ارزیابی مدل تحلیل عاملی تائیدی بایفکتر از بعدپذیری و ارزش خرده - دامنه‌های مقیاس‌های روانشناختی

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دکتری روان‌شناسی تربیتی، مدرس دانشگاه فرهنگیان، پردیس ورامین، ورامین، ایران.

2 دانشیار گروه روان‌شناسی، واحد گرمسار، دانشگاه آزاد اسلامی، گرمسار، ایران.

چکیده

مقدمه: کاربرد روش‌­هایی مانند مدل­‌یابی معادله ساختاری (SEM) یا نظریة پرسش و پاسخ (IRT) برای عملیاتی‌سازی سازه‌­های روان‌شناختی، مستلزم بررسی مفروضه «استقلال موضعی» در داده­‌ها است. هدف از این پژوهش، ارزیابی بعدپذیری و ارزش افزوده خرده - دامنه‌­های مقیاس‌­های روان‌شناختی با استفاده از مدل تحلیل عاملی تأییدی بایفکتر بود.
روش: این مطالعه  از نوع مروری بود که پس از معرفی مدل تحلیل عاملی تأییدی بایفکتر، از بستة آماری BifactorIndicesCalculator در نرم‌افزار  R نسخة 3/3/4 برای ارزیابی بعدپذیری  و ارزش افزوده خرده - دامنه­های مقیاس­های روان‌شناختی استفاده شد. داده­ها از 512 نفر از دانشجویان دانشگاه آزاد اسلامی واحد گرمسار در سال تحصیلی 1402-1403 جمع‌آوری شدند.  این دانشجویان با روش نمونه‌­گیری در دسترس انتخاب شده و  به پرسش‌های مقیاس خوب زیستن یوسفی پاسخ دادند.
نتایج: اگر شاخص واریانس مشترک تبیین شده کل، کمتر از 60/0 باشد، مقیاس چند بعدی در نظر گرفته می‌شود و اگر 90/0 و بیشتر باشد، مقیاس به حد کفایت تک‌بعدی تلقی می‌شود. همچنین اگر دو شاخص واریانس مشترک تبیین شده کل و درصد همبستگی­های آلوده نشده‌، دستکم 70/0 باشد، مقیاس تک‌بعدی محسوب می‌شود. اگر شاخص واریانس مشترک تبیین شده کل حداقل 60/0 باشد، لازم است دو شاخص درصد همبستگی‌های آلوده نشده و ضریب امگا سلسله مراتبی نیز حداقل 70/0 باشند تا مقیاس به حد کفایت تک‌بعدی درنظر گرفته شود.
بحث و نتیجه‏‌گیری: با توجه به نتایج این مطالعه، پژوهشگران می­توانند از  مدل تحلیل عاملی تأییدی بایفکتر برای ارزیابی بعدپذیری و ارزش خرده دامنه‌­های مقیاس­‌های روان‌شناختی بهره ببرند.

کلیدواژه‌ها

عنوان مقاله [English]

Evaluation of the Bifactor Confirmatory Factor Analysis Model of Dimensionality and Value of Sub-Domains of Psychological Scale

نویسندگان [English]

  • Noorellah Yousefi 1
  • Alireza Pirkhaefi 2
1 Ph.D in Educational Psychology, Farhangian University Lecturer, Varamin Campus, Varamin, Iran.
2 Associate Professor, Department of Psychology, Garmsar Branch, Islamic Azad University, Garmsar, Iran.
چکیده [English]

