Last revised: 13-5-1999
ASSIGNMENT 1: NORMAL MODELS
The Second Task Force on Blood Pressure Control reported the 90th percentile of systolic blood pressure in single years of age from age 1-18 based on prior studies. The data are given for boys in the following table:
| AGE (x) | SBP(y) | AGE(x) | SBP(y) | AGE(x) | SBP(y) |
|
1 |
105 |
7 |
112 |
13 |
124 |
|
2 |
106 |
8 |
114 |
14 |
126 |
|
3 |
107 |
9 |
115 |
15 |
129 |
|
4 |
108 |
10 |
117 |
16 |
131 |
|
5 |
109 |
11 |
119 |
17 |
134 |
|
6 |
111 |
12 |
121 |
18 |
136 |
A...Fit the following models on BUGS:
ìi = á + âXi + ãXi2 , Õi ~ N( ìi , ó2 )
ìi=á+âXi , Õi ~ N( ìi , ó2 )
B...Give the statistics and histograms for the model coefficients with a brief comment. Check Convergence for each coefficient. Give brief interpretation for each parameter. Compare the Bayesian estimates with the classical MLE estimates (fitted on any statistical program).
C...Give the Residuals, st.residuals and probability of more extreme values for each model. Are there any outliers?
D... Which of the two models seems to be better according to deviance and approximate Bayes Factor?.
One Company wants to hire an experienced secretary. Two of the applicants have better qualifications than all the others but the manager cannot decide which of these two is the best. The manager decides to test them in three different kinds of typewriting (1=typewritter, 2=word for windows and 3=latex) and record their performance (words per minute). The results are given in the following table
| * | * |
Type |
* |
|
Secretary |
Typewriter(1) |
Word(2) |
Latex(3) |
|
1 |
42 |
45 |
30 |
|
2 |
40 |
35 |
31 |
A...Fit the following model on BUGS:
ìij = ì + ái + âj , Õij ~ N( ìij , ó2 ), i=1,2, j=1,2,3
Use Corner and Sum to Zero Constraints.
B...Give the statistics and histograms for the model coefficients with a brief comment. Check Convergence for each coefficient. Give brief interpretation for each parameter. Which typewritist is better? Compare the Bayesian estimates with the classical MLE estimates (fitted on any statistical program).
C...Give the Residuals, st.residuals and probability of more extreme values for each model. Are there any outliers?
The data below were obtained as part of a health survey in the US investigating cholesterol levels in women from two states - Iowa (1) and Nebraska (2). The question here is whether there are real differences in cholesterol levels among women from the two states allowing for age differences. (Source: Snedecor;1956) The problem is to assess the relationship of cholesterol with age in the two groups and if possible use it to deduce what the difference between the two groups would have been if they had all been the same age.
| State (i) | 1 | 1 | 2 | 2 | 2 | 2 | 1 | 1 | 1 | 1 | 2 | 2 |
| Age (j) | 46 | 33 | 18 | 44 | 47 | 56 | 52 | 49 | 65 | 71 | 78 | 19 |
| Cholesterol (Y) | 181 | 201 | 137 | 190 | 196 | 196 | 228 | 121 | 249 | 224 | 241 | 189 |
A...Fit the following model on BUGS:
ìij = ì + áj + âj Xi, Õij ~ N( ìij , ó2 ), i=1,2,...,12, j=1,2.
Use Corner Constraints for the categorical factor defining the state.
B...Give the statistics and histograms for the model coefficients with a brief comment. Check Convergence for each coefficient. Give brief interpretation for each parameter. Compare the Bayesian estimates with the classical MLE estimates (fitted on any statistical program). Is there any difference between the two states? Which is the effect of age on cholesterol?
C...Give the Residuals, st.residuals and probability of more extreme values for each model. Are there any outliers?
