Bienestar psicológico en estudiantes: Adaptación cultural y revisión del modelo Ryff Min Xu 1 , Hadijah Binti Jaffri 2 , Xiaohan Yang 3 , Shih Ling Chor 4 , Xin Ma 5 1 School of Education, University Technology Malaysia, Johor, Malaysia. E-mail: lindsaysnowballs@gmail.com; ORCID ID: https://orcid.org/0009-0003-4831-5976. 2 School of Education, University Technology Malaysia, Johor, Malaysia. E-mail: hadijahjaffri@utm.my; ORCID ID: https://orcid.org/0000-0001-8620-6445. 3 School of Education, University Technology Malaysia, Johor, Malaysia. E-mail: yangxiaohan1997@gmail.com; ORCID ID: https://orcid.org/0009-0007-7619-076X, 4 School of Education, University Technology Malaysia, Johor, Malaysia. E-mail: shihling.sunshine@gmail.com; ORCID ID: https://orcid.org/0000-0002-4295-4633 5 Faculty of Management, University Technology Malaysia, Johor, Malaysia. E-mail: Chrisma0912@gmail.com; ORCID ID: https://orcid.org/0009-0007-7371-6447. Resumen. Este estudio presenta una evaluación psicométrica de la escala de Bien- estar Psicológico (PWB) de Ryff para estudiantes internacionales chinos en Malasia. Con una muestra de 335 participantes, implementamos un enfoque analítico integral que incorpora análisis de Rasch, análisis factorial confirmatorio (AFC) y análisis fac- torial exploratorio (AFE) para evaluar y refinar la estructura de la escala. El modelado inicial de Rasch en una muestra piloto (N = 110) identificó ítems problemáticos que exhibieron desajuste de medición. Al aplicar el AFC para probar el modelo original de seis factores en el estudio principal, descubrimos altas correlaciones interfactoriales y una validez discriminante inadecuada, particularmente entre cuatro dimensiones. A través de la reespecificación y validación del modelo, desarrollamos una solución de tres factores más parsimoniosa que consolidó el Dominio Ambiental, el Crecimiento Personal, el Propósito en la Vida y la Autoaceptación en un constructo unificado, manteniendo la Autonomía y las Relaciones Positivas como factores distintos. El mo- delo optimizado de 15 ítems y tres factores demostró excelentes propiedades psicomé- tricas (χ²/gl = 1,305, CFI = 0,995, TLI = 0,994, SRMR = 0,022, RMSEA = 0,030). Estos hallazgos sugieren que el bienestar psicológico podría manifestarse de forma más integrada entre los estudiantes internacionales chinos que se adaptan a entornos inter- culturales de lo que se teorizó originalmente. Este modelo perfeccionado ofrece a in- vestigadores y profesionales un instrumento más adecuado desde el punto de vista cul- Recibido: 11/03/2025 ~ Aceptado: 12/05/2025 INTERACCIÓN Y PERSPECTIVA Revista de Trabajo Social ISSN 2244-808X ~ Dep. Legal pp 201002Z43506 DOI: https://doi.org/10.5281/zenodo.16915750 Vol. 15 (3): 879 - 900 pp, 2025

880 Xu, Binti Jaffri, Yang, Ling Chor, Ma Interacción y Perspectiva. Revista de Trabajo Social Vol. 15(3): 2025 Psychological well-being in students: Cultural adaptation and revision of the Ryff model Abstract. is study presents a psychometric evaluation of Ryff’s Psychologi- cal Well-Being (PWB) scale for Chinese international students from mainland China studying in Malaysia. With a sample of 335 participants, we implemented a compre- hensive analytical approach incorporating Rasch analysis, confirmatory factor analysis (CFA), and exploratory factor analysis (EFA) to assess and refine the scale’s struc- ture. Initial Rasch modeling in a pilot sample (N = 110) identified problematic items that exhibited measurement misfit. When applying CFA to test the original six-factor model in the main study, we discovered high inter-factor correlations and inadequate discriminant validity, particularly among four dimensions. rough model respecifi- cation and validation, we developed a more parsimonious three-factor solution that consolidated Environmental Mastery, Personal Growth, Purpose in Life, and Self-Ac- ceptance into a unified construct while retaining Autonomy and Positive Relations as distinct factors. e optimized 15-item, three-factor model demonstrated excellent psychometric properties (χ²/df = 1.305, CFI = 0.995, TLI = 0.994, SRMR = 0.022, RMSEA = 0.030). ese findings suggest that psychological well-being may manifest in a more integrated manner among Chinese international students from mainland China adapting to cross-cultural environments than originally theorized. is refined model offers researchers and practitioners a more culturally appropriate and psycho- metrically sound instrument for assessing psychological well-being in international student populations, while contributing to our understanding of how cultural context may influence the structural manifestation of psychological constructs. Key words: Ryff Well-being model, Chinese International Students, psychometric property, psychological well-being, Self-acceptance. INTRODUCTION e concept of happiness has deep philosophical origins, dating back to ancient Greek think- ers (Bremner, 2011). Two major philosophical traditions—hedonism and eudaimonia—have sig- nificantly influenced current views on well-being (Deci& Ryan, 2008). Hedonism, associated with Epicurus, centers on maximizing pleasure and minimizing pain, whereas Aristotle’s notion of eudai- monia highlights the importance of living a virtuous life filled with purpose and meaning (Ryan& Deci, 2001; Waterman, 2008). ese foundational ideas continue to shape modern psychological perspectives on well-being and life satisfaction. However, the models that try to explain individual well-being are often overloaded with components and don’t always have a clear mechanism for the formation of a person’s subjective well-being (Voitenko, 2022). tural y psicométrico para evaluar el bienestar psicológico en poblaciones de estudiantes internacionales, a la vez que contribuye a nuestra comprensión de cómo el contexto cultural puede influir en la manifestación estructural de los constructos psicológicos. Palabras clave: modelo de bienestar de Ryff, estudiantes internacionales chinos, psicometría, bienestar psicológico, autoaceptación.

