Example 39.4: Logistic Regression Diagnostics
In a controlled experiment to study the
effect of the rate and volume of air inspired on a transient reflex
vaso-constriction in the skin of the digits, 39 tests under various
combinations of rate and volume of air inspired were obtained
(Finney 1947). The
end point of each test is whether or not vaso-constriction occurred.
Pregibon (1981) uses this set of data to illustrate the diagnostic
measures he proposes for detecting influential observations and to
quantify their effects on various aspects of the maximum
likelihood fit.
The vaso-constriction data are saved in the data set vaso:
data vaso;
length Response $12;
input Volume Rate Response @@;
LogVolume=log(Volume);
LogRate=log(Rate);
datalines;
3.70 0.825 constrict 3.50 1.09 constrict
1.25 2.50 constrict 0.75 1.50 constrict
0.80 3.20 constrict 0.70 3.50 constrict
0.60 0.75 no_constrict 1.10 1.70 no_constrict
0.90 0.75 no_constrict 0.90 0.45 no_constrict
0.80 0.57 no_constrict 0.55 2.75 no_constrict
0.60 3.00 no_constrict 1.40 2.33 constrict
0.75 3.75 constrict 2.30 1.64 constrict
3.20 1.60 constrict 0.85 1.415 constrict
1.70 1.06 no_constrict 1.80 1.80 constrict
0.40 2.00 no_constrict 0.95 1.36 no_constrict
1.35 1.35 no_constrict 1.50 1.36 no_constrict
1.60 1.78 constrict 0.60 1.50 no_constrict
1.80 1.50 constrict 0.95 1.90 no_constrict
1.90 0.95 constrict 1.60 0.40 no_constrict
2.70 0.75 constrict 2.35 0.03 no_constrict
1.10 1.83 no_constrict 1.10 2.20 constrict
1.20 2.00 constrict 0.80 3.33 constrict
0.95 1.90 no_constrict 0.75 1.90 no_constrict
1.30 1.625 constrict
;
In the data set vaso, the variable Response represents the
outcome of a test. The variable LogVolume
represents the log of the volume of air intake, and the variable
LogRate represents the log of the rate of air intake.
The following SAS statements invoke PROC LOGISTIC to fit a
logistic regression model to the vaso-constriction data,
where Response is the response variable, and
LogRate and LogVolume are the explanatory
variables. The INFLUENCE option and the IPLOTS option are
specified to display the regression diagnostics and the
index plots.
title 'Occurrence of Vaso-Constriction';
proc logistic data=vaso;
model Response=LogRate LogVolume/influence iplots;
run;
Results of the model fit are shown in Output 39.4.1.
Both LogRate and LogVolume are statistically significant to
the occurrence of vaso-constriction (p=0.0131 and p=0.0055,
respectively). Their positive parameter estimates indicate that
a higher inspiration rate or a larger volume
of air intake is likely to increase the
probability of vaso-constriction.
Output 39.4.1: Logistic Regression Analysis for Vaso-Constriction Data
|
| Occurrence of Vaso-Constriction |
| Model Information |
| Data Set |
WORK.VASO |
| Response Variable |
Response |
| Number of Response Levels |
2 |
| Number of Observations |
39 |
| Link Function |
Logit |
| Optimization Technique |
Fisher's scoring |
| Response Profile |
Ordered
Value |
Response |
Total
Frequency |
| 1 |
constrict |
20 |
| 2 |
no_constrict |
19 |
| Model Convergence Status |
| Convergence criterion (GCONV=1E-8) satisfied. |
| Model Fit Statistics |
| Criterion |
Intercept
Only |
Intercept
and
Covariates |
| AIC |
56.040 |
35.227 |
| SC |
57.703 |
40.218 |
| -2 Log L |
54.040 |
29.227 |
| Testing Global Null Hypothesis: BETA=0 |
| Test |
Chi-Square |
DF |
Pr > ChiSq |
| Likelihood Ratio |
24.8125 |
2 |
<.0001 |
| Score |
16.6324 |
2 |
0.0002 |
| Wald |
7.8876 |
2 |
0.0194 |
| Analysis of Maximum Likelihood Estimates |
| Parameter |
DF |
Estimate |
Standard
Error |
Chi-Square |
Pr > ChiSq |
| Intercept |
1 |
-2.8754 |
1.3208 |
4.7395 |
0.0295 |
| LogRate |
1 |
4.5617 |
1.8380 |
6.1597 |
0.0131 |
| LogVolume |
1 |
5.1793 |
1.8648 |
7.7136 |
0.0055 |
Association of Predicted Probabilities and
Observed Responses |
| Percent Concordant |
93.7 |
Somers' D |
0.874 |
| Percent Discordant |
6.3 |
Gamma |
0.874 |
| Percent Tied |
0.0 |
Tau-a |
0.448 |
| Pairs |
380 |
c |
0.937 |
|
The regression diagnostics produced by the INFLUENCE option are
shown in Output 39.4.2.
