Abstract
In this paper, we present an algorithm suitable for analysing the variance of panel data when some observations are either given in grouped form or are missed. The analysis is carried out from the perspective of ANOVA panel data models with general errors. The classification intervals of the grouped observations may vary from one to another, thus the missing observations are in fact a particular case of grouping. The proposed Algorithm (1) estimates the parameters of the panel data models; (2) evaluates the covariance matrices of the asymptotic distribution of the time-dependent parameters assuming that the number of time periods, T, is fixed and the number of individuals, N, tends to infinity and similarly, of the individual parameters when T → ∞ and N is fixed; and, finally, (3) uses these asymptotic covariance matrix estimations to analyse the variance of the panel data.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
An MY (1998) Logconcavity versus logconvexity: a complete characterization. J Econ Theory 80: 350–369
Baltagi BH (1995) Econometric analysis of panel data. Wiley, New York
Dempster AP, Laird NM, Rubin DB (1977) Maximum likelihood from incomplete data via the EM algorithm. J R Stat Soc 39(B): 1–22
Healy MJR, Westmacott M (1956) Missing values in experiments analysed on automatic computers. Appl Stat 5: 203–206
Hsiao C (2003) Analysis of panel data. Cambridge University Press, Cambridge
Laha RG, Rohatgi VK (1979) Probability theory. Wiley, New York
Lange K (1999) Numerical analysis for statistician. Springer, Berlin
Little RJA, Rubin DB (1987) Statistical analysis with missing data. Wiley, New York
Louis TA (1982) Finding observed information using the EM algorithm. J R Stat Soc 44(B): 98–130
McLachlan GJ, Krishnan T (1997) The EM algorithm and extensions. Wiley, New York
Meilijson I (1989) A fast improvement of the EM algorithm on its own terms. J R Stat Soc 51(B): 127–138
Orchard T, Woodbury MA (1972) A missing information principle: theory and applications. In: Proceedings of the sixth berkeley symposium on mathematical statistics and probability. University of California Press, Berkeley, pp 697–715
Meng XL, Rubin DB (1991) Using EM to obtain asymptotic variance-covariance matrices. J Am Stat Assoc 86: 899–909
Tanner MA (1993) Tools for statistical inference Methods for the exploration of posterior distributions and likelihood functions. Springer, Berlin
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Anido, C., Rivero, C. & Valdes, T. An algorithm for panel ANOVA with grouped data. Metrika 74, 85–107 (2011). https://doi.org/10.1007/s00184-009-0291-y
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00184-009-0291-y