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Many measurement designs produce domain factors with small variances and factor loadings. The current study investigates the cause, prevalence, and problematic consequences of such domain factors. We collected a meta-analytic sample of empirical applications, conducted a simulation study on statistical power and estimation precision, and provide a reanalysis of an empirical example. The meta-analysis shows that about a quarter of all standardized domain factor loadings is in the range of -.2<λ<.2 and about a third of all domains is measured by five or fewer indicators, resulting in small factor variances. The simulation study examines the associated difficulties concerning statistical power, trait recovery, irregular estimates, and estimation precision for a range of such realistic cases. The empirical example illustrates the challenge to develop measures that produce clearly interpretable domain factors. Study planning and interpretation need to take the (expected) sum of squared factor loadings per domain factor into account. This is relevant even if influences of domain factors are desired to be small, and equally applies to different model variants. We propose several strategies for how researchers may better unlock the bifactor model's full potential and clarify its interpretation.

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Adolescence is characterised by a peak in sensation seeking accompanied by gradually developing self-control skills. Adolescents typically show steeper delay discounting performance than other age groups; a feature that is transdiagnostically related to a variety of mental health disorders. However, delay discounting performance is not a singular mental process but involves both risk/reward and future orientation elements, usually operationalised as probability/risk and time discounting tasks, respectively. To clarify the specific relations between the risk/reward and future orientation elements of delay discounting and different types of mental health problems, two bi-factor models and a series of structural equation models (SEMs) were fitted to multi-informant (parent and adolescent self-reported) mental health data from a large UK study. A transdiagnostic promotive role of future orientation was found using bi-factor modelling to separate general and dimension-specific mental health variation; however, this was limited to parent reports. In addition, future orientation was negatively associated with conduct problems and ADHD symptoms, but positively associated with emotional problems. Risk aversion was negatively associated with conduct problems, but positively associated with emotional and peer problems. The findings highlight that risk/reward and future orientation elements of delay discounting play partly distinct roles in different mental health problems and can serve both promotive and risk roles during adolescence. Findings also illuminate which elements of delay discounting should be intervention targets for different mental health concerns.

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Nonverbal numerical ability supports individuals' numerical information processing in everyday life and is also correlated with their learning of mathematics. This ability is typically measured with an approximate number comparison paradigm, in which participants are presented with two sets of objects and instructed to choose the numerically larger set. This paradigm has multiple task variants, where the two sets are presented in different ways (e.g., two sets are presented either simultaneously or sequentially, or two sets are presented either intermixed or separately). Despite the fact that different task variants have often been used interchangeably, it remains unclear whether these variants measure the same aspects of nonverbal numerical ability. Using a latent variable modeling approach with 270 participants (Mage = 20.75 years, SDage = 2.03, 94 males), this study examined the degree to which three commonly used task variants tapped into the same construct. The results showed that a bi-factor model corresponding to the hypothesis that task variants had both commonalities and uniqueness was a better fit for the data than a single-factor model, corresponding to the hypothesis that task variants were construct equivalent. These findings suggested that task variants of approximate number comparison did not measure the same construct and cannot be used interchangeably. This study also quantified the extent to which general cognitive abilities were involved in both common and unique parts of these task variants.

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Bi-factor and second-order models based on copulas are proposed for item response data, where the items are sampled from identified subdomains of some larger domain such that there is a homogeneous dependence within each domain. Our general models include the Gaussian bi-factor and second-order models as special cases and can lead to more probability in the joint upper or lower tail compared with the Gaussian bi-factor and second-order models. Details on maximum likelihood estimation of parameters for the bi-factor and second-order copula models are given, as well as model selection and goodness-of-fit techniques. Our general methodology is demonstrated with an extensive simulation study and illustrated for the Toronto Alexithymia Scale. Our studies suggest that there can be a substantial improvement over the Gaussian bi-factor and second-order models both conceptually, as the items can have interpretations of discretized maxima/minima or mixtures of discretized means in comparison with discretized means, and in fit to data.

