Bifactor Measurement Model Research Articles

Conceptualizing Correlated Residuals as Item-Level Method Effects in Confirmatory Factor Analysis.

Conceptualizing two-variable disturbances preventing good model fit in confirmatory factor analysis as item-level method effects instead of correlated residuals avoids violating the principle that residual variation is unique for each item. The possibility of representing such a disturbance by a method factor of a bifactor measurement model was investigated with respect to model identification. It turned out that a suitable way of realizing the method factor is its integration into a fixed-links, parallel-measurement or tau-equivalent measurement submodel that is part of the bifactor model. A simulation study comparing these submodels revealed similar degrees of efficiency in controlling the influence of two-variable disturbances on model fit. Perfect correspondence characterized the fit results of the model assuming correlated residuals and the fixed-links model, and virtually also the tau-equivalent model.

Improving the Statistical Performance of Oblique Bifactor Measurement and Predictive Models: An Augmentation Approach

Oblique bifactor models, where group factors are allowed to correlate with one another, are commonly used. However, the lack of research on the statistical properties of oblique bifactor models renders the statistical validity of empirical findings questionable. Therefore, the present study took the first step to examine the statistical properties of oblique bifactor models through Monte Carlo simulations. Study 1 showed that the classic oblique bifactor measurement models had severe convergence issues in many conditions. Even for converged replications, both factor loading and group factor correlation estimates were severely biased. Study 2 further showed that the classic oblique bifactor predictive models still had serious convergence problems, and structural parameters suffered from issues of severe estimation bias and low power. Fortunately, the augmentation approach, where one or multiple indicators are specified to load onto only the general factor but not any of the group factors, was useful in ameliorating these issues in both oblique bifactor measurement and predictive models. Tentative recommendations regarding the selection between oblique and orthogonal bifactor models and the approaches to finding augmenting indicators were provided.

Portuguese Physical Literacy Assessment for adolescents (15-18 years): validation using confirmatory factor and composite analyses.

The aim of this study was to assess the construct validity and reliability of the Portuguese Physical Literacy Assessment (PPLA) instruments (a questionnaire and a tool using teacher-reported data). We also investigated the conceptual and practical implications of reflective vs. formative measurement of Physical Literacy using the PPLA. Multiple Confirmatory Factor Analysis (CFA) and Confirmatory Composite Analysis (CCA) models were used complementarily to assess construct validity in a sample of 521 grade 10-12 Portuguese students from Lisbon, Portugal. Bifactor model-based indices (ω), Explained Common Variance (ECV), and Percentage of Uncontaminated Correlations (PUC) were used to assess score reliability and adequacy. Using CFA, an asymmetrical bifactor model (S*1-1) provided the best fit to the data [Robust Comparative Fit Index = 97, Robust Root Mean Square Error Of Approximation = 0.05 (0.04-0.06), Standardized Root Mean Square Residual (SRMR) = 0.04], while CCA resulted in the best absolute fit for single first-order composite models (dG, dL, and SRMR below or borderline of their 95% critical value). Through a reflective paradigm, the total PL score should not be used in isolation (ECV = 0.49, ωH = 0.71, lower than recommended 0.80). Subscales for the Physical, Psychological, and Social domains attained acceptable reliability scores (ωs = 0.76, 0.82, 0.80, and 0.60). A general trait of PL accounts for considerable variance in all indicators. We advise calculation of a total summed PL score and domain scores, which should be interpreted conjointly in applied settings. Despite both paradigms being tenable, future research efforts should use a bifactor measurement model, which permits disentanglement of the variance attributed to the general PL trait and its domains. Overall, evidence supported the construct validity and reliability of the PPLA for its intended use as an integrated tool to measure PL as a multidimensional construct in 15- to 18-year-old Portuguese students in a physical education setting.

Urge intolerance predicts tic severity and impairment among adults with Tourette syndrome and chronic tic disorders.