The values of the explanatory variables (LogRate and
LogVolume) are listed for each observation
(Output 39.4.2). For each diagnostic, the case number,
representing the sequence number of the observation, is
displayed along with the diagnostic value. Also displayed is
a plot where the vertical axis represents the case number
and the horizontal axis represents the value of the
diagnostic statistic.
Output 39.4.2: Regression Diagnostics from the INFLUENCE Option
|
| Occurrence of Vaso-Constriction |
| Regression Diagnostics |
Case
Number |
Covariates |
Pearson Residual |
Deviance Residual |
Hat Matrix Diagonal |
Intercept DfBeta
Value |
(1 unit = 0.13)
-8 -4 0 2 4 6 8
|
LogRate DfBeta
Value |
(1 unit = 0.12)
-8 -4 0 2 4 6 8
|
LogVolume DfBeta
Value |
(1 unit = 0.13)
-8 -4 0 2 4 6 8
|
Confidence Interval Displacement C |
Confidence Interval Displacement
CBar |
Delta Deviance |
Delta Chi-Square |
| LogRate |
LogVolume |
Value |
(1 unit = 0.44)
-8 -4 0 2 4 6 8
|
Value |
(1 unit = 0.28)
-8 -4 0 2 4 6 8
|
Value |
(1 unit = 0.02)
0 2 4 6 8 12 16
|
Value |
(1 unit = 0.08)
0 2 4 6 8 12 16
|
Value |
(1 unit = 0.07)
0 2 4 6 8 12 16
|
Value |
(1 unit = 0.4)
0 2 4 6 8 12 16
|
Value |
(1 unit = 0.85)
0 2 4 6 8 12 16
|
| 1 |
-0.1924 |
1.3083 |
0.2205 |
| |* |
|
0.3082 |
| |* |
|
0.0927 |
| * |
|
-0.0165 |
| * |
|
0.0193 |
| * |
|
0.0556 |
| * |
|
0.00548 |
|* |
|
0.00497 |
|* |
|
0.1000 |
|* |
|
0.0536 |
|* |
|
| 2 |
0.0862 |
1.2528 |
0.1349 |
| * |
|
0.1899 |
| |* |
|
0.0429 |
| * |
|
-0.0134 |
| * |
|
0.0151 |
| * |
|
0.0261 |
| * |
|
0.000853 |
|* |
|
0.000816 |
|* |
|
0.0369 |
|* |
|
0.0190 |
|* |
|
| 3 |
0.9163 |
0.2231 |
0.2923 |
| |* |
|
0.4049 |
| |* |
|
0.0612 |
| * |
|
-0.0492 |
| * |
|
0.0660 |
| |* |
|
0.0589 |
| * |
|
0.00593 |
|* |
|
0.00557 |
|* |
|
0.1695 |
|* |
|
0.0910 |
|* |
|
| 4 |
0.4055 |
-0.2877 |
3.5181 |
| | *|
|
2.2775 |
| | *|
|
0.0867 |
| * |
|
1.0734 |
| | *|
|
-0.9302 |
|* | |
|
-1.0180 |
|* | |
|
1.2873 |
| *|
|
1.1756 |
| *|
|
6.3626 |
| *|
|
13.5523 |
| *|
|
| 5 |
1.1632 |
-0.2231 |
0.5287 |
| |* |
|
0.7021 |
| | * |
|
0.1158 |
| * |
|
-0.0832 |
| *| |
|
0.1411 |
| |* |
|
0.0583 |
| * |
|
0.0414 |
| * |
|
0.0366 |
|* |
|
0.5296 |
| * |
|
0.3161 |
|* |
|
| 6 |
1.2528 |
-0.3567 |
0.6090 |
| |* |
|
0.7943 |
| | * |
|
0.1524 |
| * |
|
-0.0922 |
| *| |
|