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This study aimed to investigate the factor structure and measurement invariance of the Brief Symptom Inventory-18 (BSI-18) among Chinese adults. A sample comprising 1,839 adults from four cities in Shaanxi province completed the BSI-18 and background information. The best-fitting factor structure model of the BSI-18 was verified by confirmatory factor analyses, and multigroup confirmatory factor analyses were performed to test the measurement invariance. The results indicated that the three-factor bi-factor model fitted the current data best (χ 2 = 468.861, df = 117, CFI = 0.939, TLI = 0.920, RMSEA = 0.040, BIC = 47044.977). The configural, metric, scalar, and strict invariance models all had acceptable model fit indexes across genders, and the configural, metric, scalar invariance models with different living areas and educational levels were all acceptable. Overall, the three-factor bi-factor model of the BSI-18 shows a good fit for use with Chinese adults, making it a viable tool for effectively measuring the mental health of Chinese adults.

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With the popularity of computer-based testing (CBT), it is easier to collect item response times (RTs) in psychological and educational assessments. RTs can provide an important source of information for respondents and tests. To make full use of RTs, the researchers have invested substantial effort in developing statistical models of RTs. Most of the proposed models posit a unidimensional latent speed to account for RTs in tests. In psychological and educational tests, many tests are multidimensional, either deliberately or inadvertently. There may be general effects in between-item multidimensional tests. However, currently there exists no RT model that considers the general effects to analyze between-item multidimensional test RT data. Also, there is no joint hierarchical model that integrates RT and response accuracy (RA) for evaluating the general effects of between-item multidimensional tests. Therefore, a bi-factor joint hierarchical model using between-item multidimensional test is proposed in this study. The simulation indicated that the Hamiltonian Monte Carlo (HMC) algorithm works well in parameter recovery. Meanwhile, the information criteria showed that the bi-factor hierarchical model (BFHM) is the best fit model. This means that it is necessary to take into consideration the general effects (general latent trait) and the multidimensionality of the RT in between-item multidimensional tests.

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BACKGROUND: The World Health Organization proposed a multidimensional concept of healthy aging in 2015; there was limited evidence about how the concept was constructed and measured. The current study aims to develop a health aging scale (HAS) following the WHO framework and validate it using data from the China Health and Retirement Longitudinal Study (CHARLS). METHODS: A total of 13,233 adults aged ≥ 45 years old from the CHARLS included in current study. Based on the WHO framework, 37 self-reported indicators were used to determine healthy aging. Exploratory factor analysis and second-order and bi-factor modeling, as well as psychometric coefficients, were used to examine the structure of healthy aging. To assess concurrent validity of the HAS, regression analyses were used to examine the associations of HAS and its subscales with sociodemographic characteristics, health conditions, healthcare utilization and life satisfaction in Wave 1. The predictive validity of HAS and subscales was assessed by their associations with mortality in Wave 2 follow-up using Cox regressions. RESULTS: The general HAS and its five subscales were generated according to bi-factor modeling [CFI = 0.949; TLI = 0.942; SRMSR = 0.030; and RMSEA = 0.033 (95% CI, 0.032-0.034)] and psychometric coefficients (ω = 0.903; ωH = 0.692; ECV = 0.459). The general HAS presented solid evidence of concurrent validity with various sociodemographic characteristics, health conditions, healthcare utilization and life satisfaction; and predictive validity with mortality. CONCLUSIONS: The population-based multidimensional healthy aging scale and its subscales can be used to monitor the trajectories of general healthy aging and its subdomains to support the development of healthy aging policies and interventions.

