1. An Introduction to Latent Class Analysis (LCA)
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SBM 4/11/2012
An Introduction to Latent Class Analysis (LCA)
Slides courtesy of The Methodology Center at Penn State
methodology.psu.edu
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2. Handouts provided by Methods Work, LLC
SBM 4/11/2012
Outline
Conceptual introduction to latent class analysis (LCA)
An example: Latent classes of adolescent drinking behavior
Types of research questions LCA can address
Types of data that can be used with LCA
Parameters estimated in LCA and the LCA mathematical model
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3. Handouts provided by Methods Work, LLC
SBM 4/11/2012
Abbreviations
LCA = latent class analysis
Categorical latent variable measured with categorical items
LPA = latent profile analysis
Categorical latent variable measured with continuous items
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4. Conceptual introduction to latent class analysis (LCA)
Handouts provided by Methods Work, LLC
SBM 4/11/2012
Conceptual introduction to latent class analysis (LCA)
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5. Latent variable frameworks
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Latent variable frameworks
Categorical latent variable
Continuous latent variable
Categorical observed variables
Latent Class Analysis (LCA)
Latent Trait Analysis or Item Response Theory
Continuous observed variables
Latent Profile Analysis (LPA)
Factor Analysis or Structural Equation Modeling
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6. The basic ideas underlying LCA
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The basic ideas underlying LCA
Individuals can be divided into subgroups based on unobservable construct
The construct of interest is the latent variable
Subgroups are called latent classes
True class membership is unknown
Unknown due to measurement error
Measurement of the construct is based on several categorical indicators
Latent classes are mutually exclusive & exhaustive
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7. Graphical representation
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Graphical representation C Y1 Y2 Yj …
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8. Graphical representation
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Graphical representation C Y1 Y2 Yj …
Latent class variable
Observed indicators
Arrows point from the latent variable to the observed indicators. This is because the behaviors that are observed are reflections of a person’s status on the latent variable.
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9. An example: Latent classes of adolescent drinking behavior
Handouts provided by Methods Work, LLC
SBM 4/11/2012
An example: Latent classes of adolescent drinking behavior
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10. Handouts provided by Methods Work, LLC
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Drinking in 12th grade
Data from 2004 cohort of Monitoring the Future public release
n = 2490 high school seniors who answered at least one question about alcohol use (48% boys, 52% girls)
Goals of the Lanza, Collins, Lemmon, & Schafer, 2007 study:
Investigate alcohol use behavior among U.S. 12th graders
Examine gender differences in measurement and behavior
Predict class membership from skipping school and grades
Lanza, S. T., Collins, L. M., Lemmon, D. R., & Schafer, J. L. (2007). PROC LCA: A SAS procedure for latent class analysis. Structural Equation Modeling, 14(4),
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11. Handouts provided by Methods Work, LLC
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Drinking in 12th grade
Seven items about drinking behavior
Proportion who answered ‘Yes’
Lifetime alcohol use
82%
Past-year alcohol use
73%
Past-month alcohol use
50%
Lifetime drunkenness
57%
Past-year drunkenness
49%
Past-month drunkenness
29%
5+ drinks in past 2 weeks
26%
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12. Handouts provided by Methods Work, LLC
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Here, we will…
Review the results of the first research question addressed by Lanza, Collins, Lemmon, & Schafer, 2007:
Identify and describe underlying latent classes of drinking behavior in U.S. 12th grade students
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The 5-class model
Probability of ‘Yes’ response
Item
Class 1
(18%)
Class 2
(22%)
Class 3
(9%)
Class 4
(17%)
Class 5
(34%)
Lifetime alcohol use
.00
1.00
Past-year alcohol
.61
Past-month alcohol
.39
Lifetime drunk
.24
.29
Past-year drunk
Past-month drunk
.92
5+ drinks past 2 wk
.16
.73
Note that a model selection was conducted to arrive at the 5-class model.
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14. Handouts provided by Methods Work, LLC
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The 5-class model
Probability of ‘Yes’ response
Item
Non-
Drinkers
Experi-
menters
Light
Past
Partiers
Heavy
Lifetime alcohol use
.00
1.00
Past-year alcohol
.61
Past-month alcohol
.39
Lifetime drunk
.24
.29
Past-year drunk
Past-month drunk
.92
5+ drinks past 2 wk
.16
.73
Naming the classes is the responsibility of the researcher. Similar to factor analysis, all classes must be theoretically interpretable.
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15. Types of research questions LCA can address
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Types of research questions LCA can address
Note that the following slides are designed to provide a sample of the many public health issues to which LCA can be applied.
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16. Weight control strategies (Lanza, Savage, & Birch, 2010)
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Weight control strategies (Lanza, Savage, & Birch, 2010)
What types of weight-loss strategies are used by women?
Identified classes: No Weight Loss Strategy (10%) Dietary Guidelines (27%) Guidelines + Macronutrients (39%) Guidelines + Macronutrients + Restrictive (24%)
Lanza, S. T., Savage, J. S., & Birch, L. L. (2010). Identification and prediction of latent classes of weight‐loss strategies among women. Obesity, 18(4),
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17. Substance use behaviors (Lanza, Patrick, & Maggs, 2010)
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Substance use behaviors (Lanza, Patrick, & Maggs, 2010)
What are the substance use behavior profiles among first-year college students?
