  Traditional variable selection methods could fail to be sign consistent when
irrepresentable conditions are violated. This is especially critical in
high-dimensional settings when the number of predictors exceeds the sample
size. In this paper, we propose a new semi-standard partial covariance (SPAC)
approach which is capable of reducing correlation effects from other covariates
while fully capturing the magnitude of coefficients. The proposed SPAC is
effective in choosing covariates which have direct effects on the response
variable, while eliminating the predictors which are not directly associated
with the response but are highly correlated with the relevant predictors. We
show that the proposed SPAC method with the Lasso penalty or the smoothly
clipped absolute deviation (SCAD) penalty possesses strong sign consistency in
high-dimensional settings. Numerical studies and a post-traumatic stress
disorder data application also confirm that the proposed method outperforms the
existing Lasso, adaptive Lasso, SCAD, Peter-Clark-simple algorithm, and
factor-adjusted regularized model selection methods when the irrepresentable
conditions fail.
