Autoregressive mixed effects models and an application to annual income of cancer survivors

Date created: 
Longitudinal data
Mixed models
Autoregressive models
Breast cancer
Annual net income

Longitudinal observations of income are often strongly autocorrelated, even after adjusting for independent variables. We explore two common longitudinal models that allow for residual autocorrelation: 1. the autoregressive error model (a linear mixed effects model with an AR(1) covariance structure), and 2. the autoregressive response model (a linear mixed effects model that includes the first lag of the response variable as an independent variable). We explore the theoretical properties of these models and illustrate the behaviour of parameter estimates using a simulation study. Additionally, we apply the models to a data set containing repeated (annual) observations of income and sociodemographic variables on a sample of breast cancer survivors. Our preliminary results suggest that the autoregressive response model may severely overestimate the magnitude of the effect of cancer. Our findings will guide future, comprehensive study of the short- and long-term effects of a breast cancer diagnosis on a survivor’s annual net income.

Document type: 
Graduating extended essay / Research project
This thesis may be printed or downloaded for non-commercial research and scholarly purposes. Copyright remains with the author.
Rachel Altman
Science: Department of Statistics and Actuarial Science
Thesis type: 
(Project) M.Sc.