that can reveal examinee’s degree of possession of knowledge, skill, syndrome, or pathological symp- tom. For this reason, the DCMs have been used in a variety of social sectors, including education, psychology, and clinical settings. 

One of the fundamental assumptions made in the DCMs is local item independence given a latent class. This assumption connotes that the latent class of interest provides all the necessary information about a given examinee, and after controlling for the latent variable, items are not expected to have any remaining association. While the assumption of conditional independence greatly simplifies the representation of the joint response distribution and consequently parameter estimation, it appears a strong assumption that may not always be justified. In real applications the violation of local item independence is often expected in test items involving common stimuli, similar contents or wording, order effects, speededness, etc. (Yen, 1984, 1993). Studies have shown that when local item dependence is present, parameter estimation and statistical properties of a test can be negatively impacted (see, e.g., C.-T. Chen & Wang, 2007; Kingston & Dorans, 1984; Sireci, Thissen, & Wainer, 1991; Tuerlinckx & De Boeck, 2001; Wainer & Thissen, 1996; Yen, 1984). The dependence structure, if not properly addressed, can result in biased estimation of item parameters as well as overestimation of measurement precision and reliability. 

According to W. Chen and Thissen (1997), local item dependence can be classified into two kinds: underlying dependence and surface dependence. The first type assumes that local item dependence occurs as a result of a unmodeled latent variable. It posits that there exists an extra latent parameter that is common to a set of locally dependent items and yet irrelevant to the rest of items in a test. The bifactor models (Cai, 2010; Gibbons & Hedeker, 1992) and the random- effects testlet response models (Bradlow, Wainer, & Wang, 1999; Wainer, Bradlow, & Wang, 2007; X. Wang, Bradlow, & Wainer, 2002; W. Wang & Wilson, 2005) are devised to address this type of local dependence. The bifactor models consider a secondary group factor to account for item association that cannot be explained by a primary latent factor. The testlet response models introduce a random effect parameter to model local dependence within the same testlet or item bundle. Unlike the bifactor models in which the covariance among the items (after controlling the primary factor) is attributed to within-person variance, the testlet response models ascribe local dependence to an interaction effect between a person and an item cluster. Note that both the modeling approaches evaluate local dependence in a confirmatory fashion by requiring prior 

