Deletion diagnostics in fitting a given regression model to a new observation

Abstract

A graphical diagnostic method based on multiple case deletions in a regression context is introduced by using the sampling distribution of the difference between two least squares estimators with and without multiple cases. Principal components analysis plays a key role in deriving this diagnostic method. Multiple case deletions of test statistic are also considered when a new observation is fitted to a given regression model. The result is useful for detecting influential observations in econometric data analysis, for example in checking whether the consumption pattern at a later time is the same as the one found before or not, as well as for investigating the influence of cases in the usual regression model. An illustrative example is given.

A cautionary note on the use of Cook's distance

“…Using the probabilistic behavior ofβ−β (r) through the spectral decomposition of its covariance matrix cov(β −β (r) ), Kim (2015) introduced an influence measure M r = x T r (X T X) −2 x r /(1 − h rr ) to investigate the influence of deleting an observation on the least squares estimateβ, and the problem of deleting multiple cases was considered by Kim (2016). For these three data sets, the result based on the D r values will be compared with that based on the M r values.…”