BackgroundIndividuals with Tourette Syndrome and Persistent Tic Disorders (collectively TS) often experience premonitory urges—aversive physical sensations that precede tics and are temporarily relieved by tic expression. The relationship between tics and premonitory urges plays a key role in the neurobehavioral treatment model of TS, which underlies first-line treatments such as the Comprehensive Behavioral Intervention for Tics (CBIT). Despite the efficacy of CBIT and related behavioral therapies, less than 40% of adults with TS respond to these treatments. Further examination of the relationship between premonitory urges, tic severity, and tic impairment can provide new insights into therapeutic targets to optimize behavioral treatment outcomes. This study examined whether urge intolerance—difficulty tolerating premonitory urges—predicted tic severity and tic-related impairment among adults with TS.MethodsParticipants were 80 adults with TS. Assessments characterized premonitory urge, distress tolerance, tic severity, and tic impairment. We used structural equation modeling (SEM) to examine the construct of urge intolerance—comprised of premonitory urge ratings and distress tolerance ratings. We first evaluated a measurement model of urge intolerance through bifactor modeling, including tests of the incremental value of subfactors that reflect premonitory urge severity and distress tolerance within the model. We then evaluated a structural model where we predicted clinician-rated tic severity and tic impairment by the latent variable of urge intolerance established in our measurement model.ResultsAnalyses supported a bifactor measurement model of urge intolerance among adults with TS. Consistent with theoretical models, higher levels of urge intolerance predicted greater levels of clinician-rated tic severity and tic impairment.ConclusionThis investigation supports the construct of urge intolerance among adults with TS and distinguishes it from subcomponents of urge severity and distress tolerance. Given its predictive relationship with tic severity and tic impairment, urge intolerance represents a promising treatment target to improve therapeutic outcomes in adults with TS.

Measuring the General and Specific Domains of Self-Esteem: The Short-form of the State Self-Esteem Scale.

Self-esteem is a crucial human nature feature for understanding the social dimensions of individuals' self-concept. One of its characteristics is peoples' malleability to adapt to social contexts, that is, the state self-esteem (SSE). Individuals express SES in three different factors: performance; social success; and physical appearance. Along with three studies, we present evidence of validity of the Short-Form of State Self-Esteem Scale (SSES-S) that measures contextual fluctuations in individuals' self-esteem. In Study 1 (N = 300), we found that the structure of the SSES-S was organized into three correlated factors that exhibited convergent-discriminant validity with measures of trait self-esteem and human values. In Study 2 (N = 281), confirmatory factor analysis indicated that a bifactor measurement model better fit the description of the factorial structure of the SSES-S, which also showed incremental validity concerning trait self-esteem for predicting one criterion. In Study 3 (N = 160), we experimentally manipulated contextual information about self-achievement and showed that the SSES-S is sensitive enough to detect transient fluctuations in self-esteem, especially in the achievement factor. We discussed the limitations and scope of the SSES-S, as its specific focus on measuring undergraduate students' state self-esteem and its implications distinguishing the general and particular domains of this construct.

Assessing Essential Unidimensionality of Scales and Structural Coefficient Bias.

Percentage of uncontaminated correlations (PUC), explained common variance (ECV), and omega hierarchical (ωH) have been used to assess the degree to which a scale is essentially unidimensional and to predict structural coefficient bias when a unidimensional measurement model is fit to multidimensional data. The usefulness of these indices has been investigated in the context of bifactor models with balanced structures. This study extends the examination by focusing on bifactor models with unbalanced structures. The maximum and minimum PUC values given the total number of items and factors were derived. The usefulness of PUC, ECV, and ωH in predicting structural coefficient bias was examined under a variety of structural regression models with bifactor measurement components. Results indicated that the performance of these indices in predicting structural coefficient bias depended on whether the bifactor measurement model had a balanced or unbalanced structure. PUC failed to predict structural coefficient bias when the bifactor model had an unbalanced structure. ECV performed reasonably well, but worse than ωH.