Bienestar psicológico en estudiantes: Adaptación cultural y revisión del modelo Ryff 881 Vol. 15(3) julio - diciembre 2025/ 879 - 900 Malaysia has emerged as a prominent destination for international students, with a significant increase in Chinese students enrolling in tertiary-level education. e well-established educational collaboration between China and Malaysia has fostered confidence among Chinese families regard- ing Malaysia’s higher education opportunities as reliable and credible choices (Rui & Wahab, 2022). is significant growth warrants an examination of the factors driving the increasing preference of Chinese students for Malaysia as a higher education destination. Malaysia has emerged as a promi- nent educational hub in Asia, attracting an increasing number of Chinese students for higher educa- tion (Shafaei et al., 2016). According to official statistics, in 2016, approximately 15,000 students from mainland China selected Malaysia as their study destination, making them the second-largest group among international students. Notably, this figure has shown consistent growth over the years (Malaysian Ministry of Higher Education, 2015). On the other hand, Chinese international students in Malaysia frequently encounter chal- lenges such as adjusting to a new environment, meeting academic demands, and managing cultural conflicts, all of which may adversely impact their psychological well-being (e.g., Gustems-Carnicer et al., 2019; Gan & Yuen, 2019). Given the cultural and cognitive differences among popula- tions, researchers have noted that individuals from distinct countries may perceive and interpret questionnaire items in varying ways. As a result, the psychometric attributes of such instruments, including their factor structure, validity, and reliability, may differ across diverse sample groups and cultural contexts (Vandenberg& Lance, 2000). erefore, assessing the applicability and validity of the PWBS within the cultural framework of Chinese students studying in Malaysia is essential. e Psychological Well-Being (PWB) scale, originally developed within a Western cultural context, may not accurately capture well-being in non-Western populations without adequate vali- dation. When applied across culturally distinct settings, such instruments risk measurement bias, even when translated or adapted (Byrne, 2001). us, rigorous psychometric evaluation is neces- sary to ensure their reliability and validity in diverse cultural contexts. e present study seeks to examine the psychometric properties of Ryff’s PWB scale among Chinese international students in Malaysia. Employing both classical test theory and item response theory, the research explores the scale’s factor structure and assesses its measurement invariance in a cross-cultural framework. Find- ings are anticipated to contribute to the literature on cross-cultural validation and provide practical guidance for researchers and practitioners working with international student populations. LITERATURE REVIEW Conceptual Development of Psychological Well-being Psychological well-being encompasses a comprehensive view of human flourishing that goes beyond simply experiencing pleasure or avoiding negative emotions (Keyes, 2002). Lasting well- being does not depend on constant positive feelings; rather, it involves the ability to effectively regu- late and cope with negative emotions, which is essential for maintaining mental health over time (Huppert, 2009). is form of well-being is marked by a positive psychological state characterized by confidence in facing difficulties, optimistic thinking, persistence in pursuing goals, flexibility, and resilience in the face of challenges (Luthans et al., 2007). According to Ryff (1989), happiness is the highest expression of psychological well-being and a deeply personal experience.

882 Xu, Binti Jaffri, Yang, Ling Chor, Ma Interacción y Perspectiva. Revista de Trabajo Social Vol. 15(3): 2025 Influenced by various strands of positive psychology—such as Maslow’s idea of self-actual- ization, Rogers’ concept of the fully functioning person (1968), and Allport’s view of maturity (1961)—Jahoda (1958) proposed a set of criteria for positive mental health that moved beyond merely defining well-being as the absence of illness, offering instead a richer framework for under- standing psychological health (Keyes, 2002). Another theoretical perspective on psychological well- being stems from lifespan developmental psychology, which focuses on the unique psychological challenges encountered at different stages of life. is includes Erikson’s (1959) psychosocial stage theory and Neugarten’s (1973) insights into personality changes throughout adulthood and aging. Jung (2001) further contributed to this view, describing individuation as the process through which individuals attain self-realization. Ryff (1989) argued that although earlier views on well-being were somewhat fragmented, they could be integrated into a more unified conceptual model. A closer look at various definitions of happiness reveals that many theorists focus on common themes related to positive psychologi- cal functioning. Drawing from an extensive review of literature, Ryff developed the Psychologi- cal Well-Being Scale (PWBS), grounded in research from mental health, clinical psychology, and lifespan developmental theories (Burns& Machin, 2009). Later, Ryff and Keyes (1995) identified six core dimensions that define positive mental health: self-acceptance, positive social relationships, autonomy, mastery over one’s environment, a sense of purpose, and ongoing personal growth. is multidimensional framework presents psychological well-being not simply as the absence of psycho- logical disorders, but as the presence of strengths and positive development in various areas of life. Although Ryff’s Psychological Well-Being Scale (PWBS) has been widely utilized across vari- ous populations (Abbott et al., 2006; Springer et al., 2006; Huta & Waterman, 2014), evidence supporting its factorial validity remains scarce—especially in cross-cultural settings where the scale is applied outside its original context (Byrne, 2001). e structure of psychological well-being has sparked ongoing debate, with factor analyses yielding results that range from two to fifteen factors (e.g., Burns & Machin, 2009). Factorial Validity of Cross-Cultural Adaptations of the PWB e Psychological Well-Being (PWB) scales, developed by Ryff in 1989 and revised in 2002, are widely used to assess general psychological well-being across six dimensions: personal growth, envi- ronmental mastery, purpose in life, autonomy, positive relations with others, and self-acceptance. e original instrument consists of 120 items rated on a 6-point Likert scale, with higher scores indicating greater well-being. Several shortened versions have been developed, including 84-item, 54-item, 42- item, 39-item, and 18-item versions (e.g., Abbott et al., 2006; Van Dierendonck, 2004). e factor structure of the PWB scale has been extensively debated in the literature. Research employing factor analysis has produced remarkably diverse results, identifying between 2 and 15 distinct dimensions (e.g., Kafka & Kozma, 2002; Burns & Machin, 2009; Sirigatti et al., 2009). is wide range of factorial solutions highlights the complexity of operationalizing psychological well-being across different populations and contexts. Ryff and Keyes (1995) found that the 18-item version showed strong correlations (70% to 89%) with the original 120-item version and supported a six-factor model with a second-order general well-being factor. While the original validation demonstrated high internal consistency (α = 0.86–0.93), it also revealed concerns regarding discriminant validity due to significant inter-correla-

