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Mokken’s scalability coefficients take values on the interval (−∞, 1]. The sampling distribution of scalability coefficients is skewed near the boundary, so Wald-based confidence intervals and significance tests may be biased. We introduce a transformation of the scalability coefficients and their standard errors, which can be used to construct range-preserving confidence intervals and significance tests. We demonstrated that for scalability coefficients away from the boundary, the properties of this range-preserving method are similar to the properties of the Wald-based method, but the range-preserving method outperforms the Wald-based method when the coefficient is close to unity. The range-preserving method can be applied to all types of scalability coefficients. Its implementation in software is discussed.

The thesis describes the multivariate analysis of randomized response data. Randomized response was introduced in 1965 as an interview technique to eliminate evasive response behavior (Warner, 1965). The questions are answered based on the outcome of a randomizer (a pair of dice, a deck of cards), so that the privacy of the respondents is protected. Research has shown that randomized response results in more valid answers than direct questions (van der Heijden et al., 2000 and Lensvelt-Mulders et al. 2005). During the past decade randomized response is used regularly by the Dutch administration to assess regulatory noncompliance. A well-known randomized response design is forced response (Boruch, 1971). In this design the respondent tosses two dice and answers the sensitive question based on the outcome of the two dice. If the outcome is 2, 3 or 4 the respondent has to answer is "yes", and if the outcome is 11 or 12, the respondents has to answer "no". If the outcome is 5, 6, 7, 8, 9 or 10, the respondents has answer truthfully. Since only respondent knows the outcome of the dice, confidentiality is ensured. Until recently randomized response was used to obtain a prevalence estimate of the sensitive behavior under study. Lately multivariate techniques have been developed to analyze the dependence of the sensitive behavior on other variables, like age, gender, education, etc. It has also become possible to analyze the associations between different sensitive behavior. The latest development is the estimation of self-protective response behavior, which occurs when respondents consistently give the non-sensitive response, irrespective the outcome of the randomizer. In this thesis four models for the multivariate analysis of randomized response data are presented. The models include the log-linear model, the proportional odds model, and two version of the zero-inflated Poisson model. Te models are applied to data from nationwide social welfare surveys that were conducted by the Dutch administration in the years 200, 200, 2004 and 2006.

The thesis describes the multivariate analysis of randomized response data. Randomized response was introduced in 1965 as an interview technique to eliminate evasive response behavior (Warner, 1965). The questions are answered based on the outcome of a randomizer (a pair of dice, a deck of cards), so that the privacy of the respondents is protected. Research has shown that randomized response results in more valid answers than direct questions (van der Heijden et al., 2000 and Lensvelt-Mulders et al. 2005). During the past decade randomized response is used regularly by the Dutch administration to assess regulatory noncompliance. A well-known randomized response design is forced response (Boruch, 1971). In this design the respondent tosses two dice and answers the sensitive question based on the outcome of the two dice. If the outcome is 2, 3 or 4 the respondent has to answer is "yes", and if the outcome is 11 or 12, the respondents has to answer "no". If the outcome is 5, 6, 7, 8, 9 or 10, the respondents has answer truthfully. Since only respondent knows the outcome of the dice, confidentiality is ensured. Until recently randomized response was used to obtain a prevalence estimate of the sensitive behavior under study. Lately multivariate techniques have been developed to analyze the dependence of the sensitive behavior on other variables, like age, gender, education, etc. It has also become possible to analyze the associations between different sensitive behavior. The latest development is the estimation of self-protective response behavior, which occurs when respondents consistently give the non-sensitive response, irrespective the outcome of the randomizer. In this thesis four models for the multivariate analysis of randomized response data are presented. The models include the log-linear model, the proportional odds model, and two version of the zero-inflated Poisson model. Te models are applied to data from nationwide social welfare surveys that were conducted by the Dutch administration in the years 200, 200, 2004 and 2006.