Data analysis of incomplete repeated measures using a multivariate extension of the Brown-Forsythe procedure

  1. Guillermo Vallejo Seco 1
  2. María Paula Fernández García 1
  3. Pablo Esteban Livacic Rojas 2
  4. Ellián Tuero Herrero 1
  1. 1 Universidad de Oviedo
    info

    Universidad de Oviedo

    Oviedo, España

    ROR https://ror.org/006gksa02

  2. 2 Universidad de Santiago de Chile
    info

    Universidad de Santiago de Chile

    Santiago de Chile, Chile

    ROR https://ror.org/02ma57s91

Revista:
Psicothema

ISSN: 0214-9915

Año de publicación: 2018

Volumen: 30

Número: 4

Páginas: 434-441

Tipo: Artículo

Otras publicaciones en: Psicothema

Resumen

Antecedentes: para analizar diseños de medidas parcialmente repetidas (DMPR) con matrices de covarianza arbitrarias se puede usar una extensión multivariante del enfoque de Brown-Forsythe (MBF). Una importante limitación de este enfoque es que requiere datos completos para cada sujeto. Este artículo proporciona las reglas para agrupar los resultados obtenidos tras aplicar el análisis MBF a los diferentes conjuntos de datos imputados de un DMPR. Método: se aplican técnicas de Montecarlo para evaluar la solución propuesta (IM-MBF), en términos de control de los errores Tipo I y Tipo II. Con fines comparativos, también se evalúan los resultados obtenidos con el enfoque MBF basado en los datos originales (DO-MBF), así como con el modelo de patrones de covarianza basado en asumir una matriz no estructurada (MPC-NE). Resultados: cuando se cumple el supuesto de homogeneidad, el desempeño de la prueba IM-MBF es ligeramente inferior al obtenido con la prueba MPC-NE, mientras que sucede lo contrario cuando se incumple dicho supuesto. También encontramos que se pierde poca potencia usando el enfoque MI-MBF, en lugar del enfoque DO-MBF, cuando las matrices de covarianza son heterogéneas. Conclusiones: los resultados sugieren que el enfoque MI-MBF funciona bien y podría ser de uso práctico.

Información de financiación

We thank the three anonymous reviewers for valuable comments and suggestions. This research was supported by grant PSI-2015-67630-PSIC (AEI/FEDER, UE) from the Spanish Ministry of Economy and Competitiveness, and by grant 1170642 (FONDECYT) from the Chilean National Fund for Scientific and Technological Development.

