Multiple Group IRT Modeling: Applications to Item Bias Analysis

“For discussions of the relationship between the IRT and common-factor models, see Lord and Novick (1968), Takane and de Leeuw (1987), Muthén and Lehman (1985), or McDonald (1999).”

“Scaling methods based on item response theory (IRT) that map particular items (and response categories within items) to different points upon a latent severity dimension might result in more accurate reflections of the latent traits of Anh, AS, and DT (Muthén & Lehman, 1985).”

“That is, as Zumbo (2007) and Zumbo and Rupp (2004) noted, test and item bias aim analyses at establishing the inferential limits of the test—that is, establishing for whom (and for whom not) the test or item score inferences are valid.”

“See Lord and Novick (1968), Muthén and Lehman (1985), and Thissen, Steinberg, and Wainer (1993) for a discussion on the relation between the IRT and CFA parameters.”

“Another approach to DIF assessment that has been discussed both in terms of uniform and nonuniform DIF involves the application of CFA models to item response data (Camilli & Shepard, 1994; Fleishman et al., 2002; Muthen & Lehman, 1985; Navas-Ara & Gomez-Benito, 2002; Oort, 1998).”

“Using the linear constraint, it becomes possible to assign dates to all assemblages.”

“First, it has been shown that a dichotomous factor analysis model (without exogenous covariates) is equivalent to and a reparameterization of the standard two-parameter IRT model (McDonald, 1999; Muthen & Lehman, 1985; Takane & de Leeuw, 1987).”

“Residuals in the measurement relations ( values) are taken to be multivariate normal and uncorrelated among themselves, leading to the IRT normal ogive specification.(24) The parameters estimated in this article were obtained with Mplus(24) version 2.”

“The mathematical foundation for this program was given by Muthén and Christofferson (1981), and a numerical example for one latent factor was given by Muthén and Lehman (1985).”

“The finding that factorial invariance is tenable suggests that the tests are unbiased with respect to group (Meredith, 1993; Millsap, 1997a, 1997b; Muthén & Lehman, 1985; Oort, 1996).”

“The SEM approach to detecting differential item functioning (DIF) has been explicated by Muthén & Lehman (1985) and Thissen, Steinberg & Wainer (1993).”

“CFA for DIF detection has been recommended (e.g., Muthén & Lehman, 1985) and used with polytomous items (e.g., Fleishman, Spector, & Altman, 2002; Levine et al., 2003).”

“This equivalence is exploited by Muthen and colleagues in a series of studies (Muthen, 1985, 1988; Muthen, Kao, & Burstein, 1991; Muthen & Lehman, 1985) to assess differential item functioning (DIF) within a multiple-indicator, multiple-causes (MIMIC) model (Hauser & Goldberger, 1971; J̈oreskog &…”

“…cannabis abuse and dependence criteria (Teesson et al. 2002), although examination of item characteristic curves [calculated using item response theory (IRT) criterion characteristic curves (Muthen & Lehman, 1985)] suggested some discrepancies between item properties and the DSM conceptualization.”

“To accomplish this, a multiple-group confirmatory factor model for ordered categorical responses could be applied to the facet scales (see, Muthén & Lehman, 1985; Muthén & Muthén, 1998).”

“…/df = 8.71, AIC = 1233.3, CAIC = 1882.2, and NNFI = 0.82] still indicated a serious deterioration of fit compared with those of A2, we also rejected strong factorial invariance and concluded that some or all of the tests are biased (Meredith, 1993; Millsap, 1997; Muthén & Lehman, 1985; Oort, 1996).”

“Explanation of DIF is one of the important trends in the study of DIF (Cho & Cohen, 2010; Cohen & Bolt, 2005; Cohen, Gregg, & Deng, 2005; DeAyala, Kim, Stapleton, & Dayton, 2002; Muthén, Kao, & Burstein, 1991; Muthén & Lehman, 1985; Penfield, 2010; Samuelsen, 2005; Zumbo & Gelin, 2005).”

“The limited information WLSMV approach provides fit statistics commonly found in the structural equation modeling literature and convenient and efficient algorithms for building measurement models for the purpose of detecting measurement noninvariance have been described (Jones, 2003; Muthén and Lehman, 1985; Yang and…”

“two-parameter normal ogive) and structural equation modeling of dichotomous items using a generalized least squares estimation method (non-linear factor analysis) yield equivalent item properties and trait scores ( Muthen and Lehman, 1985 ).”

“study, like that of Chen and Henning (1985), identified several vocabulary and grammar items that favored certain native language groups. Other studies that have investigated performance across native language groups include Alderman and Holland (1981), and Oltman, Stricker, and Barrows”

“…by a multiple indicators, multiple causes (MIMIC) IRT model, which is a structural equation model originally developed for continuous indicators (Zellner, 1970; Goldberger, 1972) and later extended to categorical item response data (Muthen, 1985; Muthen et al., 1991; Muthen & Lehman, 1985) .”

