Logistic Regression: A Self-learning Text, Third Edition (Statistics in the Health Sciences)

More on influential observations
including:

 How to use computer software?

 How to proceed when influential
observations are identified?

Computer Packages, e.g., SAS,
STATA, SPSS produce their
own version of influence diag-
nostics

SAS’s LOGISTIC:influenceand

iplotsoptions at end of model

statement

Large collection of regression

diagnostic information

produced, including

Dbvaluesfor each variable

and

C measuresover

all variables

SAS’s LOGISTIC:CandCbarmea-
sures (similar but not identical)

EXAMPLE

MRSA no-interaction model

Logit P(X) = a + b 1 PREVHOSP + b 2 PAMU

+ g 1 AGE + g 2 GENDER

Case 9

Case 16

C

Case 9

Case 16

1 0.00921Valve

NumberCase 0 2 4 6 8 12 16(1 unit = 0.01)C

0.008570.003040.0217

.

.

.

.

0.003600.003400.00547

0.008770.009450.1311

0.004960.02040.0260

0.004560.004560.1010

0.006690.007330.00619

0.006940.002410.0153

0.002660.01120.0271

0.007600.00760

0.0464

0.1

0.0

(^05101520) Case Number 25303540
0.2C
0.006070.002040.00261
0.01410.0661
0.003140.003090.0179
0.006460.00609
(^234)
(^567)
1089
(^111213)
(^141516)
(^171819)
(^202122)
(^232425)
(^262728)
(^293031)
(^323334)
(^353637)
(^3839)
(^414042)

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  Influence option Iplots option
  We now briefly illustrate using the MRSA
  example how to use computer software to diag-
  nose influential observations. We also discuss
  how to proceed with the analysis when influen-
  tial observations are identified.
  Most computer software packages such as
  SAS, STATA, and SPSS allow the user to obtain
  influence diagnostics for logistic regression,
  although they each have their own version of
  the program code and the statistics produced.
  For example, with SAS’s LOGISTIC procedure,
  the user can specify two options: the “influ-
  ence” option, and the “iplots” option after the
  model statement.
  Both these LOGISTIC options produce a large
  collection of regression diagnostics informa-
  tion for any fitted model. This includes Delta-
  beta measures for each variable in the model
  plus overall Cook’s distance-type measures.
  Here, we focus on the latter, which we hence-
  forth refer to as “C measures.”
  Two slightly different C measures are produced
  by the influence and iplot options, a “C” and a
  “Cbar” measure (Pregibon, 1981). These mea-
  sures typically yield similar, though not always
  identical, conclusions as to which subjects are
  “influential”.
  Theinfluenceoption produces a figure that
  vertically (on theY-axis) lists each subject and
  horizontally (on theX-axis) plots the value of
  the influence measure (C or Cbar). Theiplots
  option, on the other hand, produces a figure
  that lists the subjects horizontally and plots the
  influence measure on the vertical axis.
  The two figures on the left show the results for
  the influence measure C for the first 42 sub-
  jects in the MRSA data set for the no-interac-
  tion model shown below the figures. In both
  figures, subjects 9 and 16 appear to have C
  scores that are much higher than the other
  scores.
  Presentation: V. Influential Observations 277