Compensatory and non-compensatory multidimensional randomized item response models.

Randomized response (RR) models are often used for analysing univariate randomized response data and measuring population prevalence of sensitive behaviours. There is much empirical support for the belief that RR methods improve the cooperation of the respondents. Recently, RR models have been extended to measure individual unidimensional behaviour. An extension of this modelling framework is proposed to measure compensatory or non-compensatory multiple sensitive factors underlying the randomized item response process. A confirmatory multidimensional randomized item response theory model (MRIRT) is proposed for the analysis of multivariate RR data by modelling the response process and specifying structural relationships between sensitive behaviours and background information. A Markov chain Monte Carlo algorithm is developed to estimate simultaneously the parameters of the MRIRT model. The model extension enables the computation of individual true item response probabilities, estimates of individuals' sensitive behaviour on different domains, and their relationships with background variables. An MRIRT analysis is presented of data from a college alcohol problem scale, measuring alcohol-related socio-emotional and community problems, and alcohol expectancy questionnaire, measuring alcohol-related sexual enhancement expectancies. Students were interviewed via direct or RR questioning. Scores of alcohol-related problems and expectancies are significantly higher for the group of students questioned using the RR technique. Alcohol-related problems and sexual enhancement expectancies are positively moderately correlated and vary differently across gender and universities.

The dirichlet-multinomial model for multivariate randomized response data and small samples

In survey sampling the randomized response (RR) technique can be used to obtain truthful answers to sensitive questions. Although the individual answers are masked due to the RR technique, individual (sensitive) response rates can be estimated when observing multivariate response data. The beta-binomial model for binary RR data will be generalized to handle multivariate categorical RR data. The Dirichlet- multinomial model for categorical RR data is extended with a linear transformation of the masked individual categorical-response rates to correct for the RR design and to retrieve the sensitive categorical-response rates even for small data samples. This specification of the Dirichlet- multinomial model enables a straightforward empirical Bayes estimation of the model parameters. A constrained-Dirichlet prior will be introduced to identify homogeneity restrictions in response rates across persons and/or categories. The performance of the full Bayes parameter estimation method is verified using simulated data. The proposed model will be applied to the college alcohol problem scale study, where students were interviewed directly or interviewed via the randomized response technique about negative consequences from drinking(AU)