The Effects of Sample Size in Multilevel Models via Sub-sampling Approach

Authors

1 University Lecturer / Tarbiat Modares University

2 Tarbiat Modares University

Abstract

There are numerous research topics in different fields of study including social, medical, and agricultural sciences which contain data having intra-class correlation structure. For such data, simple linear regression models do not have acceptable applicability since they do not consider the correlation involved. Models which are suitable for data of this kind are called 'multilevel' models. Determining appropriate sample size at different levels in multilevel models is among the issues which has attracted the interest of researchers in applied sciences. In the present study, taking a sub-sampling method approach, the influence of different sizes of the sample size at the first and second levels on the estimation of fixed and random effects was studied. Furthermore, due to the close relation between determining sample size and the power of the statistical test related to the parameters under study, and also due to other factors such as design effect and significance level, different design sizes were evaluated using simulation. Results of the study indicate that increasing sample size at the second level of the two-level model increases the power of the statistical test related to the calculation of the fixed and random effects.

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References

[1] Cohen, M. (1998), Determining Sample Size for Surveys with Data Analyzed by Hierarchical Linear Models, Journal of Official Statistics, 14, 267-257. [2] Goldstein, H. (2010), Multilevel Statistical Models, (4th ed), Chichester: John Wiley and Sons. [3] Browne, W. J, Golalizadeh, M. and Parker, R. (2009), A Guide to Sample Size Calculations for Random Effect Models via
Simulation and MLPowSim Software Package, Bristol University Press, Bristol. [4] Longford, N.T. (1987), A First Scoring Algorithm for Maximum Likelihood Estimation in Unbalanced Mixed Models with Nested Effects, Biometrika, 74, 812-827. [5] Goldstein, H. and Silver, R. (1989), Multilevel and Multivariate Models in Survey Analysis, In Skinner, C. J, Holt, D. and Smith, T. M. F (ed.),
Analysis of Complex Surveys, 221-235. New York: John Wiley and Sons. [6] Snijder, T.A.B. and Bosker, R.J. (1993), Standard
Errors and Sample Size for Two-Level Research, Journal of Educational Statistics, 18, 237-259. [7] Snijder, T.A.B. and Bosker, R.J. (1999), Multilevel Analysis: An Introduction to Basic and Advanced Multilevel Modeling Multilevel StatisticalModels, Sage Publications: London. [8] Afshartous, D. (1995), Determination of Sample Size for Multilevel Model Design, Paper Presented at
the AERA meeting in San Francisco,

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History

  • Receive Date: 22 June 2013
  • Revise Date: 09 October 2013
  • Accept Date: 21 November 2013

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