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Table 8.1 on page 139.
data table8_1; input sex $1-5 age $9-13 response $14-30 frequency; datalines; women 18-23 no/little 26 women 18-23 important 12 women 18-23 very important 7 women 24-40 no/little 9 women 24-40 important 21 women 24-40 very important 15 women > 40 no/little 5 women > 40 important 14 women > 40 very important 41 men 18-23 no/little 40 men 18-23 important 17 men 18-23 very important 8 men 24-40 no/little 17 men 24-40 important 15 men 24-40 very important 12 men > 40 no/little 8 men > 40 important 15 men > 40 very important 18 ; run; proc format; picture pctfmt low-high='00.00%'; run; options nodate pageno=1 linesize=105 pagesize=60; proc tabulate data=table8_1 format=9.; class sex age response /order=data; var frequency; table (sex='sex'*age all = 'total')*frequency='', response*(sum='' rowpctsum=''*f=pctfmt9.) all='total'*sum='' / RTS=20 row=float; run;
------------------------------------------------------------------------------------------ | | response | | | |-----------------------------------------------------------| | | | no/little | important | very important | total | |------------------+-------------------+-------------------+-------------------+---------| |sex |age | | | | | | | | |--------+---------| | | | | | | | |women |18-23 | 26| 57.77%| 12| 26.66%| 7| 15.55%| 45| | |---------+---------+---------+---------+---------+---------+---------+---------| | |24-40 | 9| 20.00%| 21| 46.66%| 15| 33.33%| 45| | |---------+---------+---------+---------+---------+---------+---------+---------| | |> 40 | 5| 8.33%| 14| 23.33%| 41| 68.33%| 60| |--------+---------+---------+---------+---------+---------+---------+---------+---------| |men |18-23 | 40| 61.53%| 17| 26.15%| 8| 12.30%| 65| | |---------+---------+---------+---------+---------+---------+---------+---------| | |24-40 | 17| 38.63%| 15| 34.09%| 12| 27.27%| 44| | |---------+---------+---------+---------+---------+---------+---------+---------| | |> 40 | 8| 19.51%| 15| 36.58%| 18| 43.90%| 41| |------------------+---------+---------+---------+---------+---------+---------+---------| |total | 105| 35.00%| 94| 31.33%| 101| 33.66%| 300| ------------------------------------------------------------------------------------------
Figure 8.1 on page 140.
proc sort data = table8_1;
by sex age;
run;
proc freq data = table8_1;
weight frequency;
by sex age;
tables response/list ;
ods output onewayfreqs = list;
run;
data list;
set list;
proportion = percent/100;
run;
goptions reset = all;
symbol1 i = join v=circle c=blue;
symbol2 i = join v=dot c=black;
symbol3 i = join v = star c = red;
axis1 order = (0 to .8 by .2) minor = none label=('proportion');
proc gplot data = list;
by sex;
plot proportion*age = response /vaxis = axis1;
run;
quit;
Table 8.2 on page 141.
data table8_1a; set table8_1; x1 = (sex ='men'); x2 = (age = '24-40'); x3 = (age = '> 40'); run; proc logistic data = table8_1a ; freq frequency; class response (ref='no/little'); model response = x1 x2 x3 /link=glogit ; run;
Response Profile
Ordered Total
Value response Frequency
1 important 94
2 no/little 105
3 very important 101
Logits modeled use response='no/little' as the reference category.