 
Introduction: The application of methods such as Structural Equation Modeling (SEM) and Item Response Theory (IRT) for the operationalization of psychological constructs necessitates an examination of the assumption of "local independence" within the data. The objective of this research was to assess the dimensionality and additional value of the subdomains of psychological scales through the use of a bifactor confirmatory factor analysis model.
Method: This study employed a review methodology utilizing the bifactor confirmatory factor analysis model, implemented through the BifactorIndicesCalculator statistical package in R software version 4.3.3. The aim was to evaluate the dimensionality and added value of sub-domains of psychological scales. Data were collected from 512 students at the Islamic Azad University, Garmsar branch, during the 2022-2023 academic year. Participants were selected using an availability sampling method and completed the questions from Yousefi's Good Life Scale.
Results: If the total explained common variance index is less than 0.60, the scale is considered multidimensional. Conversely, if it is 0.90 or higher, the scale is deemed sufficiently unidimensional. Additionally, if both the total explained common variance index and the percentage of uncontaminated correlations are at least 0.70, the scale is also regarded as sufficiently unidimensional. Furthermore, if the total explained common variance index is at least 0.60, it is essential for both the percentage of uncontaminated correlations and the hierarchical omega coefficient to be a minimum of 0.70 for the scale to be classified as sufficiently unidimensional.
Discussion and conclusion: The results of the study indicate that researchers can utilize the bifactor confirmatory factor analysis model to assess the dimensionality and significance of the subdomains within psychological scales.
Extended Abstract
Introduction
Researchers employ methods such as Structural Equation Modeling (SEM) and Item Response Theory (IRT) to operationalize psychological constructs. To utilize Structural Equation Modeling (SEM) and Item Response Theory (IRT) estimates, researchers must contend with the assumption of "local independence, may not hold true in their data. If this assumption is violated, it can lead to uniqueness" or the emergence of "local dependence. result in inaccurate estimations of the underlying structure and yield misleading results from the scale. Recently, the use of the bifactor confirmatory factor analysis model to determine the dimensionality and added value of sub-domains in psychological scales has been emphasized by prominent methodologists. In a bifactor confirmatory factor analysis model, items load on both a general factor and a specific factor. Therefore, this model allows for the evaluation of dimensionality and the added value of scores from the sub-domains of the scales by partitioning the variance and covariance of the items with respect to the general factor, the covariance with the specific factor, and the variance associated with the specific factor of each item. This evaluation can be conducted using various important statistical indicators. The purpose of this research was to assess the dimensionality and added value of the sub-domains of psychological scales utilizing the bifactor confirmatory factor analysis model.
Method
This review study utilized books, articles, and theses with accessible full texts that were relevant to the bifactor confirmatory factor analysis method. In a bifactor confirmatory factor analysis model, valuable statistical indicators are derived that can significantly enhance psychometric analysis. These indicators include the omega coefficient, the omega coefficient of subscales, hierarchical omega factor, omega hierarchical subscale, explained common variance index, specific-dimension explained common variance (ECV), ECV of a specific factor with respect to itself, within-domain ECV, explained common variance-item index, percentage of uncontaminated correlations index, and average relative parameter bias index. To estimate the statistical indices of the bifactor confirmatory factor analysis model, the “BifactorIndicesCalculator” statistical package was utilized in R software version 4.3.3. This document provides instructions on how to use this statistical package in R, along with the cutoff points for the statistical indices of the bifactor confirmatory factor analysis model. These indices are essential for evaluating the dimensionality and added value of the sub-domains of psychological scales. The data were collected from 512 students (235 boys and 277 girls) at the Islamic Azad University of Garmsar branch during the academic year 2023-2024, who were selected using an available sampling method and completed Yousefi's Good Life Scale. For researchers who are not familiar with R software, the Dober Bifactor Indices Calculator, an Excel-based tool, is also introduced.
Results
