Transcript Latent Class Analaysis - Institute for Digital Research

Latent Class Analysis in
Mplus Version 3
Karen Nylund
Social Research Methods
Graduate School of Education &
Information Studies
[email protected]
Overview of Session
General description of Latent Class Analysis
(LCA) within a hypothetical example
 Two examples of LCA analysis using Mplus

Version 3
– Anti-Social Behavior
– Diabetes Diagnosis
Extensions of the LCA models
 Resources and References
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Hypothetical Example:
Identifying effective teachers
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Setting: Unsure how to identify an
effective teacher
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Possible Indicators:
– Credential or Not?
– Promotes critical thinking
– Reflective
– Professional Development (P.D.)
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What would the data look like?
Critical
Teacher Credential Thinking Reflective
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0
1
1
P.D.
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2
0
0
1
0
3
1
1
1
1
4
1
1
0
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5
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1
0
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0
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0
0
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Possible research questions:
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Are there specific characteristics that identify an
effective teacher?
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Given known ideas of what an effective teacher
is, what characteristics are important indicators?
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Are there background characteristics of the
teachers that help classify them as effective?
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What could LCA tell us?
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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
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The LCA Model
Y1
X
Y2
Y3
...
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Observed Continuous (y’s)
or Categorical Items (u’s)
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Categorical Latent Class
Variable (c)
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Continuous or Categorical
Covariates (x)
Yp
C
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How is this modeling
process conducted?
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Run through models imposing different
numbers of classes
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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.
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Evaluating the Model
Model Fit
Model Usefulness
BIC and AIC
 Substantive Interpretation
 X2 Statistic
 Classification Quality
– Classification Tables
 Lo-Mendell-Rubin Test
– Entropy
(Tech 11)
 Standardized Residuals
(Tech 10)
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1st Data Example: Anti-Social Behavior
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National Longitudinal Survey of Youth (NLSY)
Respondent ages between 16 and 23
Background information: age, gender and ethnicity
N=7,326
17 antisocial dichotomously scored behavior items:
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Damaged property
Fighting
Shoplifting
Stole <$50
Stole >$50
Use of force
Seriously threaten
Intent to injure
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Use Marijuana
Use other drug
Sold Marijuana
Sold hard drugs
‘Con’ somebody
Stole an Automobile
Broken into a building
Held stolen goods
Gambling Operation
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Anti Social Behavior Example
Damage
Property
Fighting
Shoplifting
Stole <$50
...
Gambling
Male
Race
C
Age
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Antisocial behavior Example in
Mplus Version 3
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ASB Item Probabilities
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Relationship between
class probabilities and covariate (AGE94)
Females
Males
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ASB Example Conclusions

Summary of four classes:
–
–
–
–
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Property Offense Class (9.8%)
Substance Involvement Class (18.3%)
Person Offenses Class (27.9%)
Normative Class (44.1%)
Classification Table:
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2
3
4
1
0.854
0.031
0.070
0.040
2
0.041
0.917
0.04
0
3
0.058
0.021
0.820
0.100
4
0.038
0
0.08
0.88
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nd
2
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Example: Diabetes Data
Three continuous variables:
– Glucose (y1)
– Insulin (y2)
– SSPG (Steady-stage plasma glucose, y3)
N=145
 Data from Reaven and Miller (1979)
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Diabetes Example
Glucose
Insulin
SSPG
C
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Diabetes Example in Mplus Version 3
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Diabetes Results
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Diabetes Results
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Diabetes Example Conclusions
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Summary of Three classes:
– Class 1: Overt Diabetes group (52%)
– Class 2: Chemical Diabetes group (19.6%)
– Class 3: Normal Group (28.4%)
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Classification Table:
1
2
3
1
0.929
0.001
0.071
2
0.000
0.967
0.033
3
0.053
0.010
0.937
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Extensions of the LCA Model
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Confirmatory LCA
– Constraints on Model Parameters
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Multiple LCA variables
– Multiple Measurement Instruments
– Latent Transition Analysis
Multi-level LCA
 Use Monte Carlo to explore sample size
issues
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Resources

Mplus User Guide

ATS Mplus Support
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Applied Latent Class Analysis, Edited by
Hagenaars and McCutcheon (‘02)
– http://www.statmodel.com
– http://www.ats.ucla.edu/stat/mplus/
– http://www.ats.ucla.edu/stat/seminars/ed231e/
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References
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Hagenaars, J.A & McCutcheon, A. (2002). Applied latent class
analysis. Cambridge: Cambridge University Press.
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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)
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Muthén, L. & Muthén, B. (1998-2004). Mplus user’s guide. Los Angeles, CA:
Muthén & Muthén.
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Muthén, B. & Muthén, L. (2000). Integrating person-centered and variablecentered analysis: growth mixture modeling with latent trajectory classes.
Alcoholism: Clinical and Experimental Research, 24, 882-891.
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Reaven, G.M., & Miller., R.G.(1979). “An attempt to define the nature of
chemical diabetes using multidimensional analysis,” Diabetologica, 16, 1727.
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