The Origin and Developments of Influence Measures in Regression

The understanding about influence measures is not new and certainly dates back to the first effort to detect anomalous observations that exert an unduly large impact on the regression output. The earliest development in this context that we have been able to locate is by Cook (1977). In recently the phrase ‘influence measures’ has glimpsed a great surge of research interests. In this paper the development of such measures is investigated from the early criteria of Cook’s to the present. Major influence measures treated are Cook’s distance ( i D ), Modified Cook’s distance ( * i D ), Andrew and Pregibon ( i AP ) measure, Hadi measure ( 2 i H ), Welsch and Kuh distance ( i WK ), Welsch distance ( i W ), Cook and Weisberg likelihood displacement ( i LD ) and the idea of local influence inspired by Cook (1986). The goals of these influence measures are also discussed.