Abstract: This article explores the homogeneity of coefficient functions in varying coefficient models where individuals can be classified into different subgroups for each covariate where its varying coefficients are homogeneous in the same subgroup. With repeated measurements, we use B-spline function approximations and the change point detection algorithm to identify the homogeneity. To account for the potential outliers or heavy-tailedness of the observed distribution, we propose to estimate the coefficient functions under the framework of M-estimation, and use least absolute deviation (LAD) loss as an example. Numerical results show that our estimators outperform the commonly used least squares (LS) estimators when existing outliers and heavy-tailedness of observed distribution.