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Semiparametric methods are statistical methods which make use of both parametric and nonparametric components. In particular, they avoid assumptions which fully characterize the distribution of the data while still imposing a minimal structure. Although semiparametric models offer a diverse array of statistical applications, the Cox proportional hazard model and the group-based model for latent heterogeneity in trajectories within populations are commonly used ones and have proven to be particularly valuable in gerontological research.
The notion of a semiparametric model can be understood by first observing the extreme cases of parametric and nonparametric models. Consider the problem of modeling an outcome y as a function of a set of covariates X. The standard linear regression model where y = Xβ + ϵ and the components of ϵ are i.i.d. N(0,σ2) is a simple example of a parametric model. On the other extreme are nonparametric models which assume little more than y = f(...
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