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구조방정식 모형을 활용한 매개효과 검정 방법의 비교: 백분위수 부트스트랩과 편향조정 부트스트랩

Comparison of methods for testing mediation effects under structural equation modeling framework: Percentile bootstrap and bias-corrected bootstrap

김수영|서영숙|심미경
한국심리학회 (The Korean Psychological Association)|2022.06|한국심리학회지:일반 (Korean Journal of Psychology: General)|제41권 제2호|pp. 103-131|DOI http://dx.doi.org/10.22257/kjp.2022.6.41.2.103

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참고문헌

키워드

매개효과mediation effectpower부트스트랩bootstrapmediation model매개모형1종오류검정력Type I error
주제분류심리과학

초록

매개모형이 심리학, 교육학, 경영학 등 다양한 분야에서 활발하게 이용되고 있다. 매개효과를 검정하는 방법은 Baron과 Kenny의 단계적 검정, 다변량 델타(Sobel의 방법) 등 전통적인 방법들을 거쳐 최근 부트스트랩이 표준 절차로 자리잡았다. 백분위수 부트스트랩으로 추정한 신뢰구간에 존재하는 잠재적 편향을 보완하기 위하여 편향조정 부트스트랩이 제안된 이후, 조정된 방법이 더 정확한 신뢰구간과 높은 검정력을 제공한다는 연구 결과들을 바탕으로 국내에서도 빈번히 사용되고 있다. 하지만 편향조정 부트스트랩이 검정력뿐만 아니라 1종오류 또한 더 높아 적절한 매개효과 검정 방법이 아닐 수 있다는 사실이 최근 보고되고있다. 본 연구는 매개효과의 검정에 관련된 최신 연구 흐름을 살펴보고, 잠재변수를 사용한 매개모형의 다양한 조건을 반영한 시뮬레이션을 실시하여 백분위수 부트스트랩과 편향조정 부트스트랩의 수행을 비교함으로써 매개효과 검정 방법에 대한 연구자들의 이해를 높이고자 하였다. 연구 1의 결과 편향조정 부트스트랩, 백분위수 부트스트랩, 다변량 델타 방법 순으로 검정력이 높았으며, 지표변수 개수가 많을수록, 효과크기가 클수록, 요인부하가 클수록, 표본크기가 클수록 검정력이 증가하는 경향을 보였다. 연구 2의 결과 1종오류 역시 편향조정 부트스트랩, 백분위수 부트스트랩, 다변량 델타 방법 순으로 높아 구조방정식 매개모형에서도 편향조정 부트스트랩이 가장 큰 1종오류를 발생시킨다는 것을 확인할 수 있었다. 마지막으로 본연구의 제한점을 기술하고 연구 결과를 바탕으로 한 가이드라인을 제공한다.

Abstract

Mediation models are widely used in various fields such as psychology, education, and business administration. Some traditional methods like Baron and Kenny’s approach and multivariate delta method were used before, but now bootstrap methods have become a standard procedure. Since the bias-corrected bootstrap (BC bootstrap) was proposed to correct for the potential bias in the confidence intervals (CIs) obtained by the percentile bootstrap, the BC method has been frequently used domestically based on some old research that the BC bootstrap provides more accurate CIs and higher power. However, recent studies have reported that the BC method may not be appropriate for testing mediating effects because it produces inflated Type I error rates. The goal of the present study is to enhance researchers’ understanding about testing methods for the mediation effect by examining the recent research trend of testing methods for mediating effects and by comparing the performance of the percentile bootstrap and the BC bootstrap through a series of simulations under various conditions. In Study 1, the results show that the power was high in the order of BC bootstrap, percentile bootstrap, and multivariate delta method. As the number of indicators, the effect size, the factor loading, and the sample size increased, the power also increased. Study 2 demonstrates that Type 1 error rates were also high in the order of BC bootstrap, percentile bootstrap, and multivariate delta method, confirming that the BC bootstrap also generates the highest Type 1 error in structural equation mediation models. Finally, the limitations of this study and guidelines based on the simulation results are discussed.

