Latent Class Analysis Latent Class Analysis in Min Mplusplus Version 3 Version 3

Karen NylundKaren NylundSocial Research MethodsSocial Research Methods

Graduate School of Education & Graduate School of Education & Information StudiesInformation Studiesknylund@ucla.eduknylund@ucla.edu

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Overview of SessionOverview of Session

General description of Latent Class General description of Latent Class Analysis (LCA) within a hypothetical Analysis (LCA) within a hypothetical exampleexample

Two examples of LCA analysis using Two examples of LCA analysis using MMplus Version 3plus Version 3– Anti-Social BehaviorAnti-Social Behavior– Diabetes DiagnosisDiabetes Diagnosis

Extensions of the LCA modelsExtensions of the LCA models Resources and ReferencesResources and References

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Hypothetical Example: Hypothetical Example: Identifying effective Identifying effective

teachersteachers Setting: Unsure how to identify an Setting: Unsure how to identify an

effective teachereffective teacher

Possible Indicators:Possible Indicators:– Credential or Not?Credential or Not?– Promotes critical thinkingPromotes critical thinking– ReflectiveReflective– Professional Development (P.D.)Professional Development (P.D.)

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What would the data look What would the data look like?like?

TeacheTeacherr

CredentiCredentialal

Critical Critical ThinkingThinking ReflectivReflectiv

eeP.D.P.D.

11 00 11 11 11

22 00 00 11 00

33 11 11 11 11

44 11 11 00 11

55 11 11 00 11

66 00 11 00 00

77 11 00 00 00

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Possible research questions:Possible research questions:

Are there specific characteristics that Are there specific characteristics that identify an effective teacher?identify an effective teacher?

Given known ideas of what an effective Given known ideas of what an effective teacher is, what characteristics are teacher is, what characteristics are important indicators?important indicators?

Are there background characteristics of the Are there background characteristics of the teachers that help classify them as teachers that help classify them as effective?effective?

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What could LCA tell us?What could LCA tell us? To find groups of teacher that are similar To find groups of teacher that are similar

based on observed characteristicsbased on observed characteristics

– Identify and accurately enumerate the number Identify and accurately enumerate the number of groups of teachersof groups of teachers

– Identify characteristics that indicate groups wellIdentify characteristics that indicate groups well

– Estimate the prevalence of the groupsEstimate the prevalence of the groups

– Classify teachers into classes Classify teachers into classes

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The LCA ModelThe LCA Model

Observed Continuous Observed Continuous (y’s) or Categorical (y’s) or Categorical Items (u’s)Items (u’s)

Categorical Latent Categorical Latent Class Variable (c)Class Variable (c)

Continuous or Continuous or Categorical Covariates Categorical Covariates (x)(x)

C

Y1 Y2 Y3 Yp

X

. . .

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How is this modelingHow is this modelingprocess conducted?process conducted?

Run through models imposing different Run through models imposing different numbers of classesnumbers of classes

Estimation via the EM algorithmEstimation via the EM algorithm– Start with random split of people into Start with random split of people into

classes. classes. – Reclassify based on a improvement criterionReclassify based on a improvement criterion– Reclassify until the best classification of Reclassify until the best classification of

people is found.people is found.

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Evaluating the ModelEvaluating the Model

Model FitModel Fit

BIC and AICBIC and AIC XX2 2 StatisticStatistic Lo-Mendell-Rubin Lo-Mendell-Rubin

Test (Tech 11)Test (Tech 11) Standardized Standardized

Residuals (Tech 10)Residuals (Tech 10)

Model UsefulnessModel Usefulness

Substantive Substantive InterpretationInterpretation

Classification QualityClassification Quality– Classification TablesClassification Tables– EntropyEntropy

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11stst Data Example: Anti-Social Data Example: Anti-Social BehaviorBehavior

Damaged Damaged propertyproperty

FightingFighting ShopliftingShoplifting Stole <$50Stole <$50 Stole >$50Stole >$50 Use of forceUse of force Seriously threatenSeriously threaten Intent to injureIntent to injure

Use MarijuanaUse Marijuana Use other drugUse other drug Sold MarijuanaSold Marijuana Sold hard drugsSold hard drugs ‘‘Con’ somebodyCon’ somebody Stole an AutomobileStole an Automobile Broken into a Broken into a

buildingbuilding Held stolen goodsHeld stolen goods Gambling OperationGambling Operation

National Longitudinal Survey of Youth (NLSY)National Longitudinal Survey of Youth (NLSY) Respondent ages between 16 and 23Respondent ages between 16 and 23 Background information: age, gender and ethnicityBackground information: age, gender and ethnicity N=7,326N=7,326

17 antisocial dichotomously scored behavior items:17 antisocial dichotomously scored behavior items:

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Anti Social Behavior Anti Social Behavior ExampleExample

Damage Property

Fighting Shoplifting Stole <$50 Gambling. . .

