범주형 확인적 요인분석 모형의 다집단 확장
A multi-group analysis using the categorical confirmatory factor analysis
0
조회
0
다운로드
5
인용
0
참고문헌
키워드
초록
범주형 확인적 요인분석은 심리학을 비롯한 사회과학 분야에서 빈번히 활용되는 범주형 변수(예, 리커트 척도 등)의 특성을 분석에 반영한 측정모형이다. 해당 모형의 다집단 확장에서 측정불변성을 확인하기 위해서는 단일 집단의 경우보다 모형 판별을 위하여 더 세분화된 척도화 및 제약이 수반되어야 하며, 측정불변성의 확인 단계 및 중요도 역시 연속형 지표변수를 상정한 경우와는 달라진다. 본 연구는 범주형 확인적 요인분석의 측정불변성과 관련하여 지금까지 이루어져 온 전체적인 논의를 탐색, 취합하여 연구자들이 자신의 연구 방향에 부합하는 판별 방식 및 측정불변성 확인 단계를 결정할 수 있도록 적절한 합의점을 도출하는 것을 목적으로 한다. 이를 위하여 두 가지 측면에서 논의가 이루어진다. 첫째, 모형의 판별 부분에서는 제한정보추정에 근거하여 두 종류의 잠재변수에 대한 척도화 및 다집단 분석을 위한 추가제약 방식을 다룬다. 둘째, 측정불변성 확인 단계에서는 범주형 지표변수를 상정하며 나타난 경계 모수의 동일성 확보를 중심으로 현재까지 제시되어 있는 측정불변성 확인 단계를 정리한다. 또한 앞서 제시된 판별 방식 및 측정불변성 확인 단계를 통계 프로그램을 이용하여 실제 자료 분석에 적용해 봄으로써 실질적인 활용을 도모한다. 마지막으로 판별 방식 및 측정불변성 확인 단계와 관련한 쟁점을 통합하여 각각의 상황에 부합하는 접근 방식의 특성 및 제한점을 논의한다.
Abstract
Categorical confirmatory factor analysis (CFA) is a measurement model that incorporates the categorical nature of the Likert scale, which is frequently used in the social sciences, including but not limited to psychology. The categorical CFA has quite different and complex model specification and identification as compared to the typical continuous CFA. A multi-group extension of the categorical CFA needs even more restrictions to be properly specified and identified. Moreover, the steps in checking the measurement invariance with the categorical indicator variables differ from those with the case of continuous indicator variables. The present study aims to help researchers choose proper methods and procedures for using a multi-group categorical CFA by investigating and integrating unorganized existing literature. To achieve this goal, we focus on two aspects. Based on the limited information estimation, we introduce scaling methods for the two types of latent variables, latent response variables and factors, and also address the method for parameter restrictions for multi-group analysis. Next, focusing on threshold parameters of the categorical CFA, we provide possible procedures for checking the measurement invariance. We then illustrate an application of the whole procedures using real data, and finally discuss the results.
