This is exercise 5.9 in Agresti, page 156-157. The question: does participation in Boy Scouts decrease delinquency rates? From the marginal data in the first table, it appears as if it might. . infile ses bs d count using cda157a (12 observations read) . tab bs d [freq=count] | d bs | 1 2 | Total -----------+----------------------+---------- 1 | 36 364 | 400 2 | 60 340 | 400 -----------+----------------------+---------- Total | 96 704 | 800 . loglin count ses bs d, fit(ses bs d) Variable ses = A Variable bs = B Variable d = C Margins fit: ses bs d Note: Regression-like constraints are assumed. The first level of each variable (and all iteractions with it) will be dropped from estimation. Iteration 0: Log Likelihood = -32.312744 Iteration 1: Log Likelihood = -32.206787 Iteration 2: Log Likelihood = -32.206299 Poisson regression Number of obs = 12 Goodness-of-fit chi2(0) = 0.000 Model chi2(11) = 753.583 Prob > chi2 = . Prob > chi2 = 0.0000 Log Likelihood = -32.206 Pseudo R2 = 0.9213 ------------------------------------------------------------------------------ count | Coef. Std. Err. z P>|z| [95% Conf. Interval] ---------+-------------------------------------------------------------------- A2 | .5877867 .3944053 1.490 0.136 -.1852335 1.360807 A3 | -.2231436 .4743416 -0.470 0.638 -1.152836 .706549 AB22 | -1.386294 .4859127 -2.853 0.004 -2.338666 -.4339231 AB32 | -2.772589 .8660254 -3.202 0.001 -4.469967 -1.07521 AC22 | .6061358 .4337411 1.397 0.162 -.243981 1.456253 AC32 | 1.791759 .5051815 3.547 0.000 .801622 2.781897 ABC222 | -9.91e-15 .5315192 -0.000 1.000 -1.041758 1.041758 ABC322 | 5.96e-08 .8984941 0.000 1.000 -1.761016 1.761016 B2 | 1.386294 .3535534 3.921 0.000 .6933425 2.079246 BC22 | 8.76e-15 .3952847 0.000 1.000 -.7747438 .7747438 C2 | 1.386294 .3535534 3.921 0.000 .6933425 2.079246 _cons | 2.302585 .3162278 7.281 0.000 1.68279 2.92238 ------------------------------------------------------------------------------ . loglin count ses bs d, fit(ses bs, ses d, bs d) Variable ses = A Variable bs = B Variable d = C Margins fit: ses bs, ses d, bs d Poisson regression Number of obs = 12 Goodness-of-fit chi2(2) = 0.000 Model chi2(9) = 753.583 Prob > chi2 = 1.0000 Prob > chi2 = 0.0000 Log Likelihood = -32.206 Pseudo R2 = 0.9213 ------------------------------------------------------------------------------ count | Coef. Std. Err. z P>|z| [95% Conf. Interval] ---------+-------------------------------------------------------------------- A2 | .5877867 .2638822 2.227 0.026 .0705871 1.104986 A3 | -.2231436 .3868551 -0.577 0.564 -.9813656 .5350785 AB22 | -1.386294 .1968171 -7.044 0.000 -1.772049 -1.00054 AB32 | -2.772589 .2271883 -12.204 0.000 -3.21787 -2.327308 AC22 | .6061358 .2494829 2.430 0.015 .1171583 1.095113 AC32 | 1.79176 .3897049 4.598 0.000 1.027952 2.555567 B2 | 1.386294 .2556623 5.422 0.000 .8852054 1.887383 BC22 | 5.77e-09 .2511325 0.000 1.000 -.4922107 .4922107 C2 | 1.386294 .2556623 5.422 0.000 .8852054 1.887383 _cons | 2.302585 .2486614 9.260 0.000 1.815218 2.789952 ------------------------------------------------------------------------------ . loglin count ses bs d, fit(ses bs, ses d) Variable ses = A Variable bs = B Variable d = C Margins fit: ses bs, ses d Poisson regression Number of obs = 12 Goodness-of-fit chi2(3) = 0.000 Model chi2(8) = 753.583 Prob > chi2 = 1.0000 Prob > chi2 = 0.0000 Log Likelihood = -32.206 Pseudo R2 = 0.9213 ------------------------------------------------------------------------------ count | Coef. Std. Err. z P>|z| [95% Conf. Interval] ---------+-------------------------------------------------------------------- A2 | .5877867 .2590581 2.269 0.023 .0800421 1.095531 A3 | -.2231436 .3701337 -0.603 0.547 -.9485923 .5023051 AB22 | -1.386294 .195789 -7.081 0.000 -1.770034 -1.002555 AB32 | -2.772589 .2236068 -12.399 0.000 -3.21085 -2.334328 AC22 | .6061358 .2378354 2.549 0.011 .1399871 1.072285 AC32 | 1.791759 .3593962 4.985 0.000 1.087356 2.496163 B2 | 1.386294 .1581139 8.768 0.000 1.076397 1.696192 C2 | 1.386294 .1581139 8.768 0.000 1.076397 1.696192 _cons | 2.302585 .1897367 12.136 0.000 1.930708 2.674462 ------------------------------------------------------------------------------ . loglin count ses bs d, fit(bs d) Variable ses = A Variable bs = B Variable d = C Margins fit: bs d Poisson regression