Bienestar psicológico en estudiantes: Adaptación cultural y revisión del modelo Ryff 883 Vol. 15(3) julio - diciembre 2025/ 879 - 900 tions among certain dimensions (r = 0.32–0.76), especially between self-acceptance, environmental mastery, personal growth, and purpose in life. Similarly, Clarke et al. (2001) identified an accept- able six-factor solution in their research with elderly Canadian participants. ough their analysis did not reveal problematic inter-item correlations, they did note weak factor loadings for several items, suggesting potential measurement issues within the scale’s structure. A consistent finding across multiple studies is the presence of high inter-correlations between certain dimensions. Van Dierendonck (2004) reported inter-factor correlations ranging from 0.32 to 0.76, with particularly strong associations between self-acceptance, environmental mastery, personal growth, and purpose in life. is pattern raises important questions about whether these theoretically distinct constructs are empirically separable. In addition, Lindfors et al. (2006) found results consistent with Ryff and Keyes’ (1995) origi- nal work, identifying a six-factor structure with a second-order general well-being factor as the best- fitting model. Notably, they observed a substantial correlation (r = 0.62) between self-acceptance and environmental mastery dimensions, further highlighting potential conceptual overlap between certain aspects of the scale. Springer and Hauser (2006), using multiple datasets and versions, con- sistently reported the highest inter-correlations between environmental mastery and self-acceptance, as well as between purpose in life and self-acceptance. To address these overlaps, a hierarchical model was proposed, comprising three first-order factors: one merging Environmental Mastery, Personal Growth, Purpose in Life, and Self-Acceptance (EGPS); a second representing Autonomy; and a third capturing Positive Relations with Others (Henn et al., 2016). ese three factors then loaded onto a single second-order factor reflecting overall psychological well-being—a structure that has been supported in prior studies (Burns & Machin, 2009; Van Dierendonck et al., 2008). In cross-cultural psychology research, ensuring measurement invariance is crucial to confirm that scales maintain consistent psychological structures across diverse cultural groups (Vandenberg & Lance, 2000). e psychometric properties of the PWB scales have been extensively studied across various cultural contexts, with mixed results. Kafka and Kozma (2001) found 15 distinct factors when analyzing the 120-item version with Canadian university students, with Triadó et al. (2007) reporting similar findings using a Spanish translation of the 54-item version. On the other hand, Kitamura et al. (2004) validated the original six-factor model using the Japanese version of the 84-item scale, although some items did not align with the factor structure proposed by Ryff. Cheng and Chan (2005) devel- oped a culturally adapted 28-item Chinese version that demonstrated acceptable fit for a six-factor model. Although the six-factor model has generally received weak to moderate empirical support across various studies (Burns & Machin, 2009; Fernandes et al., 2010; Van Dierendonck et al., 2008), some research has demonstrated a satisfactory model fit (Abbott et al., 2006; Cheng & Chan, 2005; Clarke et al., 2001; Kállay & Rus, 2014). Nonetheless, Springer and Hauser (2006) and Ryff (2013) argued that, despite these inconsistencies, the six-factor model outperforms competing models. e 18-item short version’s internal consistency, assessed using Cronbach’s alpha, was reported as follows for the six dimensions: autonomy (0.72), environmental mastery (0.76), positive relations with others (0.75), purpose in life (0.52), personal growth (0.73), and self-acceptance (0.51). e overall reliability of the scale was reported as 0.71 (Ryff & Keyes, 1995). Pedaprolu et al. (2021) additionally reported Cronbach’s alpha coefficients for the PWB scale, with subscale values ranging from 0.39 for “purpose in life” to 0.55 for “self-acceptance” and an overall reliability of 0.75. e 18-item short version of the PWB scale has been extensively utilized in diverse research contexts, including studies involving medical students (Nemati et al., 2023), university students in

884 Xu, Binti Jaffri, Yang, Ling Chor, Ma Interacción y Perspectiva. Revista de Trabajo Social Vol. 15(3): 2025 Iran (Sefidi & Farzad, 2012), the general population in Italy (Ruini et al., 2003), research scientists in India (Pedaprolu et al., 2021), and clinical nurses in Taiwan (Lee et al., 2019). e scale is widely recognized in the literature for its utility and effectiveness in large-scale surveys, cross-cultural stud- ies, and a variety of applied research contexts (Ryff & Keyes, 1995). However, its applicability has not been examined among Chinese international postgraduate students in Malaysian universities, where cultural and cognitive variations may influence the percep- tion and interpretation of questionnaire items. Examining the psychometric properties of the PWB scale in this population is particularly significant as Chinese international students face unique chal- lenges navigating between their heritage culture and Malaysian cultural norms (Popadiuk& Arthur, 2004; Alavi & Mansor, 2011), potentially influencing how psychological well-being manifests and is expressed. ese students often experience acculturative stress (e.g., Burris et al., 2010; Bewick et al., 2010), language barriers (e.g., Dongqi et al., 2020), and changes in social support systems that may impact their psychological well-being in ways distinct from previously studied popula- tions. Understanding the factorial structure of psychological well-being in this context could inform more culturally sensitive support services in international education settings. Additionally, as China continues to be one of the largest sources of international students globally ((Malaysian Ministry of Higher Education, 2015), research addressing the psychological measurement needs of this popula- tion has broad implications for educational institutions worldwide. Building on these insights, the present study seeks to assess the six-dimensional structure of the PWBS scale among Chinese post- graduate students in Malaysia universities and evaluate the reliability and accuracy of the PWBS-C scale in measuring psychological well-being within this specific cultural context. METHODOLOGY Content Validity Content validity refers to the extent to which the items in a given questionnaire accurately capture and represent the constructs being measured (Polit & Beck, 2006). It is closely linked to construct validity, as the process requires an initial definition of the content domain followed by an evaluation of whether the measurement scale appropriately represents that domain (Gould, 1994). According to Polit and Beck (2006), content validity relies on the scope of the measure, ensuring that the instrument includes a sufficient and representative set of items reflecting the underlying concept. Mohajan (2017) emphasizes that content validity ensures all critical aspects and dimen- sions of the concept under investigation are addressed. Typically, this form of validity is assessed by experts who determine whether the instrument’s questions or items adequately cover the intended concept (Bannigan & Watson, 2009). In the present study, two experts from the Faculty of Edu- cation at UTM will evaluate the questionnaire’s content validity prior to the formal study. Both experts possess extensive experience in teaching psychology and conducting research in the field of social science. Two educational psychology experts evaluated the questionnaire, verifying its construct valid- ity and suggesting minor wording refinements to enhance clarity. Following translation into Chi- nese, linguistic specialists conducted additional validation to ensure both measurement accuracy and cultural relevance. e instrument utilizes a seven-point Likert format, recognized for optimal psychometric properties and consistent with the original PWB structure. Content validity assess-

