### LCA and LTA in Drug Abuse Research

The Methodology Center has contributed to two important theoretical frameworks for the etiology of substance use. First, Collins (2002) proposed a methodological framework based on latent class analysis (LCA) and its longitudinal extension, latent transition analysis (LTA), for testing the gateway hypothesis of drug use onset. Maldonado and Lanza (2010) applied this framework empirically to test various gateway relations among alcohol, cigarette, and marijuana use. Second, Velicer and colleagues used LCA and LTA to test competing models of the Stages of Change theory in smoking behavior (Velicer, Martin, & Collins, 1996).

A major contribution to applied work on drug abuse is the identification of latent classes characterized by particular patterns of drug use; in other words, using LCA as a measurement model for substance use behavior. Examples include models involving stages of early substance use (e.g., Cleveland et al., 2010; Lanza, Patrick, & Maggs, 2010), stages of drug use behaviors among high-risk women (Lanza & Bray, 2010), stages involving various patterns of alcohol use (e.g., Auerbach & Collins, 2006; Lanza, Collins, Lemmon, & Schafer, 2007), and stages characterized by patterns of marijuana use and attitudes (Chung, Flaherty, & Schafer, 2006). In addition, LCA has proven to be useful for modeling closely related constructs, such as motivations of high school seniors to use alcohol (Coffman et al., 2007) and for modeling transitions in two related behaviors simultaneously over time (Bray, Lanza & Collins, 2010).

**References**

Auerbach, K. J., & Collins, L. M. (2006). A multidimensional developmental model of alcohol use during emerging adulthood. *Journal of Studies on Alcohol, 67,* 917-925.

Bray, B. C., Lanza, S. T., & Collins, L. M. (2010). Modeling relations among discrete developmental processes: A general approach to associative latent transition analysis.* Structural Equation Modeling, **17*(4), 541-569. doi:10.1080/10705511.2010.510043 PMC3094019

Chung, H., Flaherty, B. P., & Schafer, J. L. (2006). Latent class logistic regression: Application to marijuana use and attitudes among high school seniors. *Journal of the Royal Statistical Society, Series A, 169,* 723-743.

Cleveland, M. J., Collins, L. M., Lanza, S. T., Greenberg, M. T., & Feinberg, M. E. (2010). Does individual risk moderate the effect of contextual-level protective factors? A latent class analysis of substance use. *Journal of Prevention and Intervention in the Community, 38*(3), 213-228. PMCID: PMC2898733

Coffman, D. L., Patrick, M. E., Palen, L., Rhoades, B. L., & Ventura, A. K. (2007). Why do high school seniors drink? Implications for a targeted approach to intervention. *Prevention Science, 8,* 241-248.

Collins, L. M. (2002). *Using latent transition analysis to examine the gateway hypothesis. Stages and pathways of drug involvement: Examining the gateway hypothesis* (pp. 254-269). Cambridge, MA: Cambridge University Press.

Lanza, S. T., & Bray, B. C. (2010). Transitions in drug use among high-risk women: An application of latent class and latent transition analysis. *Advances and Applications in Statistical Sciences, 3,* 203-235. PMCID: PMC3171700

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. PMCID: PMC2785099

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. PMCID: PMC2909684

Maldonado, M. M., & Lanza, S. T. (2010). A framework to examine gateway relations in drug use: An application of latent transition analysis. *Journal of Drug Issues, 40, *901-924. PMCID: PMC3400537

Velicer, W. F., Martin, R. A., & Collins, L. M. (1996). Latent transition analysis for longitudinal data.* Addiction, **91 Suppl*, S197-209.

### LCA and LTA in HIV Research

Since 2008, The Methodology Center has focused more directly on the issue of HIV. LCA has played a role in this new focus. For example, Lanza and Collins (2008) identified sexual behavior latent classes among adolescents in the U.S. using data on number of dating partners, number of sexual partners, and consistency of condom use. Adolescents were followed over time, and LTA was used to model transitions between latent classes characterized by HIV risk.

Smith and Lanza (2011) integrated social network analysis into LCA. The researchers tested whether theorized social network classes could be empirically detected in a high-risk population in Namibia using LCA. The results suggested four latent classes that did not map well onto the theorized classes. The identified subgroups were the single-group members (59%), connectors (24%), single-group loyalists (15%), and selective connectors (2%).

Lanza, Kugler, and Mathur (2011) employed finite mixture regression--a variant of latent class analysis--to detect four latent classes of adolescents in the U.S. based on the effects of five risk factors (assessed in Wave I of the Add Health study) on their reported lifetime sex partners (assessed in Wave IV). The previously established risk factors for HIV-risk behavior were shown to be highly salient for latent classes characterized by fewer lifetime sex partners, but significantly less relevant for the riskiest latent class, which was characterized by nearly 80 partners on average.

**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), 446-456. PMCID: PMC2846549

Lanza, S. T, Kugler, K. C., & Mathur, C. (2011). Differential effects for sexual risk behavior: An application of finite mixture regression. *The Open Family Studies Journal, 4,* (Suppl. 1-M9), 81-88. PMCID: PMC3487167

Smith, R. A., & Lanza, S. T. (2011). Testing theoretical network classes and HIV-related correlates with latent class analysis. *AIDS Care.* Advance online publication. doi: 10.1080/09540121.2011.555747. PMCID: PMC3181093

### LCA in Risk Factors Research

Recent work on modeling multiple risk factors has demonstrated the importance of taking a more holistic approach in order to draw prevention implications. Lanza, Rhoades, Greenberg, Cox, and the Family Life Project Key Investigators (2011) compared LCA to the more common approach of a cumulative risk index to study the effect of early risk factors on the quality of the caregiving environment for infants. Also see Lanza, Rhoades, Nix, and Greenberg (2010), in which the authors used LCA to analyze 13 risk factors for children in kindergarten to predict academic and behavioral outcomes in fifth grade.

Lanza and Rhoades (2013) demonstrated how LCA can be used to construct latent classes of risk, and then treat the latent class variable as a latent moderator of treatment effect. This study led to the development of an Excel calculator that provides a model-based solution to predicting a binary distal outcome from the latent class variable, work which ultimately led to the development of a comprehensive model-based approach, packaged as SAS macro %LCA_Distal, to estimate the effect of latent class membership on a binary, continuous, count, or categorical distal outcome (Lanza, Bray, & Tan, 2011).

**References**

Lanza, S. T., Tan, X., & Bray, B. C. (2013). Latent class analysis with distal outcomes: A flexible model-based approach. *Structural Equation Modeling: A Multidisciplinary Journal*. Advance online publication. doi: 10.1080/10705511.2013.742377 PMC Journal- In Process

Lanza, S. T. & Rhoades, B. L. (2013). Latent class analysis: An alternative perspective on subgroup analysis in prevention and treatment. *Prevention Science, 14,* 157-168. PMCID: PMC3173585

Lanza, S. T., Rhoades, B. L., Greenberg, M. T., Cox, M. J., & The Family Life Project Key Investigators (2011). Modeling multiple risks during infancy: Contributions of a person-centered approach. *Infant Behavior and Development, 34*(3), 390-406. PMCID: PMC3134117

Lanza, S. T., Rhoades, B. L., Nix, R. L., Greenberg, M. T., & the Conduct Problems Prevention Research Group (2010). Modeling the interplay of multilevel risk factors for future academic and behavior problems: A person-centered approach. *Development and Psychopathology, 22,* 313-335. PMCID: PMC3005302