This paper analyzes the sum score based (SSB) formulation of the Rasch model, where items and
sum scores of persons are considered as factors in a logit model. After reviewing the evolution leading to
the equality between their maximum likelihood estimates, the SSB model is then discussed from the point
of view of pseudo-likelihood and of misspecified models. This is then employed to provide new insights
into the origin of the known inconsistency of the difficulty parameter estimates in the Rasch model. The
main results consist of exact relationships between the estimated standard errors for both models; and, for
the ability parameters, an upper bound for the estimated standard errors of the Rasch model in terms of
those for the SSB model, which are more easily available.