scholarly journals Bifactor Models for Predicting Criteria by General and Specific Factors: Problems of Nonidentifiability and Alternative Solutions

2018 ◽  
Vol 6 (3) ◽  
pp. 42 ◽  
Author(s):  
Michael Eid ◽  
Stefan Krumm ◽  
Tobias Koch ◽  
Julian Schulze
Keyword(s):  
Factor Models ◽  
Formal Proof ◽  
Bifactor Model ◽  
First Order ◽  
Applied Model ◽  
Measurement Models ◽  
Bifactor Models ◽  
Specific Factors ◽  
Order Factor ◽  
Criterion Variables

The bifactor model is a widely applied model to analyze general and specific abilities. Extensions of bifactor models additionally include criterion variables. In such extended bifactor models, the general and specific factors can be correlated with criterion variables. Moreover, the influence of general and specific factors on criterion variables can be scrutinized in latent multiple regression models that are built on bifactor measurement models. This study employs an extended bifactor model to predict mathematics and English grades by three facets of intelligence (number series, verbal analogies, and unfolding). We show that, if the observed variables do not differ in their loadings, extended bifactor models are not identified and not applicable. Moreover, we reveal that standard errors of regression weights in extended bifactor models can be very large and, thus, lead to invalid conclusions. A formal proof of the nonidentification is presented. Subsequently, we suggest alternative approaches for predicting criterion variables by general and specific factors. In particular, we illustrate how (1) composite ability factors can be defined in extended first-order factor models and (2) how bifactor(S-1) models can be applied. The differences between first-order factor models and bifactor(S-1) models for predicting criterion variables are discussed in detail and illustrated with the empirical example.

scholarly journals Can We Compare Solidarity Across Europe? What, Why, When, and How to Assess Exact and Approximate Equivalence of First- and Second-Order Factor Models

2021 ◽  
Vol 3 ◽  
Author(s):  
Vera Lomazzi
Keyword(s):  
Factor Model ◽  
Second Order ◽  
Three Dimensions ◽  
Alignment Method ◽  
Cross Sectional ◽  
Political Values ◽  
First Order ◽  
Measurement Models ◽  
European Values ◽  
Order Factor

Although measurement invariance is widely considered a precondition for meaningful cross-sectional comparisons, substantive studies have often neglected evaluating this assumption, thereby risking drawing conclusions and making theoretical generalizations based on misleading results. This study offers a theoretical overview of the key issues concerning the measurement and the comparison of socio-political values and aims to answer the questions of what must be evaluated, why, when, and how to assess measurement equivalence. This paper discusses the implications of formative and reflective approaches to the measurement of socio-political values and introduces challenges in their comparison across different countries. From this perspective, exact and approximate approaches to equivalence are described as well as their empirical translation in statistical techniques, such as the multigroup confirmatory factor analysis (MGCFA) and the frequentist alignment method. To illustrate the application of these methods, the study investigates the construct of solidarity as measured by European Values Study (EVS) and using data collected in 34 countries in the last wave of the EVS (2017–2020). The concept is captured through a battery of nine items reflecting three dimensions of solidarity: social, local, and global. Two measurement models are hypothesized: a first-order factor model, in which the three independent dimensions of solidarity are correlated, and a second-order factor model, in which solidarity is conceived according to a hierarchical principle, and the construct of solidarity is reflected in the three sub-factors. In testing the equivalence of the first-order factor model, the results of the MGCFA indicated that metric invariance was achieved. The alignment method supported approximate equivalence only when the model was reduced to two factors, excluding global solidarity. The second-order factor model fit the data of only seven countries, in which this model could be used to study solidarity as a second-order concept. However, the comparison across countries resulted not appropriate at any level of invariance. Finally, the implications of these results for further substantive research are discussed.

Issues in Estimating Interpretable Lower Order Factors in Second-Order Hierarchical Models: Commentary on Clark et al. (2021)

2021 ◽  
pp. 216770262110351
Author(s):  
Tyler M. Moore ◽  
Benjamin B. Lahey
Keyword(s):  
Lower Order ◽  
Hierarchical Modeling ◽  
Simulated Data ◽  
Second Order ◽  
General Factor ◽  
Bifactor Models ◽  
Specific Factors ◽  
Factor Modeling ◽  
Highly Correlated ◽  
Criterion Variables

In a previous issue of Clinical Psychological Science, Clark and colleagues asserted that lower order factors in second-order models are comparable with specific factors in bifactor models when residualized on the general factor. Modeling simulated data demonstrated that residualized lower order factors are correlated with bifactor-specific factors only to the extent that factor loadings are proportional. Modeling actual data with violations of proportionality showed that specific and residualized lower order factors are not always highly correlated and have differential correlations with criterion variables even when both models fit acceptably. Because proportionality constraints limit only second-order models, bifactor models should be the first option for hierarchical modeling.

scholarly journals Factor Structure and Measurement Invariance Across Gender of the Beck Depression Inventory-II in Adolescent Psychiatric Patients

