With the rise of computer- based testing, increasingly more attention has been given to response time (RT) in assessment practice and psychometric research. This study aims to reveal the rate of Type I error in the detection of preknowledge cheating behaviors, and the rate of power of Kullback–Leibler divergence (KL) measure, and  person fit statistic under different conditions via modeling patterns of response accuracy (RA) and  RT, using a joint hierarchical model. The test length,  difficulty level of the compromised items, the ratio of compromised items, and changing in RTs of the compromised items  variables were varied. KL measure has a high power and Type I error rate mean values than person fit statistics for RA and RT patterns under all conditions.