Measuring public knowledge on nuclear weapons in the post-Cold War: dimensionality and measurement invariance across eight European countries

Research on public opinion and international security has extensively examined attitudes toward nuclear weapons, but the diffusion of basic knowledge about nuclear weapons among the everyday citizens has nevertheless been mostly missed. This study proposes a working definition and advances a measurement model of knowledge on nuclear weapons in the general public. It analyzes data from two novel surveys conducted in 2018 (N = 6559) and 2019 (N = 6227) where respondents from Belgium, France, Germany, Italy, the Netherlands, Poland, Sweden, and the United Kingdom answered a web survey on attitudes and factual knowledge on nuclear weapons. Exploratory and confirmatory factor analytic models are used to examine the dimensionality and to assess the measurement invariance of a scale of knowledge about nuclear weapons. A bifactor measurement model, where a strong general factor represents the construct of interest and specific factors account for the presence of testlets due to questionnaire design, is established and validated. Configural, metric, and scalar invariance are established across the eight samples. The findings indicate that knowledge about nuclear weapons in the general, non-expert public can be reliably measured cross-nationally.

A bifactor structural model of the Hungarian Pain Catastrophizing Scale and latent classes of a clinical sample

Pain catastrophizing is an exaggerated cognitive-affective response to actual or anticipated pain, usually measured by the Pain Catastrophizing Scale (PCS). Our study aimed to test the bifactor measurement model of the Hungarian PCS and to identify a catastrophizing risk group with a clinically meaningful cut-off score.The data of 404 chronic spine-related (neck, back and low-back) pain patients (mean age: 58.61 (SD = 14.34)) were used in our cross-sectional study. Besides pain-related and demographic data, pain catastrophizing and depressive symptoms were measured with questionnaires. Confirmatory factor analyses confirmed that the bifactor model outperformed the other tested measurement models, and the general catastrophizing factor was responsible for 81.5% of the explained variance. Using latent class analysis, we found that even moderately elevated pain catastrophizing score was related to more depressive symptoms and higher perceived pain intensity, and 22 score could be used as a cut-off score. Our results support the concept of global pain catastrophizing and the validity of the Hungarian PCS. Further studies are needed to evaluate the bifactor structure of this scale and the predictive value of the proposed cut-off score.

Measuring the 7Cs of Vaccination Readiness

Abstract. Although vaccines are among the most effective interventions used in fighting diseases, vaccination readiness varies substantially among individuals. Vaccination readiness is defined as a set of components that increase or decrease AN individual’s likelihood of getting vaccinated. Building on earlier work that distinguished five components of vaccination readiness (confidence, complacency, constraints, calculation, and collective responsibility), we revised the questionnaire used to measure these components to improve its psychometric properties, specifically criterion validity. In doing so, we also developed two new components of vaccination readiness: compliance and conspiracy. Compliance is the tendency to support monitoring to control adherence to regulations; conspiracy is the tendency to endorse conspiratorial beliefs about vaccination. The newly introduced 7C scale was initially piloted in a cascade of serial cross-sectional studies and then validated with N = 681 participants from the COVID-19 Snapshot Monitoring in Denmark. We report a bifactor measurement model, convergent validity with other questionnaires, and an explanation of 85% variance in the willingness to vaccinate against COVID-19. We also present a 7-item short version of the scale. The instrument is publicly available in several languages ( www.vaccination-readiness.com ), and we seek collaboration to provide translations of our instrument into other languages.

Threat-specific maltreatment exposure: Comparison of measurement models and associations with internalizing, externalizing, and PTSD symptoms

