Conducting Confirmatory Latent Class Analysis …

1 This article was downloaded by: [University of California, Los Angeles (UCLA)]On: 28 December 2011, At: 15:49 Publisher: Psychology PressInforma Ltd Registered in England and Wales Registered Number: 1072954 Registeredoffice: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UKStructural Equation Modeling: AMultidisciplinary JournalPublication details, including instructions for authors andsubscription information: Confirmatory Latent ClassAnalysis Using MplusW. Holmes Finch a & Kendall Cotton Bronk aa Ball State UniversityAvailable online: 07 Jan 2011To cite this article: W. Holmes Finch & Kendall Cotton Bronk (2011): Conducting Confirmatory LatentClass Analysis Using Mplus , Structural Equation Modeling: A Multidisciplinary Journal, 18:1, 132-151To link to this article: SCROLL DOWN FOR ARTICLEFull terms and conditions of use: article may be used for research, teaching, and private study purposes.

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3 Holmes Finch and Kendall Cotton BronkBall State UniversityLatent Class Analysis (LCA) is an increasingly popular toolthat researchers can use to identifylatent groups in the population underlying a sample of responses to categorical observed is most commonly used in an exploratory fashion whereby no parameters are specified apriori. Although this exploratory approach is reasonable when very little prior research has beenconducted in the area under study, it can be very limiting when much is already known about thevariables and population. Confirmatory Latent Class Analysis (CLCA) provides researchers with atool for modeling and testing specific hypotheses about response patterns in the observed is based on placing specific constraints on the parameters to reflect these hypotheses.

4 Thepopular and easy-to-use Latent variable modeling softwarepackage Mpluscan be used to conduct avariety of CLCA types using these parameter constraints. This article focuses on the basic principlesunderlying the use of CLCA, and the Mplusprogramming code necessary for carrying it Class Analysis (LCA) is an increasingly popular analytic technique useful for identifyinglatent groups based on a set of observed response variables,which can be either dichotomous orpolytomous. It is important to note here that a variant of LCAknown as Latent profile analysiscan be used when the observed variables are continuous , but the focus of this article is on LCAwith dichotomous observed variables. Table 1 includes a simple taxonomy for organizing theappropriate Analysis by the type of research question to be addressed and the type of data avail-able.

5 These are merely examples of the many research questions that can be addressed by thesemodels, and are not intended to be an exhaustive list. Typically, LCA is carried out in an ex-ploratory manner where there does not exist a strong a priorihypothesis regarding the number ornature of the Latent classes underlying the data (Hoijtink,2001). In such cases, a researcher canfit several proposed models to the data with each differentiated by the number of Latent classes,and compare the resulting fit indexes to determine which bestcorresponds to the observed exploratory Analysis approach works under the implicit presumption that there is nota well-developed theory regarding the nature of Latent groups to be found in the population(Laudy, Boom, & Hoijtink, 2005).

6 However, in cases where substantive theories regardingCorrespondence should be addressed to W. Holmes Finch, Department of Educational Psychology, Ball StateUniversity, TC 521, Muncie, IN 47306, USA. E-mail: by [University of California, Los Angeles (UCLA)] at 15:49 28 December 2011 Conducting Confirmatory LCA USING MPLUS133 TABLE 1 Taxonomy of Models for Latent Categorical VariablesType of Observed VariableType ofResearch QuestionCategoricalContinuousExploratory Latent Class Analysis (How many latentclasses underlie a set of categoricalobserved variables?) Latent profile Analysis Cluster Analysis (How many Latent classes underlie aset of continuous observed variables?)ConfirmatoryConfirmatory Latent Class Analysis (Arethere three Latent classes underlying aset of categorical variables, with Group1 having higher response probabilitiesthan Group 2 and Group 3 having thelowest probabilities, as theory wouldsuggest?)

7 Confirmatory Latent profile Analysis (Arethere three Latent classes underlying aset of observed continuous variablessuch that Group 1 has the highestmean values, followed by Group 2,which in turn has higher means thanGroup 3, as theory would suggest?) research questions associated with each Analysis are shown in number and nature of these Latent classes have been developed, exploratory LCA mightbe inefficient, not taking advantage of this prior knowledge. Confirmatory LCA (CLCA) isan alternative approach to Latent Class modeling that allows for the formulation of specifichypotheses regarding the nature and number of Latent classes in the data. These hypothesesare expressed as a set of parameter constraints for an estimated LCA model (Croon, 1990).

8 The goal of this article is to demonstrate how such parameterconstraints can be used in acommon Latent variable modeling software package, Mplus,to carry out CLCA. First, webriefly introduce the basic LCA model, and then describe how constraining parameter valuescan be used to express specific hypotheses regarding Latent classes in the population. We willthen present several examples of CLCA using a set of dichotomous items taken from a surveyon adolescent Class ANALYSISThe basic LCA model is described in some detail by McCutcheon(2002). Assume that datahave been collected for four observed, dichotomous variables,X1,X2,X3, andX4, and thatthere exists a Latent categorical variableY, which accounts for the relationships among thesefour observed variables.

9 The LCA model linking the Latent and observed variables can then beexpressed as: X1X2X3X4 YijkltD Yt X1jYit X2jYjt X3jYkt X4jYlt(1)where YtDProbability that a randomly selected individual will be in Latent classtof latentvariableY X1jYitDProbability that a member of Latent classtwill provide a response ofifor observedvariableX1 Downloaded by [University of California, Los Angeles (UCLA)] at 15:49 28 December 2011 134 FINCH AND BRONK X2jYjtDProbability that a member of Latent classtwill provide a response ofjfor observedvariableX2 X3jYktDProbability that a member of Latent classtwill provide a response ofkfor observedvariableX3 X4jYltDProbability that a member of Latent classtwill provide a response oflfor observedvariableX4 The LCA model in Equation 1 asserts that the observed variables are conditionally indepen-dent given a particular Class inY(Goodman, 2002).

10 This notion of conditional independenceis very similar to local independence in the context of item response theory, which statesthat when the Latent trait influencing responses to items on an instrument is held constant,individuals responses to any two items are statistically independent. As an example, take anindividual from the population who has the following probability values for the three classesinY: Y1D0:6, Y2D0:25, and Y3D0:15. These results indicate that the individual is mostlikely to be in Class 1 of the Latent variable , with only a 1/4 chance of being in Class 2 anda less than 1/5 chance of being in Class 3. In addition, assumethat observed variableX1is asurvey item asking whether an individual hopes to pursue a career helping other people afterfinishing college.