The purpose of this study was to investigate whether simulated differential motivation between the stakes for operational tests and anchor items produces an invalid linking result if the Rasch model is used to link the operational tests. This was done for an external anchor design and a variation of a pretest design. The study also investigated whether a constrained mixture Rasch model could identify latent classes in such a way that one latent class represented high‐stakes responding while the other represented low‐stakes responding. The results indicated that for an external anchor design, the Rasch linking result was only biased when the motivation level differed between the subpopulations to which the anchor items were administered. However, the mixture Rasch model did not identify the classes representing low‐stakes and high‐stakes responding. When a pretest design was used to link the operational tests by means of a Rasch model, the linking result was found to be biased in each condition. Bias increased as percentage of students showing low‐stakes responding to the anchor items increased. The mixture Rasch model only identified the classes representing low‐stakes and high‐stakes responding under a limited number of conditions.