2020 ◽  
Vol 11 ◽  
Author(s):  
Ferdinand Keller ◽  
Inken Kirschbaum-Lesch ◽  
Joana Straub
Keyword(s):  
Measurement Invariance ◽  
Beck Depression Inventory ◽  
Factor Structure ◽  
Goodness Of Fit ◽  
Clinical Sample ◽  
Factor Models ◽  
Bifactor Model ◽  
General Factor ◽  
Factor Analyses ◽  
Specific Factors

The revised version of the Beck Depression Inventory (BDI-II) is one of the most frequently applied questionnaires not only in adults, but also in adolescents. To date, attempts to identify a replicable factor structure of the BDI-II have mainly been undertaken in adult populations. Moreover, most of the studies which included minors and were split by gender lacked confirmatory factor analyses and were generally conducted in healthy adolescents. The present study therefore aimed to determine the goodness of fit of various factor models proposed in the literature in an adolescent clinical sample, to evaluate alternative solutions for the factor structure and to explore potential gender differences in factor loadings. The focus was on testing bifactor models and subsequently on calculating bifactor statistical indices to help clarify whether a uni- or a multidimensional construct is more appropriate, and on testing the best-fitting factor model for measurement invariance according to gender. The sample comprised 835 adolescent girls and boys aged 13–18 years in out- and inpatient setting. Several factor models proposed in the literature provided a good fit when applied to the adolescent clinical sample, and differences in goodness of fit were small. Exploratory factor analyses were used to develop and test a bifactor model that consisted of a general factor and two specific factors, termed cognitive and somatic. The bifactor model confirmed the existence of a strong general factor on which all items load, and the bifactor statistical indices suggest that the BDI-II should be seen as a unidimensional scale. Concerning measurement invariance across gender, there were differences in loadings on item 21 (Loss of interest in sex) on the general factor and on items 1 (Sadness), 4 (Loss of pleasure), and 9 (Suicidal Thoughts) on the specific factors. Thus, partial measurement invariance can be assumed and differences are negligible. It can be concluded that the total score of the BDI-II can be used to measure depression severity in adolescent clinical samples.

Evaluating Bifactor Models of Psychopathology Using Model-Based Reliability Indices

2019 ◽  
Author(s):  
Matthew Constantinou ◽  
Peter Fonagy
Keyword(s):  
Bifactor Model ◽  
Common Variance ◽  
Reliability Indices ◽  
Bifactor Models ◽  
Study Characteristics ◽  
Specific Factors ◽  
P Factor ◽  
Explained Common Variance ◽  
Internalizing And Externalizing ◽  
Variance Explained

There is has been a rapid increase in quantitative researchers applying the bifactor model to psychopathology data. The bifactor model, which typically includes a general p factor and internalizing and externalizing residual factors, consistently demonstrates superior model fit to competing models, including the correlated factors model, which typically includes internalizing and externalizing factors. However, the bifactor model’s superior fit might stem from its tendency to overfit noise and flexibly fit most datasets. An alternative approach to evaluating bifactor models that does not rely on fit statistics is model-based reliability assessment. Reliability indices, including omega/omega hierarchical, explained common variance, and percent uncontaminated correlations can be used to determine the viability of the general and specific psychopathology factors and the extent that the underlying data structure and its measurement is multidimensional. In this methodological review, we identified 49 studies published between 2009 and 2019 that applied the bifactor model to at least two separate symptom domains and calculated reliability indices from the standardized factor loading matrices. We also predicted variation in the p factor’s strength, indexed by the explained common variance, from study characteristics. We found that psychopathology measures tend to be multidimensional, with 57% of the variance explained by the p factor and the remaining variance explained by specific factors. By contrast, most of the variance in observed total scores (74%) was explained by the p factor, while relatively little of the variance in in observed subscale scores (37%) was explained by specific factors beyond the p factor. Finally, 62% of the variability in the p factor’s strength could be predicted by study characteristics, most notably the informant (in a simultaneous regression model), but also age, percent uncontaminated correlations, and the number of items (in separate regression models). We conclude that the latent structure of psychopathology is multidimensional, but its measurement is governed by a single dimension, the strength of which is predicted by study characteristics, particularly the informant.

Confirmatory Factor Analysis of the Group Environment Questionnaire with an Intercollegiate Sample

1996 ◽  
Vol 18 (1) ◽  
pp. 49-63 ◽  
Author(s):  
Fuzhong Li ◽  
Peter Harmer
Keyword(s):  
Factor Analysis ◽  
Confirmatory Factor Analysis ◽  
Group Cohesion ◽  
Factor Models ◽  
Second Order ◽  
First Order ◽  
Confirmatory Factor ◽  
Group Environment ◽  
Order Factor ◽  
Group Environment Questionnaire