Identified classes: Non-users (58%) Cigarette Smokers (5%) Binge Drinkers (29%) Bingers + Marijuana Users (8%)
Lanza, S. T., Patrick, M. E., & Maggs, J. L. (2010). Latent transition analysis: Benefits of a latent variable approach to modeling transitions in substance use. Journal of Drug Issues, 40(1),
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18. Risky sexual behavior (Lanza & Collins, 2008)
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Risky sexual behavior (Lanza & Collins, 2008)
What are the profiles of dating and sexual risk-taking behaviors among adolescents and young adults?
Identified classes: Non-Daters (19%) Daters (29%) Monogamous (12%) Multi-partner Safe Sex (23%) Multi-Partner STI-Exposed Sex (18%)
Lanza, S. T., & Collins, L. M. (2008). A new SAS procedure for latent transition analysis: Transitions in dating and sexual risk behavior. Developmental Psychology, 44(2), 446.
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19. Ecological risk profiles (Lanza & Rhoades, 2013)
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Ecological risk profiles (Lanza & Rhoades, 2013)
What are the patterns of ecological risk factors experienced by adolescents that may help explain differential response to intervention?
Identified classes: Low Risk (31%) Peer Risk (28%) Economic Risk (20%) Household + Peer Risk (12%) Multi-context Risk (8%)
Lanza, S. T., & Rhoades, B. L. (2013). Latent class analysis: An alternative perspective on subgroup analysis in prevention and treatment. Prevention Science, 14(2),
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20. Social network roles (Smith & Lanza, 2011)
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Social network roles (Smith & Lanza, 2011)
Do people's social connections fall into types of social capital that represent theorized network roles relevant for HIV intervention in Namibia?
Identified classes: Single-Group Members (59%) Connectors (24%) Single-Group Loyalists (15%) Selective Connectors (2%)
Smith, R. A., & Lanza, S. T. (2011). Testing theoretical network classes and HIV-related correlates with latent class analysis. AIDS Care, 23(10),
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21. Types of data that can be used with LCA
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Types of data that can be used with LCA
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22. Individuals’ responses to multiple items…
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Individuals’ responses to multiple items…
Using all categorical indicators usually called LCA
Interested in latent class prevalences and item-response probabilities
Using all continuous indicators usually called LPA
Interested in latent profile prevalences and item-response means (and variances)
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23. How many indicators can be used?
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How many indicators can be used?
When many indicators with many response options are used, it can be difficult to identify reliably the maximum likelihood estimates
When few indicators with few response options are used, only a very small number of latent classes can be identified
Practically speaking, it is often a good idea to start with 5-12 binary indicators
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A note on missing data
Most LCA software can handle missing data
Missing data mechanisms:
MAR (missing at random)
Missingness is completely random, or related to observed items
MNAR (missing not at random)
Missingness is related to unobserved items
Software assumes data are MAR
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25. Parameters estimated in LCA and the LCA mathematical model
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Parameters estimated in LCA and the LCA mathematical model
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26. Handouts provided by Methods Work, LLC
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Estimated parameters
Latent class prevalences
e.g., probability of membership in EXPERIMENTERS latent class
Item-response probabilities
e.g., probability of reporting PAST-YEAR ALCOHOL USE given membership in EXPERIMENTERS latent class
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27. Handouts provided by Methods Work, LLC
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Latent class notation
Y represents the vector of all possible response patterns
y represents a particular response pattern
Example response pattern for the 7 items from the example of drinking in 12th grade: y = (Y, Y, N, N, N, N, N)
X represents the vector of all covariates of interest
x represents a particular covariate
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Latent class notation
The latent class model can be expressed as where
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29. Handouts provided by Methods Work, LLC
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Latent class notation
…with (c = 1,2,…,K) latent classes and (m = 1,2,…,M) indicators, each with (rm = 1,2,…,Rm) response options. = probability of membership in latent class c (latent class membership probabilities) = probability of response rm to indicator m, conditional on membership in latent class c (item-response probabilities)
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30. Item-response probabilities
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SBM 4/11/2012
Item-response probabilities
parameters express the relation between…
the discrete latent variable in an LCA and
the observed indicator variables
Similar conceptually to factor loadings
Basis for interpretation of latent classes
Are probabilities (between 0 and 1)
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31. Item-response probabilities
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SBM 4/11/2012
Item-response probabilities
parameters analogous to factor loadings; both…
express the relation between manifest and latent variables
form the basis for interpreting latent structure
But…
Factor loadings are -weights
parameters are probabilities
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32. Exercise 1
Fitting a latent class model
Interpreting the parameters

33. References
Lanza, S. T., & Collins, L. M. (2008). A new SAS procedure for latent transition analysis: Transitions in dating and sexual risk behavior. Developmental Psychology, 44(2), 446. Lanza, S. T., Collins, L. M., Lemmon, D. R., & Schafer, J. L. (2007). PROC LCA: A SAS procedure for latent class analysis. Structural Equation Modeling, 14(4), Lanza, S. T., Patrick, M. E., & Maggs, J. L. (2010). Latent transition analysis: benefits of a latent variable approach to modeling transitions in substance use. Journal of Drug Issues, 40(1), Lanza, S. T., & Rhoades, B. L. (2013). Latent class analysis: An alternative perspective on subgroup analysis in prevention and treatment. Prevention Science, 14(2), Lanza, S. T., Savage, J. S., & Birch, L. L. (2010). Identification and prediction of latent classes of weight‐loss strategies among women. Obesity, 18(4), Smith, R. A., & Lanza, S. T. (2011). Testing theoretical network classes and HIV-related correlates with latent class analysis. AIDS Care, 23(10),