Advanced Data Analysis, II

36-402  Homework 3  Spring, 1996

Homework due — In class, Thursday March 14.

The following problems are taken from the book “The Analysis of Cross-Classified Categorical Data” by Fienberg. The data are available in the directory /afs/andrew/hss/stat/data/402.

1. Plackett presented the data below on a random sample of diabetic patients. Fit appropriate loglinear models to these data and comment on the influence of family history of diabetes on the other two variables, and on the relationship between the other two variables. Data in t312.dat.

Family History of Diabetes  Yes  No
Dependence on Insulin Injections Yes No Yes No
Age at Onset < 45  6 1 16 2
≥ 45  6 36  8 48

2. In a survey of a large American city, respondents were asked the question: “Are the radio and TV networks doing a good job, just a fair job, or a poor job?” Data for the responses it this question were broken down by the color of the respondent, and the question was asked in two separate years. Data

in t316.dat.

Response

Year Color Good Fair Poor
1959 Black  81 23  4
White  325 253  54
1971 Black  224 144  24
White  600 636 158

(a) Which variables are explanatory?

(b) Which loglinear models provide an acceptable fit to the data?

(c) In your most parsimonious model that fits the data, look at the residuals and fitted values to decide if you like this model.

(d) Interpret your results.

3. More challenging problem. The following data presents information about British coal miners between the ages of 20 and 64 years who were smokers but did not show radiological signs of pheumoconiosis. The data, consisting of information on two symptoms (breathlessness and wheeze) and age are given below. Find a model which fits the data, and describe what the model means. Be careful to take into account explanatory and response variables. Data in t43.dat.

Age group  Breathlessness  No Breathlessness
in years  Wheeze No wheeze Wheeze No wheeze
20–24  9  7  95  1841
25–29  23  9  105  1654
30–34  54  19  177  1863
35–39  121  48  257  2357
40–44  169  54  273  1778
45–49  269  88  324  1712
50–54  404  117  245  1324
55–59  406  152  225  967
60–64  372  106  132  526

Let me know how things are going!