate item and population parameters in longitudinal studies. Our pairwise method effectively reduces the dimensionality of the problem and hence is applicable to longitudinal IRT data with high-dimensional latent variables, which are challenging for classical methods. And in the low-dimensional case, our simulation study shows that it performs comparably with the classical methods. We further illustrate the implementation of the pairwise method using a development study of mathematics levels of junior high school students in which the response data are collected from 65 classes of 8 schools from 4 different school districts in China.     

Stress assessment during adolescence: Psychometric properties and measurement invariance of the Student Stress Inventory-Stress Manifestations across gender and age

The main purpose of this study was to analyze the psychometric properties and measurement invariance across gender and age of the Student Stress Inventory-Stress Manifestations (SSI-SM) scores in a large sample of adolescents. The sample was comprised by a total of 1108 students (482 were male), with a mean age of 14.61 years (SD = 1.71). The results indicated that the SSI-SM scores presented adequate psychometric properties from both classical test theory and Item Response Theory (IRT). Confirmatory factorial analysis (CFA), showed that both the bifactor model and a three-factor model (emotional, physiological, and behavioural) were adequate. Multi-group CFA showed that the three-factor model had strong measurement invariance across gender and age. Statistically significant differences in gender were found between latent means as well as raw scores of SSI-SM. Ordinal alpha was .78 for Physiological, .90 for the Emotional, and .79 for the Behavioural subscales. Using IRT, the SSI-SM provides more accuracy information at the medium level of the latent trait. SSI-SM subscales were associated with emotional and behavioural problems. These results provided new sources of validity evidence of the SSI-SM scores in adolescents from general population. The SSI-SM appears to be a useful, brief, and easy to administrate self-report instrument for the screening of stress manifestations at school and educational settings.     

The construct of psychophysiological reactivity: Statistical and psychometric issues

The purpose of this paper is to review major statistical and psychometric issues impacting the study of psychophysiological reactivity and discuss their implications for applied developmental researchers. We first cover traditional approaches such as the observed difference score (DS) and the observed residual score (RS), including a review of classic and recent research on their reliability and validity from two related bodies of work: the measurement of change and the Law of Initial Values. Second, we review several types of latent variable modeling in this context: latent difference score (LDS) models, latent residual score (LRS) models, latent state-trait (LST) models, and latent growth curve (LGC) models. Finally, we provide broad guidelines for applied researchers broken down by key stages of a psychophysiological project: study planning, data analysis, and reporting of results. Our recommendations highlight the need for (1) increased attention to the ubiquitous nature of measurement error in observed variables and the importance of employing latent variable models when possible, and (2) increased specification of theories relating to the construct of reactivity, especially in regards to the distinction between baseline arousal and change over time in broader systems of variables.