Bidimensional latent regression item response models for the assessment of financial knowledge in the presence of ‘Don’t Know’ responses

Increasing attention has been recently paid to assessing individuals’ financial competence. Financial knowledge appears as a complex and not directly observable phenomenon, whose measurement is usually based on answers to a set of multiple-choice items. The option ‘Don’t Know’ (DK) is usually included among the possible answers to capture uncertainty or lack of knowledge. Its presence represents an element of noise that can affect the measurement of financial knowledge. DK responses are usually considered as incorrect answers or missing values; however, these naive approaches may lead to biased financial knowledge measures. In this study, we address the issue of estimating the latent knowledge construct accounting for the DK option, through a bidimensional latent dregression two-parameter logistic model. The model at issue relies on the assumption that the response process may be disentangled in two consecutive steps driven by two latent variables: propensity to provide a substantive answer and financial knowledge. In the first step, both latent variables affect the probability of providing a substantive response. In the second step, conditionally on the selection of a substantive response, financial knowledge affects the probability of a correct answer vs. an incorrect one. Individual characteristics are also considered to explain the two latent traits.