4. Each essay rating is multiplied by 10, and then the rescaled 0-100 essay ratings are analyzed with the MCQ items. Since onlyevery 10th category of the 0-100 essay rating scale is observed,the analysis must allow for structurally present, but empiricallyabsent, categories (Wilson RMT 5:1 p. 128). Again, standard errorswill need to be inflated about 75% due to the effect of thefictitious categories. Only one essay difficulty will be reported,but it will not be at the same location on the variable as the 0-10essay would have been. By convention, the difficulty of a ratingscale item is chosen so that the sum of the step difficulties iszero, i.e., at the location on the variable where the highest andlowest possible ratings on the item are equally probable. If thedifficulty of the 0-10 essay item is D logits from the center ofthe person ability distribution, the difficulty of the 0-100 essayitem will be much closer to the mean ability, only about D/10logits away. This makes the construct harder to understand, andcan be confusing if the assigned weights are changed.
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