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Although satisfying friendships are crucial for well-being throughout adulthood, measures of friendship satisfaction have been limited by: (1) item content relevant to children only, (2) a focus on single relationships rather than the friendship network, and (3) disagreement about the number of dimensions necessary to capture the construct. To overcome these limitations, we assembled an item pool from a number of existing measures, created additional items drawn from research on friendships, and then examined the structure and psychometric properties of those items in two online surveys of over 2000 respondents each. Factor analyses consistently identified two correlated factors-closeness and socializing-but bi-factor modeling revealed that scores on both subscales load strongly on a general factor, suggesting that the multifaceted content can be scored efficiently as a unidimensional composite. Analyses using item response theory (IRT) supported the creation of a reliable 14-item instrument that demonstrated adequate convergent and predictive validity. Thus, the Friendship Network Satisfaction (FNS) Scale is a psychometrically sound tool to advance research on friendships across the lifespan.

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This research investigated the psychometric properties of the Prosociality Scale and its cross-cultural validation and generalizability across five different western and non-western countries (China, Chile, Italy, Spain, and the United States). The scale was designed to measure individual differences in a global tendency to behave in prosocial ways during late adolescence and adulthood. Study 1 was designed to identify the best factorial structure of the Prosociality Scale and Study 2 tested the model's equivalence across five countries (N = 1,630 young adults coming from China, Chile, Italy, Spain and the United States; general M age = 21.34; SD = 3.34). Findings supported a bifactor model in which prosocial responding was characterized by a general latent factor (i.e., prosociality) and two other specific factors (prosocial actions and prosocial feelings). New evidence of construct validity of the Prosociality Scale was provided.

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BACKGROUND: Neuroticism and stress are important vulnerability factors in the development and outcome of anxiety symptoms. However, as neuroticism is a heterogeneity trait, it is still unclear how different neuroticism factors contribute to anxiety symptoms independently or in conjunction with stress. Thus, different factors of neuroticism were extracted in the present longitudinal study using the bi-factor model. The prediction effect of these different factors on anxiety symptoms and their combined effects with stress in both adolescent and adult samples were examined. METHOD: Participants (592 adolescents and 638 young adults) in Hunan China were included. In the initial assessment in our longitudinal study, participants were asked to complete measurements that assessed neuroticism, stress, and anxiety symptoms. Next, a monthly assessment of stress and anxiety symptoms was completed for the subsequent 6 months. The bi-factor model was used to extract different factors of neuroticism. The hierarchical linear model was used to analyze longitudinal multi-wave data. RESULT: Several model fit indices were used to evaluate the bi-factor model fit for neuroticism (adolescent: Tucker-Lewis index (TLI) = 0.957, comparative fit index (CFI) = 0.973, RMSEA = 0.040, Chi-Square = 80.471; early adults: TLI = 0.957, CFI = 0.973, RMSEA = 0.042, Chi-Square = 88.465). The results of hierarchical linear modeling analyses indicated that the general factor of neuroticism possessed a predictive effect on anxiety symptoms (adolescents: F = 36.77, p < 0.0001, early adults: F = 30.44, p < 0.0001); The negative effect factor only had the prediction effect on anxiety symptoms in early adults (adolescents: F = 0.65, p > 0.05; early adults: F = 4.84, p < 0.05); No prediction of self-reproach factor was found on anxiety symptoms (adolescents: F = 3.79, p > 0.05; early adults: F = 0.02, p > 0.05); the interactive effects of the general factor and stress on anxiety symptoms were only found in early adulthood (adolescents: F = 0.13, p > 0.05; early adults: F = 11.55, p < 0.01). CONCLUSION: Our results suggested that the bi-factor model achieved a satisfactory fit for neuroticism measurement and supported that the anxiety symptoms were induced by the main effects of the general factor in both age samples and the negative factor only in adults. The general factor of neuroticism, but not the negative factor could make an additive effect for anxiety symptoms in face of stress, which meant that the homogeneity of neuroticism played a more significant role in further anxiety symptoms than heterogeneity when coping with stress.