Number of obs = 12 Goodness-of-fit chi2(6) = 218.614 Model chi2(5) = 534.970 Prob > chi2 = 0.0000 Prob > chi2 = 0.0000 Log Likelihood = -141.513 Pseudo R2 = 0.6540 ------------------------------------------------------------------------------ count | Coef. Std. Err. z P>|z| [95% Conf. Interval] ---------+-------------------------------------------------------------------- A2 | .1823215 .0856349 2.129 0.033 .0144803 .3501628 A3 | -7.75e-08 .0894427 -0.000 1.000 -.1753046 .1753044 B2 | .5108255 .2108185 2.423 0.015 .0976289 .9240222 BC22 | -.5790338 .2239037 -2.586 0.010 -1.017877 -.1401906 C2 | 2.313635 .1747141 13.242 0.000 1.971201 2.656068 _cons | 2.420368 .174722 13.853 0.000 2.077919 2.762817 ------------------------------------------------------------------------------ . loglin , ir Poisson regression Number of obs = 12 Goodness-of-fit chi2(6) = 218.614 Model chi2(5) = 534.970 Prob > chi2 = 0.0000 Prob > chi2 = 0.0000 Log Likelihood = -141.513 Pseudo R2 = 0.6540 ------------------------------------------------------------------------------ count | IRR Std. Err. z P>|z| [95% Conf. Interval] ---------+-------------------------------------------------------------------- A2 | 1.2 .1027619 2.129 0.033 1.014586 1.419299 A3 | .9999999 .0894427 -0.000 1.000 .8392014 1.191609 B2 | 1.666667 .3513641 2.423 0.015 1.102554 2.519404 BC22 | .5604396 .1254845 -2.586 0.010 .3613613 .8691926 C2 | 10.11111 1.766554 13.242 0.000 7.179297 14.24019 ------------------------------------------------------------------------------ . loglin count ses bs d, fit(bs d) resid Variable ses = A Variable bs = B Variable d = C Margins fit: bs d Poisson regression Number of obs = 12 Goodness-of-fit chi2(6) = 218.614 Model chi2(5) = 534.970 Prob > chi2 = 0.0000 Prob > chi2 = 0.0000 Log Likelihood = -141.513 Pseudo R2 = 0.6540 ------------------------------------------------------------------------------ count | Coef. Std. Err. z P>|z| [95% Conf. Interval] ---------+-------------------------------------------------------------------- A2 | .1823215 .0856349 2.129 0.033 .0144803 .3501628 A3 | -7.75e-08 .0894427 -0.000 1.000 -.1753046 .1753044 B2 | .5108255 .2108185 2.423 0.015 .0976289 .9240222 BC22 | -.5790338 .2239037 -2.586 0.010 -1.017877 -.1401906 C2 | 2.313635 .1747141 13.242 0.000 1.971201 2.656068 _cons | 2.420368 .174722 13.853 0.000 2.077919 2.762817 ------------------------------------------------------------------------------ count ses bs d cellhat resid stdres 10 1 1 1 11.250 -1.250 -0.373 40 1 1 2 113.750 -73.750 -6.915 40 1 2 1 18.750 21.250 4.907 160 1 2 2 106.250 53.750 5.215 18 2 1 1 13.500 4.500 1.225 132 2 1 2 136.500 -4.500 -0.385 18 2 2 1 22.500 -4.500 -0.949 132 2 2 2 127.500 4.500 0.399 8 3 1 1 11.250 -3.250 -0.969 192 3 1 2 113.750 78.250 7.337 2 3 2 1 18.750 -16.750 -3.868 48 3 2 2 106.250 -58.250 -5.651 . loglin count ses bs d, fit(ses bs, ses d) resid Variable ses = A Variable bs = B Variable d = C Margins fit: ses bs, ses d Poisson regression Number of obs = 12 Goodness-of-fit chi2(3) = 0.000 Model chi2(8) = 753.583 Prob > chi2 = 1.0000 Prob > chi2 = 0.0000 Log Likelihood = -32.206 Pseudo R2 = 0.9213 ------------------------------------------------------------------------------ count | Coef. Std. Err. z P>|z| [95% Conf. Interval] ---------+-------------------------------------------------------------------- A2 | .5877867 .2590581 2.269 0.023 .0800421 1.095531 A3 | -.2231436 .3701337 -0.603 0.547 -.9485923 .5023051 AB22 | -1.386294 .195789 -7.081 0.000 -1.770034 -1.002555 AB32 | -2.772589 .2236068 -12.399 0.000 -3.21085 -2.334328 AC22 | .6061358 .2378354 2.549 0.011 .1399871 1.072285 AC32 | 1.791759 .3593962 4.985 0.000 1.087356 2.496163 B2 | 1.386294 .1581139 8.768 0.000 1.076397 1.696192 C2 | 1.386294 .1581139 8.768 0.000 1.076397 1.696192 _cons | 2.302585 .1897367 12.136 0.000 1.930708 2.674462 ------------------------------------------------------------------------------ count ses bs d cellhat resid stdres 10 1 1 1 10.000 0.000 0.000 40 1 1 2 40.000 0.000 0.000 40 1 2 1 40.000 0.000 0.000 160 1 2 2 160.000 0.000 0.000 18 2 1 1 18.000 0.000 0.000 132 2 1 2 132.000 -0.000 -0.000 18 2 2 1 18.000 0.000 0.000 132 2 2 2 132.000 -0.000 -0.000 8 3 1 1 8.000 0.000 0.000 192 3 1 2 192.000 0.000 0.000 2 3 2 1 2.000 0.000 0.000 48 3 2 2 48.000 0.000 0.000