  Defect models are analytical models that are used to build empirical theories
that are related to software quality. Prior studies often derive knowledge from
such models using interpretation techniques, such as ANOVA Type-I. Recent work
raises concerns that prior studies rarely remove correlated metrics when
constructing such models. Such correlated metrics may impact the interpretation
of models. Yet, the impact of correlated metrics in such models has not been
investigated. In this paper, we set out to investigate the impact of correlated
metrics, and the benefits and costs of removing correlated metrics on defect
models. Through a case study of 15 publicly-available defect datasets, we find
that (1) correlated metrics impact the ranking of the highest ranked metric for
all of the 9 studied model interpretation techniques. On the other hand,
removing correlated metrics (2) improves the consistency of the highest ranked
metric regardless of how a model is specified for all of the studied
interpretation techniques (except for ANOVA Type-I); and (3) negligibly impacts
the performance and stability of defect models. Thus, researchers must (1)
mitigate (e.g., remove) correlated metrics prior to constructing a defect
model; and (2) avoid using ANOVA Type-I even if all correlated metrics are
removed.