Bienestar psicológico en estudiantes: Adaptación cultural y revisión del modelo Ryff 885 Vol. 15(3) julio - diciembre 2025/ 879 - 900 ment employed the Content Validation Index (CVI), with both experts rating all items as content valid (scores of 3-4), yielding a perfect CVI of 1.0 that substantially exceeds the 0.8 threshold re- quired for adequate content validity. TABLE 1. CVI for Adapted PWB Measurement scale Total number Expert 1 Expert 2 Overall CVI Valid items Invalid items CVI Valid items Invalid items CVI 1 Adapted PWB 16 16 0 1 16 0 1 1 Pilot Study e pilot study employed eory (IRT), the Rasch model, to evaluate the psychometric prop- erties of the instrument (Wright& Masters, 1982). is approach converts ordinal data into inter- val-scale measurements expressed in logits, allowing for more precise assessment of item functioning and producing comparable measurements with defined units (Sondergeld & Johnson, 2014; Boone et al., 2011). Additionally, the Rasch model enables the removal of irrelevant items, identifies items with high accuracy, and detects potential item bias (Cooke & Michie, 1997). ConQuest version 2 software was utilized for the Rasch analysis due to its powerful capabilities in handling a wide range of measurement models and its ability to process both dichotomous and polytomous item responses efficiently. e software provides comprehensive item fit statistics and allows for clear interpretation of results through well-structured output formats. ConQuest is particularly effective for educational and psychological measurement applications, making it suitable for analyzing instruments such as the one examined in this study (Koyuncu& Şata, 2023). Data from 110 Chinese postgraduate students at Universiti Teknologi Malaysia were analyzed using ConQuest version 2. is sample size aligns with established guidelines for polytomous Rasch models, which recommend approximately 100-200 participants to achieve stable item parameter es- timates due to the increased complexity of item scoring with multiple response categories (Briggs& Wilson, M. (2003). e sample size of 110 participants was determined to be sufficient for obtain- ing meaningful results in this pilot phase while maintaining adequate statistical power. To evaluate item fit, Mean Square (MNSQ) values were examined, with acceptable ranges between 0.6 and 1.4 (Bond & Fox, 2007), and T statistics, with values between ±2.0 indicating acceptable fit (Linacre, 1994). ese criteria help identify items that may not be functioning as expected within the measurement model. Item 3 was removed from the final scale due to statistical misfit based on Rasch analysis (See Table 2). e item demonstrated significant deviation from the measurement model expectations with weighted MNSQ of 1.23 and a T value of 2.2, exceeding the recommended threshold of ±2.0. is elevated T statistic indicates the item exhibited more unpredictable response patterns than the model predicts, suggesting it may be measuring a different construct or contains confusing wording that introduces construct-irrelevant variance. Removal of this item improves the overall psychometric integrity of the scale while maintaining sufficient con- tent coverage of the underlying construct.

886 Xu, Binti Jaffri, Yang, Ling Chor, Ma Interacción y Perspectiva. Revista de Trabajo Social Vol. 15(3): 2025 TABLE 2. Item Parameter Estimates of PWB PWB Unweighted Fit Weighted Fit Item Estimate error MNSQ CI T MNSQ CI T 1 -0.064 0.07 0.92 (0.73, 1.27) -0.6 0.9 (0.74, 1.26) -0.8 2 0.013 0.069 1.01 (0.73, 1.27) 0.1 1.01 (0.74, 1.26) 0.1 3 -0.212 0.041 1.27 (0.73, 1.27) 1.9 1.23 (0.81, 1.19) 2.2 4 0.197 0.077 1.21 (0.74, 1.26) 1.5 1.17 (0.73, 1.27) 1.2 5 0.051* 0.098 1.15 (0.74, 1.26) 1.1 1.17 (0.74, 1.26) 1.2 6 -0.139 0.058 1.16 (0.74, 1.26) 1.2 1.12 (0.74, 1.26) 0.9 7 0.291 0.043 0.94 (0.74, 1.26) -0.4 0.94 (0.80, 1.20) -0.6 8 -0.368 0.077 0.76 (0.74, 1.26) -1.9 0.77 (0.73, 1.27) -1.8 9 0.171* 0.109 0.96 (0.74, 1.26) -0.2 0.95 (0.73, 1.27) -0.3 10 -0.079* 0.059 1.03 (0.74, 1.26) 0.3 1.01 (0.76, 1.24) 0.1 11 0.271 0.066 0.79 (0.74, 1.26) -1.6 0.86 (0.71, 1.29) -1 12 0.089 0.064 1.03 (0.74, 1.26) 0.3 1.06 (0.72, 1.28) 0.5 13 0.053 0.06 1.16 (0.74, 1.26) 1.1 1.16 (0.74, 1.26) 1.1 14 -0.360* 0.092 1.16 (0.74, 1.26) 1.2 1.2 (0.72, 1.28) 1.4 15 0.24 0.074 1.2 (0.74, 1.26) 1.5 1.15 (0.74, 1.26) 1.1 16 0.086* 0.084 1.01 (0.74, 1.26) 0.1 1.03 (0.71, 1.29) 0.3 17 0.1 0.076 0.95 (0.74, 1.26) -0.3 0.96 (0.73, 1.27) -0.2 18 -0.340* 0.106 0.92 (0.74, 1.26) -0.6 0.97 (0.74, 1.26) -0.2 e analysis of the 18-item instrument revealed that most items demonstrated acceptable fit to the Rasch model, with one item (Item 3) showing potential misfit with a weighted MNSQ of 1.23 and a T value of 2.2, exceeding the recommended threshold. As the purpose of the pilot was to refine the instrument, this item was removed to improve the overall measurement properties of the scale before proceeding to the main study. Participants and procedure e main study sampled 335 Chinese international postgraduate students from a Malaysian university, exceeding the minimum required sample size (160) based on the 1:10 item-to-sample ra- tio for SEM. From 366 initial questionnaires, 31 were eliminated through systematic outlier detec- tion using Mahalanobis distance analysis (p<.001) (Mahalanobis, 2018; Hair, 2011), standard de-