Model Fit Statistics
Intercept
Intercept and
Criterion Only Covariates
AIC 662.544 596.702
SC 669.952 626.332
-2 Log L 658.544 580.702
Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 77.8419 6 <.0001
Score 74.9761 6 <.0001
Wald 62.9703 6 <.0001
Type III Analysis of Effects
Wald
Effect DF Chi-Square Pr > ChiSq
x1 2 6.4173 0.0404
x2 2 17.5366 0.0002
x3 2 47.5933 <.0001
Analysis of Maximum Likelihood Estimates
Standard Wald
Parameter response DF Estimate Error Chi-Square Pr > ChiSq
Intercept important 1 -0.5908 0.2840 4.3286 0.0375
Intercept very important 1 -1.0391 0.3305 9.8843 0.0017
x1 important 1 -0.3881 0.3005 1.6677 0.1966
x1 very important 1 -0.8129 0.3210 6.4122 0.0113
x2 important 1 1.1283 0.3416 10.9059 0.0010
x2 very important 1 1.4780 0.4009 13.5912 0.0002
x3 important 1 1.5876 0.4029 15.5270 <.0001
x3 very important 1 2.9165 0.4229 47.5594 <.0001
Odds Ratio Estimates
Point 95% Wald
Effect response Estimate Confidence Limits
x1 important 0.678 0.376 1.223
x1 very important 0.444 0.236 0.832
x2 important 3.090 1.582 6.037
x2 very important 4.384 1.998 9.620
x3 important 4.892 2.221 10.775
x3 very important 18.477 8.066 42.327
Table 8.3 on page 142.
proc sql; create table table8_1b as select *, sum(frequency) as total from table8_1a group by sex, age; quit; proc logistic data = table8_1b ; freq frequency; class response (ref='no/little'); model response = x1 x2 x3 /link=glogit ; output out = table8_3 p=p ; run; data table8_3; set table8_3; fitted = p*total; pres = (frequency-fitted)/sqrt(fitted); if response=_level_; run; proc sort data = table8_3 ; run; proc print data = table8_3; var sex age response frequency p fitted pres; run;
Obs sex age response frequency p fitted pres 1 men 18-23 no/little 40 0.65246 42.4102 -0.37010 2 men 18-23 important 17 0.24515 15.9346 0.26690 3 men 18-23 very important 8 0.10239 6.6552 0.52128 4 men 24-40 important 15 0.40753 17.9312 -0.69220 5 men 24-40 very important 12 0.24149 10.6254 0.42171 6 men 24-40 no/little 17 0.35099 15.4435 0.39608 7 men > 40 important 15 0.32034 13.1340 0.51489 8 men > 40 very important 18 0.50537 20.7201 -0.59756 9 men > 40 no/little 8 0.17429 7.1460 0.31948 10 women 18-23 very important 7 0.18546 8.3455 -0.46576 11 women 18-23 important 12 0.29034 13.0654 -0.29475 12 women 18-23 no/little 26 0.52420 23.5891 0.49639 13 women 24-40 very important 15 0.36388 16.3747 -0.33971 14 women 24-40 important 21 0.40153 18.0687 0.68959 15 women 24-40 no/little 9 0.23459 10.5566 -0.47908 16 women > 40 no/little 5 0.09759 5.8557 -0.35361 17 women > 40 very important 41 0.63798 38.2788 0.43983 18 women > 40 important 14 0.26443 15.8655 -0.46836
Table 8.4 on page 148.
data table8_1c; set table8_1a; if response = 'no/little' then resnum = 1; if response = 'important' then resnum = 2; if response = 'very important' then resnum = 3; run; proc logistic data = table8_1c descending ; freq frequency; model resnum = x1 x2 x3 /scale = none aggregate; run;
Score Test for the Proportional Odds Assumption
Chi-Square DF Pr > ChiSq
0.7139 3 0.8699
Deviance and Pearson Goodness-of-Fit Statistics
Criterion DF Value Value/DF Pr > ChiSq
Deviance 7 4.5321 0.6474 0.7169
Pearson 7 4.5641 0.6520 0.7130
Number of unique profiles: 6
Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 77.2485 3 <.0001
Score 70.0452 3 <.0001
Wald 68.0278 3 <.0001
Analysis of Maximum Likelihood Estimates
Standard Wald
Parameter DF Estimate Error Chi-Square Pr > ChiSq
Intercept 3 1 -1.6546 0.2536 42.5742 <.0001
Intercept 2 1 -0.0433 0.2303 0.0354 0.8508
x1 1 -0.5762 0.2261 6.4936 0.0108
x2 1 1.1468 0.2773 17.1079 <.0001
x3 1 2.2322 0.2904 59.0806 <.0001
Odds Ratio Estimates
Point 95% Wald
Effect Estimate Confidence Limits
x1 0.562 0.361 0.875
x2 3.148 1.828 5.421
x3 9.320 5.275 16.467
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