| Local influence analysis suggested by Cook (1986) employs a simultaneous perturbation scheme and has an advantage in that it can detect joint influence of observations and thus can identify some masking effects (Lawrance,1988). However, when there exist strong masking effects in the data, such those caused by a group of outliers or influential observations, the local influence analysis will fail to identify such influential patterns, as noted by Bruce and Martin (1989, p420) in time series models and our studies in this paper. In local influence analysis, although the observations are jointly detected, when one observation is highly influential, the associated local diagnostic for this point will have higher value, which will down-weights the effects of other influential observations if there are a mutual influence among influential observations. As a result, the masking effect will remain when down-weighting is serious.In this paper we suggest a new local influence method, which we call stepwise local influence analysis. The main idea is follows:First we perform local influence analysis using full perturbation cheme. By removing the effects of any highly influential observations identified by perturbing all observations in the first time step, and then performing a local influence analysis that is based on a subset perturbation scheme in which the influential observations identified in the first step are excluded. In this way, any influential observations masked by the first step can be identified in this new step. The procedure continues iteratively until no further influential observations can be found. We also discuss the issues of constraint on perturbation vector and bench-mark determinations on local influence analysis. The method is applied to linear model, mixed linear model and time series ARIMA model, and the analysis of four examples shows that this technique is very effective for identifying outliers or influential observations and uncovering masking effects.
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