This program replicates an analysis based on the works of Jorgenson (1961) and Frome et al. (1971). It compares the results of Poisson regression models (Poisson distribution) without an intercept (noint). The script tests the Fisher Scoring optimization algorithm (limited to 10 iterations) with an identity link then a logarithmic link, and then compares with the default optimization technique (Newton-Raphson).
Data Analysis
Type : CREATION_INTERNE
The 'failures' data (x1, x2, y) are generated directly in the code via the DATALINES statement.
1 Code Block
DATA STEP Data
Explanation :
Creation of the SAS table 'failures' containing explanatory variables x1, x2 and the response variable y (number of failures) via internal data.
Creation of the SAS table 'failures' containing explanatory variables x1, x2 and the response variable y (number of failures) via internal data.
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| 1 | DATA failures; |
| 2 | INPUT x1 x2 y; |
| 3 | DATALINES; |
| 4 | 33.3 25.3 15 |
| 5 | 52.2 14.4 9 |
| 6 | 64.7 32.5 14 |
| 7 | 137.0 20.5 24 |
| 8 | 125.9 97.6 27 |
| 9 | 116.3 53.6 27 |
| 10 | 131.7 56.6 23 |
| 11 | 85.0 87.3 18 |
| 12 | 91.9 47.8 22 |
| 13 | ; |
2 Code Block
PROC GLIMMIX
Explanation :
Execution of two GLIMMIX models with the 'Fisher Scoring' optimization method (scoring=10 option). The first model uses an identity link and the second a logarithmic link. ODS Graphics display is enabled to visualize residuals.
Execution of two GLIMMIX models with the 'Fisher Scoring' optimization method (scoring=10 option). The first model uses an identity link and the second a logarithmic link. ODS Graphics display is enabled to visualize residuals.
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| 1 | ods html; |
| 2 | ods graphics on; |
| 3 | title1 '*** Fisher Scoring optimization technique up to iteration 10 ***'; |
| 4 | title2 '*** Identity Link ***'; |
| 5 | PROC GLIMMIX DATA=failures scoring=10 plots=residualpanel; |
| 6 | model y = x1 x2 / noint dist=poisson link=identity covb s; |
| 7 | RUN; |
| 8 | |
| 9 | title1 '*** Fisher Scoring optimization technique up to iteration 10 ***'; |
| 10 | title2 '*** Logarithm Link ***'; |
| 11 | PROC GLIMMIX DATA=failures scoring=10 plots=residualpanel; |
| 12 | model y = x1 x2 / noint dist=poisson link=log covb s; |
| 13 | RUN; |
| 14 | ods graphics off; |
| 15 | ods html close; |
3 Code Block
PROC GLIMMIX
Explanation :
Execution of a third GLIMMIX model using default optimization (Newton-Raphson) with an identity link for comparison with previous results.
Execution of a third GLIMMIX model using default optimization (Newton-Raphson) with an identity link for comparison with previous results.
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| 1 | title '*** Newton-Raphson optimization technique. Hessian is used ***'; |
| 2 | PROC GLIMMIX DATA=failures; |
| 3 | model y = x1 x2 / noint dist=poisson link=identity covb s; |
| 4 | RUN; |
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