참고문헌 (80)

  1. Alwin, D. F., "The decomposition of effects in path analysis", American Sociological Review, 40, pp.37~47 (1975)[DOI]
  2. Bae, B., "Structural equation modeling with Mplus 7.0" (2016), Chungram
  3. Baron, R. M., "The moderator-mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations", Journal of Personality and Social Psychology, 51(6), pp.1173~1182 (1986)[DOI]
  4. Biesanz, J. C., "Assessing mediational models: Testing and interval estimation for indirect effects", Multivariate Behavioral Research, 45, pp.661~701 (2010)[DOI]
  5. Bollen, K. A., "Structural equations with latent variables" (1989), John Wiley & Sons
  6. Bollen, K. A., "Direct and indirect effects: Classical and bootstrap estimates of variability", Sociological Methodology, 20, pp.115~140 (1990)[DOI]
  7. Caron, P. -O., "A comparison of the type I error rates of three assessment methods for indirect effects", Journal of Statistical Computation and Simulation, 89(8), pp.1343~1356 (2019)[DOI]
  8. Chen, D., "Comparing alternative corrections for bias in the bias-corrected bootstrap test of mediation", Evaluation & the Health Professions, 44(4), pp.416~427 (2021)[DOI]
  9. Cerin, E., "A commentary on current practice in mediating variable analyses in behavioural nutrition and physical activity", Public Health Nutrition, 12(8), pp.1182~1188 (2009)[DOI]
  10. Cheung, G. W., "Testing mediation and suppression effects of latent variables: Bootstrapping with structural equation models", Organizational Research Methods, 11(2), pp.296~325 (2008)[DOI]
  11. Cheung, M. W. L., "Comparison of approaches to constructing confidence intervals for mediating effects using structural equation models", Structural Equation Modeling: A Multidisciplinary Journal, 14(2), pp.227~246 (2007)[DOI]
  12. Cohen, J., "Statistical power analysis for the behavioral sciences" (1988), Routledge
  13. correlation analysis for the behavioral sciences, "Applied multiple regression", pp.1983, Cohen, J.
  14. Cramer, H., "Mathematical methods of statistics" (1946), Princeton University Press
  15. DiCiccio, T. J., "Bootstrap confidence intervals", Statistical Science, 11(3), pp.189~228 (1996)[DOI]
  16. Duckworth, A. L., "A stitch in time: Strategic self-control in high school and college students", Journal of Educational Psychology, 108(3), pp.329~341 (2016)[DOI]
  17. Efron, B., "Bootstrap methods: Another look at the Jackknife", The Annals of Statistics, 7(1), pp.1~26 (1979)
  18. Efron, B., "Better bootstrap confidence intervals", Journal of the American Statistical Association, 82, pp.171~185 (1987)[DOI]
  19. Efron, B., "Bootstrap methods for standard errors, confidence intervals, and other measures of statistical accuracy", Statistical Science, 1(1), pp.54~75 (1986)
  20. Fairchild, A. J., "R2 effect-size measures for mediation analysis", Behavior Research Methods, 41, pp.486~498 (2009)[DOI]
  21. Fairchild, A. J., "Best (but oft-forgotten) practices: mediation analysis", The American Journal of Clinical Nutrition, 105(6), pp.1259~1271 (2017)[DOI]
  22. Falk, C. F., "Inference and interval estimation methods for indirect effects with latent variable models", Structural Equation Modeling: A Multidisciplinary Journal, 22(1), pp.24~38 (2015)[DOI]
  23. Fritz, M. S., "Required sample size to detect the mediated effect", Psychological Science, 18(3), pp.233~239 (2007)[DOI]
  24. Fritz, M. S., "Explanation of two anomalous results in statistical mediation analysis", Multivariate Behavioral Research, 47(1), pp.61~87 (2012)[DOI]
  25. Hair, J. F., "Multivariate data analysis" (2018), Cengage Learning, EMEA
  26. Hayes, A. F., "Introduction to mediation, moderation, and conditional process analysis. A regression-based approach" (2018), Guilford Press
  27. Hayes, A. F., "The relative trustworthiness of inferential tests of the indirect effect in statistical mediation analysis:Does method really matter?", Psychological Science, 24(10), pp.1918~1927 (2013)[DOI]
