Physical activity is an important component to a healthy lifestyle. However, it is difficult to create physical activity recommendations because it is difficult to track people's physical activity throughout time. This makes it difficult to assess whether people adhere to recommendations or not. Additionally, lack of measurement error-free data makes it difficult to understand the relationships between physical activity and health outcomes.

We address these three issues in this dissertation. First, we construct a flexible measurement error model that uses free knot splines to model the relationship between less expensive measurements and the truth. Because the truth is latent, we model it with a Dirichlet Process mixture prior. We give a calibration algorithm which can be used to eliminate biases in future measurements once this model is fit. Second, we develop a model that allows us to estimate the proportion of people in adherence to the Physical Activity Guidelines (PAG). Additionally, we estimate the entire distribution of usual activity levels which allows us to understand differences among different demographic groups. We find large differences in results using the Physical Activity Measurement Survey (PAMS) from Iowa compared to the 2003-2006 National Health and Nutrition Examination Survey (NHANES), a nationally representative survey. Finally, we construct a model that looks at the relationship between minutes in moderate to vigorous physical activity (MVPA) and Metabolic Syndrome (MetS) and its risk factor components. This model accounts for measurement error as well as the complex data structure. Using the 2003-2006 NHANES data, we find the probability of being diagnosed with MetS goes from 40\% to 23\% when one participates in 20 minutes of MVPA compared to 0 minutes.