Correlation between residuals in confirmatory factor analysis: a brief guide to their use and interpretation
Abstract
Introduction: The inclusion of correlations between residuals in measurement models is a common practice in psychometric research and is predominantly oriented to the statistical improvement of the model through increase (for example, IFC) or decrease (for example, RMSEA) of the magnitude of certain adjustment indices, rather than understanding the nature of these associations. This methodological report aims to present to the reader the modeling, management, and interpretation of correlated residuals in a framework of confirmatory factor analysis and poor specifications. Method: Using data from a previously presented study of 521 psychology students at a private university in Metropolitan Lima (75.8% women). The Flowering Scale is used to perform the analyses. Results and Discussion: These specifications would not have a real impact on the relationship of the elements with the construct they evaluate, so they do not contribute modifications to the understanding of the model. Therefore, specifying correlations between residuals could mask a poorly specified model, or with internal failures, by increasing spurious adjustment rates.
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Bonifay, W., Lane, S.P., & Reise, S.P. (2017). Three concerns with applying a bifactor model as a structure of psychopathology. Clinical Psychological Science, 5(1), 184 – 186. doi: 10.1177/2167702616657069
Brady, B., Kneebone, I. I., & Bailey, P. E. (2019). Validation of the Emotion Regulation Questionnaire in older community‐dwelling adults. British Journal of Clinical Psychology, 58(1), 110-122. doi:10.1111/bjc.12203
Brown, T. (2015). Confirmatory Factor Analysis for Applied Research (2nd Ed.). New York: The Guilford Press.
Byrne, B. M. (2009). Structural equation modeling with AMOS: Basic concepts, applications, and programming. New York, NY: Routledge & Taylor & Francis.
Calderón-De la Cruz, G., Dominguez-Lara, S., & Arroyo-Rodríguez, F. (2018). Análisis psicométrico preliminar de una medida breve de autoeficacia profesional en trabajadores peruanos: AU-10. Psicogente, 21(39), 12-24. doi: 10.17081/psico.21.39.2819
Calderón-De la Cruz, G., Lozano, F., Cantuarias, A., & Ibarra, L. (2018). Validación de la Escala Satisfacción con la Vida en trabajadores peruanos. Liberabit, 24(2), 249-264. doi: 10.24265/liberabit.2018. v24n2.06
Cassaretto, M., & Martínez, P. (2017). Validación de las escalas de bienestar, de florecimiento y afectividad. Pensamiento Psicológico, 15(1), 19-31. Recuperado a partir de //revistas.javerianacali.edu.co/index.php/pensamientopsicologico/article/view/1255
Caycho-Rodríguez, T., Ventura-León, J., Noe-Grijalva, M., Barboza-Palomino, M., Arias, W., Reyes-Bossio, M., & Rojas-Jara, C. (2018). Evidencias psicométricas iniciales de una medida breve sobre preocupación por el cáncer. Psicooncología, 15(2), 315-325. doi: 10.5209/PSIC.61438
Crede, M. (2018). Questionable research practices when using confirmatory factor analysis. Journal of Managerial Psychology, 34(1), 18-30. doi: 10.1108/JMP-06-2018-0272
Diener, E., Wirtz, D., Tov, W., Kim-Prieto, C., Choi, D., Oishi, S. & Biswas-Diener, R. (2010). New Well-Being Measures: Short Scales to Assess Flourishing and Positive and Negative Feelings. Social Indicators Research, 97(2), 143-156. doi: 10.1007/s11205-009-9493-y
DiStefano, C., Liu, J., Jiang, N., & Shi, D. (2018). Examination of the weighted root mean square residual: Evidence for trustworthiness? Structural Equation Modeling, 25(3), 453-466. Doi: 10.1080/10705511.2017.1390394
Dominguez-Lara, S. (2016). Errores correlacionados y estimación de la fiabilidad en estudios de validación: comentarios al trabajo validación de la escala ehealth literacy (eheals) en población universitaria española. Revista Española de Salud Pública, 90(9), e1-e2. Recuperado desde: http://scielo.isciii.es/pdf/resp/v90/1135-5727-resp-90-e60002.pdf
Dominguez-Lara, S. (2018a). Propuesta de puntos de corte para cargas factoriales: una perspectiva de fiabilidad de constructo. Enfermería Clínica, 28(6), 401. doi: 10.1016/j.enfcli.2018.06.002
Dominguez-Lara, S. (2018b). Sobre carretas, caballos, y otras cuestiones psicométricas. Interacciones, 4(3), 199-200. doi: 10.24016/2017.v4n3.152
Dominguez-Lara, S. & De la Cruz-Contreras, F. (2017). Análisis estructural y desarrollo de una versión breve de la versión en español del Inventario de Ansiedad ante Exámenes (TAI-E) en universitarios de Lima. Interacciones, 3(1), 7-17. doi: 10.24016/2017.v3n1.50
Dominguez-Lara, S. & Merino-Soto, C. (2017). Una modificación del coeficiente alfa de Cronbach por errores correlacionados. Revista Médica de Chile, 145, 269-274. Doi: 10.4067/S003498872017000200018.
