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Consensus theory for mixed response formats. (English) Zbl 1416.62646
Summary: Measuring shared beliefs, expert consensus, or the details of a crime in eyewitness testimony represents a psychometric challenge. In expert interviews, for example, the correct responses representing the expert consensus (i.e., the answer key) are initially unknown and experts may differ in their contribution to this consensus. I propose the variable-response model, an extension of latent-trait models. The model allows the estimation of the answer key and the latent trait for continuous, categorical, or mixed responses. I describe some minimal requirements for the addition of new response formats to the model. I further propose a Markov chain Monte Carlo algorithm to estimate the model parameters. The results of a simulation study demonstrate that the algorithm accurately recovers the data-generating parameters. I also present an application of the variable-response model to the empirical data of a geography test. In this application, the parameter estimates correspond well with the true answer key.

MSC:
62P15 Applications of statistics to psychology
62D05 Sampling theory, sample surveys
Software:
R
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