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BACKGROUND: The SF-8 is a short form of the SF-36 Health Survey, which is used for generic assessment of physical and mental aspects of health-related quality of life (HRQoL). Each of the 8 dimensions of the SF-36 is covered by a single item in the SF-8. The aim of the study was to examine the latent model structure of the SF-8. METHOD: One-, two- and three dimensional as well as bi-factor structural models were defined and estimated adopting the ML- as well as the WLSMV-algorithm for ordinal data. The data were collected in a German general population sample (N = 2545 persons). RESULTS: A two- (physical and mental health) and a three-dimensional CFA structure (in addition overall health) represent the empirical data information adequately [CFI = .987/.995; SRMR = .024/.014]. If a general factor is added, the resulting bi-factor models provide a further improvement in data fit [CFI = .999/.998; SRMR = .001]. The individual items are much more highly associated with the general HRQoL factor (loadings: .698 to .908) than with the factors physical, mental, and overall health (loadings: -.206 to .566). CONCLUSIONS: In the SF-8, each item reflects mainly general HRQoL (general factor) as well as one of the three components physical, mental, and overall health. The findings suggest in particular that the evaluation of the information of the SF-8 items can be validly supplemented by a general value HRQoL.

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Aims: The Dutch Four-Dimensional Symptom Questionnaire (4DSQ) measures distress, depression, anxiety and somatisation, facilitating the distinction between stress-related problems and psychiatric disorder in primary and occupational health care. The aim of the study was to examine the measurement equivalence across the Danish and Dutch 4DSQ. Methods: Danish 4DSQ data were obtained from a cohort of Danish citizens on sick leave for mental-health problems. Dutch 4DSQ data were obtained from a cohort of Dutch employees on sick leave and a cohort of general practice attenders suspected of having mental-health problems. The study samples were matched on age and sex. The 4DSQ scales were assessed for essential unidimensionality using confirmatory factor analysis. Measurement equivalence of the 4DSQ across the groups was assessed using differential item and test functioning (DIF and DTF) analysis. Results: The study groups each consisted of 1363 people (63% female, Mage=42 years). The 4DSQ scales proved essentially unidimensional. DIF was detected in 20 items. In terms of Cohen's effect size, DIF was mostly small or moderate. In terms of effect size, the mean effect on the scale score (DTF) was negligible. Nevertheless, it is recommended to adjust some of the cut-off points for two Danish 4DSQ scales to retain the meaning of these cut-off points in Dutch respondents. Conclusions: The Danish version of the 4DSQ measures the same constructs as the original Dutch questionnaire. Twenty items functioned differently in Danish respondents than in Dutch respondents, but this had only a small impact on the scale scores.

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INTRODUCTION: The Clinical Dementia Rating (CDR) is widely used in Alzheimer's disease research studies and has well established reliability and validity. To facilitate the development of an online, electronic CDR (eCDR) for more efficient clinical applications, this study aims to produce a shortened version of the CDR, and to develop the statistical model for automatic scoring. METHODS: Item response theory (IRT) was used for item evaluation and model development. An automatic scoring algorithm was validated using existing CDR global and domain box scores as the reference standard. RESULTS: Most CDR items discriminate well at mild and very mild levels of cognitive impairment. The bi-factor IRT model fits best and the shortened CDR still demonstrates very high classification accuracy (81%∼92%). DISCUSSION: The shortened version of the CDR and the automatic scoring algorithm has established a good foundation for developing an eCDR and will ultimately improve the efficiency of cognitive assessment.

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The Symptom Checklist 90-R (SCL-90-R) is a popular instrument, accessing nine different symptom clusters of psychopathology, although its original factor structure is widely questioned. However, most validation studies seem to ignore the possible effect of comorbidity. We aimed at validating the factor structure of the SCL-90-R and to draw additional information about the role of comorbidity in the factor structure of mental disorders. We thus introduced a comorbidity index within the SCL-90-R and validated the Greek version of the SCL-90-R in a sample of 914 participants, consisting of 688 individuals from the general population and 226 psychiatric outpatients. We showed that the original 9-factor model was superior to the second order factor and the bi-factor model. This may reflect lower comorbidity traits in our sample, rather than the accuracy of the original 9-factor structure of the SCL-90-R, which has to be further assessed by concurrent validity for each individual scale on selected samples. In this regard, we showed that the depression subscale was an excellent screening tool in a subgroup of patients with a confirmed major depressive episode.