Bienestar psicológico en estudiantes: Adaptación cultural y revisión del modelo Ryff 887 Vol. 15(3) julio - diciembre 2025/ 879 - 900 viation review, boxplot visualization, and screening for straight-lining patterns (Reuning& Plutzer, 2020). Data collection followed formal institutional protocols with official authorization from the Faculty of Educational Sciences and Technology, adhered to methodological guidelines (Sng et al., 2016), and maintained ethical standards including informed consent and participant rights protec- tion (Felzmann, 2009). All participants provided informed consent voluntarily and were fully aware of their involvement in the research process (Felzmann, 2009; Ederio et al., 2023). e consent form ensured participants’ rights to withdraw at any point, guaranteed complete anonymity for privacy protection, and mitigated the risk of deception (Sil & Das, 2017). Data Analysis Procedure Mplus software was selected for this analysis due to its effectiveness in handling categorical data through the integration of the WLSMV estimator (Harrington, 2009). As the instruments in this study utilized a seven-point Likert scale—an ordinal measurement format—factor analysis was con- ducted using Mplus version 8 with the WLSMV estimation approach. erefore, Mplus 8 (v1.6.1) is employed for confirmatory factor analysis (CFA) testing the models, and SmartPLS 4 (v4.1.0.9) is to test the inner model fit: evaluating reliability, convergent validity, and discriminant validity of the adapted PWB. Findings Goodness-of-fit for measurement model Multiple fit indices were examined to evaluate model adequacy. e Standardized Root Mean Square Residual (SRMR), an absolute fit index, was assessed with values between 0.05-0.10 con- sidered acceptable and values below 0.05 indicating good fit (Schermelleh-Engel et al., 2003). For incremental fit measures, the Comparative Fit Index (CFI) values exceeding 0.95 represent good fit, while values above 0.90 are deemed acceptable (Byrne, 2013; Hair et al., 2019). Similarly, the Tucker-Lewis Index (TLI), a non-normed fit index, values greater than 0.90 indicate good fit (Whittaker & Schumacker, 2022). Additionally, the Root Mean Square Error of Approximation (RMSEA) values below 0.08 and normed chi-square (χ²/df ) between 1.0-5.0 are considered satisfac- tory thresholds for model evaluation (Hair et al., 2011). TABLE 3. Goodness-of-fit for measurement model PWB Model χ2 df χ2/df P-Value CFI TLI SRMR RMSEA Estimate 90 Percent C.I. Probability RMSEA <= .05 M1 628.655 119 5.283 0.0000 0.870 0.852 0.067 0.146 0.135 0.157 0.000 M2 132.684 104 1.276 0.0303 0.993 0.990 0.021 0.037 0.012 0.055 0.879 M3 139.848 116 1.206 0.0652 0.994 0.993 0.022 0.032 0.000 0.050 0.952 M4 113.545 87 1.305 0.0296 0.995 0.994 0.022 0.030 0.010 0.045 0.990

888 Xu, Binti Jaffri, Yang, Ling Chor, Ma Interacción y Perspectiva. Revista de Trabajo Social Vol. 15(3): 2025 e analysis began with an evaluation of Ryff’s original six-factor Psychological Well-Being (PWB) scale. rough rigorous Confirmatory Factor Analysis (CFA), the structural validity of the model was examined. e results demonstrated exceptional model fit, with highly favorable overall fit indices: Root Mean Square Error of Approximation (RMSEA) of 0.037 (90% Confidence Inter- val [0.012, 0.055]), Comparative Fit Index (CFI) of 0.993, Tucker-Lewis Index (TLI) of 0.990, and Standardized Root Mean Square Residual (SRMR) of 0.021. ese metrics provide strong empirical support for the six-factor structure, indicating that the model effectively represents the underlying psychological construct of well-being. Nevertheless, further examination revealed significant discriminant validity concerns. e Heterotrait-Monotrait ratio (HTMT) analysis showed extremely high correlations between Envi- ronmental Mastery (EM), Personal Growth (PG), Purpose in Life (PL), and Self-Acceptance (SA), with HTMT values approaching or exceeding 1.0 (ranging from 0.999 to 1.009) (Sarstedt et al., 2021). Such high values indicate these four dimensions are statistically almost indistinguishable, despite their conceptual differences. Addressing persistent discriminant validity challenges highlighted in previous research and the current investigation, an alternative three-factor model was proposed. is model combined four highly correlated dimensions—Environmental Mastery (EM), Personal Growth (PG), Purpose in Life (PL), and Self-Acceptance (SA)—into a single composite factor labeled as Merged Four, while maintaining Autonomy (AU) and Positive Relations (PR) as distinct factors. As a result, M3(merged) shows comparable excellence with a slightly better χ²/df ratio of 1.206 (χ² = 139.848, df = 116), non-significant p-value (0.0652), marginally higher incremental indices (CFI = 0.994, TLI = 0.993), and slightly improved residual indices (SRMR = 0.022, RMSEA = 0.032, 90% CI [0.000-0.050], probability RMSEA ≤ .05 = 0.952) than M2. While M3(merged) demonstrates slight statistical advantages across several indices, particularly in its non-significant p- value and higher probability of close fit, the differences between the models are minor, suggesting that both adequately represent the underlying structure of the data. Construct reliability and validity To ensure methodological rigor in our measurement models, a comprehensive approach was implemented to evaluate convergent validity and reliability, following the established guidelines of Hair et al. (2019). e assessment centered on four critical statistical parameters: 1) item factor loadings, 2) Cronbach’s alpha, 3) composite reliability, and 4) average variance extracted (AVE). Stringent criteria were applied throughout the validation process. Specifically, factor loadings were required to exceed 0.60 to establish item validity (Hair et al., 2019). Internal consistency was rigorously examined through both Cronbach’s alpha and composite reliability, with thresh- old values set above 0.70 to confirm satisfactory reliability (Fornell & Larcker, 1981; Hair et al., 2019). Additionally, AVE was incorporated as a complementary validity indicator, with values of at least 0.50 considered sufficient to demonstrate convergent validity, in accordance with Hair et al. (2019). To address potential statistical complications, variance inflation factor (VIF) values were also scrutinized. VIF values below 5 were deemed to represent acceptable multicollinearity levels, while values exceeding 10 indicated significant multicollinearity issues (Hair et al., 2019; Becker et al., 2015).

