This article is concerned with the technique called discrete-time noncausal linear periodically time-varying (LPTV) scaling for robust stability analysis. Noncausal LPTV scaling has already been shown to be effective for reducing the conservativeness of robustness analysis in theoretical and numerical ways. However, there still remain some issues to be resolved for further understanding and exploiting noncausal LPTV scaling, e. g. its relationship with the conventional analysis approach of causal linear time-invariant scaling. In this article, by introducing the key idea of shift-invariance in lifting-timing, we discuss the difference and corresponding relationship between the conventional approach and noncausal LPTV scaling.