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st: Pregibon's beta
To detect influential cases in binary regression, Long & Freese (2003: 128)
and Long (1997:101) mention Pregibon?s beta, a statistic that is "the
counterpart to Cook?s distance for the linear regression model." In Stata,
you get Pregibon's betas by using -predict- with the option dbeta.
Long and Freese do not give any particular rule of thumb about what value
of this statistic would be a good threshold (i.e., above that value we
worry, below that value we don?t). Long (1997) seems to imply that .06 is
too low and Long & Freese that .2 is high. But I wonder if that depends on
the particular samples they were looking at. I checked Pregibon (1981) and
also Cook (1979), but I couldn't spot any rules of thumb.
Beyond the basic interpretation that large values of this statistic
indicate more influential cases, are there any clues to evaluate how high
values have to be before we take a closer look at them? I anticipate that
the answer is "no, it depends on sample size and other issues", but I'd
appreciate any enlightenment on this particular statistic.
Department of Sociology
Louisiana State University
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