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Teachers' autonomy support (AS) in physical education (PE) has positive effects on students' affective and behavioral outcomes in PE. Even though the existence of three different dimensions of AS, namely cognitive, organizational and procedural AS has been suggested in educational settings, there is a lack of multidimensional instruments for the assessment of autonomy-supportive teaching in PE. The aim of this study was to validate the German Multi-Dimensional Perceived Autonomy Support Scale for Physical Education (MD-PASS-PE). The sample comprised 1030 students of grades 6 through 10. Internal consistency was used to test the reliability of the assumed subscales. Factorial validity and measurement invariance across gender and age were examined by confirmatory factor analyses. Structural equation modeling was used to evaluate criterion validity. The subscales exhibited acceptable to good internal consistency. The assumed three-factor structure was confirmed within a bi-factor model including a general factor and three specific group factors. Results strongly supported measurement invariance across gender while tentatively suggesting measurement invariance across age. Criterion validity was supported as the MD-PASS-PE explained 15% and 14% of the variance in the constructs of self-efficacy and intrinsic value, respectively. The German MD-PASS-PE provides PE teachers with deeper insights into their autonomy-supportive teaching behavior, helping them to support their students' autonomy in a holistic way.

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BACKGROUND: The phenotypic and aetiological architecture of depression symptomatology has been mostly studied in Western samples. In this study, we conducted a genetically informed factor analysis to elucidate both the phenotypic and aetiological architectures of self-reported depression among a Japanese adult twin sample. METHODS: Depressive symptoms assessed by Zung's Self-rating Depression Scale were self-rated by 425 twin pairs (301 monozygotic and 124 dizygotic twin pairs) in a community sample in Japan. RESULTS: An exploratory factor analysis extracted three symptom domains representing cognitive, affective and somatic symptomatology. A confirmatory factor analysis demonstrated that a bi-factor solution fitted better than the alternative solutions, implying that depression may be defined as a combination of a single general construct and three factors specific to each of the three symptom domains. A multivariate genetic analysis with the bi-factor solution showed that the general factor was substantially heritable (47%), and that only the affective symptom domain was significantly heritable (29%) among the three specific factors, their remaining variance being explained by non-shared environmental influences. CONCLUSIONS: Depression symptomatology appears to be adequately captured by a substantially heritable general factor. The heritability of this factor (47%) in a Japanese adult sample is in line with commonly reported heritability estimates for depression. The three specific factors - cognitive, affective and somatic - are mostly explained by non-shared environmental factors, which include measurement error. The extent to which these specific factors are uniquely associated with correlates of depression when the general factor is accounted for should be investigated in future studies.

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Recently, large-scale testing programs have an increasing interest in providing examinees with more accurate diagnostic information by reporting overall and domain scores simultaneously. However, there are few studies focusing on how to report and interpret reliable total scores and domain scores based on bi-factor models. In this study, the authors introduced six methods of reporting overall and domain scores as weighted composite scores of the general and specific factors in a bi-factor model, and compared their performance with Yao's MIRT (multidimensional item response theory) method using both simulated and empirical data. In the simulation study, four factors were considered: test length, number of dimensions, correlation between dimensions, and sample size. Major findings are that Bifactor-M4 and Bifactor-M6, the methods utilizing discrimination parameters of the specific dimensions to compute the weights, provided the most accurate and reliable overall and domain scores in most conditions, especially when the test was long, the correlation between dimensions was high and the number of dimensions was large; additionally, Bifactor-M4 recovered the relationship of true ability parameters the best of all the proposed methods; On the contrary, Bifactor-M2, the method with equal weights, performed poor on the overall score estimation; Bifactor-M3 and Bifactor-M5, the methods where weights were computed using the discrimination parameters of all the dimensions, performed poor on the domain score estimation; Bifactor-M1, the original factor method, obtained the worst estimations.