참고문헌 (97)
- Asparouhov, T, "Robust chi square difference testing with mean and variance adjusted test statistics", Matrix, 1(5), pp.1~6 (2006)
- Asparouhov, T, "Simple second order chi-square correction" (2010)
- Asparouhov, T, "Auxiliary variables in mixture modeling: Three-step approaches using M plus", Structural Equation Modeling, 21(3), pp.329~341 (2014)
- Baas, K. D, "Measurement invariance with respect to ethnicity of the Patient Health Questionnaire-9(PHQ-9)", Journal of Affective Disorders, 129(1-3), pp.229~235 (2011)
- Batinic, B, "Construction and Factorial Structure of a Short Version of the Trendsetting Questionnaire (TDS-K) A Cross-Validation Using Multigroup Confirmatory Factor Analyses", European Journal of Psychological Assessment, 24(2), pp.88~94 (2008)
- Beauducel, A, "On the performance of maximum likelihood versus means and variance adjusted weighted least squares estimation in CFA", Structural Equation Modeling, 13(2), pp.186~203 (2006)
- Bernstein, I. H, "Factoring items and factoring scales are different : Spurious evidence for multidimensionality due to item categorization", Psychological Bulletin, 105(3), pp.467~477 (1989)
- Bollen, K. A, "A new incremental fit index for general structural equation models", Sociological Methods & Research, 17(3), pp.303~316 (1989)
- Byrne, B. M, "Stuctural equation modeling with Mplus : Basic concepts, applications, and programming" (2012), Taylor & Francis Group
- Byrne, B. M, "Testing for the equivalence of factor covariance and mean structures: The issue of partial meausrement invariance", Psychological Bulletin, 105(3), pp.456~466 (1989)
- Chen, F. F, "Sensitivity of goodness of fit indexes to lack of measurement Invariance", Structural Equation Modeling, 14(3), pp.464~504 (2007)
- Cheung, G. W, "Assessing extreme and acquiescence response sets in cross-cultural research using structural equations modeling", Journal of Cross-Cultural Psychology, 31(2), pp.187~212 (2000)
- Cheung, G. W, "Evaluating goodness-of-fit indexes for testing measurement invariance", Structural Equation Modeling, 9(2), pp.233~255 (2002)
- 최수미, "부정문항이 포함된 척도의 요인구조 및 방법효과 검증과 남녀 간의 차이 비교: Rosenberg 자기존중감 척도를 중심으로", 한국심리학회지:일반, 32(3), pp.571~589 (2013), 한국심리학회
- Christoph, G, "Adolescents' computer performance : The role of self-concept and motivational aspects", Computers & Education, 81, pp.1~12 (2015)
- Cooke, D. J, "Psychopathy and ethnicity : Structural, item, and test generalizability of the Psychopathy Checklist-Revised(PCL-R)in Caucasian and African American Participants", Psychological Assessments, 13(4), pp.531~542 (2001)
- Dimitrov, D. M, "Testing for factorial invariance in the context of construct validation", Measurement and Evaluation in Counseling and Development, 43(2), pp.121~149 (2010)
- Diniz, A, "Cognitive abilities, sociocultural background and academic achievement", Psicothema, pp.695~700 (2011)
- Dolan, C. V, "Factor analysis of variables with 2, 3, 5 and 7 response categories : A comparison of categorical variable estimators using simulated data", British Journal of Mathematical and Statistical Psychology, 47(2), pp.309~326 (1994)
- Edwards, M. C, "Handbook of structural equation modeling", pp.195~208 (2012), The Guilford Press
- Elosua, P, "Subjective values of quality of life dimensions in elderly people. A SEM preference model approach", Social indicators research, 104(3), pp.427~437 (2011)
- Flora, D. B, "An empirical evaluation of alternative methods of estimation for confirmatory factor analysis with ordinal data", Psychological methods, 9(4), pp.466~491 (2004)
- Forbush, K. T, "Development and validation of the Eating Pathology Symptoms Inventory(EPSI)", Psychological Assessment, 25(3), pp.859~878 (2013)
- Forero, C. G, "Factor analysis with ordinal indicators : A Monte Carlo study comparing DWLS and ULS estimation", Structural Equation Modeling, 16(4), pp.625~641 (2009)