Bienestar psicológico en estudiantes: Adaptación cultural y revisión del modelo Ryff 889 Vol. 15(3) julio - diciembre 2025/ 879 - 900 TABLE 4. Construct reliability and validity and collinearity (VIF) PWB Items Outer Loading Cronbach’s alpha Composite Reliability AVE VIF Autonomy 0.912 0.944 0.85 AU1 0.920 2.902 AU2 0.921 3.268 AU3 0.925 3.439 Merged Four 0.978 0.980 0.817 SA1 0.907 4.629 SA2 0.907 4.662 SA3 0.902 4.479 EM1 0.892 4.031 EM2 0.913 5.125 EM3 0.898 4.213 PG1 0.920 5.493 PG2 0.904 4.522 PG3 0.904 4.589 PL2 0.904 4.650 PL3 0.892 4.062 Personal relationship 0.926 0.953 0.871 PR1 0.938 4.161 PR2 0.931 3.834 PR3 0.931 3.365 Despite the strong overall performance of the three-factor model (M3), minor multicollinear- ity issues persisted for items EM2 (VIF = 5.125) and PG1 (VIF = 5.403) (Hair et al., 2019; Becker et al., 2015) (see Table 4). Consequently, these items were removed to improve model fit, resulting in the refined M4 model. e fit indices for M4 indicate excellent structural validity: χ² = 113.545 with 87 degrees of freedom (χ²/df = 1.305), CFI = 0.995, TLI = 0.994, SRMR = 0.022, and RM- SEA = 0.030 (90% CI [0.010, 0.045]). e probability of RMSEA ≤ 0.05 is notably high at 0.990, suggesting strong model fit. In addition, the psychometric assessment of the three-factor Psychological Well-Being (PWB) scale demonstrates excellent measurement properties across all dimensions. e Autonomy factor (three items: AU1-AU3) exhibits high outer loadings (0.920-0.925), strong reliability (Cronbach’s alpha = 0.912, composite reliability = 0.944), robust convergent validity (AVE = 0.85), and accept- able multicollinearity levels (VIF = 2.902-3.439). Similarly, the Personal Relationship factor (three items: PR1-PR3) shows very high loadings (0.931-0.938), excellent reliability (Cronbach’s alpha = 0.926, composite reliability = 0.953), strong convergent validity (AVE = 0.871), and acceptable multicollinearity (VIF = 3.365-4.161). e Merged Four factor, consolidating items from Self- Acceptance, Environmental Mastery, Personal Growth, and Purpose in Life dimensions, demon- strates consistently high loadings (0.892-0.920), outstanding reliability (Cronbach’s alpha = 0.978, composite reliability = 0.980), and robust convergent validity (AVE = 0.817).

890 Xu, Binti Jaffri, Yang, Ling Chor, Ma Interacción y Perspectiva. Revista de Trabajo Social Vol. 15(3): 2025 Comparative analysis between M3 and M4 reveals subtle improvements in the refined model. While both demonstrate strong fit statistics, M4 shows marginally better performance across key indicators, including lower RMSEA (0.030 vs. 0.032), higher CFI (0.995 vs. 0.994), and higher TLI (0.994 vs. 0.993). e most notable improvement appears in the probability value of RMSEA ≤ 0.05 (0.990 vs. 0.952), indicating M4’s stronger confidence of good fit. Additionally, M4’s more parsimonious structure is reflected in its reduced degrees of freedom (87 vs. 116), suggesting a more efficient measurement model while maintaining excellent psychometric properties. Discriminant validity Discriminant validity refers to the extent to which constructs in a measurement model are empirically distinct from one another (Fornell& Larcker, 1981). It is a critical methodological re- quirement for accurately analyzing relationships among latent variables (Hair et al., 2019). Accord- ing to established criteria, discriminant validity is confirmed only when a latent construct explains more variance in its own indicators than it shares with other constructs within the model (Hair et al., 2019). In this study, discriminant validity was assessed using multiple complementary approaches. First, the Heterotrait-Monotrait Ratio (HTMT) of correlations was employed, which is consid- ered a more reliable criterion than the traditional Fornell-Larcker method (see Table. 5). Based on Henseler et al.’s (2015) guidelines, HTMT values below 0.85 indicate strong discriminant validity, while values below 0.90 are deemed acceptable. Second, the Fornell-Larcker criterion was applied, which requires that the square root of the average variance extracted (AVE) for each construct should exceed its correlation with any other construct in the model (Haji-Othman& Yusuff, 2022). Finally, the cross-loadings of all indicators across constructs were examined to verify that each indicator loaded highest on its intended construct with substantially lower loadings on all other constructs (Henseler et la., 2015), confirming that items were appropriately assigned to their respective latent variables (Chin, 1998). e results from all three approaches consistently demonstrated adequate discriminant validity among the study’s constructs. e initial HTMT assessment of the proposed three-factor psychological well-being model (M3)—in which the four related dimensions of Environmental Mastery, Personal Growth, Purpose in Life, and Self-Acceptance were consolidated into a single “Merged four” construct—indicated acceptable though borderline discriminant validity between certain constructs. Most notably, the HTMT coefficient between Autonomy (AU) and the Merged four reached 0.879, approaching the upper acceptable limit of 0.90. Other relationships demonstrated more comfortable values: 0.591 between AU and Positive Relations (PR), and 0.721 between PR and Merged four. ough these findings generally supported acceptable discriminant validity, the relatively high AU–Merged four correlation suggested possible theoretical overlap between these constructs, indicating the need for additional model refinement to strengthen construct distinctiveness. HTMT analysis of the refined M4 model demonstrated notable improvements in discrimi- nant validity measures: the AU–Merged four coefficient reduced considerably from 0.879 to 0.779, the PR–Merged four value decreased from 0.721 to 0.691, and the AU–PR relationship improved slightly from 0.591 to 0.574. e most significant enhancement occurred in the previously prob- lematic AU–Merged four relationship, which shifted from borderline acceptable to comfortably within the recommended threshold (below 0.85), providing strong evidence of improved construct separation and theoretical distinctiveness.