Referencias bibliográficas

  • Austin, P.C. (2009). Type I error rates, coverage of confidence intervals, and variance estimation in propensity-score matched analyses. The International Journal of Biostatistics, 5, 13-38. doi.org/10.2202/1557-4679.1146
  • Bathke, A.C., Schabenberger, O., Tobias, R.D., & Madden, L.V. (2009). Greenhouse-Geisser adjustment and the ANOVA-type statistic: Cousins or twins? The American Statistician, 63, 239-246. doi. org/10.1198/tast.2009.08187
  • Bono, R., Blanca, M.J., Arnau, J., & Gómez-Benito, J. (2017). Non-normal distributions commonly used in health, education, and social sciences: A systematic review. Frontiers in Psychology, 8. doi.org/10.3389/ fpsyg.2017.01602
  • Blanca, M. J., Arnau, J., López-Montiel, D., Bono, R., & Bendayan, R. (2013). Skewness and kurtosis in real data samples. Methodology, 9, 78-84. doi.org/10.1027/1614-2241/a000057
  • Brunner, E., Munzel, U., & Puri, M.L. (2002). The multivariate nonparametric Behrens-Fisher problem. Journal of Statistical Planning and Inference, 108, 37-53. doi.org/10.1191/0962280205sm392oa
  • Cain, M.K., Zhang, Z., & Yuan, K.H. (2017). Univariate and multivariate skewness and kurtosis for measuring nonnormality: Prevalence, influence and estimation. Behavior Research Methods, 49, 1716-1735. doi.org/10.3758/s13428-016-0814-1
  • Fitzmaurice, G., Laird, N., & Ware, J. (2011). Applied longitudinal analysis (2nd edition). Hoboken, NJ: Wiley.
  • Friedrich, S., Konietschke, F., & Pauly, M. (2017). A wild bootstrap approach for nonparametric repeated measurements. Computational Statistics & Data Analysis, 113, 38-52. doi.org/10.1016/j.csda.2016.06.016
  • Grund, S., Lüdtke, O., & Robitzsch, A. (2016). Pooling ANOVA results from multiply imputed datasets: A simulation study. Methodology, 12, 75-88. doi.org/10.1027/ 1614-2241/a000111
  • Hertzog, C., Lindenberger, U., Ghisletta, P., & von Oertzen, T. (2008). Evaluating the power of latent growth curve models to detect individual differences in change. Structural Equation Modeling, 15, 541-563. doi. org/10.1080/10705510802338983
  • Kenward, M., & Carpenter, J. (2007). Multiple imputation: Current perspectives. Statistical Methods in Medical Research, 16, 199-218. doi.org/10.1177/0962280206075304
  • Kowalchuk, R.K., Keselman, H.J., & Algina, J. (2003). Repeated measures interaction test with aligned ranks. Multivariate Behavioral Research, 38, 433-461.doi.org/10.1207/ s15327906mbr3804_2
  • Li, K.H., Meng, X L., Raghunathan, T.E., & Rubin, D.B. (1991). Significance levels from repeated p-values with multiply imputed data. Statistica Sinica, 1, 65-92.
  • Li, K.H., Raghunathan, T.E., & Rubin, D.B. (1991). Large-sample signifi cance levels from multiply imputed data using moment-based statistic and an F-reference distribution. Journal of the American Statistical Association, 86, 1065-73. doi.org/10.1080/ 01621459.1991.10475152
  • Livacic-Rojas, P.E., Vallejo, G. Fernández, P., & Tuero-Herrero, E. (2017). Power of modified Brown-Forsythe and mixed-model approaches in split-plot designs. Methodology, 13, 9-22. doi.org/10.1027/1614-2241/ a000124
  • Lix, L.M., Algina, J., & Keselman, H.J. (2003). Analyzing multivariate repeated measures designs: A comparison of two approximate degrees of freedom procedures. Multivariate Behavioral Research, 38, 403431. doi.org/10.1207/s15327906mbr3804_1
  • Meng, X.L., & Rubin, D.B. (1992). Performing likelihood ratio tests with multiply imputed data set. Biometrika, 79, 103-111. doi.org/10.1093/ biomet/79.1.103
  • Oliver-Rodríguez, J.C., & Wang, X.T. (2015). Non-parametric three-way mixed ANOVA with aligned rank tests. British Journal of Mathematical and Statistical Psychology, 68, 23-42. doi.org/10.1111/bmsp.12031
  • Paniagua, D., Amor, P.J., Acheburúa, E., & Abad, F.J. (2017). Comparison of methods for dealing with missing values in the EPV-R. Psicothema, 29, 384-389. doi.org/10.7334/psicothema2016.75
  • Raghunathan, T. (2016). Missing Data Analysis in Practice. Boca Raton, FL: Chapman and Hall/CRC.
  • Raghunathan, T., & Dong, Q. (2011). Analysis of variance from multiply imputed data sets. Unpublished manuscript, Survey Research Center, Institute for Social Research, University of Michigan, Ann Arbor, Michigan. Retrieved from http://www-personal.umich.edu/_teraghu/ Raghunathan-Dong.pdf.
  • Ripley, B E. (1987). Stochastic Simulation. New York: Wiley. Rubin, D.B. (1987). Multiple Imputation for Nonresponse in Surveys. New York: Wiley. Rubin, D.B., & Schenker, N. (1986). Multiple imputation for interval estimation from simple random samples with ignorable nonresponse. Journal of the American Statistical Association, 81, 366-374. doi.org/ 10.1080/01621459.1986.10478280
  • SAS Institute, Inc (2017). SAS/STAT® 14.3 user’s guide. Cary, NC: SAS Institute, Inc.
  • Schafer, J. L. (1997). Analysis of Incomplete Multivariate Data. London: Chapman & Hall.
  • Vallejo, G., & Ato, M. (2006). Modifi ed Brown-Forsythe procedure for testing interaction effects in split-plot designs. Multivariate Behavioral Research, 41, 549-578.
  • Vallejo, G., & Ato, M. (2012). Robust tests for multivariate factorial designs under heteroscedasticity. Behavior Research Methods, 44, 471-489. doi.org/10.1207/s15327906mbr4104_6
  • Vallejo, G., Arnau, J., & Ato, M. (2007). Comparative robustness of recent methods for analyzing multivariate repeated measures. Educational & Psychological Measurement, 67, 1-27. doi. org/10.1177/0013164406294777
  • Vallejo, G., Fernández, P., Herrero, F.J., & Conejo, N. M. (2004). Alternative procedures for testing fixed effects in repeated measures designs when assumptions are violated. Psicothema, 16, 498-508.
  • Vallejo, G., Ato, M., Fernández, M. P., & Livacic-Rojas, P.E. (in press). Sample size estimation for heterogeneous growth curve models with attrition. Behavior Research Method. doi.org/10.3758/s13428-0181059-y
  • Vallejo, G., Fernández, M.P., Livacic-Rojas, P.E., & Tuero-Herrero, E. (2011a). Comparison of modern methods for analyzing unbalanced repeated measures data with missing values. Multivariate Behavioral Research, 46, 900-937. doi.org/10.1080/00273171.201 1.625320
  • Vallejo, G., Fernández, M.P., Livacic-Rojas, P.E., & Tuero-Herrero, E. (2011b). Selecting the best unbalanced repeated measures model. Behavior Research Methods, 43, 18-36. doi.org/10.3758/s13428-0100040-1
  • Vallejo, G., Moris, J., & Conejo, N. (2006). A SAS/IML program for implementing the modified Brown-Forsythe procedure in repeated measures designs. Computer Methods & Programs in Biomedicine, 83, 169-177. doi.org/10.1016/j.cmpb.2006.06.006
  • Van Ginkel, J.R., & Kroonenberg, P.M. (2014). Analysis of variance of multiply imputed data. Multivariate Behavioral Research, 49, 78-91. doi.org/10.1080/00273171.2013.855890
  • Weerahandi, S. (2004). Generalized Inference in Repeated Measures: Exact Methods in MANOVA and Mixed Models. New Jersey, NJ: John Wiley & Sons.
  • Xu, L.W. (2015). Parametric bootstrap approaches for two-way MANOVA with unequal cell sizes and unequal cell covariance matrices. Journal of Multivariate Analysis, 133, 291-303. doi.org/10.1016/j. jmva.2014.09.015