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Multilevel analysis is an appropriate tool for the analysis of hierarchically structured data. There may, however, be reasons to ignore one of the levels of nesting in the data analysis. In this article a three level model with one predictor variable is used as a reference model and the top or intermediate level is ignored in the data analysis. Analytical results show that this has an effect on the estimated variance components and that standard errors of regression coefficients estimators may be overestimated, leading to a lower power of the test of the effect of the predictor variable. The magnitude of these results depends on the ignored level and the level at which the predictor variable varies, and on the values of the variance components and the sample sizes.

This article deals with optimal sample sizes for experimental studies with individuals nested within clusters. Examples are multicenter clinical trials with patients nested within clinics or family practices, studies on absence due to illness with employees nested within work sites, or school-based smoking prevention interventions with pupils nested within schools. Optimal sample sizes are given for models with continuous or binary outcomes and for 1 or 2 treatment factors. Because individuals are nested within clusters, not only the total number of individuals needed to obtain a specified power of the test of treatment effect has to be established but also the number of clusters and the number of individuals per cluster. We show that different outcome variables lead to different optimal sample sizes. Furthermore, the statistically optimal design is not always feasible in practice because of certain limitations, and we show how to calculate the optimal design given restrictions on the sample sizes at both...

To predict macrofaunal community composition from environmental data a two-step approach is often followed: (1) the water samples are clustered into groups on the basis of the macrofauna data and (2) the groups are related to the environmental data, e.g. by discriminant analysis. For the cluster analysis in step 1 many hard, seemingly arbitrary choices have to be made that nevertheless influence the solution (similarity measure, clustering strategy, number of clusters). The stability of the solution is often of concern, e.g. in clustering by the twinspan program. In the discriminant analysis of step 2 it can occur that a water sample is misclassified on the basis of the environmental data but on further inspection happens to be a borderline case in the cluster analysis. One would then rather reclassify such a sample and iterate the two steps. Bayesian latent class analysis is a flexible, extendable model-based cluster analysis approach that recently has gained popularity in the statistical literature and that has the potential to address these problems. It allows the macrofauna and environmental data to be modelled and analyzed in a single integrated analysis. An exciting extension is to incorporate in the analysis prior information on the habitat preferences of the macrofauna taxa such as is available in lists of indicator values. The output of the analysis is not a hard assignment of water samples to clusters but a probabilistic (fuzzy) assignment. The number of clusters is determined on the basis of the Bayes factor. A standard feature of the Bayesian method is to make predictions and to assess their uncertainty. We applied this approach to a data set consisting of 70 water samples, 484 macrofauna taxa and four environmental variables for which previously a five cluster solution had been proposed. The standard for Bayesian estimation, the Gibbs sampler, worked fine on a subset with only 12 selected taxa but did not converge on the full set with 484 taxa. This is due to many configurations in which the assignment probabilities are all very close to either 0 or 1. This convergence problem is comparable with the local optima problem in classical cluster optimization algorithms, including the EM algorithm used in Latent Gold, a Windows program for latent class analysis. The convergence problem needs to be solved before the benefits of Bayesian latent class analysis can come to fruition in this application. We discuss possible solutions.

The subject of this thesis is the analysis of randomized response (RR) data and the analysis of data that are subject to the post randomization method (PRAM). RR is an interview technique that can be used when sensitive questions have to be asked and respondents are reluctant to answer directly. RR variables can be seen as misclassified categorical variables where conditional misclassification probabilities are known. The misclassification protects the privacy of the individual respondent. The idea of RR can also be used to protect data that have already been collected. PRAM can be seen as an application of RR where the misclassification is applied using a computer. The thesis investigates how statistical models such as the log-linear model and the linear regression model should be adapted to take the misclassification into account. In addition, measures of disclosure risk are discussed when PRAM is applied.

The subject of this thesis is the analysis of randomized response (RR) data and the analysis of data that are subject to the post randomization method (PRAM). RR is an interview technique that can be used when sensitive questions have to be asked and respondents are reluctant to answer directly. RR variables can be seen as misclassified categorical variables where conditional misclassification probabilities are known. The misclassification protects the privacy of the individual respondent. The idea of RR can also be used to protect data that have already been collected. PRAM can be seen as an application of RR where the misclassification is applied using a computer. The thesis investigates how statistical models such as the log-linear model and the linear regression model should be adapted to take the misclassification into account. In addition, measures of disclosure risk are discussed when PRAM is applied.

Various methods exist to calculate confidence intervals for the benchmark dose in risk analysis. This study compares the performance of three such methods in fitting nonlinear dose-response models: the delta method, the likelihood-ratio method, and the bootstrap method. A data set from a developmental toxicity test with continuous, ordinal, and quantal dose-response data is used for the comparison of these methods. Nonlinear dose-response models, with various shapes, were fitted to these data. The results indicate that a few thousand runs are generally needed to get stable confidence limits when using the bootstrap method. Further, the bootstrap and the likelihood-ratio method were found to give fairly similar results. The delta method, however, resulted in some cases in different (usually narrower) intervals, and appears unreliable for nonlinear dose-response models. Since the bootstrap method is more time consuming than the likelihood-ratio method, the latter is more attractive for routine dose-response analysis. In the context of a probabilistic risk assessment the bootstrap method has the advantage that it directly links to Monte Carlo analysis.

This study aimed at comparing the stability of three methods for two-dimensional sociometric status determination, including (1) the recently developed SSrat technique (Maassen, Akkermans, & Van der Linden, 1996), as well as (2) the procedure of Howes (1988), which is based on the algorithm and classification criteria of Coie and Dodge (1983), and (3) a procedure applied by Cillessen, van IJzendoorn, Van Lieshout, and Hartup (1992) based on the algorithm and criteria of Newcomb and Bukowski (1983). The latter two techniques can be regarded as nomination methods eliciting unlimited numbers of nominations from the participants. In the present study, 83 pupils (ages ranging from 5.8 to 8.8 years) participated in the 3-point rating procedure of Asher, Singleton, Tinsley, and Hymel (1979). They were asked to rate how much they liked to play with each of their classmates. The ratings data were processed in three ways according to the methods mentioned above. The techniques of Howes and of Cillessen et al. showed higher stability than previously ever reported using the nomination procedures of Coie and Dodge or Newcomb and Bukowski. Nevertheless, the rating scale procedure SSrat proved to have even higher stability.

The sub-scales of the SF-36 in the Dutch National Study are investigated with respect to unidimensionality and reliability. It is argued that these properties deserve separate treatment. For unidimensionality we use a non-parametric model from item response theory, called the Mokken scaling model, and compute the corresponding scalability coefficients. We estimate reliability under the Mokken model, assuming that the items are double homogeneous, and compare it to Cronbach's α. The scalability of the sub-scale general health perceptions is medium (H = 0.46), and for the other sub-scales it is strong (H ≥ 0.6). The reliability in terms of α indicates that all sub-scales can be used in basic research (α > 0.70), but that only physical functioning can be used for clinical applications of quality of life (α > 0.90). The relative merits of our approach are discussed.