## TVEM With Normal and Binary Outcomes

The time-varying effect model developed by Methodology Center researchers allows researchers to estimate the time-varying effects of coefficients. A natural extension of linear regression models, TVEM allows coefficients to vary over time. This flexible approach allows the mean trajectory and effects of covariates to vary with time without assuming parametric (e.g., linear or quadratic) functions.

**References**

Tan, Shiyko, Li, Li, & Dierker (2012) provides a detailed introduction to time-varying effect models for audiences in the psychological sciences. An empirical demonstration of the %TVEM macro appears in Shiyko, Lanza, Tan, Li, & Shiffman (2012). Both articles make use of the %TVEM SAS macro, developed by Center scientists to enable applied researchers to employ TVEM.

Patrick, M. E., Evans-Polce, R., Kloska, D. D., Maggs, J. L., & Lanza, S. T. (2017). Age-related changes in associations between reasons for alcohol use and high-intensity drinking across young adulthood. *Journal Of Studies On Alcohol And Drugs, 78*(4), 558-5

Vasilenko, S. A., Piper, M. E., Lanza, S. T., Liu, X., Yang, J., & Li, R. (2014). Time-varying processes involved in smoking lapse in a randomized trial of smoking cessation therapies. *Nicotine & Tobacco Research, 16,* S135-143.

Lanza, S. T., Vasilenko, S., Liu, X., Li, R., & Piper, M. (2014). Advancing the understanding of craving during smoking cessation attempts: A demonstration of the time-varying effect model*. Nicotine and Tobacco Research, 16,* S127-134.

Yao, W., & LI, R. (2013). New local estimation procedure for nonparametric regression function of longitudinal data*. Journal of the Royal Statistical Society, Series B*, 75, 123-138. PMCID: PMC3607647

Tan, X., Shiyko, M. P., Li, R., Li, Y., & Dierker, L. (2012). A time-varying effect model for intensive longitudinal data. *Psychological Methods, 17*, 61-77. PMCID: PMC3288551

Shiyko, M. P., Lanza, S. T., Tan, X., Li, R., & Shiffman, S. (2012). Using the time-varying effect model (TVEM) to examine dynamic associations between negative affect and self-confidence on smoking urges: Differences between successful quitters and relapsers. *Prevention Science, 13*, 288-299. PMCID: PMC3171604

Tan, X., Dierker, L., Rose, J., Li, R., & Tobacco Etiology Research Network. (2011). How spacing of data collection may impact estimates of substance use trajectories. *Substance Use & Misuse, 46*(6), 758-68. doi: 10.1007/s11121-011-0217-6

Kai, B., Li, R., & Zou, H. (2011). New efficient estimation and variable selection methods for semiparametric varying-coefficient partially linear models. *Annals of Statistics, 39*, 305-332. PMCID: PMC3109949

Fan, J. Huang, T., & Li, R. (2007). Analysis of longitudinal data with semiparametric estimation of covariance function. *Journal of American Statistical Association. 102*, 632-641. PMCID: PMC2730591

Qu, A. P., & Li, R. (2006). Quadratic inference functions for varying-coefficient models with longitudinal data. *Biometrics, 62*, 379-391. PMCID: PMC2680010

Fan, J., & Li, R. (2004). New estimation and model selection procedures for semiparametric modeling in longitudinal data analysis. *Journal of the American Statistical Association, 99,* 710-723.

## TVEM With Ordinal Outcomes

Ordinal TVEM is time-varying effect model for an ordinal response. Ordinal variables differ from categorical variables in that, for ordinal responses, the categories have an order (e.g., first second, third,), and they must be treated differently in computation. Methodology Center researchers have developed a SAS macro to estimate Ordinal TVEM. See Dziak, Li, Zimmerman, & Bu (2014) for more information.

**References**

Dziak, J. J., Li, R., Zimmerman, M., & Buu, A. (2014). Time-varying effect models for ordinal responses with applications in substance abuse research. *Statistics In Medicine, 33*(29), 5126-37.

## Mixture TVEM

MixTVEM estimates time varying effect models that allow heterogeneous subgroups within the data set to have different coefficient functions. Effectively, there are latent classes, each containing its own TVEM. Methodology Center researchers have developed a SAS macro and an R function to estimate Mixture TVEM. See Dziak, Li, Shiffman, & Shiyiko (2015) for more information.

**References**

Dziak, J. J., Li, R., Tan, X., Shiffman, S., & Shiyko, M. P. (2015). Modeling Intensive Longitudinal Data With Mixtures of Nonparametric Trajectories and Time-Varying Effects. P*sychological Methods.* http://doi.org/10.1037/met0000048