Summary
In longitudinal research studies, the allocation and selection of the number of time points will influence the variance of the estimated model parameters. Optimal designs for fixed effects models with uncorrelated errors are well documented in the statistical literature. In this paper optimal designs will be discussed for mixed effects models. Optimal designs for mixed effects models are only locally optimal, i.e. for a fixed combination of parameter values. Another problem is that optimal designs depend on the specified model. To circumvent both the local optimality problem and the dependency on the specified model, we propose to apply a maximin procedure. The results show that it is possible to find maximin designs that are highly efficient for a variety of parameter values and different models.
This is a preview of subscription content, log in via an institution to check access.
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
Abt, M., Liski, E.P., Mandai, N.K. and Sinha, B. K. (1997). Correlated model for linear growth: Optimal designs for slope parameter estimation and growth prediction. Journal of Statistical Planning and Inference, 64, 141–150.
Atkins, J.E. and Cheng, C.S. (1999). Optimal regression designs in the presence of random block effects. Journal of Statistical Planning and Inference, 77, 321–335.
Atkinson, A.C. and Donev, A.N. (1996). Optimum experimental designs. Oxford: Clarendon Press.
Berger, M.P.F., King, C.Y., and Wong, W.K. (2000). Minimax D-optimal designs for item response theory models. Psychometrika, 65, 377–390.
Bischoff, W. (1993). On D-optimal designs for linear models under correlated observations with an application to a linear model with multiple response. Journal of Statistical Planning and Inference, 37, 69–80.
Bunke, H. and Bunke O. (1986). Statistical inference in lineair models. New York: John Wiley.
Diggle, P.J., Liang, K.-Y.,and Zeger, S.L. (1994). Analysis of longitudinal data. Oxford: Clarendon Press.
Federov, V.V. (1980). Convex design theory. Mathematische Operations Forschung und Statistics. Series Statistics, 11, 403–413.
Mentré, F., Mallet, A. and Baccar, D. (1997). Optimal design in random effect regression models. Biometrika, 84, 429–442.
Moerbeek, M. Van Breukelen, G.J.P. and Berger, M.P.F. (2001). Optimal experimental designs for multilevel models with covariates. Communications in Statistics, Theory and Methods, 30, 12, 2683–2697.
Ouwens, J.N.M., Tan, F.E.S. and Berger, M.P.F. (2001). On the maximin designs for logistic random effects models with covariates. In B. Klein and L. Korshom (Eds.), New trends in Statistical Modelling. ( The Proceedings of the 16th International Workshop on Statistical modelling, Odense, Denmark, pp. 321–328 ).
Tan, F.E.S. and Berger, M.P.F. (1999). Optimal allocation of time points for the random effects model. Communications in Statistics, Simulation and Computation, 28, 517–540.
Wong, W.K. (1992). A unified approach to the construction of minimax designs. Biometrika, 79, 611–619.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2003 Springer Japan
About this paper
Cite this paper
Berger, M.P.F., Ouwens, M.J.N.M., Tan, F.E.S. (2003). Robust designs for longitudinal mixed effects models. In: Yanai, H., Okada, A., Shigemasu, K., Kano, Y., Meulman, J.J. (eds) New Developments in Psychometrics. Springer, Tokyo. https://doi.org/10.1007/978-4-431-66996-8_38
Download citation
DOI: https://doi.org/10.1007/978-4-431-66996-8_38
Publisher Name: Springer, Tokyo
Print ISBN: 978-4-431-66998-2
Online ISBN: 978-4-431-66996-8
eBook Packages: Springer Book Archive