“medical and psychiatric research, is reviewed elsewhere [14, 25, 34].”

“In Ogasawara (2002), it was shown that item response functions were possible to estimate accurately in spite of unstable item parameter estimates while the expected information functions were more affected by unstable item parameter estimates.”

“With this potentially serious limitation of that approach in mind, a researcher may be willing to consider instead dropping from the instrument or modifying the item(s) for which DIF has been found with the method of this article (or with other procedures; see also Muthén & Lehman, 1985).”

“Parameters from CFA can be converted into a 2 parameter logistic item response model (Muthén and Lehman, 1985) characterized by discrimination and difficulty.”

“This comparison can be carried out in several different ways: (1) by calculating the area between ICC’s (Linn et al., 1981; Raju, 1988, 1990; Rudner, 1977; Rudner et al., 1980); (2) by studying the goodness of fit of an IRT model to the focal group with parameters estimated in the combined (or reference) group (Linn a…”

“6 To do so, we use the multiple group approach (Muthen & Lehman, 1985) estimated via the EM algorithm (Bock & Aitkin, 1981) as implemented in mirt (Chalmers, 2012).”

“However, readers interested in more coverage may consult additional references (see, for example, Forero & Maydeu-Olivares, 2009; Kamata & Bauer, 2008; B. Muthén & Asparouhov, 2002; B. Muthén & Lehman, 1985; Takane & de Leeuw, 1987).”

“In situations in which the same set of dichotomously scored items is administered to more than one class of persons, items many not be invariant across the classes (Muthén & Lehman, 1985) — for instance, due to DIF.”

“We note that the model coincides with a MIMIC model (Jöreskog & Goldberger, 1975) for manifest DIF analysis (Muthen & Lehman, 1985; Muthén, 1989; Woods, 2009; Woods & Grimm, 2011) when conditioning on the latent class ξ i (i.e., viewing ξ i as observed).”

“One can also use the robust maximum likelihood estimator (MLE), which produces slightly more efficient estimates than WLSMV when dealing with item response data (Muthén & Lehman, 1985).”

“…of Research in Education, 14 an IRT model assumes that given θ, there is no interaction between items and intervening variables such as gender and course content; Muthén (1987) and Muthén and Lehman (1985) compare the fit of structural models that do and do not posit their conditional effects.”

“The following results are an extension of those derived by B. Muthén and Lehman (1985) for the unidimensional case.”

“This equivalence was used in a series of studies (e.g., Muthén, 1985, Muthén, Kao, & Burstein, 1991; Muthén & Lehman, 1985; Raykov et al., 2015; Woods & Grimm, 2011) to test for DIF in the framework of CFA under the multiple-indicator, multiple-causes (MIMIC) model (Jöreskog & Goldberger, 1975).”

“Finally, we believe that the acceptable fit is a noticeable result, as models of the type considered here are usually intended to make a detailed scrutiny of small sets of 5 to 10 items (B. O. Muthén & Lehman, 1985).”

“Analyses of ordered categorical variable in multiple-group settings have been described elsewhere (Muthén and Christofferson 1981; Muthén and Lehman 1985; Muthén 1989; Muthén and Asparouhov 2002; Millsap and YunTein 2004).”

“In the present context, the multiple-group model estimates a separate mean ability and variance for each diagnostic group and allows for a direct test of whether the measurement model is invariant across the different groups (Muthe´n & Lehman, 1985).”

“(18) It should be pointed out that Muthén and Lehman (1985) obtained similar results in the context of multiple group measurements at a single point in time.”

“Differential item/criterion functioning (DCF; Muthen & Lehman, 1985) is a formal test of whether the factor loading/ discrimination and the threshold/difficulty of certain criteria vary across subgroups of individuals, such as men and women, or in individuals with co-occurring MDD.”

“It is difficult to allow the same set of covariates to effect both the measurement and structural part of the model without some issues of identifiability, although such a model is possible provided there are some items for which there is no direct effect.(50,51) Ordinal SEMs with covariates are usually fitted by a mu…”

“If the subjects’ populationmembership is known, multiplegroup IRT models (e. g., B. Muthén & Lehman, 1985) can be used.”

“The construct in question is the latent variable measured on items formed based on indicators as variables observed in the factor analysis model (Muthen & Lehman, 1985; Thissen et al., 1993).”

“IRT is a mild nonlinearization of standard factor analy- sis, and indeed this connection has been recognized since the initial formulation of IRT (Lord & Novick, 1968; Muthén & Lehman, 1985; Takane & de Leeuw, 1987; McDonald, 1999; Kamata & Bauer, 2008; Bartholomew, Knott, & Moustaki, 2011).”