BackgroundChild maltreatment is associated with short- and long-term mental health sequelae. Extant research has demonstrated that exposure characteristics (i.e., severity, frequency, duration, onset) are important in the measurement of maltreatment experiences. Emerging research has highlighted the contributions of these characteristics on symptom outcomes. ObjectiveThe current study used multiple exposure characteristics of threat-specific types of maltreatment (i.e., physical abuse, sexual abuse, witnessing domestic violence) to examine three distinct measurement models of maltreatment and their relation to symptoms. Participants and settingA racially and ethnically diverse sample of treatment-seeking youth (74 % female) ages 4–17 (N = 348) participated in the study. The majority of the youth (61 %) endorsed experiencing more than one type of threat-specific maltreatment. MethodUsing Structural Equation Modeling, we tested one-factor, three-factor, and bifactor models of maltreatment characteristics, and hypothesized that the bifactor model would yield the best fitting model based on prior studies supporting family violence as an underlying factor for child physical abuse and domestic violence. ResultsThe bifactor measurement model fit the data better than the three- and one-factor models. In the bifactor structural model that included symptom outcomes, physical abuse was significantly and positively associated with child internalizing and externalizing symptoms, whereas sexual abuse and witnessing domestic violence were associated with externalizing symptoms and PTSD. ConclusionOur findings support the inclusion of multiple exposure characteristics in the measurement of maltreatment and suggest that specific types of threat-specific maltreatment may have distinct associations with mental health sequelae.

General Factor Mean Difference Estimation in Bifactor Models with Ordinal Data

ABSTRACT A simulation study was conducted to explore robustness of general factor mean difference estimation in bifactor measurement models with ordered-categorical measures. Common analysis misspecifications in which generated bifactor data were fitted using a unidimensional model and/or ordered-categorical data were treated as continuous were compared under generation conditions varying by sample size, number of response categories, effect size of the general factor mean difference, and loadings on the specific factors. Fitting bifactor data using unidimensional models resulted in estimation bias in the general factor mean difference, with magnitude largely determined by degree of unidimensionality and size of the general factor mean difference. Although bifactor models produced less estimation bias, estimates were less precise. Modeling the data as categorical and employing the WLSMV estimator provided somewhat more power, whereas modeling the data as continuous and applying MLR produced relatively less estimation bias when unidimensional models were specified for strongly bifactor data.

Self-Concept Focus: A Tendency to Perceive Autobiographical Events as Central to Identity

Self-Concept Focus is a 15-item measure of the disposition to make autobiographical memories central to one's self-concept and thus to rehearse them more frequently. In studies with 400 MTurk workers and 299 undergraduates, Self-Concept Focus had high reliability (α ∼.83), good test-retest stability (r = .66) that did not decline between 7 and 54 days, good psychometric properties in a bifactor measurement model, and results that replicated across studies. A factor analysis of nine measures relevant to self-concept resulted in two factors. Self-Concept Focus, Reflection, Reappraisal and Private Self-Consciousness all loaded on one factor, suggesting an underlying dimension of elaborative rehearsal of memories and emotion regulation. Self-Concept Focus also correlated with PTSD symptoms for a single very negative event and thus with opportunities to modify such memory-based symptoms. Given its association with elaborative rehearsal and emotion regulation, Self-Concept Focus has potential applied relevance in clinical, forensic and consumer contexts.

Using a Bifactor Model to Measure Food Insecurity in Households with Children

In this study, we explored the dimensionality of U.S. food security measures using bifactor measurement models estimated on a sample of low-income households with children from the CPS Food Security Supplement. The U.S. Department of Agriculture defines food security as access at all times to enough food for an active, healthy lifestyle. In the United States, food security is measured by the Household Food Security Survey Module (HFSSM) which is an 18-item survey module that asks information about the food security of a household’s adult and child members, if present. Previous research suggests the HFSSM may exhibit multidimensionality among households with children. Employing bifactor models in this study allowed us to explore the dimensionality of the HFSSM and identify potential subscales. Our findings suggest the HFSSM captures a single dimension of food security for households with children. The reliability of specific factor scores reflecting subscales for the adult and child items were very low, and the analyses suggest that caution should be used when interpreting separate subscale scores.

Cumulative Lifetime Adversity in a National Sample of Hispanic/Latino Immigrants: Exploring Construct Validity Across Six Hispanic/Latino Groups Using Data From the HCHS/SOL Sociocultural Ancillary Study.