Bienestar psicológico en estudiantes: Adaptación cultural y revisión del modelo Ryff 891 Vol. 15(3) julio - diciembre 2025/ 879 - 900 e observed improvements—evidenced by reductions in HTMT ratios and enhanced model fit indices—offer strong support for the refined three-factor model (M4) as a more statistically sound and conceptually parsimonious representation of psychological well-being. Table 5 provides a comparative overview of HTMT coefficients before and after item removal (M3 vs. M4), where values outside parentheses correspond to the refined model (M4), and those within parentheses re- flect the original estimates from M3. Following the exclusion of two items with VIF values slightly exceeding 5, both the HTMT analysis and model fit metrics demonstrated marked enhancement. ese results collectively validate the item removal as a judicious and efficient refinement of the measurement model. TABLE 5. HTMT Results for PWB The Fornell-Larcker section confirms this with square roots of AVE (diagonal values: AU=0.922, PR=0.933, Merged four=0.903) exceeding inter-construct correlations in their respective rows and columns ((Fornell & Larcker, 1981). The Fornell-Larcker criterion results for the three-factor Psychological Well-Being (PWB) model demonstrate strong discriminant validity among the constructs (see Table 6). Each construct has stronger correlations with its own indicators than with those of other constructs, indicating that it shares more variance with its associated measures than with unrelated ones in the model. Specifically, the correla- tion between AU and PR is 0.544, between AU and Merged four is 0.734, and between PR and Merged four is 0.685. The highest correlation (0.734 between AU and Merged four) remains below the square root of AVE for both constructs, further supporting discriminant validity. These findings provide statistical evidence that the three PWB dimensions are empiri- cally distinct from one another, despite their conceptual relationships, reinforcing the struc- tural validity of the three-factor model. TABLE 6. Fornell-Lacker Criterion for PWB As shown in Table 6, the cross-loading matrix confirms that each item predominantly loads on its theoretically assigned factor. Items measuring Autonomy exhibit high loadings on their intended construct (0.920–0.925), with only moderate cross-loadings on unrelated factors. Positive Relations HTMT Results AU PR Merged four AU PR 0.574 (0.591) Merged four 0.779 (0.879) 0.691(0.721) Fornell- Lacker Criterion AU PR Merged four 0.922 0.544 0.933 0.734 0.685 0.903

892 Xu, Binti Jaffri, Yang, Ling Chor, Ma Interacción y Perspectiva. Revista de Trabajo Social Vol. 15(3): 2025 items similarly show strong primary loadings (0.931–0.938), while the indicators from the merged dimensions—Environmental Mastery, Personal Growth, Purpose in Life, and Self-Acceptance— demonstrate consistently substantial loadings (0.894–0.907) on the combined “Merged four” factor. ese results collectively affirm that the revised 15-item, three-factor model successfully addresses the discriminant validity limitations of both the original six-factor structure and the earlier 17-item three-factor model, while retaining solid psychometric robustness. TABLE 7. Cross loading for PWB AU PR merged 4 AU1 0.920 0.502 0.728 AU1 0.920 0.502 0.728 AU2 0.921 0.509 0.642 AU2 0.921 0.509 0.642 AU3 0.925 0.494 0.655 AU3 0.925 0.494 0.655 EM1 0.652 0.637 0.894 EM1 0.652 0.637 0.894 EM3 0.661 0.599 0.899 EM3 0.661 0.599 0.899 PG2 0.656 0.609 0.907 PG2 0.656 0.609 0.907 PG3 0.662 0.627 0.906 PG3 0.662 0.627 0.906 PL2 0.659 0.623 0.906 PL2 0.659 0.623 0.906 PL3 0.664 0.594 0.896 PL3 0.664 0.594 0.896 PR1 0.517 0.938 0.632 PR1 0.517 0.938 0.632 PR2 0.476 0.931 0.608 PR2 0.476 0.931 0.608 PR3 0.528 0.931 0.676 PR3 0.528 0.931 0.676 SA1 0.666 0.614 0.905 SA1 0.666 0.614 0.905 SA2 0.667 0.634 0.907 SA2 0.667 0.634 0.907 SA3 0.673 0.628 0.906 SA3 0.673 0.628 0.906

Bienestar psicológico en estudiantes: Adaptación cultural y revisión del modelo Ryff 893 Vol. 15(3) julio - diciembre 2025/ 879 - 900 DISCUSSION is study provides important insights into the psychometric properties of the Psychological Well-Being (PWB) scale when applied to Chinese international students studying in Malaysia. Our findings raise significant questions about the empirical distinctiveness of Ryff’s theoretical six-factor structure, particularly in light of the substantial overlap observed between certain dimensions when used with this specific cross-cultural population. e high inter-factor correlations revealed through our HTMT analysis between Environ- mental Mastery, Personal Growth, Purpose in Life, and Self-Acceptance (with values approaching or exceeding 1.0) suggest these dimensions are statistically nearly indistinguishable in our sample of Chinese international students, despite their conceptual differences. is finding aligns with previ- ous research that has questioned the distinctiveness of these dimensions. Van Dierendonck (2004) similarly reported high inter-factor correlations, particularly among these same four dimensions. While Clarke et al. (2001) and Lindfors et al. (2006) found support for the six-factor structure, they too observed substantial correlations between certain dimensions, notably Self-Acceptance and Environmental Mastery. It is important to note that the original six-factor structure still demonstrated acceptable model fit indices in our study, confirming the overall value and validity of Ryff’s theoretical framework. e six-factor conceptualization offers rich theoretical insights into the multidimensional nature of psychological well-being and has proven useful across numerous studies and diverse populations. Our findings do not invalidate this model but rather suggest that in the specific context of Chinese international students navigating cross-cultural adaptation in Malaysia, certain dimensions may be experienced in a more integrated manner. e methodological approach employed in this study represents a significant strength. Begin- ning with Rasch analysis in the pilot phase allowed for early identification of problematic items (Frances& Solon, 2014), such as PL1, which demonstrated substantial misfit with the measurement model. It should be noted that our Rasch analysis was conducted using the original dimensional structure and focused primarily on item parameter estimation. e limited sample size in our pi- lot study (n=110) was insufficient for robust DIF analysis, which typically requires larger groups for meaningful comparisons across cultural or demographic categories. is integration of Item Response eory with traditional factor analytic techniques provided a more comprehensive assess- ment of the scale’s psychometric properties than either approach alone could offer. CONCLUSION is study presents a rigorous psychometric assessment of the Psychological Well-Being (PWB) scale through the integration of multiple analytical frameworks. In the preliminary pilot phase, Rasch analysis grounded in Item Response eory (IRT) was employed to detect measurement anomalies. e exclusion of item PL1 was warranted due to its substantial misfit with the model (weighted MNSQ = 1.23, T = 2.2), suggesting that its response pattern was misaligned with the intended latent construct. e application of Rasch analysis at this early stage facilitated the detec- tion of item-level irregularities that may not have been identifiable using traditional classical test theory alone. is Rasch-informed refinement laid a more psychometrically robust foundation for the subsequent main analysis.

