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An important problem in multilevel modeling is what constitutes a sufficient sample size for accurate estimation. In multilevel analysis, the major restriction is often the higher-level sample size. In this paper, a simulation study is used to determine the influence of different sample sizes at the group level on the accuracy of the estimates (regression coefficients and variances) and their standard errors. In addition, the influence of other factors, such as the lowest-level sample size and different variance distributions between the levels (different intraclass correlations), is examined. The results show that only a small sample size at level two (meaning a sample of 50 or less) leads to biased estimates of the second-level standard errors. In all of the other simulated conditions the estimates of the regression coefficients, the...
A multilevel problem concerns a population with a hierarchical structure. A sample from such a population can be described as a multistage sample. First, a sample of higher level units is drawn (e.g. schools or organizations), and next a sample of the sub-units from the available units (e.g. pupils in schools or employees in organizations). In such samples, the individual observations are in general not completely independent. Multilevel analysis software accounts for this dependence and in recent years these programs have been widely accepted. Two problems that occur in the practice of multilevel modeling will be discussed. The first problem is the choice of the sample sizes at the different levels. What are sufficient sample sizes for accurate estimation? The second problem is the normality assumption of the level-2 error distributio...
Hierarchical structured data cause problems in analysis, because the usual assumptions of independently and identically distributed variables are violated. Muthn (1989) described an estimation method for multilevel factor and path analysis with hierarchical data. This article assesses the robustness of the method with unequal groups, small sample sizes at both the individual and the group level, in the presence of a low or a high intraclass correlation (ICC). The within-groups part of the model poses no problems. The most important problem in the between-groups part of the model is the occurrence of inadmissible estimates, especially when group level sample size is small (50) while the intracluster correlation is low. This is partly compensated by using large group sizes. When an admissible solution is reached, the factor loadings are ...
Many experiments aim at populations with persons nested within clusters. In the design stage of such experiments one has to decide whether to randomize complete clusters or persons within clusters to treatment conditions. Furthermore, the optimal sample sizes have to be calculated. In this article these two design issues will be dealt with for logistic models with a binary treatment condition and a binary covariate. The multilevel model is used to relate treatment condition and the covariate to the binary outcome. The optimal design is analytically derived for first order Marginal Quasi Likelihood (MQL) by linearizing the model using a Taylor series expansion. A simulation study shows results for second order Penalized Quasi Likelihood, (PQL), which is known to produce less biased estimates. The results show that person level randomiza...
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