Hispanic/Latino immigrants often experience significant adversity before, during, and after migrating to the United States. However, no extant studies have tested the construct validity of a cumulative measure of lifetime adversity with Hispanic/Latino immigrants. Our objective was to assess the construct validity of a comprehensive measurement model of lifetime adversity (i.e., adverse childhood experiences, adult chronic stress, adult perceived stress, adult acculturation stress, and lifetime ethnic discrimination) with a national sample of Hispanic/Latinos born outside the mainland United States. Guided by the life course perspective, we examined the (a) dimensionality of cumulative lifetime adversity; (b) extent to which the functioning of this measurement model differed across various Hispanic/Latino subgroups including Mexicans, Cubans, Puerto Ricans, Dominicans, Central Americans, and South Americans; and (c) association between cumulative lifetime adversity and other constructs (e.g., anxiety and depression). We used existing data from the Hispanic Community Health Survey/Study of Latinos-Sociocultural Ancillary Study, a national survey of Hispanic/Latinos living in the United States (N = 3,296). Results from confirmatory factor analyses indicated that a five-factor bifactor measurement model for cumulative lifetime adversity fit the data adequately (e.g., comparative fit index = .91, root mean square error of approximation = .04, standardized root mean square residual = .07). Results from multigroup confirmatory factor analyses suggested that the measurement model functioned similarly across Hispanic/Latino subgroups, providing evidence for measurement invariance. The model also displayed convergent and discriminant validity based on associations with other constructs. We discuss implications for advancing the precision of assessment instruments for lifetime adversity with populations with high within-group diversity.

Gender differences in self-esteem, unvarnished self-evaluation, future orientation, self-enhancement and self-derogation in a U.S. national sample

American men tend to score slightly higher on measures of self-esteem than American women. We ask whether this is because of gender differences in responsiveness to the positive and negative phrasing of self-related survey statements used to assess self-esteem. We argue that self-enhancing and self-derogatory tendencies can be inferred from wording valence effects that are common to both self-esteem and optimism. Including latent factors for those response tendencies in a bifactor measurement model transforms the latent factors for self-esteem and optimism into “unvarnished” forms of self-evaluation and future orientation. The bifactor model is shown to fit data from the National Survey of Midlife Development in the United States (MIDUS) better than a conventional measurement model. Although we observe a gender difference in self-esteem, as identified in the conventional model, no gender difference is observed in unvarnished self-evaluation identified in the bifactor model. Our results are consistent with the idea that self-esteem differs by gender due to a greater tendency for men to agree with positively worded self-statements, and a greater tendency for women to agree with negatively worded self-statements. We argue that those tendencies can be interpreted respectively as reflecting unconscious dispositions to self-enhance and self-derogate.

Abstract WMP89: Examining the Constructs of the Patient Health Questionnaire (PHQ-8) in the Stroke Population

Introduction: Most existing screening tools used for post-stroke depression were not originally developed for stroke patients, but the same criteria for identifying depression are usually applied. For instance, the common use of the total score of the Patient Health Questionnaire (PHQ) assumes a unidimentional construct of depression, which may result in distorted performance in the presence of the complexity of stroke. This study aims to test a bifactor measurement model (a depression factor and a stroke-specific factor) using the PHQ-8 in a population-based sample of stroke patients. Methods: The study sample consisted of 613 first-ever stroke patients from the Brain Attack Surveillance in Corpus Christi project (2011-2015). Depressive symptoms at 90 days after stroke were assessed by the PHQ-8. A bifactor measurement model was proposed based on existing knowledge of stroke symptoms, and investigation of depressive symptoms in the study sample. The model included a general depression factor that influences all eight symptoms, and a stroke-specific factor that influences symptoms that frequently overlap between depression and stroke (Figure). The model fit was evaluated using confirmatory factor analysis, and compared with the unidimensional model. Results: The sample was equally distributed by sex, with a mean age of 65.7 (SD=11.0). Fifty-seven percent were Mexican Americans and 38.3% were non-Hispanic Whites. The bifactor model showed statistically significant better fit than the unidimensional model (P<0.001). Conclusion: Future research should explore whether a bifactor measurement model for the PHQ-8, which may result in a different scoring and classification scheme, improves the accuracy of depression screening among stroke survivors.

