Goodness of fit in confirmatory factor analysis: The effects of sample size and model parsimony

Abstract There is a series of conventions governing how Confirmatory Factor Analysis gets applied, from minimum sample size to the number of items representing each factor, to estimation of factor loadings so they may be interpreted. In their implementation, these rules sometimes lead to unjustified decisions, because they sideline important questions about a model’s practical significance and validity. Conducting a Monte Carlo simulation study, the present research shows the compensatory effects of sample size, number of items, and strength of factor loadings on the stability of parameter estimation when Confirmatory Factor Analysis is conducted. The results point to various scenarios in which bad decisions are easy to make and not detectable through goodness of fit evaluation. In light of the findings, these authors alert researchers to the possible consequences of arbitrary rule following while validating factor models. Before applying the rules, we recommend that the applied researcher conduct their own simulation studies, to determine what conditions would guarantee a stable solution for the particular factor model in question.

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Confirmatory Factor Analysis of the Long and Short Forms of the Worry Domains Questionnaire

European Journal of Psychological Assessment ◽

10.1027/1015-5759.25.4.239 ◽

2009 ◽

Vol 25 (4) ◽

pp. 239-243

Author(s):

Roberto Nuevo ◽

Andrés Losada ◽

María Márquez-González ◽

Cecilia Peñacoba

Keyword(s):

Factor Analysis ◽

Confirmatory Factor Analysis ◽

Factor Structure ◽

Goodness Of Fit ◽

Factorial Validity ◽

Fit Indices ◽

Short Forms ◽

Confirmatory Factor ◽

Positive Correlations ◽

Future Work

The Worry Domains Questionnaire was proposed as a measure of both pathological and nonpathological worry, and assesses the frequency of worrying about five different domains: relationships, lack of confidence, aimless future, work, and financial. The present study analyzed the factor structure of the long and short forms of the WDQ (WDQ and WDQ-SF, respectively) through confirmatory factor analysis in a sample of 262 students (M age = 21.8; SD = 2.6; 86.3% females). While the goodness-of-fit indices did not provide support for the WDQ, good fit indices were found for the WDQ-SF. Furthermore, no source of misspecification was identified, thus, supporting the factorial validity of the WDQ-SF scale. Significant positive correlations between the WDQ-SF and its subscales with worry (PSWQ), anxiety (STAI-T), and depression (BDI) were found. The internal consistency was good for the total scale and for the subscales. This work provides support for the use of the WDQ-SF, and potential uses for research and clinical purposes are discussed.

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512 Confirmatory Factor Analysis of the Sleep Inertia Questionnaire in a Clinical Sample with Sleep Disorders

SLEEP ◽

10.1093/sleep/zsab072.511 ◽

2021 ◽

Vol 44 (Supplement_2) ◽

pp. A201-A202

Author(s):

Kristina Puzino ◽

Susan Calhoun ◽

Allison Harvey ◽

Julio Fernandez-Mendoza

Keyword(s):

