Multilevel modelling of complex survey longitudinal data with time varying random effects

Longitudinal observations consist of repeated measurements on the same units over a number of occasions, with fixed or varying time spells between the occasions. Each vector observation can be viewed therefore as a time series, usually of short length. Analyzing the measurements for all the units permits the fitting of low-order time series models, despite the short lengths of the individual series. We illustrate this paradigm using simulated data that follow the rotation scheme of the Israel Labor Force Survey (LFS). This survey employs a rotating panel sampling scheme of two quarters in the sample, two quarters out of the sample and then two quarters in again. The model consists of two-level linear models for single time points that are connected by allowing the second level effects (corresponding to households) and the first level residuals (corresponding to individuals) to evolve stochastically over time. The likelihood of the model is easily constructed by employing the time series properties of the combined model. However, in view of the large number of unknown parameters, direct maximization of the likelihood could yield unstable estimators. Therefore, a two-stage procedure is adopted. At the first stage, a separate two-level model is fitted for each time point, thus yielding estimators for the fixed effects and the variances. At the second stage, the time series likelihood is maximized only with respect to the time series model parameters. This two-stage procedure has the further advantage of permitting appropriate first and second level weighting to account for possible informative sampling effects. Empirical results when fitting the model to data collected by the Israel LFS are also presented

[1]  Malcolm Hill,et al.  The Panel Study of Income Dynamics , 1991 .

[2]  Aldo V. Vecchia,et al.  Fitting Continuous ARMA Models to Unequally Spaced Spatial Data , 1993 .

[3]  Richard H. Jones,et al.  Serial correlation in unequally spaced longitudinal data , 1990 .

[4]  Richard H. Jones.  Longitudinal data with serial correlation , 1993 .

[5]  G. Tunnicliffe Wilson,et al.  Parameterization of continuous time autoregressive models for irregularly sampled time series data , 1994 .

[6]  R. P. Chakrabarty,et al.  SURVEY OF INCOME AND PROGRAM PARTICIPATION , 1990 .

[7]  Dale L. Zimmerman,et al.  Structured Antedependence Models for Longitudinal Data , 1997 .

[8]  P. Diggle.  Analysis of Longitudinal Data , 1995 .

[9]  D. Binder.  On the variances of asymptotically normal estimators from complex surveys , 1983 .

[10]  Richard H. Jones,et al.  Longitudinal Data with Serial Correlation : A State-Space Approach , 1994 .

[11]  R. H. Jones,et al.  Unequally spaced longitudinal data with AR(1) serial correlation. , 1991, Biometrics.

[12]  Chris J. Skinner,et al.  Analysis of complex surveys , 1991 .

[13]  R. Day,et al.  Empirical Bayes Analysis for Systems of Mixed Models with Linked Autocorrelated Random Effects , 1991 .

[14]  D. Pfeffermann,et al.  The use of sampling weights for survey data analysis , 1996, Statistical methods in medical research.

[15]  Greg J. Duncan,et al.  Issues of design and analysis of surveys across time , 1987 .

[16]  H Goldstein,et al.  Multilevel time series models with applications to repeated measures data. , 1994, Statistics in medicine.

[17]  Andrew Harvey,et al.  Forecasting, Structural Time Series Models and the Kalman Filter , 1990 .

[18]  J. N. K. Rao,et al.  Some recent advances in model-based small area estimation , 1999 .

[19]  H. Goldstein.  Multilevel Statistical Models , 2006 .

[20]  David A. Harville,et al.  Best Linear Recursive Estimation for Mixed Linear Models , 1981 .