- French, B. F, "Confirmatory factor analytic procedures for the determination of measurement invariance", Structural Equation Modeling, 13(3), pp.378~402 (2006)
- Glanville, J. L, "The measurement of school engagement : Assessing dimensionality and measurement invariance across race and ethnicity", Educational and Psychological Measurement, 67(6), pp.1019~1041 (2007)
- Glockner-Rist, A, "The best of both worlds : Factor analysis of dichotomous data using item response theory and structural equation modeling", Structural Equation Modeling, 10(4), pp.544~565 (2003)
- Hempel, L. M, "Scripture, sin and salvation : Theological conservatism reconsidered", Social Forces, 86(4), pp.1647~1674 (2008)
- Hoe, M, "Testing measurement invariance of the 11-tiem Korean version CES-D scale", Meantal Health and Social Work, 43(2), pp.313~339 (2015)
- Hutchinson, S. R, "Behavior of descriptive fit indexes in confirmatory factor analysis using ordered categorical data", Structural Equation Modeling, 5(4), pp.344~364 (1998)
- Johnson, D. R, "Ordinal measures in multiple indicator models: A simulation study of categorization error", American Sociological Review, 48(3), pp.398~407 (1983)
- Kamata, A, "A note on the relation between factor analytic and item response theory models", Structural Equation Modeling, 15(1), pp.136~153 (2008)
- Katsikatsou, M, "Pairwise likelihood estimation for factor analysis models with ordinal data", Computational Statistics & Data Analysis, 56(12), pp.4243~4258 (2012)
- Kim, E. S, "Measurement invariance testing with many groups : a comparison of five approaches", Structural Equation Modeling, 24(4), pp.524~544 (2017)
- Kim, E. S, "Testing measurement invariance : A comparison of multiple-group categorical CFA and IRT", Structural Equation Modeling, 18(2), pp.212~228 (2011)
- Kline, R. B, "Principles and practice of structural equation modeling" (2016), Guilford publications
- Kim, S.-Y, "Fundamentals and extensions of structural equation modeling" (2016), Hakjisa
- Koğar, H, "Comparison of different estimation methods for categorical and ordinal data in confirmatory factor analysis", Eğitimde ve Psikolojide Ölçme ve Değerlendirme Dergisi, 6(2), pp.351~364 (2015)
- Lawrence, J. W, "Perceived stigmatization and social comfort : Validating the constructs and their measurement among pediatric burn survivors", Rehabilitation Psychology, 55(4), pp.360~371 (2010)
- 이주연, "정상체중 중학생의 체형인식이 자아존중감에 미치는 영향: 체형만족도의 매개효과와 성별 차이", 한국청소년연구, 26(4), pp.267~297 (2015), 한국청소년정책연구원[DOI]
- 이필석, "중간보기 “?” 의 차별적 사용에 대한 한국과 미국 간 비교 문화적 검증: 혼합 문항반응분석의 적용", 한국심리학회지:일반, 33(3), pp.647~669 (2014), 한국심리학회
- 이순묵, "캐나다 도박행동 척도에서 개념적 구조 및 심리측정적 특성의 일반화 가능성: 남녀간 다집단 분석", 한국심리학회지:일반, 31(1), pp.1~26 (2012), 한국심리학회
- 이순묵, "탐색적 요인분석: 어떻게 달라지나?", 한국심리학회지:일반, 35(1), pp.217~255 (2016), 한국심리학회[DOI]
- Lee, S. Y, "Structural equation models with continuous and polytomous variables", Psychometrika, 57(1), pp.89~105 (1992)
- Looij-Jansen, P. M, "Confirmatory factor analysis and factorial invariance analysis of the adolescent self‐report Strengths and Difficulties Questionnaire : How important are method effects and minor factors?", British Journal of Clinical Psychology, 50(2), pp.127~144 (2011)
- Lopez Rivas, G. E, "The effects of referent item parameters on differential item functioning detection using the free baseline likelihood ratio test", Applied Psychological Measurement, 33(4), pp.251~265 (2009)
- Little, T. D, "Mean and covariance structures(MACS)analyses of cross-cultural data : Practical and theoretical issues", Multivariate Behavioral Research, 32(1), pp.53~76 (1997)
- Marsh, H. W, "The scholarship of teaching and learning in higher education: An evidence-based perspective", pp.319~383 (2007), Springer
- Mathyssek, C. M, "Does the Revised Child Anxiety and Depression Scale(RCADS)measure anxiety symptoms consistently across adolescence? The TRAILS study", International Journal of Methods in Psychiatric Research, 22(1), pp.27~35 (2013)