Factor Analysis ◽

Confirmatory Factor Analysis ◽

Construct Validity ◽

Sleep Disorders ◽

Goodness Of Fit ◽

Criterion Validity ◽

Clinical Samples ◽

Sleep Inertia ◽

Confirmatory Factor ◽

Sensitivity Specificity

Abstract Introduction The Sleep Inertia Questionnaire (SIQ) was developed and validated in patients with mood disorders to evaluate difficulties with becoming fully awake after nighttime sleep or daytime naps in a multidimensional manner. However, few data are available regarding its psychometric properties in clinical samples with sleep disorders. Methods 211 patients (43.0±16.4 years old, 68% female, 17% minority) evaluated at the Behavioral Sleep Medicine (BSM) program of Penn State Health Sleep Research & Treatment Center completed the SIQ. All patients were diagnosed using ICSD-3 criteria, with 111 receiving a diagnosis of chronic insomnia disorder (CID), 48 of a central disorder of hypersomnolence (CDH), and 52 of other sleep disorders (OSD). Structural equation modelling was used to conduct confirmatory factor analysis (CFA) of the SIQ. Results CFA supported four SIQ dimensions of “physiological”, “cognitive”, “emotional” and “response to” (RSI) sleep inertia with adequate goodness-of-fit (TLI=0.90, CFI=0.91, GFI=0.85, RMSEA=0.08). Internal consistency was high (α=0.94), including that of its dimensions (physiological α=0.89, cognitive α=0.94, emotional α=0.67, RSI α=0.78). Dimension inter-correlations were moderate to high (r=0.42–0.93, p<0.01), indicating good construct validity. Convergent validity showed moderate correlations with Epworth sleepiness scale (ESS) scores (r=0.38) and large correlations with Flinders fatigue scale (FFS) scores (r=0.65). Criterion validity showed significantly (p<0.01) higher scores in subjects with CDH (69.0±16.6) as compared to those with CID (54.4±18.3) or OSD (58.5±20.0). A SIQ cut-off score ≥57.5 provided a sensitivity/specificity of 0.77/0.65, while a cut-off score ≥61.5 provided a sensitivity/specificity of 0.71/0.70 to identify CDH vs. ESS<10 (AUC=0.76). Conclusion The SIQ shows satisfactory indices of reliability and construct validity in a clinically-diverse sleep disorders sample. Its criterion validity is supported by its divergent association with hypersomnia vs. insomnia disorders, as well as its adequate sensitivity/specificity to identify patients with CDH. The SIQ can help clinicians easily assess the complex dimensionality of sleep inertia and target behavioral sleep treatments. Future studies should confirm the best SIQ cut-off score by including good sleeping controls, while clinical studies should determine its minimal clinically important difference after pharmacological or behavioral treatments. Support (if any):

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Assessing teacher leadership in physical education: the Spanish version of the transformational teaching questionnaire

Anales de Psicología ◽

10.6018/analesps.34.2.291711 ◽

2018 ◽

Vol 34 (2) ◽

pp. 405 ◽

Cited By ~ 3

Author(s):

Octavio Alvarez ◽

Ines Tomas ◽

Isaac Estevan ◽

Javier Molina-García ◽

Ana Queralt ◽

...

Keyword(s):

Factor Analysis ◽

Transformational Leadership ◽

Physical Education ◽

Confirmatory Factor Analysis ◽

Goodness Of Fit ◽

Leadership Theory ◽

Spanish Version ◽

Transformational Teaching ◽

Confirmatory Factor ◽

Gender Groups

Drawing from the transformational leadership theory, this study aims to translate and analyse the psychometric properties of a Spanish version of the Transformational Teaching Questionnaire (TTQ).A cohort sample of 2107 adolescents (997 males and 1110 females) from 82 secondary schools voluntarily participated in the research.In Study 1 ((n = 1066), the exploratory factor analysis informed a one-factor solution. In Study 2 (n = 1041), the confirmatory factor analysis showed the single-factor and the four-factor models showed satisfactory and adequate goodness of fit indices, respectively. Confirmatory factor analysis demonstrated that the four-factor structure of transformational teaching with a high second-order factor, previously found in Canadian adolescents, was replicated in this study. Internal consistency was high in all subscales and in the total scale. The expected pattern of significant relationships with other variables was supported, and evidence of measurement invariance across gender groups was obtained.This study provides evidence for the cross-cultural validation of the TTQ, a questionnaire designed to assess students’ perceptions of their teachers’ behaviours from the perspective of transformational leadership theory. These findings suggested that the Spanish version of TTQ would be useful for assessing transformational teaching in Spanish adolescents in physical education classes.

