Determining sample size requirements in Latent Growth Models

Recently, latent growth models (LGMs) have been widely used in education or psychology for analyzing behavioral change over time. Although there have been a plethora of methodological research for the last couple of decades, required sample sizes for the model under various conditions still remains unclear for most substantive researchers. The present study carried out a series of Monte Carlo simulations with three mostly used types of LGM and tried to provide general guidelines for minimum required sample sizes for accurate estimation. According to the results, larger sample sizes were required when the number of measurement occasions were small, when missing responses were present, and when a binary outcome variable was included in the model. In particular, when the complex conditions were combined, very large sample sizes were required showing interactions between those conditions. Additionally, we discovered that quadratic growth models required remarkably larger sample sizes compared to linear or lambda-estimated growth models with minimal number of time points. Finally, we discussed how to apply the simulation results to determining appropriate sample sizes in practical situations.

keywords: Latent growth model, Quadratic latent growth model, Sample size, Simulation, 잠재성장모형, 2차 함수 잠재성장모형, 표본크기, 몬테카를로 시뮬레이션

Reference

권선중, 임숙희, 김영호 (2015). 청소년의 게임관련 신념과 게임 중독의 관계에 대한 재탐색: 잠재성장모형을 활용한 단기 종단연구. 한국심리학회지: 건강, 20(1), 267-283.

노성호 (2009). 청소년 비행의 추세분석과 전망. 형사정책연구, 20(1).

박순미, 손지아, 배성우 (2009). 노인의 생활만족도 변화에 대한 종단적 접근 - 인구사회학적 변인을 중심으로. 사회과학연구, 25(3), 1-24.

박현수, 박성훈, 정혜원 (2009). 청소년비행에있어 낙인의 효과에 대한 경험적 연구:비공식 낙인을 중심으로. 한국청소년연구, 20(1), 227-251.

서미정 (2009). 초기 청소년의 외현적 공격성변화와 비행, 우울/불안 및 학업성취감:잠재성장분석. 한국청소년연구, 20(2), 141-167.

송태민, 이주열, 안지영 (2010). 금연 실천과니코틴 의존도의 변화과정에 관한 연구. 보건교육건강증진학회지, 27(4), 123-129.

정소희 (2009). 청소년비행의 발달궤적과 이에영향을 주는 요인. 한국청소년연구, 20(2). 31-64.

조윤주 (2010). 청소년의 인터넷일탈에 관한종단적 연구: 잠재성장모형의 적용. 청소년학연구, 17(6), 171-195.

주혜선, 이나빈, 민문경, 안현의 (2014). 대학생의 우울증상 진행경로에 미치는 정서조절곤란과 외상 기억 특성의 효과: 잠재성장모형을 통한 단기종단연구. 한국심리학회지: 상담 및 심리치료, 26(3), 617-636.

10.

Algina, J, Keselman, H. J., Penfield, R. D. (2005). An Alternative to Cohen's Standardized Mean Difference Effect Size: A Robust Parameter and Confidence Interval in the Two Independent Groups Case. Psychological Methods, 10(3), 317-328.

11.

Bentler, P. M. (1990). Comparative fit indexes in structural models. Psychological Bulletin, 107(2), 238-246.

12.

Bentler, P. M., & Yuan, K.-H. (1999). Structural equation modeling with small samples: Test statistics. Multivariate Behavioral Research, 34, 183-199.

13.

Blozis, S. A., Harring, J. R., & Mels, G. (2008). Using LISREL to fit nonlinear latent curve models. Structural Equation Modeling: A Multidisciplinary Journal, 15(2), 346-369.

14.

Bollen, K. A., & Curran, P. J. (2006). Latent curve models: A structural equation modeling perspective. New Jersey: John Wiley.

15.

Boomsma, A. (2000). Reporting analyses of covariance structures. Structural Equation Modeling: A Multidisciplinary Journal, 7, 461-481.

16.

Bradley, J. V. (1978). Robustness? British Journal of Mathematical and Statistical Psychology, 31, 144-152.

17.

Cheong, J., MacKinnon, D. P., & Khoo, S. T. (2003). Investigation of mediational processes using parallel process latent growth curve modeling. Structural Equation Modeling: A Multidisciplinary Journal, 10(2), 238-262.

18.

Coffman, D. L., & Millsap, R. E. (2006). Evaluating latent growth curve models using individual fit statistics. Structural Equation Modeling: A Multidisciplinary Journal, 13(1), 1-27.

19.

Grimm, K. J., & Ram, N. (2009). Nonlinear growth models in Mplus and SAS. Structural Equation Modeling: A Multidisciplinary Journal, 16(4), 676-701.

20.

Grimm, K. J., Steele, J. S., Ram, N., & Nesselroade, J. R. (2013). Exploratory latent growth models in the structural equation modeling framework. Structural Equation Modeling: A Multidisciplinary Journal, 20(4), 568-591.