0.1710 |
| |* |
|
0.0381 |
| * |
|
0.0787 |
| * |
|
0.0667 |
| * |
|
0.6976 |
| * |
|
0.4376 |
| * |
|
| 7 |
-0.2877 |
-0.5108 |
-0.0328 |
| * |
|
-0.0464 |
| * |
|
0.00761 |
|* |
|
-0.00280 |
| * |
|
0.00274 |
| * |
|
0.00265 |
| * |
|
8.321E-6 |
|* |
|
8.258E-6 |
|* |
|
0.00216 |
|* |
|
0.00109 |
|* |
|
| 8 |
0.5306 |
0.0953 |
-1.0196 |
| * | |
|
-1.1939 |
| * | |
|
0.0559 |
| * |
|
-0.1444 |
| *| |
|
0.0613 |
| |* |
|
0.0570 |
| * |
|
0.0652 |
| * |
|
0.0616 |
| * |
|
1.4870 |
| * |
|
1.1011 |
| * |
|
| 9 |
-0.2877 |
-0.1054 |
-0.0938 |
| * |
|
-0.1323 |
| * |
|
0.0342 |
| * |
|
-0.0178 |
| * |
|
0.0173 |
| * |
|
0.0153 |
| * |
|
0.000322 |
|* |
|
0.000311 |
|* |
|
0.0178 |
|* |
|
0.00911 |
|* |
|
| 10 |
-0.7985 |
-0.1054 |
-0.0293 |
| * |
|
-0.0414 |
| * |
|
0.00721 |
|* |
|
-0.00245 |
| * |
|
0.00246 |
| * |
|
0.00211 |
| * |
|
6.256E-6 |
|* |
|
6.211E-6 |
|* |
|
0.00172 |
|* |
|
0.000862 |
|* |
|
| 11 |
-0.5621 |
-0.2231 |
-0.0370 |
| * |
|
-0.0523 |
| * |
|
0.00969 |
| * |
|
-0.00361 |
| * |
|
0.00358 |
| * |
|
0.00319 |
| * |
|
0.000014 |
|* |
|
0.000013 |
|* |
|
0.00274 |
|* |
|
0.00138 |
|* |
|
| 12 |
1.0116 |
-0.5978 |
-0.5073 |
| *| |
|
-0.6768 |
| * | |
|
0.1481 |
| * |
|
-0.1173 |
| *| |
|
0.0647 |
| |* |
|
0.1651 |
| |* |
|
0.0525 |
| * |
|
0.0447 |
| * |
|
0.5028 |
| * |
|
0.3021 |
|* |
|
| 13 |
1.0986 |
-0.5108 |
-0.7751 |
| * | |
|
-0.9700 |
| * | |
|
0.1628 |
| * |
|
-0.0931 |
| *| |
|
-0.00946 |
| * |
|
0.1775 |
| |* |
|
0.1395 |
| * |
|
0.1168 |
| * |
|
1.0577 |
| * |
|
0.7175 |
| * |
|
| 14 |
0.8459 |
0.3365 |
0.2559 |
| |* |
|
0.3562 |
| |* |
|
0.0551 |
| * |
|
-0.0414 |
| * |
|
0.0538 |
| * |
|
0.0527 |
| * |
|
0.00404 |
|* |
|
0.00382 |
|* |
|
0.1307 |
|* |
|
0.0693 |
|* |
|
| 15 |
1.3218 |
-0.2877 |
0.4352 |
| |* |
|
0.5890 |
| | * |
|
0.1336 |
| * |
|
-0.0940 |
| *| |
|
0.1408 |
| |* |
|
0.0643 |
| |* |
|
0.0337 |
|* |
|
0.0292 |
|* |
|
0.3761 |
| * |
|
0.2186 |
|* |
|
| 16 |
0.4947 |
0.8329 |
0.1576 |
| * |
|
0.2215 |
| |* |
|
0.0402 |
| * |
|
-0.0198 |
| * |
|
0.0234 |
| * |
|
0.0307 |
| * |
|
0.00108 |
|* |
|
0.00104 |
|* |
|
0.0501 |
|* |
|
0.0259 |
|* |
|
| 17 |
0.4700 |
1.1632 |
0.0709 |
| * |
|
0.1001 |
| * |
|
0.0172 |
| * |
|
-0.00630 |
| * |
|
0.00701 |
| * |
|
0.00914 |
| * |
|
0.000089 |
|* |
|
0.000088 |
|* |
|
0.0101 |
|* |
|