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PURPOSE: This paper presents two studies exploring the latent structure of item sets used in the development of the Recovering Quality of Life mental health outcome measures: ReQoL-10 and ReQoL-20. METHOD: In study 1, 2262 participants completed an initial set of 61 items. In study 2, 4266 participants completed a reduced set of 40 items. Study 2 evaluated two formats of the questionnaires: one version where the items were intermingled and one where the positively worded and negatively worded items were presented as two separate blocks. Exploratory and confirmatory factor analyses were conducted on both datasets where models were specified using ordinal treatment of the item responses. Dimensionality based on the conceptual framework and methods effects reflecting the mixture of positively worded and negatively worded items were explored. Factor invariance was tested across the intermingled and block formats. RESULTS: In both studies, a bi-factor model (study 1: RMSEA = 0.061; CFI = 0.954; study 2: RMSEA = 0.066; CFI = 0.971) with one general factor and two local factors (positively worded questions and negatively worded questions) was preferred. The loadings on the general factor were higher than on the two local factors suggesting that the ReQoL scale scores can be understood in terms of a general factor. Insignificant differences were found between the intermingled and block formats. CONCLUSIONS: The analyses confirmed that the ReQoL item sets are sufficiently unidimensional to proceed to item response theory analysis. The model was robust across different ordering of positive and negative items.

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BACKGROUND: A study conducted as part of the development of the Eleventh International Classification of Mental Disorders for Primary Health Care (ICD-11 PHC) provided an opportunity to test the relationships among depressive, anxious and somatic symptoms in PHC. METHOD: Primary care physicians participating in the ICD-11 PHC field studies in five countries selected patients who presented with somatic symptoms not explained by known physical pathology by applying a 29-item screening on somatic complaints that were under study for bodily stress disorder. Patients were interviewed using the Clinical Interview Schedule-Revised and assessed using two five-item scales that measure depressive and anxious symptoms. Structural models of anxious-depressive symptoms and somatic complaints were tested using a bi-factor approach. RESULTS: A total of 797 patients completed the study procedures. Two bi-factor models fit the data well: Model 1 had all symptoms loaded on a general factor, along with one of three specific depression, anxiety and somatic factors [x2 (627) = 741.016, p < 0.0011, RMSEA = 0.015, CFI = 0.911, TLI = 0.9]. Model 2 had a general factor and two specific anxious depression and somatic factors [x2 (627) = 663.065, p = 0.1543, RMSEA = 0.008, CFI = 0.954, TLI = 0.948]. CONCLUSIONS: These data along with those of previous studies suggest that depressive, anxious and somatic symptoms are largely different presentations of a common latent phenomenon. This study provides support for the ICD-11 PHC conceptualization of mood disturbance, especially anxious depression, as central among patients who present multiple somatic symptoms.

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The drinking motives questionnaire (DMQ, Cooper, 1994) has been a very useful measurement tool for understanding why people drink alcohol. Recent attempts to examine drinking motives used the DMQ within a person-centered analysis framework. However, latent profiles identified in previous research largely presented level effects without strong shape effects, which consequently restricted meaningful interpretations and effective applications of drinking-motive profiles. To address this limitation, we applied a new alternative methodology for the study of drinking motives that integrated variable- and person-centered approaches. Our research clearly demonstrated that controlling for an overarching general drinking-motive construct provided a clearer disaggregation of shape and level effects. Four latent profiles were identified that represented a combination of shape and level effects. Each profile predicted different patterns of alcohol use. Theoretical as well as practical implications are discussed.

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