ARTICLE
ABSTRACT
The purpose of this article is to account for informative sampling in fitting superpopulation model for multivariate observations, and in particular multivariate normal distribution, for longitudinal survey data. The idea behind the proposed approach is to extract the model holding for the sample data as a function of the model in the population and the first order inclusion probabilities, and then fit the sample model using maximum likelihood, pseudo maximum likelihood and estimating equations methods. As an application of the results, we fit the general linear model for longitudinal survey data under informative sampling using different covariance structures: the exponential correlation model, the uniform correlation model, and the random effect model, and using different conditional expectations of first order inclusion probabilities given the study variable. The main feature of the present estimators is their behaviours in terms of the informativeness parameters.
KEYWORDS
General Linear Model, Informative sampling, Longitudinal Survey Data, Maximum Likelihood , and Sample distribution.
REFERENCES
BIRNBAUM Z.W., PAULSON E., and ANDREWS F.C. (1950). On the Effect of Selection Performed on Some Coordinates of a Multi-Dimensional Population. Psychometrika, 15, pp 191-204.
CHAMBERS, R. and SKINNER, C. (2003). Analysis of Survey Data. New York: John Wiley.
DIGGLE, P. J., LIANG, K. Y, and ZEGER, S. L. (1994). Analysis of Longitudinal Data. Oxford: Science Publication.
EIDEH A.H. (2008). Estimation and Prediction of Random Effects Models for Longitudinal Survey Data under Informative Sampling. Statistics in Transition - New Series .Volume 9, Number 3, December 2008, pp 485-502.
EIDEH, A. H. and NATHAN, G. (2009). Two-Stage Informative Cluster Sampling with application in Small Area Estimation. Journal of Statistical Planning and Inference.139, pp 3088-3101.
EIDEH, A. H. and NATHAN, G. (2006) Fitting Time Series Models for Longitudinal Survey Data under Informative Sampling. Journal of Statistical Planning and Inference, 136, 3052-3069.
FAHRMEIR, L. and TUTZ, G. (2001). Multivariate statistical modeling based on generalized linear models, 2nd edn. New York: Springer.
HERRIOT, R.A., and KASPRZYK, D. (1984). The survey of income and program participation. American Statistical Association, Proceedings of the Social Statistics Section, pp.107-116.
HOEM, J.M. (1989). The issue of weights in panel surveys of individual behaviors. In Panel Surveys, (Eds.), Kasprzyk, D., Duncan, G.J., Kalton, G., and Singh, M.P., New York: Wiley, pp. 539-565.
LOHNSON, R.A., and WICHERN, D.W. (1998). Applied Multivariate Statistical Analysis, 4th edn. New Jersey: Prentice Hall.
KASPRZYK, D., DUNCAN, G.J, KALTON, G., and SINGH, M.P. (Eds.) (1989). Panel Surveys. New York: Wiley.
