The Effects of Educational Diversity in a National Sample of Law Students: Fitting Multilevel Latent Variable Models in Data With Categorical Indicators

Abstract

Controversy surrounding the use of race-conscious admissions can be partially resolved with improved empirical knowledge of the effects of racial diversity in educational settings. We use a national sample of law students nested in 64 law schools to test the complex and largely untested theory regarding the effects of educational diversity on student outcomes. Social scientists who study these outcomes frequently encounter both latent variables and nested data within a single analysis. Yet, until recently, an appropriate modeling technique has been computationally infeasible, and consequently few applied researchers have estimated appropriate models to test their theories, sometimes limiting the scope of their research question. Our results, based on disaggregated multilevel structural equation models, show that racial diversity is related to a reduction in prejudiced attitudes and

Gender inequality and the use of maternal healthcare services in rural sub-Saharan Africa

“…The system of equations was estimated simultaneously using Mplus 6.11. Standard errors were estimated using the maximum likelihood method with the MLR estimator based on the expectation maximisation algorithm (Gottfredson et al, 2009). This is a robust estimator in cases of non-normality of dependent variables (Muthén andMuthén, 1998-2010).…”

A Bayesian Approach to Multilevel Structural Equation Modeling With Continuous and Dichotomous Outcomes

“…For instance, multilevel measurement modeling with categorical indicators represents the basis of multilevel item response theory (IRT; Fox, 2010;Fox & Glas, 2001;Muthén & Asparouhov, 2012b). There are a number of applications of multilevel SEM with categorical outcomes in the research literature using both frequentist (e.g., Gottfredson et al, 2009;Little, 2013;Mitchell & Bradshaw, 2013) and Bayesian (e.g., Diya, Li, Heede, Sermeus, & Lesaffre, 2013;Goldstein, Bonnet, & Rocher, 2007) approaches, yet simulation research has not been conducted to determine whether the sample size recommendations that have been put forth for continuous outcomes also hold for categorical outcomes. Moreover, a Bayesian approach is uniquely beneficial in the context of categorical data because it can be used to estimate categorical variable models that cannot be analyzed with currently available frequentist approaches (see, e.g., Ansari & Jedidi, 2000;Dunson, 2000;Muthén & Asparouhov, 2012b;Steele & Goldstein, 2006).…”

“…Despite the growing number of applications of multilevel SEM with categorical variables (e.g., Diya et al, 2013;Goldstein et al, 2007;Gottfredson et al, 2009;Little, 2013;Mitchell & Bradshaw, 2013;Steele & Goldstein, 2006), the simulation studies that have been conducted to develop lower bounds on sample size in multilevel SEM have been based solely on models with continuous variables. It is not yet known how different types of outcomes-most notably, categorical-affect parameter recovery in multilevel SEM.…”

“…In the former example, biased estimates might be obtained if constructs measured by multiple indicators are represented with composite scores instead of latent variables (Lüdtke, Marsh, Robitzsch, & Trautwein, 2011); in the latter, parameter estimates could be inaccurate if the hierarchical structure of the data is ignored (Julian, 2001;Muthén & Satorra, 1995). To deal with the shortcomings of each approach, methodologists have combined features of MLM and SEM into a flexible framework that extends conventional latent variable modeling to accommodate hierarchical data, called multilevel SEM (Gottfredson, Panter, Daye, Allen, & Wightman, 2009;Johnson, Burlingame, Olsen, Davies, & Gleave, 2005;Marsh et al, 2012).…”

The Shaping of Postcollege Colorblind Orientation Among Whites: Residential Segregation and Campus Diversity Experiences

“…Previous research on cross-racial interactions and race relations on historically white campuses has uncovered the positive benefits of racial diversity for decreasing reported prejudicial attitudes and discrimination (Davies, Tropp, Aron, Pettigrew, & Wright, 2011;Gottfredson, Panter, Daye, Allen, & Wightman, 2009), higher levels of cultural awareness (Antonio, 2001), and increased pluralistic orientation (Engberg & Hurtado, 2011;Hurtado, 2005;Jayakumar, 2008). Improvement on these aforementioned outcomes in particular is often pursued under the presumption that they will contribute to positive race relations, and result in more inclusive social conditions and equity for people of color.…”