An Introduction to Latent Class Analysis (LCA) Handouts provided by Methods Work, LLC SBM 4/11/2012 An Introduction to Latent Class Analysis (LCA) Slides courtesy of The Methodology Center at Penn State methodology.psu.edu Learn. Apply. Innovate. www.methodswork.com

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 Learn. Apply. Innovate. www.methodswork.com

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 Learn. Apply. Innovate. www.methodswork.com

Conceptual introduction to latent class analysis (LCA) Handouts provided by Methods Work, LLC SBM 4/11/2012 Conceptual introduction to latent class analysis (LCA) Learn. Apply. Innovate. www.methodswork.com

Latent variable frameworks Handouts provided by Methods Work, LLC SBM 4/11/2012 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 Learn. Apply. Innovate. www.methodswork.com

The basic ideas underlying LCA Handouts provided by Methods Work, LLC SBM 4/11/2012 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 Learn. Apply. Innovate. www.methodswork.com

Graphical representation Handouts provided by Methods Work, LLC SBM 4/11/2012 Graphical representation C Y1 Y2 Yj … Learn. Apply. Innovate. www.methodswork.com

Graphical representation Handouts provided by Methods Work, LLC SBM 4/11/2012 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. Learn. Apply. Innovate. www.methodswork.com

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 Learn. Apply. Innovate. www.methodswork.com

Handouts provided by Methods Work, LLC SBM 4/11/2012 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), 671-694. Learn. Apply. Innovate. www.methodswork.com

Handouts provided by Methods Work, LLC SBM 4/11/2012 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% Learn. Apply. Innovate. www.methodswork.com

Handouts provided by Methods Work, LLC SBM 4/11/2012 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 Learn. Apply. Innovate. www.methodswork.com

Handouts provided by Methods Work, LLC SBM 4/11/2012 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. Learn. Apply. Innovate. www.methodswork.com

Handouts provided by Methods Work, LLC SBM 4/11/2012 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. Learn. Apply. Innovate. www.methodswork.com

Types of research questions LCA can address Handouts provided by Methods Work, LLC SBM 4/11/2012 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. Learn. Apply. Innovate. www.methodswork.com

Weight control strategies (Lanza, Savage, & Birch, 2010) Handouts provided by Methods Work, LLC SBM 4/11/2012 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), 833-840. Learn. Apply. Innovate. www.methodswork.com

Substance use behaviors (Lanza, Patrick, & Maggs, 2010) Handouts provided by Methods Work, LLC SBM 4/11/2012 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), 93-120. Learn. Apply. Innovate. www.methodswork.com

Risky sexual behavior (Lanza & Collins, 2008) Handouts provided by Methods Work, LLC SBM 4/11/2012 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. Learn. Apply. Innovate. www.methodswork.com

Ecological risk profiles (Lanza & Rhoades, 2013) Handouts provided by Methods Work, LLC SBM 4/11/2012 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), 157-168. Learn. Apply. Innovate. www.methodswork.com

Social network roles (Smith & Lanza, 2011) Handouts provided by Methods Work, LLC SBM 4/11/2012 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), 1274-1281. Learn. Apply. Innovate. www.methodswork.com

Types of data that can be used with LCA Handouts provided by Methods Work, LLC SBM 4/11/2012 Types of data that can be used with LCA Learn. Apply. Innovate. www.methodswork.com

Individuals’ responses to multiple items… Handouts provided by Methods Work, LLC SBM 4/11/2012 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) Learn. Apply. Innovate. www.methodswork.com

How many indicators can be used? Handouts provided by Methods Work, LLC SBM 4/11/2012 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 Learn. Apply. Innovate. www.methodswork.com

Handouts provided by Methods Work, LLC SBM 4/11/2012 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 Learn. Apply. Innovate. www.methodswork.com

Parameters estimated in LCA and the LCA mathematical model Handouts provided by Methods Work, LLC SBM 4/11/2012 Parameters estimated in LCA and the LCA mathematical model Learn. Apply. Innovate. www.methodswork.com

Handouts provided by Methods Work, LLC SBM 4/11/2012 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 Learn. Apply. Innovate. www.methodswork.com

Handouts provided by Methods Work, LLC SBM 4/11/2012 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 Learn. Apply. Innovate. www.methodswork.com

Handouts provided by Methods Work, LLC SBM 4/11/2012 Latent class notation The latent class model can be expressed as where Learn. Apply. Innovate. www.methodswork.com

Handouts provided by Methods Work, LLC SBM 4/11/2012 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) Learn. Apply. Innovate. www.methodswork.com

Item-response probabilities Handouts provided by Methods Work, LLC 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) Learn. Apply. Innovate. www.methodswork.com

Item-response probabilities Handouts provided by Methods Work, LLC 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 Learn. Apply. Innovate. www.methodswork.com

Exercise 1 Fitting a latent class model Interpreting the parameters

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), 671-694. 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), 93-120. Lanza, S. T., & Rhoades, B. L. (2013). Latent class analysis: An alternative perspective on subgroup analysis in prevention and treatment. Prevention Science, 14(2), 157-168. 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), 833-840. Smith, R. A., & Lanza, S. T. (2011). Testing theoretical network classes and HIV-related correlates with latent class analysis. AIDS Care, 23(10), 1274-1281.