Last revised: 13-5-1999
ASSIGNMENT 3: POISSON MODELS
In the following contingency table we have 79 patients cross-classified by three factors: A= the condition of the patient, B = whether the patient received antitoxin or not and C = whether the patient survived or not. Prime interest is given on the effect of antitoxin to deaths from tetanus.
| * | * |
SURVIVAL |
* |
| (A) CONDITION | (B) ANTITOXIN | No (deaths) | Yes (survivors) |
| More Severe | Yes | 15 | 06 |
| More Severe | No | 22 | 04 |
| Less Severe | Yes | 05 | 15 |
| Less Severe | No | 07 | 05 |
There are two ways of analysing these sets of data. We either use binary response models (logistic, probit or clog-log regression ) or log-linear models for contingency tables. In each kind of analysis different relationships are under investigation.
A...Fit the following model on BUGS:
log(ëijk)=ì + ái + âj + ãk + áâij + áãik+ âãjk , Õijk ~ Poisson(ëijk), i,j,k=1,2,
where Õijk are the number of patients with i condition, j antitoxin and k survival. Use ONLY Sum to zero Constraints.
Note: Log-linear models work with a different way than all the other models. Typically ‘response’ variable is the number of counts for each cell of the contingency table. In reality, there is not any response variable. The log-linear model is used to find the associations between the ‘explanatory’ variables. Each interaction denotes association of the corresponding factors.
B...Write a report including statistics and histograms for the model coefficients. Check Convergence for each coefficient.. Produce the posterior distribution of the ODDS (plots & statistics) and Odds Ratios.
C...Give the Residuals, st.residuals and probability of more extreme values for each model. Are there any outliers? Summarise the residual results in a diagram of the 95% confidence intervals (for residuals and st. residuals).
D... Compare the log-linear model with the logistic regression model of the first task. What is the relationship of the coefficients between the two models? · Write a complete report, with detailed answrers. You should also check convergence and include any appropriate plots. Any plots that do not interest the non-technical reader but statistician should be placed only at the appendix.