This study was designed to assess the factorial construct validity of the Group Environment Questionnaire (GEQ; Carron, Widmeyer, & Brawley, 1985) within a hypothesis-testing framework. Data were collected from 173 male and 148 female intercollegiate athletes. Based on Carron et al.’s (1985) conceptual model of group cohesion, the study examined (a) the extent to which the first-order four-factor model could be confirmed with an intercollegiate athlete sample and (b) the degree to which higher order factors could account for the covariation among the four first-order factors. The a priori models of GEQ, including both the first- and second-order factor models, were tested through confirmatory factor analysis (CFA). CFA results showed that the theoretically specified first- and second-order factor models fit significantly better than all alternative models. These results demonstrated that the GEQ possesses adequate factorial validity and reliability as a measure of the sport group cohesion construct for an intercollegiate athlete sample.

scholarly journals Viability of a MSQOL-54 general health-related quality of life score using bifactor model

2021 ◽  
Vol 19 (1) ◽  
Author(s):  
Andrea Giordano ◽  
Silvia Testa ◽  
Marta Bassi ◽  
Sabina Cilia ◽  
Antonio Bertolotto ◽  
...  
Keyword(s):  
Quality Of Life ◽  
Sexual Function ◽  
Factor Models ◽  
Bifactor Model ◽  
Health Related Quality ◽  
Hrqol Score ◽  
Related Quality ◽  
Health Related ◽  
Order Factor

Abstract Background MSQOL-54 is a multidimensional, widely-used, health-related quality of life (HRQOL) instrument specific for multiple sclerosis (MS). Findings from the validation study suggested that the two MSQOL-54 composite scores are correlated. Given this correlation, it could be assumed that a unique total score of HRQOL may be calculated, with the advantage to provide key stakeholders with a single overall HRQOL score. We aimed to assess how well the bifactor model could account for the MSQOL-54 structure, in order to verify whether a total HRQOL score can be calculated. Methods A large international database (3669 MS patients) was used. By means of confirmatory factor analysis, we estimated a bifactor model in which every item loads onto both a general factor and a group factor. Fit of the bifactor model was compared to that of single and two second-order factor models by means of Akaike information and Bayesian information criteria reduction. Reliability of the total and subscale scores was evaluated with Mc Donald’s coefficients (omega, and omega hierarchical). Results The bifactor model outperformed the two second-order factor models in all the statistics. All items loaded satisfactorily (≥ 0.40) on the general HRQOL factor, except the sexual function items. Omega coefficients for total score were very satisfactory (0.98 and 0.87). Omega hierarchical for subscales ranged between 0.22 to 0.57, except for the sexual function (0.70). Conclusions The bifactor model is particularly useful when it is intended to acknowledge multidimensionality and at the same time take account of a single general construct, as the HRQOL related to MS. The total raw score can be used as an estimate of the general HRQOL latent score.

scholarly journals Exploratory Bifactor Measurement Models in Vocational Behavior Research

2020 ◽  
Author(s):  
Casey Giordano
Keyword(s):  
Performance Feedback ◽  
Bifactor Model ◽  
Vocational Psychology ◽  
Measurement Models ◽  
Vocational Behavior ◽  
Bifactor Models ◽  
Developmental Performance

We provide an overview of and guidance for applying exploratory bifactor models to vocational research. First, we describe bifactor models and highlight their potential and actual applications in vocational psychology. Second, we review the theoretical bases of bifactor models and offer methodological guidance to correctly implement and interpret these models in practice. Third, we estimate a bifactor model in two vocational datasets to illustrate the concepts reviewed in this manuscript. The resulting models highlight novel insights in careers research (e.g., developmental performance feedback and personality [conscientiousness] modeling) that are made possible by leveraging bifactor measurement models. Overall, this manuscript provides a useful introduction to bifactor models to facilitate vocational behavior scholars and practitioners in thoughtfully producing and consuming bifactor models in their own research.

Challenging the Multidimensional Conception of Perceived Person-Environment Fit

2020 ◽  
pp. 1-9
Author(s):  
Julian M. Etzel ◽  
Gabriel Nagy
Keyword(s):  
Higher Education ◽  
University Students ◽  
Educational Outcomes ◽  
Factor Model ◽  
Higher Order ◽  
Substantial Proportion ◽  
Unique Variance ◽  
First Order ◽  
Person Environment Fit ◽  
Order Factor

Abstract. In the current study, we examined the viability of a multidimensional conception of perceived person-environment (P-E) fit in higher education. We introduce an optimized 12-item measure that distinguishes between four content dimensions of perceived P-E fit: interest-contents (I-C) fit, needs-supplies (N-S) fit, demands-abilities (D-A) fit, and values-culture (V-C) fit. The central aim of our study was to examine whether the relationships between different P-E fit dimensions and educational outcomes can be accounted for by a higher-order factor that captures the shared features of the four fit dimensions. Relying on a large sample of university students in Germany, we found that students distinguish between the proposed fit dimensions. The respective first-order factors shared a substantial proportion of variance and conformed to a higher-order factor model. Using a newly developed factor extension procedure, we found that the relationships between the first-order factors and most outcomes were not fully accounted for by the higher-order factor. Rather, with the exception of V-C fit, all specific P-E fit factors that represent the first-order factors’ unique variance showed reliable and theoretically plausible relationships with different outcomes. These findings support the viability of a multidimensional conceptualization of P-E fit and the validity of our adapted instrument.

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