Male

Race

Age

C

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Antisocial behavior Example in Antisocial behavior Example in MMplus plus Version 3Version 3

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ASB Item ProbabilitiesASB Item Probabilities

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Relationship between Relationship between class probabilities and covariate class probabilities and covariate

(AGE94)(AGE94)Females Males

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ASB Example ConclusionsASB Example Conclusions

Summary of four classes:Summary of four classes:– Property Offense Class (9.8%)Property Offense Class (9.8%)– Substance Involvement Class (18.3%)Substance Involvement Class (18.3%)– Person Offenses Class (27.9%)Person Offenses Class (27.9%)– Normative Class (44.1%) Normative Class (44.1%)     

Classification Table:Classification Table:

11 22 33 44

11 0.850.8544

0.0310.031 0.0700.070 0.0400.040

22 0.0410.041 0.910.9177

0.040.04 00

33 0.0580.058 0.0210.021 0.820.8200

0.1000.100

44 0.0380.038 00 0.080.08 0.880.88

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22nd nd Example: Diabetes DataExample: Diabetes Data

Three continuous variables:Three continuous variables:– Glucose (y1)Glucose (y1)– Insulin (y2)Insulin (y2)– SSPG (Steady-stage plasma glucose, y3)SSPG (Steady-stage plasma glucose, y3)

N=145N=145 Data from Reaven and Miller (1979)Data from Reaven and Miller (1979)

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Diabetes ExampleDiabetes Example

C

Glucose Insulin SSPG

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Diabetes Example in MDiabetes Example in Mplus plus Version 3Version 3

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Diabetes ResultsDiabetes Results

2020

Diabetes ResultsDiabetes Results

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Diabetes Example Diabetes Example ConclusionsConclusions

Summary of Three classes:Summary of Three classes:– Class 1: Class 1: Overt Diabetes group (52%)– Class 2: Chemical Diabetes group Class 2: Chemical Diabetes group

(19.6%)(19.6%)– Class 3: Normal Group (28.4%)Class 3: Normal Group (28.4%)

Classification Table:Classification Table:11 22 33

11 0.920.9299

0.0010.001 0.0710.071

22 0.0000.000 0.9670.967 0.0330.033

33 0.0530.053 0.0100.010 0.9370.937

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Extensions of the LCA Extensions of the LCA ModelModel

Confirmatory LCAConfirmatory LCA– Constraints on Model ParametersConstraints on Model Parameters

Multiple LCA variablesMultiple LCA variables– Multiple Measurement InstrumentsMultiple Measurement Instruments– Latent Transition AnalysisLatent Transition Analysis

Multi-level LCAMulti-level LCA Use Monte Carlo to explore sample Use Monte Carlo to explore sample

size issuessize issues

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ResourcesResources MMplus plus User GuideUser Guide

– http://www.statmodel.comhttp://www.statmodel.com

ATS MATS Mplusplus Support Support– http://www.ats.ucla.edu/stat/mplus/http://www.ats.ucla.edu/stat/mplus/– http://www.ats.ucla.edu/stat/seminars/ed231e/http://www.ats.ucla.edu/stat/seminars/ed231e/

Applied Latent Class Analysis, Edited by Applied Latent Class Analysis, Edited by Hagenaars and McCutcheon (‘02)Hagenaars and McCutcheon (‘02)

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ReferencesReferences Hagenaars, J.A & McCutcheon, A. (2002).  Applied latent class

analysis.  Cambridge: Cambridge University Press.

Muthén, B. (2001). Latent variable mixture modeling. In G. A. Marcoulides & R. E. Schumacher (eds.), New Developments and Techniques in Structural Equation Modeling (pp. 1-33). Lawrence Erlbaum Associates. (#86)

Muthén, L. & Muthén, B. (1998-2004). Mplus user’s guide. Los Angeles, CA: Muthén & Muthén.

Muthén, B. & Muthén, L. (2000). Integrating person-centered and variable-centered analysis: growth mixture modeling with latent trajectory classes. Alcoholism: Clinical and Experimental Research, 24, 882-891.

Reaven, G.M., & Miller., R.G.(1979). “An attempt to define the nature of chemical diabetes using multidimensional analysis,” Diabetologica, 16, 17-27.