Abstract
Misspecification effects (meffs) measure the effect on the sampling variance of an estimator of incorrect specification of both the sampling scheme and the model considered. We assess the effect of various features of complex sampling schemes on the inferences drawn from models for panel data using meffs. Many longitudinal social survey designs employ multistage sampling, leading to some clustering, which tends to lead to meffs greater than unity. An empirical study using data from the British Household Panel Survey is conducted, and a simulation study is performed. Our results suggest that clustering impacts are stronger for longitudinal studies than for cross-sectional studies, and that meffs for the regression coefficients increase with the number of waves analysed. Hence, estimated standard errors in the analysis of panel data can be misleading if any clustering is ignored.
References
1.
Binder, D.A. 1983. “On the Variances of Asymptotically Normal Estimators from Complex Surveys.” International Statistical Review 51: 279–292. Doi: https://dx-doi-org.web.bisu.edu.cn/10.2307/1402588.
2.
Binder, D.A. and G.R. Roberts. 2003. “Design-Based and Model-Based Methods for Estimating Model Parameters.” In Analysis of Survey Data , edited by R.L. Chambers and C.J. Skinner. 29–48. Chichester: Wiley.
3.
Chambers, R.L. and C.J. Skinner. 2003. Analysis of Survey Data . Chichester: Wiley.
4.
Diggle, P.J., P. Heagerty, K. Liang, and S.L. Zeger. 2002. Analysis of Longitudinal Data , 2nd ed. Oxford: Oxford University Press.
5.
Feder, M., “Fitting Regression Models to Complex Survey Data – Gelman’s Estimator Revisited.” International Statistical Institute, Proceedings of the 58th World Statistical Congress, Session CPS028, 21–26 August 2011, Dublin, Ireland. Available at: http://2011.isiproceedings.org/ (accessed January 2016).
6.
Feder, M., G. Nathan, and D. Pfeffermann. 2000. “Multilevel Modelling of Complex Survey Longitudinal Data with Time Varying Random Effects.” Survey Methodology 26: 53–65.
7.
Fitzmaurice, G.M., M.N. Laird, and J.H. Ware. 2004. Applied Longitudinal Analysis . Hoboken, NJ: Wiley.
8.
Holt, D. and A.J. Scott. 1981. “Regression Analysis Using Survey Data.” The Statistician 30: 169–178. Doi: https://dx-doi-org.web.bisu.edu.cn/10.2307/2988047.
9.
Kish, L. and M.R. Frankel. 1974. “Inference from Complex Samples.” Journal of the Royal Statistical Society, Series B 36: 1–37.
10.
Liang, K. and S.L. Zeger. 1986. “Longitudinal Data Analysis Using Generalized Linear Models.” Biometrika 73: 13–22. Doi: https://dx-doi-org.web.bisu.edu.cn/10.1093/biomet/73.1.13.
11.
Lynn, P. and D. Lievesley. 1991. Drawing General Population Samples in Great Britain . London: Social and Community Planning Research.
12.
Nathan, G. and D. Holt. 1980. “The Effect of Survey Design on Regression Analysis.” Journal of the Royal Statistical Society, Series B 42: 377–386.
13.
Pfeffermann, D. 2011. “Modelling of Complex Survey Data: Why is it a Problem? How Should We Approach It?” Survey Methodology 37: 115–136.
14.
Roberts, G., Q. Ren, and J.N.K. Rao. 2009. “Using Marginal Mean Models for Data from Longitudinal Surveys with a Complex Design: Some Advances in Methods.” In Methodology of Longitudinal Surveys , edited by P. Lynn. 351–366. Chichester: Wiley.
15.
Salgueiro, M.F., P.W.F. Smith, and M.D.T. Vieira. 2013. “A Multi-Process Second-Order Latent Growth Curve Model for Subjective Well-Being.” Quality and Quantity 47: 735–752. Doi: https://dx-doi-org.web.bisu.edu.cn/10.1007/s11135-011-9541-y.
16.
Scott, A.J. and D. Holt. 1982. “The Effect of Two-Stage Sampling on Ordinary Least Squares Methods.” Journal of the American Statistical Association 77: 848–854. Doi: https://dx-doi-org.web.bisu.edu.cn/10.1080/01621459.1982.10477897.
17.
Skinner, C.J. 1986. “Design Effects of Two-Stage Sampling.” Journal of the Royal Statististical Society, Series B 48: 89–99.
18.
Skinner, C.J. 1989a. “Introduction to Part A.” In Analysis of Complex Surveys , edited by C.J. Skinner, D. Holt, and T.M.F. Smith. 23–58. Chichester: Wiley.
19.
Skinner, C.J. 1989b. “Domain Means, Regression and Multivariate Analysis.” In Analysis of Complex Surveys , edited by C.J. Skinner, D. Holt, and T.M.F. Smith. 59–87. Chichester: Wiley.
20.
Skinner, C.J. and D. Holmes. 2003. “Random Effects Models for Longitudinal Survey Data.” In Analysis of Survey Data , edited by R.L. Chambers and C.J. Skinner. 205–219. Chichester: Wiley.
21.
Skinner, C.J., D. Holt, and T.M.F. Smith. 1989. Analysis of Complex Surveys . Chichester: Wiley.
22.
Skinner, C. and M.D.T. Vieira. 2007. “Variance Estimation in the Analysis of Clustered Longitudinal Survey Data.” Survey Methodology 33: 3–12.
23.
Smith, P., P. Lynn, and D. Elliot. 2009. “Sample Design for Longitudinal Surveys.” In Methodology of Longitudinal Surveys , edited by P. Lynn. 21–33. Chichester: Wiley.
24.
Sutradhar, B.C. and M. Kovacevic. 2000. “Analysing Ordinal Longitudinal Survey Data: Generalised Estimating Equations Approach.” Biometrik 87: 837–848. Doi: https://dx-doi-org.web.bisu.edu.cn/10.1093/biomet/87.4.837.
25.
Taylor, M.F. (ed.), J. Brice, N. Buck, and E. Prentice-Lane. 2010. British Household Panel Survey User Manual Volume A: Introduction, Technical Report and Appendices . Colchester: University of Essex.
26.
UK Data Service. UK Data Service . Available at: http://ukdataservice.ac.uk (accessed January 2016).
27.
Vieira, M.D.T. 2009. Analysis of Longitudinal Survey Data , 1st ed. Saarbrücken: VDM Verlag.
28.
Vieira, M.D.T. and C.J. Skinner. 2008. “Estimating Models for Panel Survey Data under Complex Sampling.” Journal of Official Statistics 24: 343–364.