This study is interesting that the extreme response style is modeled into the multidimensional item response probability. It fixes the slop parameter to represent the extreme response properties. In the section illustrating Real PISA Science data, we can see the model three (two substantive trait and one ERS theta fixed the category slopes on 1, -1, -1, 1) has the best model data fit indices. Then we can observe the model property via figure 1 ,that is, the increased bias followed at theta rising as ERS is positive. that means the person responding many 5 points actually should responds 4 point via his true latent trait because of the ERS causes he intend to extreme response. Furthermore, the more than two substantive trait is needed. The effect between the one and two trait was seen at simulation study.
Comment:
1) I am curious the phenomena in figure 2. It seems there is a implicit line at ENJ W/VAL=-0.8 and +0.8. Subsequently, as ENJ_ALONE=-0.8/ +0.8, it is almost the same value between ENJ_ALONE and ENJ W/VAL. Perhaps, it implicates that the estimate theta=-0.8/ +0.8 will always be ERS=0 calculated in this model.
2) The second substantive trait is important because we need to have additional information to discriminate the real high/low theta from the extreme response style. It is very similar with the problem of force choice model.
3) To compare with the RE-RSM, I think this MNRM is like the RE-RSM with fixed person category random effect on negative value at centered region categories, and fixed positive value at extreme categories.
Sorry, the thinking in the comment 3 is wrong.
This MNRM put ERS effect in (1, -1, -1, 1) slopes of theta. It can't reflect to any parameter in RE-RSM. Perhaps It is more similar with the Kuan-Yu's model that put a person slope at item category parameter. The ERS in MNRM directly affects the probability of each category even if the threshold disordered appears. When ERS is very large positive value, the probability of 2 and 3 categories will be close to zero.