0.00511 |
|* |
|
| 18 |
0.3471 |
-0.1625 |
2.9062 |
| | * |
|
2.1192 |
| | * |
|
0.0954 |
| * |
|
0.9595 |
| | * |
|
-0.8279 |
| * | |
|
-0.8477 |
| * | |
|
0.9845 |
| * |
|
0.8906 |
| * |
|
5.3817 |
| * |
|
9.3363 |
| * |
|
| 19 |
0.0583 |
0.5306 |
-1.0718 |
| * | |
|
-1.2368 |
| * | |
|
0.1315 |
| * |
|
-0.2591 |
| * | |
|
0.2024 |
| | * |
|
-0.00488 |
| * |
|
0.2003 |
| * |
|
0.1740 |
| * |
|
1.7037 |
| * |
|
1.3227 |
| * |
|
| 20 |
0.5878 |
0.5878 |
0.2405 |
| |* |
|
0.3353 |
| |* |
|
0.0525 |
| * |
|
-0.0331 |
| * |
|
0.0421 |
| * |
|
0.0518 |
| * |
|
0.00338 |
|* |
|
0.00320 |
|* |
|
0.1156 |
|* |
|
0.0610 |
|* |
|
| 21 |
0.6931 |
-0.9163 |
-0.1076 |
| * |
|
-0.1517 |
| *| |
|
0.0373 |
| * |
|
-0.0180 |
| * |
|
0.0158 |
| * |
|
0.0208 |
| * |
|
0.000465 |
|* |
|
0.000448 |
|* |
|
0.0235 |
|* |
|
0.0120 |
|* |
|
| 22 |
0.3075 |
-0.0513 |
-0.4193 |
| *| |
|
-0.5691 |
| * | |
|
0.1015 |
| * |
|
-0.1449 |
| *| |
|
0.1237 |
| |* |
|
0.1179 |
| |* |
|
0.0221 |
|* |
|
0.0199 |
|* |
|
0.3437 |
| * |
|
0.1956 |
|* |
|
| 23 |
0.3001 |
0.3001 |
-1.0242 |
| * | |
|
-1.1978 |
| * | |
|
0.0761 |
| * |
|
-0.1961 |
| *| |
|
0.1275 |
| |* |
|
0.0357 |
| * |
|
0.0935 |
| * |
|
0.0864 |
| * |
|
1.5212 |
| * |
|
1.1355 |
| * |
|
| 24 |
0.3075 |
0.4055 |
-1.3684 |
| * | |
|
-1.4527 |
| * | |
|
0.0717 |
| * |
|
-0.1281 |
| *| |
|
0.0410 |
| * |
|
-0.1004 |
| *| |
|
0.1558 |
| * |
|
0.1447 |
| * |
|
2.2550 |
| * |
|
2.0171 |
| * |
|
| 25 |
0.5766 |
0.4700 |
0.3347 |
| |* |
|
0.4608 |
| | * |
|
0.0587 |
| * |
|
-0.0403 |
| * |
|
0.0570 |
| * |
|
0.0708 |
| |* |
|
0.00741 |
|* |
|
0.00698 |
|* |
|
0.2193 |
| * |
|
0.1190 |
|* |
|
| 26 |
0.4055 |
-0.5108 |
-0.1595 |
| * |
|
-0.2241 |
| *| |
|
0.0548 |
| * |
|
-0.0366 |
| * |
|
0.0329 |
| * |
|
0.0373 |
| * |
|
0.00156 |
|* |
|
0.00147 |
|* |
|
0.0517 |
|* |
|
0.0269 |
|* |
|
| 27 |
0.4055 |
0.5878 |
0.3645 |
| |* |
|
0.4995 |
| | * |
|
0.0661 |
| * |
|
-0.0327 |
| * |
|
0.0496 |
| * |
|
0.0788 |
| |* |
|
0.0101 |
|* |
|
0.00941 |
|* |
|
0.2589 |
| * |
|
0.1423 |
|* |
|
| 28 |
0.6419 |
-0.0513 |
-0.8989 |
| * | |
|
-1.0883 |
| * | |
|
0.0647 |
| * |
|
-0.1423 |
| *| |
|
0.0617 |
| |* |
|
0.1025 |
| |* |
|
0.0597 |
| * |
|
0.0559 |
| * |
|
1.2404 |
| * |
|
0.8639 |
| * |
|
| 29 |
-0.0513 |
0.6419 |
0.8981 |
| | * |
|
1.0876 |
| | * |
|
