Influence analysis with homogeneous linear restrictions

We discuss the problem of influence analysis for the particular situation in which the observations must satisfy a set of homogeneous linear restrictions. We present the proof of a theoretical result showing, that for this situation, we can define a system of orthogonal influence directions, as in the unrestricted problem. As an illustration, we discuss a linear regression model where some of the explanatory variables are in the form of proportions, giving also an example with a numerical data set. Our example shows that the influence measure that is here discussed can be quite effective in identifying relevant perturbations.