- Maydeu-Olivares, A, "Multidimensional item response theory modeling of binary data : Large sample properties of NOHARM estimates", Journal of Educational and Behavioral Statistics, 26(1), pp.51~71 (2001)
- Maydeu-Olivares, A, "A cautionary note on using G2(dif)to assess relative model fit in categorical data analysis", Multivariate Behavioral Research, 41(1), pp.55~64 (2006)
- McKelvey, R. D, "A statistical model for the analysis of ordinal level dependent variables", Journal of Mathematical Sociology, 4(1), pp.103~120 (1975)
- Meade, A. W, "Power and sensitivity of alternative fit indices in tests of measurement invariance", Journal of Applied Psychology, 93(3), pp.568~592 (2008)
- Mellenbergh, G. J, "Item bias and item response theory", International journal of educational research, 13(2), pp.127~143 (1989)
- Meredith, W, "Notes on factorial invariance", Psychometrika, 29(2), pp.177~185 (1964)
- Meredith, W, "Measurement invariance, factor analysis and factorial invariance", Psychometrika, 58(4), pp.525~543 (1993)
- Meuleman, B, "Measuring attitudes toward immigration in Europe : The cross-cultural validity of the ESS immigration scales", Research & Methods, 21(1), pp.5~29 (2012)
- Millsap, R. E, "The Wiley Handbook of Psychometric Testing: A Multidisciplinary Reference on Survey, Scale and Test Development", pp.847~884 (2018), Wiley
- Millsap, R. E, "Assessing factorial invariance in ordered-categorical measures", Multivariate Behavioral Research, 39(3), pp.479~515 (2004)
- Moor, M. H, "Assessment of borderline personality features in population samples : Is the Personality Assessment Inventory-Borderline Features scale measurement invariant across sex and age?", Psychological Assessment, 21(1), pp.125~130 (2009)
- Morin, A. J, "Factorial validity of the ADHD Adult Symptom Rating Scale in a French community sample : results from the ChiP-ARD study", Journal of Attention Disorders, 20(6), pp.530~541 (2016)
- Muthén, B, "A general structural equation model with dichotomous, ordered categorical, and continuous latent variable indicators", Psychometrika, 49(1), pp.115~132 (1984)
- "Model fit indices for two-part growth model" (2006)[URL]
- "DIFFTEST related" (2009)[URL]
- "Multiple group analysis with categorical variables" (2011)[URL]
- Muthén, B, "Latent variable analysis with categorical outcomes : Multiple-group and growth modeling in Mplus", Mplus web notes, 4(5), pp.1~22 (2002)
- Muthén, B. O, "Robust interference using weighted least squares and quadratic estimating equations in the latent variable modeling with categorical and continuous outcomes" (1997), University of California
- Muthen, B, "A comparison of some methodologies for the factor analysis of non‐normal Likert variables : A note on the size of the model", British Journal of Mathematical and Statistical Psychology, 45(1), pp.19~30 (1992)
- Muthén, L, "Mplus (Version 7)" (2019), Muthén &Muthén
- Nussbeck, F. W, "Analyzing multitrait-multimethod data with sturctural equation models for ordinal variables applying the WLSMV estimator:What sample size is needed for valid results", British Journal of Mathematical and Statistical Psychology, 59(1), pp.195~213 (2006)
- Potthast, M. J, "Confirmatory factor analysis of ordered categorical variables with large models", British Journal of Mathematical and Statistical Psychology, 46(2), pp.273~286 (1993)
- Reise, S. P, "Confirmatory factor analysis and item response theory : Two approaches for exploring measurement invariance", Psychological Bulletin, 114(3), pp.552~566 (1993)
- Rhemtulla, M, "When can categorical variables be treated as continuous? A comparison of robust continuous and categorical SEM estimation methods under suboptimal conditions", Psychological Methods, 17(3), pp.354~373 (2012)