Desired Ageing Well: Predictive validity for consumers aged 50–80

Ageing well currently represents a major challenge for consumers and marketers, but this concept needs further investigation. To address this issue, we introduce the concept of Desired Ageing Well (DAW), which refers to the psychological, physical, social and financial objectives of ageing well. We provide a reliable and valid bifactor measurement model (general factor and specific factors) in which general DAW is accompanied by three specific factors, namely, physical DAW, social DAW and financial DAW. Together with age, DAW proves to be of value for explaining consumption in four sectors: e-health, cosmetic surgery, leisure and financial investment. The results obtained suggest that ageing well marketing should be developed to better design and promote products and services favouring successful ageing.

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

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.

Self-reported depression symptoms in haemodialysis patients: Bi-factor structures of two common measures and their association with clinical factors.

To validate the factor structure of two common self-report depression tools in a large sample of haemodialysis (HD) patients and to examine their demographic and clinical correlates, including urine output, history of depression and transplantation. Factor structures of the Beck Depression Inventory (BDI-II) and Patient Health Questionnaire (PHQ-9) were evaluated using confirmatory factor analysis (CFA). Data was utilised from the screening phase (n = 709) of a placebo-controlled feasibility randomised control trial (RCT) of sertraline in HD patients with mild to moderate Major Depressive Disorder. Alternative factor models including bi-factor models for the BDI-II and PHQ-9 were evaluated. Coefficient omega and omega-hierarchical were calculated. For both measures, bi-factor measurement models had the overall best fit to the data, with dominant general depression factors. Omega-hierarchical for the general BDI-II and PHQ-9 factors was 0.94 and 0.88 respectively. Both general factors had high reliability (coefficient omega = 0.97 and 0.94 respectively) and explained over 85% of the explained common variance within their respective models. BDI-II and PHQ-9 general depression factors were negatively associated with age and urine output and positively with a history of depression, antidepressant use within the last 3 months and a history of failed transplantation. In adjusted regression models, age, urine output and a history of depression remained significant. These data suggest that both the BDI-II and PHQ-9 are sufficiently unidimensional to warrant the use of a total score. Younger age, lower urine output and a history of depression appear consistent correlates of depression severity among HD patients.

Evidence for the interpretation of Social, Academic, and Emotional Behavior Risk Screener (SAEBRS) scores: An argument-based approach to screener validation

In accordance with an argument-based approach to validation, the purpose of the current study was to yield evidence relating to Social, Academic, and Emotional Behavior Risk Screener (SAEBRS) score interpretation. Bifactor item response theory analyses were performed to examine SAEBRS item functioning. Structural equation modeling (SEM) was used to simultaneously evaluate intra- and inter-scale relationships, expressed through (a) a measurement model specifying a bifactor structure to SAEBRS items, and (b) a structural model specifying convergent and discriminant relations with an outcome measure (i.e., Behavioral and Emotional Screening System [BESS]). Finally, hierarchical omega coefficients were calculated in evaluating the model-based internal reliability of each SAEBRS scale. IRT analyses supported the adequate fit of the bifactor model, indicating items adequately discriminated moderate and high-risk students. SEM results further supported the fit of the latent bifactor measurement model, yielding superior fit relative to alternative models (i.e., unidimensional and correlated factors). SEM analyses also indicated the latent SAEBRS-Total Behavior factor was a statistically significant predictor of all BESS subscales, the SAEBRS-Academic Behavior predicted BESS Adaptive Skills subscales, and the SAEBRS-Emotional Behavior predicted the BESS Internalizing Problems subscale. Hierarchical omega coefficients indicated the SAEBRS-Total Behavior factor was associated with adequate reliability. In contrast, after accounting for the total scale, each of the SAEBRS subscales was associated with somewhat limited reliability, suggesting variability in these scores is largely driven by the Total Behavior scale. Implications for practice and future research are discussed.