The IRT model that fits the data determines the score rule of the measurement instrument. If, for instance, a one-parameter model does not fit the data, but a two-parameter model does, the sum score where the items scores are weighted with their respective discrimination parameters is a sufficient statistic for θj (Lord and Novick 1968). So some items can be more important or sensitive indicators of a trait than others. Modelling the item data in a variance decomposition analysis allows the separate evaluation of model fit regarding the measurement model and the variance decomposition model.
