Complexity being one of the main limitations of LPV methods, the need for efficient model reduction techniques is highly motivated. Yet, so far, there exists no convex formulation of the general problem of finding a reduced model of any given complexity. In this paper, we focus on the case when the reduced model is supposed to have a special structure and we then derive convex conditions. Thus, for a system modeled by an LFT on a repeated scalar parameter structure, we prove that the problem can be formulated as an LMI optimization problem in the case when the reduced model is supposed to depend only on some parameters of the original system in the same manner as the plant whereas the dependence on the other parameters has been removed. The method is applicable to quadratically stable systems. A complete construction procedure is provided and a measure of the associated model reduction error is given. The method is illustrated in the context of missile control.