Latent Class Analysis in Mplus Version 3 Karen Nylund Social Research Methods Graduate School of Education & Information Studies Graduate School of Education & Information

2 Overview of Session General description of Latent Class Analysis (LCA) within a hypothetical example General description of Latent Class Analysis (LCA) within a hypothetical example Two examples of LCA analysis using Mplus Version 3 Two examples of LCA analysis using Mplus Version 3 –Anti-Social Behavior –Diabetes Diagnosis Extensions of the LCA models Extensions of the LCA models Resources and References Resources and References

3 Hypothetical Example: Identifying effective teachers Setting: Unsure how to identify an effective teacher Setting: Unsure how to identify an effective teacher Possible Indicators: Possible Indicators: –Credential or Not? –Promotes critical thinking –Reflective –Professional Development (P.D.)

4 What would the data look like? TeacherCredential Critical Thinking ReflectiveP.D

5 Possible research questions: Are there specific characteristics that identify an effective teacher? Are there specific characteristics that identify an effective teacher? Given known ideas of what an effective teacher is, what characteristics are important indicators? Given known ideas of what an effective teacher is, what characteristics are important indicators? Are there background characteristics of the teachers that help classify them as effective? Are there background characteristics of the teachers that help classify them as effective?

6 What could LCA tell us? To find groups of teacher that are similar based on observed characteristics To find groups of teacher that are similar based on observed characteristics –Identify and accurately enumerate the number of groups of teachers –Identify characteristics that indicate groups well –Estimate the prevalence of the groups –Classify teachers into classes

7 The LCA Model Observed Continuous (y’s) or Categorical Items (u’s) Observed Continuous (y’s) or Categorical Items (u’s) Categorical Latent Class Variable (c) Categorical Latent Class Variable (c) Continuous or Categorical Covariates (x) Continuous or Categorical Covariates (x) C Y1Y1 Y2Y2 Y3Y3 YpYp X...

8 How is this modeling process conducted? Run through models imposing different numbers of classes Run through models imposing different numbers of classes Estimation via the EM algorithm Estimation via the EM algorithm –Start with random split of people into classes. –Reclassify based on a improvement criterion –Reclassify until the best classification of people is found.

9 Evaluating the Model Model Fit BIC and AIC BIC and AIC X 2 Statistic X 2 Statistic Lo-Mendell-Rubin Test (Tech 11) Lo-Mendell-Rubin Test (Tech 11) Standardized Residuals (Tech 10) Standardized Residuals (Tech 10) Model Usefulness Substantive Interpretation Substantive Interpretation Classification Quality Classification Quality –Classification Tables –Entropy

10 1 st Data Example: Anti-Social Behavior Damaged property Damaged property Fighting Fighting Shoplifting Shoplifting Stole <$50 Stole <$50 Stole >$50 Stole >$50 Use of force Use of force Seriously threaten Seriously threaten Intent to injure Intent to injure Use Marijuana Use Marijuana Use other drug Use other drug Sold Marijuana Sold Marijuana Sold hard drugs Sold hard drugs ‘Con’ somebody ‘Con’ somebody Stole an Automobile Stole an Automobile Broken into a building Broken into a building Held stolen goods Held stolen goods Gambling Operation Gambling Operation National Longitudinal Survey of Youth (NLSY) National Longitudinal Survey of Youth (NLSY) Respondent ages between 16 and 23 Respondent ages between 16 and 23 Background information: age, gender and ethnicity Background information: age, gender and ethnicity N=7,326 N=7, antisocial dichotomously scored behavior items:

11 Anti Social Behavior Example Damage Property FightingShopliftingStole <$50Gambling... Male Race Age C

12 Antisocial behavior Example in Mplus Version 3

13 ASB Item Probabilities

14 Relationship between class probabilities and covariate (AGE94) FemalesMales

15 ASB Example Conclusions Summary of four classes: Summary of four classes: –Property Offense Class (9.8%) –Substance Involvement Class (18.3%) –Person Offenses Class (27.9%) –Normative Class (44.1%) –Normative Class (44.1%) Classification Table: Classification Table:

16 2 nd Example: Diabetes Data Three continuous variables: Three continuous variables: –Glucose (y1) –Insulin (y2) –SSPG (Steady-stage plasma glucose, y3) N=145 N=145 Data from Reaven and Miller (1979) Data from Reaven and Miller (1979)

17 Diabetes Example C GlucoseInsulinSSPG

18 Diabetes Example in Mplus Version 3

19 Diabetes Results

20 Diabetes Results

21 Diabetes Example Conclusions Summary of Three classes: Summary of Three classes: –Class 1: –Class 1: Overt Diabetes group (52%) –Class 2: Chemical Diabetes group (19.6%) –Class 3: Normal Group (28.4%) Classification Table: Classification Table:

22 Extensions of the LCA Model Extensions of the LCA Model Confirmatory LCA Confirmatory LCA –Constraints on Model Parameters Multiple LCA variables Multiple LCA variables –Multiple Measurement Instruments –Latent Transition Analysis Multi-level LCA Multi-level LCA Use Monte Carlo to explore sample size issues Use Monte Carlo to explore sample size issues

23 Resources Mplus User Guide Mplus User Guide – ATS Mplus Support ATS Mplus Support – – Applied Latent Class Analysis, Edited by Hagenaars and McCutcheon (‘02) Applied Latent Class Analysis, Edited by Hagenaars and McCutcheon (‘02)

24References 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. ( ). 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, Reaven, G.M., & Miller., R.G.(1979). “An attempt to define the nature of chemical diabetes using multidimensional analysis,” Diabetologica, 16,