The Individual True and Error Model: Getting the Most out of Limited Data

True and Error Theory (TET) is a modern latent variable modeling approach for analyzing sets of preferences held by people. Individual True and Error Theory (iTET) allows researchers to estimate the proportion of the time an individual truly holds a particular underlying set of preferences without assuming complete response independence in a repeated measures experimental design. iTET is thus suitable for investigating research questions such as whether an individual ever is truly intransitive in their preferences (i.e. they prefer a to b, b to c, and c to a). While current iTET analysis methods provide the means of investigating such questions they require a lot of data to achieve satisfactory power for hypothesis tests of interest. This paper overviews the performance and shortcomings of the current analysis methods in efficiently utilizing data, while providing new analysis methods that offer substantial gains in power and efficiency.