Journal of Educational Measurement Fall 2011, Vol. 48, No. 3, pp. 313–332 Spurious Latent Classes in the Mixture Rasch Model Natalia Alexeev, Jonathan Templin and Allan S. Cohen University of Georgia Mixture Rasch models have been used to study a number of psychometric issues such as goodness of fit, response strategy differences, strategy shifts, and multidimen- sionality. Although these models offer the potential for improving understanding of the latent variables being measured, under some conditions overextraction of latent classes may occur, potentially leading to misinterpretation of results. In this study, a mixture Rasch model was applied to data from a statewide test that was initially calibrated to conform to a 3-parameter logistic (3PL) model. Results suggested how latent classes could be explained and also suggested that these latent classes might be due to applying a mixture Rasch model to 3PL data. To support this latter con- jecture, a simulation study was presented to demonstrate how data generated to fit a one-class 2-parameter logistic (2PL) model required more than one class when fit with a mixture Rasch model. Mixture IRT models offer the potential for providing increased information about examinees’ abilities as well as their response strategies not captured by traditional single class (or group) IRT models (Mislevy & Verhelst, 1990; Rost, 1990). For example, in educational measurement, mixture IRT models have been used for de- tecting latent classes that differ in patterns of item difficulty that are indicative of differences in strategy use (e.g., Bolt, Cohen, & Wollack, 2001; De Boeck, Wilson, & Acton, 2005; Embretson, 2007; Mislevy & Verhelst, 1990; Rost, 1990). Traditional IRT models are defined by several assumptions: unidimensionality, in- variance, local independence, monotonicity, and existence of a continuous function that describes the relationship between the probability of correct response to a test item and latent trait of the examinee and characteristics of the test item (Reckase, 2009). IRT models have been found to be useful, but they are not always robust to violations of these assumptions. When violations do occur, more complex mod- els may be needed to “more accurately reflect the complexity of the interactions between examinees and test items’’ (Reckase, 2009, p. 53). If the first assumption (unidimensionality) is violated, then a multidimensional IRT model may be applied. If the invariance assumption is violated, mixture IRT models may be applied (von Davier, Rost, & Carstensen, 2007). Mixture distribution IRT models belong to the family of discrete (or finite) mix- ture distribution models (McLachlan & Peel, 2000). Although finite mixture mod- els have a long history that began with the fundamental paper of Pearson (1894), most model development has happened in the last twenty to thirty years, following the development of the EM algorithm (Dempster, Laird, & Rubin, 1977). Mixture models are considered to be a semiparametric compromise between nonparametric and parametric models, attaining the flexibility of the former and advantages of the latter, such as reducing the dimension space to a reasonable size (McLachlan & Peel, Copyright c  2011 by the National Council on Measurement in Education 313