Homework Set 3

Due Tuesday, February 4, 1997

Last updated 29-Jan-97 14:23

1. Below is a data set published by Karl Pearson in 1910 (in Biometrika, Vol. 7, p. 257), that gives data collected by Dr. John Brownlee on the relationship between the severity of an attack of smallpox and the length of time since vaccination. There are five degrees of severity, from most severe (Haemorrhagic) to least (very sparse). Note that these data are confined to people who have experienced some form of attack, and that because the ages of the people are not given there is confounding of age and years-since-vaccination (no young people could have been vaccinated 45 years before the attack, and it is conceivable that older people are over-represented in the unvaccinated group). Analyze these data. (Data are available by rows in the data set vacc.raw [Source:S Stigler])
[See the asthma example for explanation of how to use the predict command in Stata and how to calculate residuals from a Poisson regression.]

1. Treating the table as a whole, test the hypothesis of no association, both with the Chisquare test and with the loglikelihood ratio test.
2. Form a table of the same form of the Pearson residuals, and look for patterns of deviation. What conclusions do you draw?
3. Use the estimated parameters from Stata's poisson command to calculate fitted values for the second and fourth entries in row 2 of the table. Compare your calculations with the result of the Stata's predict command.
4. Repeat the test of no association for the reduced table consisting of the first two rows only. Presumably the people here are more similar in age. Do your conclusions differ? Can you explain why they might?
```                                   Severity of Attack
Years since    Haemorrhagic  Confluent  Abundant  Sparse   Very  Totals
Vacination                                                Sparse
-----------------------------------------------------------------------
0- 10                0        1         6        11      12       30
10 - 25              5       37       114       165     136      457
25 - 45             29      155       299       268     181      932
Over 45             11       35        48        33      28      155
Unvaccinated         4       61        41         7       2      115
-----------------------------------------------------------------------
Totals              49      289       508       484     359     1689
```

2. Agresti, Exercise 4.2

3. Agresti, Exercise 4.3

4. Agresti, Exercise 4.6

Notes

• The textbook is on two-hour reserve in Eckhart library.