0.1682 |
| * |
|
0.2367 |
| | * |
|
-0.1950 |
| * | |
|
0.0286 |
| * |
|
0.1961 |
| * |
|
0.1631 |
| * |
|
1.3460 |
| * |
|
0.9697 |
| * |
|
| 30 |
-0.9163 |
0.4700 |
-0.0992 |
| * |
|
-0.1400 |
| * |
|
0.0507 |
| * |
|
-0.0224 |
| * |
|
0.0227 |
| * |
|
0.0159 |
| * |
|
0.000554 |
|* |
|
0.000526 |
|* |
|
0.0201 |
|* |
|
0.0104 |
|* |
|
| 31 |
-0.2877 |
0.9933 |
0.6198 |
| |* |
|
0.8064 |
| | * |
|
0.2459 |
| *|
|
0.1165 |
| |* |
|
-0.0996 |
| *| |
|
0.1322 |
| |* |
|
0.1661 |
| * |
|
0.1253 |
| * |
|
0.7755 |
| * |
|
0.5095 |
| * |
|
| 32 |
-3.5066 |
0.8544 |
-0.00073 |
| * |
|
-0.00103 |
| * |
|
0.000022 |
|* |
|
-3.22E-6 |
| * |
|
3.405E-6 |
| * |
|
2.48E-6 |
| * |
|
1.18E-11 |
|* |
|
1.18E-11 |
|* |
|
1.065E-6 |
|* |
|
5.324E-7 |
|* |
|
| 33 |
0.6043 |
0.0953 |
-1.2062 |
| * | |
|
-1.3402 |
| * | |
|
0.0510 |
| * |
|
-0.0882 |
| *| |
|
-0.0137 |
| * |
|
-0.00216 |
| * |
|
0.0824 |
| * |
|
0.0782 |
| * |
|
1.8744 |
| * |
|
1.5331 |
| * |
|
| 34 |
0.7885 |
0.0953 |
0.5447 |
| |* |
|
0.7209 |
| | * |
|
0.0601 |
| * |
|
-0.0425 |
| * |
|
0.0877 |
| |* |
|
0.0671 |
| |* |
|
0.0202 |
|* |
|
0.0190 |
|* |
|
0.5387 |
| * |
|
0.3157 |
|* |
|
| 35 |
0.6931 |
0.1823 |
0.5404 |
| |* |
|
0.7159 |
| | * |
|
0.0552 |
| * |
|
-0.0340 |
| * |
|
0.0755 |
| |* |
|
0.0711 |
| |* |
|
0.0180 |
|* |
|
0.0170 |
|* |
|
0.5295 |
| * |
|
0.3091 |
|* |
|
| 36 |
1.2030 |
-0.2231 |
0.4828 |
| |* |
|
0.6473 |
| | * |
|
0.1177 |
| * |
|
-0.0867 |
| *| |
|
0.1381 |
| |* |
|
0.0631 |
| * |
|
0.0352 |
|* |
|
0.0311 |
|* |
|
0.4501 |
| * |
|
0.2641 |
|* |
|
| 37 |
0.6419 |
-0.0513 |
-0.8989 |
| * | |
|
-1.0883 |
| * | |
|
0.0647 |
| * |
|
-0.1423 |
| *| |
|
0.0617 |
| |* |
|
0.1025 |
| |* |
|
0.0597 |
| * |
|
0.0559 |
| * |
|
1.2404 |
| * |
|
0.8639 |
| * |
|
| 38 |
0.6419 |
-0.2877 |
-0.4874 |
| *| |
|
-0.6529 |
| * | |
|
0.1000 |
| * |
|
-0.1395 |
| *| |
|
0.1032 |
| |* |
|
0.1397 |
| |* |
|
0.0293 |
|* |
|
0.0264 |
|* |
|
0.4526 |
| * |
|
0.2639 |
|* |
|
| 39 |
0.4855 |
0.2624 |
0.7053 |
| | * |
|
0.8987 |
| | * |
|
0.0531 |
| * |
|
0.0326 |
| * |
|
0.0190 |
| * |
|
0.0489 |
| * |
|
0.0295 |
|* |
|
0.0279 |
|* |
|
0.8355 |
| * |
|
0.5254 |
| * |
|
|
The index plots produced by the IPLOTS option are essentially
the same plots as those produced by the INFLUENCE option with a