  28. Judd, C. M., "Process analysis: Estimating mediation in treatment evaluations", Evaluation review, 5(5), pp.602~619 (1981)[DOI]
  29. Kenny, D. A., "The handbook of social psychology (Vol. 1)", pp.233~265 (1998), McGraw-Hill
  30. 김하형, "비일관적 매개효과 모형의 해석 방향 탐색", 한국심리학회지:일반, 39(1), pp.91~115 (2020), 한국심리학회[DOI]
  31. 김현우, "다중매개모델에서 bootstrapping기법을 이용한 흡수능력의 매개효과 분석", 한국시뮬레이션학회 논문지, 24(4), pp.89~96 (2015), 한국시뮬레이션학회
  32. Kim, S. -Y., "Sample size requirements in single- and multiphase growth mixture models: A Monte Carlo simulation study", Structural Equation Modeling: A Multidisciplinary Journal, 19(3), pp.457~476 (2012)[DOI]
  33. Kim, S.-Y., "Fundamentals and extensions of structural equation modeling: With Mplus examples" (2016), Hakjisa
  34. Kirby, K. N., "BootES: An R package for bootstrap confidence intervals on effect sizes", Behavior Research Methods, 45, pp.905~927 (2013)[DOI]
  35. Kline, R. B., "Principles and practices of structural equation modeling" (2016), The Guilford Press
  36. Lachowicz, M. J., "A novel measure of effect size for mediation analysis", Psychological Methods, 23(2), pp.244~261 (2018)[DOI]
  37. Lee, H., "Analysis of mediating effect, moderating effect, and moderated mediating effect using Mplus" (2018), Shinyoungsa
  38. Liu, X., "Sample size planning for detecting mediation effects: A power analysis procedure considering uncertainty in effect size estimates", Multivariate Behavioral Research, 54(6), pp.822~839 (2019)[DOI]
  39. Lockman, J. D., "Testing the predictions of the existential constructivist theory of suicide in a college student sample", Journal of Counseling Psychology, 65(3), pp.294~307 (2018)[DOI]
  40. Lomnicki, Z. A., "On the distribution of products of random variables", Journal of the Royal Statistical Society, Series B (Statistical Methodology), 29(3), pp.513~524 (1967)[DOI]
  41. MacKinnon, D. P., "Introduction to statistical mediation analysis" (2008), Routledge
  42. Mackinnon, D. P., "Estimating mediated effects in prevention studies", Evaluation Review, 17(2), pp.144~158 (1993)[DOI]
  43. MacKinnon, D. P., "Distribution of the product confidence limits for the indirect effect: Program PRODCLIN", Behavior Research Methods, 39, pp.384~389 (2007)[DOI]
  44. MacKinnon, D. P., "A comparison of methods to test mediation and other intervening variable effects", Psychological Methods, 7(1), pp.83~104 (2002)[DOI]
  45. MacKinnon, D. P., "Confidence limits for the indirect effect: Distribution of the product and resampling methods", Multivariate Behavioral Research, 39(1), pp.99~128 (2004)[DOI]
  46. Malone, J. C., "Midlife Eriksonian psychosocial development: Setting the stage for late-life cognitive and emotional health", Developmental Psychology, 52(3), pp.496~508 (2016)[DOI]
  47. Meeker, W. Q., "Selected tables in mathematical statistics:The product of two normally distributed random variables" (1981), American Mathematical Society
  48. Meeker, W. Q., "An algorithm to compute the CDF of the product of two normal random variables", Communications in Statistics-Simulation and Computation, 23(1), pp.271~280 (1994)[DOI]
  49. Miočević, M., "Power in Bayesian mediation analysis for small sample research", Structural Equation Modeling: A Multidisciplinary Journal, 24(5), pp.666~683 (2017)[DOI]
  50. Miočević, M., "Statistical properties of four effect-size measures for mediation models", Behavior Research Methods, 50, pp.285~301 (2018)[DOI]
  51. "Bias-corrected bootstrap" (2014)[URL]
  52. Muthen, B. O., "Causal effects in mediation modeling: An introduction with applications to latent variables", Structural Equation Modeling: A Multidisciplinary Journal, 22(1), pp.12~23 (2015)[DOI]
  53. "Which kind of bootstrapping?" (2014)[URL]
  54. Muthén, L. K., "Mplus user’s guide" (1998), Muthén & Muthén
