Derivation of metric scales from ordinal data with Guttman-Goode’s scaling

Psychometric methods have been argued to not be able to test the assumption that the underlying latent scale is really an interval scale. More specifically, the Rasch model was accused to provide an interval scale only because it fits measurement error, an issue known as the "Rasch paradox". Regardless of whether the Rasch paradox is real or not, it would be interesting to be able to derive interval, or even ratio, scales from ordinal data. The aim of the present study is to propose a procedure that combines the probabilistic Guttman scaling with Goode’s method to obtain either an interval or a ratio scale from dichotomous psychometric data. We present how the procedures are combined to derive the metric scales and how fit to the data can be calculated using RMSE. Final considerations note the limitations of the procedure, but also value its potentials.