we usually remove uni-variate outliers (Influential & extreme) by box-plot & other techniques.What we should do in case Multi-variate outliers of Structure equation modeling(AMOS) which can be easily obtained by Mahalanobis d square method. How to determine which outlier is influential and extreme. By removing one a new outliers crop up.Hence, by continuing with this approach, we may lost important data point.This is why I like to know whether there is any logic behind removing Multi-variate outliers by this approach.
You get better model fit if you remove all the data that don't fit the model. That's clear. What is not clear is why you are getting your data to fit a model rather than finding a model to fit your data.
Outliers require to be understood. They may reflect important but uncommon data generation processes, such as the existence of small groups with higher or lower values. Removing them is almost certain to leave you with data that do not actually represent the behaviour of the variables you are interested in, and which will have very questionable generalisability.
In case of outliers, I would suggest that we should firstly try to meet the assumptions of multivariate analysis (Normality, Homoscedasticity, linearity and uncorrelated errors). If these assumptions are met then we can get good model fit. In case of Mahalanobis D square distance, initially if we find outliers based on distance , after removing theses outliers, then, it will show next set of observations as distant from the rest of data.
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