A Dirichlet random coefficient regression model for quality indicators

We present a random coefficient regression model in which a response is linearly related to some explanatory variables with random coefficients following a Dirichlet distribution. These coefficients can be interpreted as weights because they are nonnegative and add up to one. The proposed estimation procedure combines iteratively reweighted least squares and the maximization on an approximated likelihood function. We also present a diagnostic tool based on a residual Q–Q plot and two procedures for estimating individual weights. The model is used to construct an index for measuring the quality of the railroad system in Spain.