- Rutkowski, L, "Assessing the hypothesis of measurement invariance in the context of large-scale international surveys", Educational and Psychological Measurement, 74(1), pp.31~57 (2014)
- Rutkowski, L, "Measurement invariance in international surveys : Categorical indicators and fit measure performance", Applied Measurement in Education, 30(1), pp.39~51 (2017)
- Sass, D. A, "Handbook of quantitative methods for educational research", pp.315~345 (2013), Sense Publishers
- Sass, D. A, "Evaluating model fit with ordered categorical data within a measurement invariance framework : A comparison of estimators", Structural Equation Modeling, 21(2), pp.167~180 (2014)
- Satorra, A, "A scaled difference chi-square test statistic for moment structure analysis", Psychometrika, 66(4), pp.507~514 (2001)
- Satterthwaite, F. E, "Synthesis of variance", Psychometrika, 6(5), pp.309~316 (1941)
- Schlotz, W, "The perceived stress reactivity scale : Measurement invariance, stability, and validity in three countries", Psychological assessment, 23(1), pp.80~94 (2011)
- Schreiber, J. B, "Reporting structural equation modeling and confirmatory factor analysis results : A review", The Journal of educational research, 99(6), pp.323~338 (2006)
- Selig, J. P, "Multilevel analysis of individuals and cultures", pp.93~119 (2008), Taylor & Francis
- Seo, D, "Item response theory approach using item factor anlaysis in the development of psycholgocial test", A packet for the Korean Psychological Association, 137 (2017)
- Stark, S, "Examining assumptions about item responding in personality assessment : Should ideal point methods be considered for scale development and scoring?", Journal of Applied Psychology, 91(1), pp.25~39 (2006)
- Steenkamp, J. B. E, "Assessing measurement invariance in cross-national consumer research", Journal of consumer research, 25(1), pp.78~90 (1998)
- Temme, D, "International advertising and communication: Current insights and empirical findings", pp.455~472 (2006), Springer Science &Business Media
- Vandenberg, R. J, "A review and synthesis of the measurement invariance literature: Suggestions, practices, and recommendations for organizational research", Organizational Research Methods, 3(1), pp.4~70 (2000)
- Wang, W. C, "Effects of anchor item methods on differential item functioning detection with the likelihood ratio test", Applied Psychological Measurement, 27(6), pp.479~498 (2003)
- Widaman, K. F, "Modeling longitudinal and multilevel data: Practical issues, applied approaches, and specific examples", pp.163~281 (2000), Lawrence Erlbaum Associates Publishers
- Widaman, K. F, "The science of prevention:Methodological advances from alchol and substance abuse research", pp.281~324 (1997), American Psychologocal Association
- Wu, H, "Identification of confirmatory factor analysis models of different levels of invariance for ordered categorical outcomes", Psychometrika, 81(4), pp.1014~1045 (2016)
- Xing, C, "Confirmatory factor analysis and measurement invariance testing with ordinal data : An application in revising the flirting styles inventory", Communication Methods and Measures, 9(3), pp.123~151 (2015)
- Yang, Y, "A note on structural equation modeling estimates of reliability", Structural Equation Modeling, 17(1), pp.66~81 (2010)
- Yang-Wallentin, F, "Confirmatory factor analysis of ordinal variables with misspecified models", Structural Equation Modeling, 17(3), pp.392~423 (2010)
- Yoon, M, "Detecting violations of factorial invariance using data-based specification searches : A Monte Carlo study", Structural Equation Modeling, 14(3), pp.435~463 (2007)
- Liu, Y, "Testing measurement invariance in longitudinal data with ordered-categorical measures", Psychological Methods, 22(3), pp.486~506 (2017)
- Zimprich, D, "Openness to experience, fluid intelligence, and crystallized intelligence in middle-aged and old adults", Journal of Research in Personality, 43(3), pp.444~454 (2009)