Dominguez-Lara, S., & Merino-Soto, C. (2018). Evaluación de las malas especificaciones en modelos de ecuaciones estructurales. Revista Argentina de Ciencias del Comportamiento, 10(2), 19 – 24. doi: 10.32348/1852.4206.v10.n2.19595
Dominguez-Lara, Merino-Soto y Gutiérrez-Torres (2018). Estudio Estructural de una Medida Breve de Inteligencia Emocional en Adultos: El EQ-i-M20. Revista Iberoamericana de Diagnóstico y Evaluación – e Avaliação Psicológica, 49(4), 5-21. doi: 10.21865/RIDEP49.4.01
Dunn, T. J., Baguley, T. & Brunsden, V. (2014). From alpha to omega: A practical solution to the pervasive problem of internal consistency estimation. British Journal of Psychology, 105(3), 399-412. doi: 10.1111/bjop.12046
Fernández-Arata, M., Juárez-García, A., & Merino-Soto, C. (2015). Análisis estructural e invarianza de medición del MBI-GS en trabajadores peruanos. Liberabit, 21(1), 9-20. Recuperado de http://www.scielo.org.pe/scielo.php?script=sci_arttext&pid=S1729-48272015000100002&lng=es&tlng=es.
Gu, F., Little, T. D., & Kingston, N. M. (2013). Misestimation of reliability using coefficient alpha and structural equation modeling when assumptions of tau-equivalence and uncorrelated errors are violated. Methodology, 9(1), 30–40. doi:10.1027/1614-2241/a000052
Green, S.B. (2003). A coefficient alpha for test-retest data. Psychological Methods, 8(1), 88–101. doi: 10.1037/1082-989X.8.1.88
Haslam, D., Filus, A., Morawska, A., Sanders, M. R., & Fletcher, R. (2015). The Work–Family Conflict Scale (WAFCS): Development and initial validation of a self-report measure of work–family conflict for use with parents. Child Psychiatry & Human Development, 46(3), 346-357. doi: 10.1007/s10578-014-0476-0
Jöreskog, K. G. (1993). Testing structural equation models. 294–316 in: Bollen, K. A. and Long, J. S. (eds.) Testing Structural Equation Models. Beverly Hills: Sage.
Kline, R.B. (2016). Principles and practice of structural equation modeling. New York: The Guilford Press.
Loera, B., Converso, D., & Viotti, S. (2014) Evaluating the Psychometric Properties of the Maslach Burnout Inventory-Human Services Survey (MBI-HSS) among Italian Nurses: How Many Factors Must a Researcher Consider? PLoS ONE, 9(12): e114987. doi:10. 1371/journal.pone.0114987
McDonald, R.P., & Ho, M..H. R. (2002). Principles and practice in reporting structural equation analyses. Psychological Methods, 7, 64–82. doi: 10.1037/1082-989X.7.1.64
Moreta-Herrera, R., López-Calle, C., Ramos-Ramírez, M. & López-Castro, J. (2018). Estructura factorial y fiabilidad del Cuestionario de Salud General de Goldberg (GHQ-12) en universitarios ecuatorianos. Revista Argentina de Ciencias del Comportamiento, 10(3), 35-42. doi: 10.32348/1852.4206.v10.n3.20405
Moscoso, M.S., Merino-Soto, C., Dominguez-Lara, S., Chau, C.B., & Claux, M. (2016). Análisis factorial confirmatorio del inventario multicultural de la expresión de la ira y hostilidad. Liberabit, 22(2), 137-152. Recuperado de http://www.scielo.org.pe/scielo.php?script=sci_arttext&pid=S1729-48272016000200002&lng=es&tlng=es.