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Maladaptive and Adaptive Cognitions About the Self and Others: Confirmatory Factor Analysis of the Brief Core Schemas Scales

Psychological Reports ◽

10.1177/00332941211063602 ◽

2022 ◽

pp. 003329412110636

Author(s):

Bruno Faustino

Keyword(s):

Factor Analysis ◽

Confirmatory Factor Analysis ◽

Goodness Of Fit ◽

Factor Model ◽

Well Being ◽

The Self ◽

Fit Indices ◽

Portuguese Population ◽

Dysfunctional Cognitions ◽

Confirmatory Factor

The presence of dysfunctional cognitions about how individuals see themselves and others is a hallmark of psychopathology. The Brief Core Schemas Scale (BCSS) was developed to evaluate adaptive and dysfunctional beliefs about the self and others. This study describes the first psychometric analysis of the BCSS in the Portuguese population. Participants were recruited from community ( N = 320, Mage=27.31, DP = 12.75). Confirmatory factor analysis (CFA) was used to confirm the BCSS factorial structure. Four-factor model revealed moderate to adequate goodness-of-fit indices (χ2/df = 717.1, (246) p = .01; SRMR = .044; RMSEA = .077; CFI/TLI < .90). Negative views of the self and others correlated positively with early maladaptive schemas, distress, and symptomatology and correlated negatively with psychological well-being. An inversed correlational pattern was found with the positive views of the self and others. Despite the model's moderate adherence to the data, results suggest that the BCSS may be an asset in the assessment of dysfunctional and adaptive cognitions about the self and others. Further analysis is required to deepen the psychometric properties of the BCSS in the Portuguese population.

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Confirmatory Factor Analysis (CFA), Exploratory Structural Equation Modeling (ESEM), and Set-ESEM: Optimal Balance Between Goodness of Fit and Parsimony

Multivariate Behavioral Research ◽

10.1080/00273171.2019.1602503 ◽

2019 ◽

Vol 55 (1) ◽

pp. 102-119 ◽

Cited By ~ 13

Author(s):

Herbert W. Marsh ◽

Jiesi Guo ◽

Theresa Dicke ◽

Philip D. Parker ◽

Rhonda G. Craven

Keyword(s):

Factor Analysis ◽

Structural Equation Modeling ◽

Confirmatory Factor Analysis ◽

Structural Equation ◽

Goodness Of Fit ◽

Equation Modeling ◽

Exploratory Structural Equation Modeling ◽

Optimal Balance ◽

Confirmatory Factor

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The Self-Transcendence Scale

Journal of Holistic Nursing ◽

10.1177/0898010111429849 ◽

2011 ◽

Vol 30 (3) ◽

pp. 147-159 ◽

Cited By ~ 19

Author(s):

Gørill Haugan ◽

Toril Rannestad ◽

Helge Garåsen ◽

Randi Hammervold ◽

Geir Arild Espnes

Keyword(s):

Factor Analysis ◽

Confirmatory Factor Analysis ◽

Goodness Of Fit ◽

Factor Model ◽

Well Being ◽

The Self ◽

Mean Square ◽

Confirmatory Factor ◽

Self Transcendence ◽

Fit Index

Purpose: Self-transcendence, the ability to expand personal boundaries in multiple ways, has been found to provide well-being. The purpose of this study was to examine the dimensionality of the Norwegian version of the Self-Transcendence Scale, which comprises 15 items. Background: Reed’s empirical nursing theory of self-transcendence provided the theoretical framework; self-transcendence includes an interpersonal, intrapersonal, transpersonal, and temporal dimension. Design: Cross-sectional data were obtained from a sample of 202 cognitively intact elderly patients in 44 Norwegian nursing homes. Results: Exploratory factor analysis revealed two and four internally consistent dimensions of self-transcendence, explaining 35.3% (two factors) and 50.7% (four factors) of the variance, respectively. Confirmatory factor analysis indicated that the hypothesized two- and four-factor models fitted better than the one-factor model (c x2, root mean square error of approximation, standardized root mean square residual, normed fit index, nonnormed fit index, comparative fit index, goodness-of-fit index, and adjusted goodness-of-fit index). Conclusions: The findings indicate self-transcendence as a multifactorial construct; at present, we conclude that the two-factor model might be the most accurate and reasonable measure of self-transcendence. Implications: This research generates insights in the application of the widely used Self-Transcendence Scale by investigating its psychometric properties by applying a confirmatory factor analysis. It also generates new research-questions on the associations between self-transcendence and well-being.

