This thesis explores the homogeneity of coefficient functions in nonlinear models with functional coefficients, and identifies the semiparametric modelling structure. With initial kernel estimate of each coefficient function, we combine the classic hierarchical clustering method and a generalised version of the information criterion to estimate the number of clusters each of which has the common functional coefficient and determine the indices within each cluster. To specify the semi-varying coefficient modelling framework, we further introduce a penalised local least squares method to determine zero coefficient, non-zero constant coefficients and functional coefficients varying with the index variable. Through the nonparametric kernel-based cluster analysis and the penalised approach, the number of unknown parametric and nonparametric components in the models can be substantially reduced and the aim of dimension reduction can be achieved. Under some regularity conditions, we establish the asymptotic properties for the proposed methods such as consistency of the homogeneity pursuit and sparsity. Some numerical studies including simulation and two empirical applications are given to examine the finite-sample performance of our methods