The results indicated that if the scale adheres to a bifactor model based on the underlying theoretical foundations and the collected data, a total explained common variance (ECV) index of less than 0.60 suggests that the scale is multidimensional. Conversely, if the total explained common variance (ECV) index is 0.90 or higher, the scale is considered sufficiently unidimensional. If the total explained common variance (ECV) index falls between 0.60 and 0.90, the researcher should consider additional indicators to assess the dimensionality of the scale. Specifically, if the ECV index is at least 0.70, the percentage of uncontaminated correlations (PUC) must also be a minimum of 0.70 to ensure that the scale is sufficiently unidimensional. If the total explained common variance index is at least 0.60, the percentage of uncontaminated correlations (PUC) index and the hierarchical omega coefficient must each be at least 0.70 for the scale to be considered sufficiently unidimensional. If a researcher intends to utilize the scores from the sub-domains in a bifactor model, it is essential to make decisions based on the omega coefficients of the subscales. When the reliability of a sub-domain is low, specifically when the omega coefficient (ωS) is at least 0.60, a value of at least 0.45 for the Explained Common Variance (ECV) coefficient of the specific factor (ECVSS) is adequate. This indicates that the sub-domain has a good likelihood of providing significant added value beyond the total score (ωS ≥ 0.60 and ECVSS ≥ 0.45). For an average reliability coefficient (ωS ≥ 0.80), an ECVSS coefficient value of at least 0.30 is necessary for the subscale to have a strong likelihood of providing significant added value beyond the total score (ωS ≥ 0.80 and ECVSS ≥ 0.30). Also, when the reliability of the sub-domain is low, specifically when it is at least 0.60 (ωS ≥ 0.60), a minimum OmegaHS coefficient of 0.25 is sufficient for the sub-domains to have a good chance of providing high added value in relation to the total score (ωS ≥ 0.60 and ωHS ≥ 0.25). Conversely, for an average reliability coefficient (ωS ≤ 0.80), a minimum value of 0.20 is adequate for the sub-domains to have a good chance of delivering high added value in relation to the total score (ωS ≥ 0.80 and ωHS ≥ 0.20). If the obtained values of the explained common variance-item index (I-ECV) for each scale item exceed 0.80 or 0.85, the researcher can utilize these items to create a short, concise, and unidimensional tool.
Conclusion
If a researcher is examining the factor structure of a psychological scale that has a total score reflecting its underlying theoretical foundations—specifically, a general factor—it is essential to estimate the bifactor model in addition to evaluating the unidimensional confirmatory factor analysis (CFA) model, the CFA model of correlated traits, and the higher-order CFA model. When comparing these estimated models, researchers should not solely rely on the goodness-of-fit indices to select the final model. In other words, if the data collected by the scale adheres to a bifactor model and the goodness-of-fit indices for this model are optimal, albeit slightly lower than those of competing models, it is advisable for the researcher to choose the bifactor model as the final model. They should also utilize various statistical coefficients from the bifactor model to assess the psychometric properties of the scale. Researchers need to pay attention to this point when their final bifactor confirmatory factor analysis model has two sub-domains, and their intention is to estimate the reliability of each sub-domain in order to use the scores of each sub-domain, it is not possible to use the cut points presented in this article for them; That is, the researcher can use the cut points presented in this article to estimate the reliability and use the score of each sub-domain when the researcher's final bifactor model is at least three sub-domains. According to the results of the study, researchers can use the bifactor confirmatory factor analysis model to evaluate the dimensionality and value of the subdomains of psychological scales.
Ethical Considerations
Compliance with Ethical Guidelines: Compliance with ethical guidelines: In the current study, ethical considerations such as informing about the research objectives, obtaining informed consent and agreement to participate in the study, not forcing participants to participate in the study, keeping the participants' information confidential and maintaining confidentiality were observed.
Funding: The present study was carried out without any financial support from any particular organization.
Authors’ contribution: Both researchers were involved in drafting, rewriting and revising the article.
Conflict of interest: The authors of the article declare that they have no conflict of interest.
Acknowledgments: We hereby express our gratitude to all the dear ones who helped us in carrying out this study; We are especially grateful to the students of Islamic Azad University of Garmsar branch.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

کلیدواژه‌ها [English]

  • Scale Dimensions
  • Local Independence
  • Bifactor Model
  • Omega Reliability Coefficient
  • Explained Common Variance Index
  • Total Score
  • Sub-Scale Score

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    [In Persian]

روانشناسی بالینی و شخصیت
دوره 23، شماره 1 - شماره پیاپی 44
فروردین 1404
صفحه 215-244

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