894 Xu, Binti Jaffri, Yang, Ling Chor, Ma Interacción y Perspectiva. Revista de Trabajo Social Vol. 15(3): 2025 e main study commenced with a traditional six-factor confirmatory factor analysis (CFA), which produced fit indices that, while within acceptable ranges, indicated less-than-optimal model performance and raised concerns regarding its structural validity. A closer inspection highlighted substantial issues with discriminant validity. Specifically, the Heterotrait-Monotrait (HTMT) ratio analysis revealed exceedingly high inter-factor correlations among Environmental Mastery (EM), Personal Growth (PG), Purpose in Life (PL), and Self-Acceptance (SA). ese elevated values sug- gest that, despite their theoretical distinctiveness, the four dimensions were statistically indistin- guishable within the measurement model. In light of the observed discriminant validity issues, a revised three-factor model was proposed wherein the highly interrelated dimensions—Environmental Mastery, Personal Growth, Purpose in Life, and Self-Acceptance—were consolidated into a single latent construct labeled “Merged four,” while Autonomy and Positive Relations were retained as separate factors. is restructured model (M3) yielded improved psychometric properties and model fit. Further refinement involved the removal of two items (PG1 and EM2) with variance inflation factors exceeding 5.0, culminating in the final model (M4), which comprises 15 items distributed across three latent variables. e opti- mized model demonstrated excellent fit indices (χ²/df = 1.305, CFI = 0.995, TLI = 0.994, SRMR = 0.022, RMSEA = 0.030), along with enhanced discriminant validity, as indicated by reduced HTMT values. Limitations Several limitations of this study should be acknowledged. e cross-sectional design limits our ability to assess the stability of the factor structure over time (e.g., Levin, 2006), particularly for international students whose psychological well-being may evolve throughout their cross-cultural adaptation process (Zhou et al., 2008). Additionally, our use of convenience sampling means that the findings may not fully represent the broader population of Chinese international students in Malaysia (e.g., Jager et al., 2017). e sample was also drawn from specific universities, potentially limiting the generalizability of our findings. A methodological limitation of this study is that Rasch analysis was only employed during the pilot phase, whereas the main analyses relied exclusively on Classical Test eory (CTT) ap- proaches. Although the sample size in the main study (n = 335) would have been adequate for con- ducting Differential Item Functioning (DIF) analysis, the shift to CTT-based methods precluded further examination of measurement invariance across demographic subgroups. is decision was guided by the study’s primary focus on factorial structure but reflects a trade-off between the depth of item-level diagnostics and the broader dimensional validation. Moreover, while the study identi- fied structural inconsistencies in the PWB scale within this population, it did not investigate the underlying cultural or contextual factors that may account for the limited empirical distinctiveness of certain dimensions among Chinese international students in Malaysia. Implications and Future Directions ese findings have important implications for how psychological well-being is conceptualized and measured in cross-cultural contexts, particularly for Chinese international students navigating adaptation to a foreign educational environment. Although Ryff’s six dimensions may not demon- strate perfect distinctiveness in this population, with considerable overlap observed among certain aspects, this does not necessarily indicate a flaw in the theoretical framework. Rather, it suggests that

Bienestar psicológico en estudiantes: Adaptación cultural y revisión del modelo Ryff 895 Vol. 15(3) julio - diciembre 2025/ 879 - 900 Chinese international students may experience psychological well-being in a more integrated man- ner than originally conceptualized, with specific components exhibiting stronger interconnections than anticipated in the original model. e three-factor model identified in this study (Autonomy, Positive Relations, and the “Merged four” composite) may provide a more parsimonious and culturally appropriate framework for as- sessing psychological well-being among Chinese international students. is streamlined model could offer practitioners and researchers a more efficient tool for assessing well-being in this group. Future research should investigate whether similar patterns of dimensional overlap emerge in dif- ferent international student populations, which could help determine whether our findings reflect characteristics specific to Chinese international students in Malaysia or more fundamental issues with the scale’s structure in cross-cultural settings. Additionally, longitudinal studies examining how the factor structure might change throughout the cultural adaptation process would provide valu- able insights into the dynamic nature of psychological well-being for international students. Future studies could benefit from integrating Rasch modeling, DIF testing, and qualitative approaches to more comprehensively explore how cultural variables shape both the experience and measurement of psychological well-being. BIBLIOGRAPHIC REFERENCES • Abbott, R. A., Ploubidis, G. B., Huppert, F. A., Kuh, D., Wadsworth, M. E., & Croudace, T. J. (2006). Psychometric evaluation and predictive validity of Ryff’s psychological well-being items in a UK birth cohort sample of women. Health and quality of life outcomes, 4, 1-16. • Bannigan, K., & Watson, R. (2009). Reliability and validity in a nutshell. Journal of clinical nursing, 18(23), 3237-3243. • Bewick, B., Koutsopoulou, G., Miles, J., Slaa, E., & Barkham, M. (2010). Changes in un- dergraduate students’ psychological well‐being as they progress through university. Studies in Higher Education, 35(6), 633–645. https://doi.org/10.1080/03075070903216643 • Bond, T. G., & Fox, C. M. (2013). Applying the Rasch model: Fundamental measurement in the human sciences. Psychology Press. https://doi.org/10.4324/9781410614575 • Boone, W. J., Townsend, J. S., & Staver, J. (2011). Using Rasch theory to guide the practice of survey development and survey data analysis in science education and to inform science re- form efforts: An exemplar utilizing STEBI self‐efficacy data. Science Education, 95(2), 258-280. https://doi.org/10.1002/sce.20413 • Bremner, R. H. (2011). eories of happiness: On the origins of happiness and our contemporary conception (Doctoral dissertation, Universitäts-und Landesbibliothek Bonn). • Briggs, D. C., & Wilson, M. (2003). An introduction to multidimensional measurement us- ing Rasch models. • Burns, R. A., & Machin, M. A. (2009). Investigating the structural validity of Ryff’s psycho- logical well-being scales across two samples. Social indicators research, 93, 359-375. • Burris, J. L., Brechting, E. H., Salsman, J., & Carlson, C. R. (2009). Factors associated with the psychological well-being and distress of university students. Journal of American College Health, 57(5), 536–544. https://doi.org/10.3200/jach.57.5.536-544 • Byrne, B. M. (2013). Structural equation modeling with Mplus: Basic concepts, applications, and programming. routledge.

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