A Linear Variable-θ Model for Measuring Individual Differences in Response Precision

Models for measuring individual response precision have been proposed for binary and graded responses. However, more continuous formats are quite common in personality measurement and are usually analyzed with the linear factor analysis model. This study extends the general Gaussian person-fluctuation model to the continuous-response case and develops a linear model: the Pseudo-Congeneric model. Two experimentally indistinguishable variants of the model are differentiated and discussed from a substantive point of view. At the applied level, the model is very simple and can be calibrated using standard factor analysis software. Estimation of person estimates (particularly individual fluctuation) is also very simple, and this allows for further developments that were quite difficult with previous models. All the proposals are illustrated using two empirical examples.