  We generalize Levene's test for variance (scale) heterogeneity between $k$
groups for more complex data, which includes sample correlation and group
membership uncertainty. Following a two-stage regression framework, we show
that least absolute deviation regression must be used in the stage 1 analysis
to ensure a correct asymptotic $\chi^2_{k-1}/(k-1)$ distribution of the
generalized scale ($gS$) test statistic. We then show that the proposed $gS$
test is independent of the generalized location test, under the joint null
hypothesis of no mean and no variance heterogeneity. Consequently, we
generalize the recently proposed joint location-scale ($gJLS$) test valuable in
settings where there is an interaction effect, but one interacting variable is
not available. We evaluate the proposed method via an extensive simulation
study, and two genetic association application studies.

Methodology