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Gauging the Auditory Dimensions of Dysarthric Impairment: Reliability and Construct Validity of the Bogenhausen Dysarthria Scales (BoDyS)

Journal of Speech Language and Hearing Research ◽

10.1044/2017_jslhr-s-16-0336 ◽

2017 ◽

Vol 60 (6) ◽

pp. 1516-1534 ◽

Cited By ~ 3

Author(s):

Wolfram Ziegler ◽

Anja Staiger ◽

Theresa Schölderle ◽

Mathias Vogel

Keyword(s):

Factor Analysis ◽

Confirmatory Factor Analysis ◽

Construct Validity ◽

Convergent Validity ◽

Goodness Of Fit ◽

Discriminant Validity ◽

Measurement Model ◽

Interrater Agreement ◽

Speech Impairment ◽

Confirmatory Factor

Purpose Standardized clinical assessment of dysarthria is essential for management and research. We present a new, fully standardized dysarthria assessment, the Bogenhausen Dysarthria Scales (BoDyS). The measurement model of the BoDyS is based on auditory evaluations of connected speech using 9 scales (traits) assessed by 4 elicitation methods. Analyses of the BoDyS' reliability and construct validity were performed to test this model, with the aim of gauging the auditory dimensions of speech impairment in dysarthria. Method Interrater agreement was examined in 70 persons with dysarthria. Construct validity was examined in 190 persons with dysarthria using a multitrait-multimethod design with confirmatory factor analysis. Results Interrater agreement of < 1 on a 5-point scale was found in 91% of cases across listener pairs and scales. Average reliability was .85. Inspection of the multitrait-multimethod matrix pointed at a high convergent and discriminant validity. Modeling of the BoDyS trait and method factors using confirmatory factor analysis yielded high goodness of fit. Model coefficients confirmed high discriminant and convergent validity and revealed meaningful relationships between scales and methods. Conclusions The 9 auditory scales of the BoDyS provide a reliable and valid profile of dysarthric impairment. They permit standardized measurement of clinically relevant dimensions of dysarthric speech.

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Mengakomodasi Efek Metode dalam Pengujian Validitas Konstruk Melalui Analisis Faktor Konfirmatori

Psikologia Jurnal Psikologi ◽

10.21070/psikologia.v1i1.478 ◽

2017 ◽

Vol 1 (1) ◽

pp. 37

Author(s):

Wahyu Widhiarso

Keyword(s):

Factor Analysis ◽

Confirmatory Factor Analysis ◽

Structural Equation ◽

Goodness Of Fit ◽

Equation Modeling ◽

Fit Indices ◽

Method Effect ◽

Confirmatory Factor ◽

Method Effects ◽

Item Writing

Literatures in the field of psychometrics recommend researchers to employvarious of methods on measuring individual attributes. Ideally,each methods are complementary and measuresthe construct designed to be measured. However, some problems arise when among the methods is unique and unrelated to the construct being measured. The uniqueness of method can lead what is called the method effect. In testing construct validity using confirmatory factor analysis, the emergence of this effect tend to reducing the goodness of fit indices of the model. There are many ways to solve these problem, one of themis controling the method effects and accommodate it to the model. This paper introduces how to accommodate method effecton the confirmatory factor analysis using structural equation modeling. In the application section, author identify the emergence of method effects due to the differences item writing direction (favorable-unfavorable). The analysis showed that method effectemerge from different writing direction.

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