This thesis is an extension of the longitudinal data analysis of the association between externalizing behavior in early childhood and body mass index (BMI) from age 2 to 12 years conducted in Anderson et al. (2010). Externalizing behaviors problems are characterized by aggressive, oppositional, disruptive, or inattentive behaviors beyond those that would be expected given a child's age and development. The aim of the thesis is to estimate the children's BMI trajectory and to evaluate to what extent the externalizing behavior is related to BMI using semiparametric and nonparametric time-varying coefficient models. Some valuable insights into how the externalizing behavior and BMI are associated will be provided.