21.

Grimm, K. J., & Widaman, K. F. (2010). Residual structures in latent growth curve modeling. Structural Equation Modeling: A Multidisciplinary Journal, 17(3), 424-442.

22.

Jackson, D. L. (2001). Sample size and number of parameter estimates in maximum likelihood confirmatory factor analysis: A Monte Carlo investigation. Structural Equation Modeling: A Multidisciplinary Journal, 8, 205-223.

23.

Jackson, D. L. (2003). Revisiting sample size and the number of parameter estimates: Some support for the n:q hypothesis. Structural Equation Modeling: A Multidisciplinary Journal, 10, 128-141.

24.

Jöreskog, K. G. (1969). A general approach to confirmatory maximum likelihood factor analysis. Psychometrika, 34(2), 183-202.

25.

Kim, S. -Y. (2012). Sample size requirements in single- and multi-phase growth mixture models: A Monte Carlo simulation study. Structural Equation Modeling: A Multidisciplinary Journal, 19, 457-476.

26.

Kline, R. B. (2011). Principles and practice of structural equation modeling. New York: The Guilford Press.

27.

Little, R. J. A., & Rubin, D. B. (2002). Statistical analysis with missing data, 2nd ed. Hoboken, NJ: Wiley.

28.

McArdle, J. J. (1986). Latent variable growth within behavior genetic models. Behavior Genetics, 16, 163-200.

29.

McDonald, R. P., & Ho, M. -H. R. (2002). Principles and practice in reporting structural equation analyses. Psychological Methods, 7(1), 64-82.

30.

Meredith, W., & Tisak, J. (1984). “Tuckerzing”curves. Paper presented at the annual meeting of the Psychometric Society, Santa Barbara, CA.

31.

Meredith, W., & Tisak, J. (1990). Latent curve analysis. Psychometrika, 55(1), 107-122.

32.

Muthén, B. (1989). Latent variable modeling in heterogeneous populations. Psychometrika, 54, 557-585.

33.

Muthén, B. (2001a). Latent variable mixture modeling. In G. A. Marcoulides & R. E. Schumacker (Eds.), New developments and techniques in structural equation modeling (pp. 1-33). Mahwah: NJ: Erlbaum.

34.

Muthén, B. (2001). Second-generation structural equation modeling with a combination of categorical and continuous latent variables:New opportunities for latent class/latent growth modeling. In L. Collins & A. Sayer (Eds.), New methods for the analysis of change (pp.291-322). Washington, DC: American Psychological Association.

35.

Muthén, B. (2004). Latent variable analysis:Growth mixture modeling and related techniques for longitudinal data. In D. Kaplan (Ed.), Handbook of quantitative methodology for the social sciences (pp.345-368). Newbury Park, CA: Sage.

36.

Muthén, B., & Asparouhov, T. (2012). Bayesian SEM: A more flexible representation of substantive theory. Psychological Methods, 17(3), 313-335.

37.

Muthén, B., & Shedden, K. (1999). Finite mixture modeling with mixture outcomes using the EM algorithm. Biometrics, 55, 463-469.

38.

Muthén, L., & Muthén, B. (2002). How to use a Monte Carlo study to decide on sample size and determine power. Structural Equation Modeling: A Multidisciplinary Journal, 4, 599-620.

39.

Muthén, L., & Muthén, B. (2013). Mplus (Version 7). Los Angeles, CA: Muthén & Muthén.

40.

Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical linear models: Applications and data analysis methods. Thousand Oaks, CA: Sage Publications, Inc.

41.

Steiger, J. H., & Lind, J. C. (1980, May). Statistically-based tests for the number of common factors. Paper presented at the annual Spring meeting of the Psychometric Society, Iowa City, IA.

42.

Team, R. D. C. (2014). R: A language and environment for statistical computing [Computer software manual]. Vienna, Austria. Retrieved from http://www.R-project.org

43.

Tournagngeau, K., Nord, C., Lê, T., Sorongon, A. G., & Najarian, M. (2009). Early childhood longitudianl study, kindergarten class of 1998-99(ECLS-K), combined user’s manual for the ECLS-K eighth-grade and K-8 full sample data files and electronic codebooks (NCES 2009-004). National Center for Education Statistics, Institute of Education Sciences, U.S. Department of Education, Washington, DC.’

44.

von Soest, T., & Hagtvet, K. A. (2011). Mediation analysis in a latent growth curve modeling framework. Structural Equation Modeling: A Multidisciplinary Journal, 18(2), 289-314.

45.

Wu, W., West, S. G., & Taylor, A. B. (2009). Evaluating model fit for growth curve models:Integration of fit indices from SEM and MLM frameworks. Psychological Methods, 14(3), 183-201.

바로가기메뉴

Article Contents

Vol.34 No.2

Determining sample size requirements in Latent Growth Models

Abstract

Reference

Korean Journal of Psychology: General