Muñiz, J., & Fonseca-Pedrero, E. (2019). Diez pasos para la construcción de un test. Psicothema, 31(1), 7 - 16. doi: 10.7334/psicothema2018.291
Muthén, L.K., & Muthén, B.O. (1998-2015). Mplus User’s guide (7th ed.). Los Angeles, CA: Muthén & Muthén.
Navarro-Loli, J.S., & Dominguez-Lara, S. (2019). Propiedades psicométricas de la Escala de Autoeficacia Percibida Específica de Situaciones Académicas en adolescentes peruanos. Psychology, Society, & Education, 11(1), 53-68. doi: 10.25115/psye.v10i1.1985
Reise, S. P., Waller, N. G., & Comrey, A. L. (2000). Factor analysis and scale revision. Psychological Assesment, 12, 287-297. doi:10.1037/1040-3590.12.3.287
Sanders, M. R., Morawska, A., Haslam, D. M., Filus, A., & Fletcher, R. (2014). Parenting and Family Adjustment Scales (PAFAS): validation of a brief parent-report measure for use in assessment of parenting skills and family relationships. Child Psychiatry & Human Development, 45(3), 255-272. doi: 10.1007/s10578-013-0397-3
Saris, W.E, Satorra, A., & van der Veld, W.M. (2009). Testing structural equation modeling or detection of misspecifications? Structural Equation Modeling, 16, 561 – 582. doi: 10.1080/10705510903203433
Schaufeli, W. B., Bakker, A. B., Hoogduin, K., Schaap, C., & Kladler, A. (2001). On the clinical validity of the Maslach Burnout Inventory and the Burnout Measure. Psychology & Health, 16(5), 565-582. doi: 10.1080/08870440108405527.
Seo, J. W., & Kwon, S. M. (2018). Preliminary Validation of a Korean Version of the Acquired Capability for Suicide Scale‐Fearlessness About Death. Suicide and Life‐Threatening Behavior, 48(3), 305-314. doi: 10.1111/sltb.12360
Solano, C. & Copez-Lonzoy, A. (2017). Análisis preliminar del cuestionario señales de alerta de recaída (AWARE) en drogodependientes peruanos. Interacciones, 3(2), 87-94. doi: 10.24016/2017.v3n2.65
Sörbom, D. (1989). Model modification. Psychometrika, 54(3), 371-384. doi: 10.1007/BF02294623
Sullman, M.J.M, Stephens, A.N., & Kuzu D. (2013). The expression of anger amongst Turkish taxi drivers. Accident Analysis and Prevention, 56, 42 50. doi: 10.1016/j.aap.2013.03.013
Sullman, M.J.M., Stephens, A.N., & Yong, M. (2015). Anger, aggression and road rage behaviour in Malaysian drivers. Transportation Research Part F: Traffic Psychology and Behaviour, 29, 70 – 82. doi: 10.1016/j.trf.2015.01.006
Ventura-León, J., Jara-Avalos, S., Garcia-Pajuelo, C., & Ortiz-Saenz, C. (2018). Validación de una escala de perfeccionismo en niños peruanos. Actualidades en Psicología, 32(124), 16-33. Recuperado de https://www.scielo.sa.cr/pdf/ap/v32n124/2215-3535-ap-32-124-16.pdf
Viladrich, C., Angulo-Brunet, A., & Doval, E. (2017). A journey around alpha and omega to estimate internal consistency reliability. Anales de Psicología, 33(3), 755-782. doi: 10.6018/analesps.33.3.268401
West, S.G., Taylor, A.B., & Wu, W. (2012). Model fit and model selection in structural equation modeling. In R. H. Hoyle (Ed.), Handbook of Structural Equation Modeling (pp. 209–231). New York, NY: Guilford
Williams, L. J., Vandenberg, R. J., & Edwards, J.R. (2009). Structural equation modeling in management research: A guide for improved analysis. Academy of Management Annals, 3, 543-604. doi: 10.1080/19416520903065683
Wu, Y., Zuo, B., Wen, F., & Yan, L. (2017). Rosenberg Self-Esteem Scale: Method effects, factorial structure and scale invariance across migrant child and urban child populations in China. Journal of Personality Assessment, 99(1), 83-93. doi: 10.1080/00223891.2016.1217420
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