Summary
A mixed-effects multivariate adaptive splines model is presented for analyzing longitudinal or growth curves data that may or may not have been collected through a regular measurement schedule. The MASAL (an acronym for multivariate adaptive splines for the analysis of longitudinal data) algorithm by Zhang [19, 20, 21] is used to determine the nonparametric fixed-effects in the mixed-effects multivariate adaptive splines model. The original MASAL algorithm requires the characterization and specification of the within subject autocorrelation structure, which is usually a tedious while not always rewarding process. In contrast, the idea of mixed-effects is introduced to the MASAL algorithm in this work, leading to an automated procedure for analysis of longitudinal and growth curves data. To demonstrate the great potential of this new procedure, I re-analyzed a data set on the effect of cocaine use by pregnant women on the growth of their infants after birth. The numerical results are remarkable as opposed to a previously published analysis by [21] in terms of the dissection of random effects.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Altman, N. S. (1992). An iterated Cochrane-Orcutt procedure for nonparametric regression. Journal of Statistical Computation and Simulation 40, 93–108.
Carlin, B.P. and Louis, T.A. (1996) Bayes and Empirical Bayes Methods for Data Analysis, New York: Chapman and Hall.
Crowder, M. J. and Hand, D. J. (1991). Analysis of Repeated Measures, New York: Chapman and Hall.
Diggle, P.J., Liang, K.Y., and Zeger, S.L. (1994). Analysis of Longitudinal Data. New York: Oxford University Press, Inc.
Efron, B. and Tibshirani, R. (1993) An Introduction to the Bootstrap, Chapman and Hall, New York.
Fan, J. and Lin, S.K. (1998) “Test of significance when data are curves,” Journal of the American Statistical Association, 93, 1007–1021.
Friedman, J. H. (1991). Multivariate adaptive regression splines. The Annals of Statistics 19, 1–141.
Hoover, D.R., Rice, J.A., Wu, CO., and Yang, L.P. (1998). Nonparametric smoothing estimates of time-varying coefficient models with longitudinal data. Biometrika 85, 809–822.
Laird, N.M. and Ware, J.H. (1982). Random-effects models for longitudinal data. Biometrics 38, 963–974.
Lin, D.Y. and Ying, Z. (2000). Semiparametric and nonparametric regression analysis of longitudinal data. Journal of the American Statistical Association, in press.
Lin, X.H. and Carroll, R.J. (2000). Nonparametric function estimation for clustered data when the predictor is measured without/with error. Journal of the American Statistical Association 95, 520–534.
Meredith, W. and Tisak, J. (1990). Latent curve analysis. Psychometrika, 55, 107–122.
Neider, J.A. and Mead, R. (1965) A simplex method for function minimisation. The Computer Journal 7, 303–313.
Robinson, G.K. (1991) That BLUP is a good thing: The estimation of random effects. Statistical Science, 6, 15–51.
Stier, D.M., Leventhal, J.M., Berg, A.T., Johnson, L., and Mezger, J. (1993). Are children born to young mothers at increased risk of maltreatment? Pediatrics 91, 642–648.
Truong, Y. K. (1991). Nonparametric curve estimation with time series errors. Journal of Statistical Planning and Inference 28, 167–183.
Wasserman, D.R. and Leventhal, J.M. (1993). Maltreatment of children born to cocaine-dependent mothers. American Journal of Diseases of Children 147, 1324–1328.
Zeger, S.L. and Diggle, P.J. (1994). Semi-parametric models for longitudinal data with application to CD4 cell numbers in HIV seroconverters. Biometrics 50, 689–699.
Zhang, H. P. (1994). Maximal correlation and adaptive splines. Technometrics 36, 196–201.
Zhang, H. P. (1997). Multivariate adaptive splines for the analysis of longitudinal data. Journal of Computational and Graphical Statistics 6, 74–91.
Zhang, H. P. (1999). Analysis of infant growth curves using multivariate adaptive splines. Biometrics 55, 452–459.
Zhang, H. P. (2000). Mixed-effects multivariate adaptive splines models. Amer. Statist. Assoc. 2000 Proceedings of the Biometrics Section, 20-29.
Zhang, H. P. and Singer, B. (1999). Recursive Partitioning in the Health Sciences, Springer, New York.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer Science+Business Media New York
About this chapter
Cite this chapter
Zhang, H. (2003). Mixed-Effects Multivariate Adaptive Splines Models. In: Denison, D.D., Hansen, M.H., Holmes, C.C., Mallick, B., Yu, B. (eds) Nonlinear Estimation and Classification. Lecture Notes in Statistics, vol 171. Springer, New York, NY. https://doi.org/10.1007/978-0-387-21579-2_18
Download citation
DOI: https://doi.org/10.1007/978-0-387-21579-2_18
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-95471-4
Online ISBN: 978-0-387-21579-2
eBook Packages: Springer Book Archive