90-degree rotation and perhaps on a more refined scale.
The vertical axis of an index plot represents
the value of the diagnostic and the horizontal axis represents
the sequence (case number) of the observation. The index plots
are useful for identification of extreme values.
|
---------------+----+----+----+----+----+----+----+----+---------------
RESCHI | |
P 4 + +
e | * |
a | |
r | * |
s | |
o 2 + +
n | |
| |
R | * * * * |
e | * * * ** * * * *** |
s 0 + * * *** ** * * * * +
i | * * * |
d | * * * |
u | * * ** * |
a | |
l -2 + +
| |
---------------+----+----+----+----+----+----+----+----+---------------
0 5 10 15 20 25 30 35 40
Case Number INDEX
|
---------------+----+----+----+----+----+----+----+----+---------------
D RESDEV | |
e 4 + +
v | |
i | |
a | |
n | * |
c 2 + * +
e | |
| * |
R | ** * *** * |
e | * * *** * * * |
s 0 + * * *** * * * * +
i | * * |
d | ** * |
u | * * * * * * |
a | * |
l -2 + +
| |
---------------+----+----+----+----+----+----+----+----+---------------
0 5 10 15 20 25 30 35 40
Case Number INDEX
|
|
|
----------------+----+----+----+----+----+----+----+----+-----------------
H | |
0.3 + +
| |
H | |
a | * |
t | |
0.2 + +
D | |
i | * * * |
a | * * * |
g | * * |
o 0.1 + * * * * +
n | * ** |
a | * * * * **** * *** * * |
l | * * * * |
| * |
0.0 + * ** * +
| |
----------------+----+----+----+----+----+----+----+----+-----------------
0 5 10 15 20 25 30 35 40
Case Number INDEX
|
--------------+----+----+----+----+----+----+----+----+---------------
DFBETA0 | |
I 1.5 + +
n | |
t | |
e | * |
r 1.0 + * +
c | |
e | |
p | |
t 0.5 + +
| |
D | * |
f | * |
B 0.0 + *** * *** * ** ** *** * * ** * +
e | ** * ** * * * * * *** |
t | * * |
a | |
-0.5 + +
--------------+----+----+----+----+----+----+----+----+---------------
0 5 10 15 20 25 30 35 40
Case Number INDEX
|
|
|
--------------+----+----+----+----+----+----+----+----+---------------
DFBETA1 | |
0.5 + +
L | |
o | |
g | * * |
R | * * * * ** ** * * ***** |
a 0.0 + ** * *** * ** ** * ** * ** * +
t | * |
e | * |
| |
D | |
f -0.5 + +
B | |
e | |
t | * |
a | * |
-1.0 + +
| |
--------------+----+----+----+----+----+----+----+----+---------------
0 5 10 15 20 25 30 35 40
Case Number INDEX
|
--------------+----+----+----+----+----+----+----+----+---------------
DFBETA2 | |
L 0.5 + +
o | |
g | |
V | ** |
o | * * * * ** * * * ** * ***** |