  55. Muthén, L. K., "How to use a Monte Carlo study to decide on sample size and determine power", Structural Equation Modeling: A Multidisciplinary Journal, 9(4), pp.599~620 (2002)[DOI]
  56. "Test indirect effect using bootstrap" (2008)[URL]
  57. 오미화, "정신질환자 가족의 스트레스와 가족적응 간의 관계에서 낙인지각과 가족건강성의 매개효과", 정신간호학회지, 27(3), pp.274~283 (2018), 한국정신간호학회[DOI]
  58. 박선미, "매개효과 연구의 동향분석과 새로운 방향 탐색", 교육심리연구, 28(1), pp.41~70 (2014), 한국교육심리학회
  59. 박세영, "병원간호사의 직무 스트레스와 투약안전간호수행 간 관계에서 피로의 매개효과", 성인간호학회지, 33(3), pp.283~293 (2021), 한국성인간호학회[DOI]
  60. Preacher, K. J., "SPSS and SAS procedures for estimating indirect effects in simple mediation models", Behavior Research Methods, Instruments, & Computers, 36(4), pp.717~731 (2004)[DOI]
  61. Preacher, K. J., "Asymptotic and resampling strategies for assessing and comparing indirect effects in multiple mediator models", Behavior Research Methods, 40, pp.879~891 (2008)[DOI]
  62. Preacher, K. J., "The Sage sourcebook of advanced data analysis methods for communication research", pp.13~54 (2008), Sage
  63. Preacher, K. J., "Effect size measures for mediation models: Quantitative strategies for communicating indirect effects", Psychological Methods, 16(2), pp.93~115 (2011)[DOI]
  64. Preacher, K. J., "Advantages of Monte Carlo confidence intervals for indirect effects", Communication Methods and Measures, 6(2), pp.77~98 (2012)[DOI]
  65. Rucker, D. D., "Mediation analysis in social psychology: Current practices and new recommendations", Social and Personality Psychology Compass, 5(6), pp.359~371 (2011)[DOI]
  66. Serlin, R. C., "Testing for robustness in Monte Carlo studies", Psychological Methods, 5(2), pp.230~240 (2000)[DOI]
  67. Shrout, P. E., "Mediation in experimental and nonexperimental studies: New procedures and recommendations", Psychological Methods, 7(4), pp.422~445 (2002)[DOI]
  68. Sim, M., "Sample size requirements for simple and complex mediation models", Educational and Psychological Measurement, 82(1) (2022)[DOI]
  69. Sobel, M. E., "Asymptotic confidence intervals for indirect effects in structural equation models", Sociological Methodology, 13, pp.290~312 (1982)[DOI]
  70. Sobel, M. E., "Direct and indirect effects in linear structural equation models", Sociological Methods & Research, 16(1), pp.155~176 (1987)[DOI]
  71. Springer, M. D., "The distribution of independent random variables", SIAM Journal on Applied Mathematics, 14(3), pp.511~526 (1966)[DOI]
  72. Stone, C. A., "The robustness of estimates of total indirect effects in covariance structure models estimated by maximum", Psychometrika, 55(2), pp.337~352 (1990)[DOI]
  73. Taylor, A. B., "Tests of the three-path mediated effect", Organizational Research Methods, 11(2), pp.241~269 (2008)[DOI]
  74. Tofighi, D., "Indirect effects in sequential mediation models: Evaluating methods for hypothesis testing and confidence interval formation", Multivariate Behavioral Research, 55(2), pp.188~210 (2020)[DOI]
  75. Tofighi, D., "RMediation: An R package for mediation analysis confidence intervals", Behavior Research Methods, 43(3), pp.692~700 (2011)[DOI]
  76. Valente, M. J., "A note on testing mediated effects in structural equation models:Reconciling past and current research on the performance of the test of joint significance", Educational and Psychological Measurement, 76(6), pp.889~911 (2016)[DOI]
  77. Van Rossum, G., "Python 3Reference Manual" (2009), CreateSpace
  78. Yuan, K. -H., "Reliable and more powerful methods for power analysis in structural equation modeling", Structural Equation Modeling: A Multidisciplinary Journal, 24(3), pp.315~330 (2017)[DOI]
  79. Yuan, Y., "Bayesian mediation analysis", Psychological methods, 14(4), pp.301~322 (2009)[DOI]
  80. Zhao, X., "Reconsidering Baron and Kenny: Myths and truths about mediation analysis", Journal of Consumer Research, 37(2), pp.197~206 (2010)[DOI]

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