  The $\gamma$-divergence is well-known for having strong robustness against
heavy contamination. By virtue of this property, many applications via the
$\gamma$-divergence have been proposed. There are two types of \gd\ for
regression problem, in which the treatments of base measure are different. In
this paper, we compare them and pointed out a distinct difference between these
two divergences under heterogeneous contamination where the outlier ratio
depends on the explanatory variable. One divergence has the strong robustness
under heterogeneous contamination. The other does not have in general, but has
when the parametric model of the response variable belongs to a location-scale
family in which the scale does not depend on the explanatory variables or under
homogeneous contamination where the outlier ratio does not depend on the
explanatory variable. \citet{hung.etal.2017} discussed the strong robustness in
a logistic regression model with an additional assumption that the tuning
parameter $\gamma$ is sufficiently large. The results obtained in this paper
hold for any parametric model without such an additional assumption.
