Questionnaire (EPQ)-Revised (EPQ-R; S. B. G. Eysenck, Eysenck, & Barrett, 1985), a widely used survey for measuring individual differences in personality across different cultures. The question- naire assesses personality traits of an individual in aspects of Psychoticism, Extraversion, Neuroti- cism, and Lie. Psychoticism (P) implies an inclination toward being impersonal, aggressive, lacking in empathy, and incompliant with rules. Extraversion (E) is characterized by sociability, activity, and impulsiveness. Neuroticism (N) is associated with high levels of negative perception such as being nervous, apprehensive, and highly-strung. Lie (L) is related to faking good of scores on the other scales. The question inventory has 100 yes/no items in its full-scale version (H. J. Eysenck & Eysenck, 1975) and 48 items in its short version (S. B. G. Eysenck et al., 1985). The present study focuses on a test set of 36 items from the short scale version, excluding the L scale that measures consistency in item responses. Each of the personality dimensions was measured on a continuous scale by 12 items. In this particular analysis, we aimed to classify observed response patterns in terms of a small number of latent classes by defining each scale on a binary status. Each status indicates whether or not a subject possesses a propensity for a particular scale. A similar strategy has been practiced in the DCM literature, for example, for diagnosing pathological gamblers (Templin & Henson, 2006) or evaluating language proficiency (Jang, 2009; Roussos, DiBello, Henson, Jang, & Templin, 2010). To evaluate the fit of the GDCM, we compared the observed log-likelihood to an empirical distri- bution obtained via parametric bootstrapping under the presumed model. The detailed procedure is described as follows. Let ( ˆ B , ˆ Φ , ˆ π ) denote the maximal pseudo-likelihood estimates of the fitted model. The logarithm of the joint likelihood given the estimated parameters is then calculated as where ( x$_{1}$ , . . . , x$_{N}$ ) is the set of observed responses. The plausibleness of the observed log- likelihood value, l $^{o}$, can be evaluated by comparing it against an empirical distribution of log- likelihoods predicted by the fitted model. In this study 500 independent bootstrap data sets were 6.2 Goodness-of-fit l o = log N ∏ i =1 f ( x$_{i}$ | ˆ B , ˆ Φ , ˆ π ) = N ∑ i =1 log$^{(}$ ∑ α ˆ π$_{α}$ exp$^{(}$ x ⊤ i ˆ B α + 1 2 x ⊤ i ˆ Φx$_{i}$$^{)}$$^{)}$ − log z ( ˆ B , ˆ Φ ) , 21