l 0.0 + * ** *** ** * * * * ** ** * +
u | * |
m | |
e | |
| |
D -0.5 + +
f | |
B | |
e | * |
t | |
a -1.0 + * +
| |
--------------+----+----+----+----+----+----+----+----+---------------
0 5 10 15 20 25 30 35 40
Case Number INDEX
|
|
|
----------------+----+----+----+----+----+----+----+----+-----------------
C C | |
o 1.5 + +
n | |
f | * |
i | |
d | |
e 1.0 + * +
n | |
c | |
e | |
| |
I 0.5 + +
n | |
t | |
e | * * * * |
r | * * ** * * * * |
v 0.0 + *** * * *** **** *** *** * * *** ** +
a | |
l ----------------+----+----+----+----+----+----+----+----+-----------------
0 5 10 15 20 25 30 35 40
D
Case Number INDEX
|
----------------+----+----+----+----+----+----+----+----+----------------
C CBAR | |
o 1.5 + +
n | |
f | |
i | * |
d | |
e 1.0 + +
n | * |
c | |
e | |
| |
I 0.5 + +
n | |
t | |
e | * * |
r | * * * ** * * * * |
v 0.0 + *** * * **** **** *** *** * * *** ** +
a | |
l ----------------+----+----+----+----+----+----+----+----+----------------
0 5 10 15 20 25 30 35 40
D
Case Number INDEX
|
|
|
---------------+----+----+----+----+----+----+----+----+---------------
DIFDEV | |
8 + +
D | |
e | |
l | * |
t 6 + +
a | * |
| |
D | |
e 4 + +
v | |
i | |
a | * |
n 2 + * +
c | * * * * |
e | * * * * * |
| ** * * * * *** * |
0 + *** * *** * ** ** ** * * +
---------------+----+----+----+----+----+----+----+----+---------------
0 5 10 15 20 25 30 35 40
Case Number INDEX
|
--------------+----+----+----+----+----+----+----+----+--------------
DIFCHISQ | |
D 15 + +
e | * |
l | |
t | |
a | |
10 + +
C | * |
h | |
i | |
S | |
q 5 + +
u | |
a | |
r | * * |
e | * * * * ** * * * |
0 + *** *** **** **** *** *** * * *** * +
| |
--------------+----+----+----+----+----+----+----+----+--------------
0 5 10 15 20 25 30 35 40
Case Number INDEX
|
|
The index plots of the Pearson residuals and the deviance residuals indicate
that case 4 and case 18 are poorly accounted for by the model. The index
plot of the diagonal elements of the hat matrix suggests that
case 31 is an extreme point in the design space. The index plots of
DFBETAS indicate that case 4 and case 18 are causing instability
in all three parameter estimates. The other four index plots also
point to these two cases as having a large impact on the
coefficients and goodness of fit.
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.
