1. Generalized linear models
Unfortunately the standard REGRESSION in SPSS does not give these statistics so…….
Need to use
Analyze
Generalized Linear Models…..

2. Generalized linear models. Default is linear
Add Min LDL achieved as dependent as in REGRESSION in SPSS
Next go to predictors…..

3. Generalized linear models: Predictors
WARNING!
Make sure you add the predictors in the correct box
Categorical in FACTORS box
Continuous in COVARIATES box

4. Generalized linear models: Model
Add all factors and covariates in the model as main effects

5. Generalized Linear Models Parameter Estimates
Note identical to REGRESSION output

6. Generalized Linear Models Goodness-of-fit
Note output gives log likelihood and AIC = 2835
(AIC = -2x x7= 2835)
Footnote explains smaller AIC is ‘better’

7. Let Science or Clinical factors guide selection: ‘Optimal’ model
The log likelihood is a measure of GOODNESS-OF-FIT
Seek ‘optimal’ model that maximises the log likelihood or minimises the AIC
Model
2LL p
AIC
1 Full Model 7
2835.6
2 Non-significant variables removed 4
2837.2
Change is 1.6

8. 1) Let Science or Clinical factors guide selection
Key points:
Results demonstrate a significant association with baseline LDL, Age and Adherence
Difficult choices with Gender, smoking and BMI
AIC only changes by 1.6 when removed
Generally changes of 4 or more in AIC are considered important

9. 1) Let Science or Clinical factors guide selection
Key points:
Conclude little to chose between models
AIC actually lower with larger model and consider Gender, and BMI important factors so keep larger model but have to justify
Model building manual, logical, transparent and under your control

10. 2) Use automatic selection procedures
These are based on automatic mechanical algorithms usually related to statistical significance
Common ones are stepwise, forward or backward elimination
Can be selected in SPSS using ‘Method’ in dialogue box

11. 2) Use automatic selection procedures (e.g Stepwise)
Select Method = Stepwise

12. 2) Use automatic selection procedures (e.g Stepwise)
1st step
2nd step
Final Model

13. 2) Change in AIC with Stepwise selection
Note: Only available from Generalized Linear Models
Step
Model
Log Likelihood
AIC
Change in AIC
No. of Parameters p 1
Baseline LDL
2852.2 - 2
+Adherence
2844.1
8.1 3
+Age
2837.2
6.9 4

14. 2) Advantages and disadvantages of stepwise
Simple to implement
Gives a parsimonious model
Selection is certainly objective
Disadvantages
Non stable selection – stepwise considers many models that are very similar
P-value on entry may be smaller once procedure is finished so exaggeration of p-value
Predictions in external dataset usually worse for stepwise procedures – tends to add bias

15. 2) Automatic procedures: Backward elimination
Backward starts by eliminating the least significant factor form the full model and has a few advantages over forward:
Modeller has to consider the ‘full’ model and sees results for all factors simultaneously
Correlated factors can remain in the model (in forward methods they may not even enter)
Criteria for removal tend to be more lax in backward so end up with more parameters

16. 2) Use automatic selection procedures (e.g Backward)
Select Method = Backward

17. 2) Backward elimination in SPSS
1st step
Gender removed
2nd step BMI removed
Final Model

18. Summary of automatic selection
Automatic selection may not give ‘optimal’ model (may leave out important factors)
Different methods may give different results (forward vs. backward elimination)
Backward elimination preferred as less stringent
Too easily fitted in SPSS!
Model assessment still requires some thought

19. 3) A mixture of automatic procedures and self selection
Use automatic procedures as a guide
Think about what factors are important
Add ‘important’ factors
Do not blindly follow statistical significance
Consider AIC for ‘best’ model

20. Summary of Model selection
Selection of factors for Multiple Linear regression models requires some judgement
Automatic procedures are available but treat results with caution
They are easily fitted in SPSS
Check AIC or log likelihood for fit

21. Summary
Multiple regression models are the most used analytical tool in quantitative research
They are easily fitted in SPSS
Model assessment requires some thought
Parsimony is better – Occam’s Razor
Donnelly LA, Palmer CNA, Whitley AL, Lang C, Doney ASF, Morris AD, Donnan PT. Apolipoprotein E genotypes are associated with lipid lowering response to statin treatment in diabetes: A Go-DARTS study. Pharmacogenetics and Genomics, 2008; 18:

22. Remember Occam’s Razor
‘Entia non sunt multiplicanda praeter necessitatem’
‘Entities must not be multiplied beyond necessity’
William of Ockham 14th century Friar and logician

23. Practical on Multiple Regression
Read in ‘LDL Data.sav’
Try fitting multiple regression model on Min LDL obtained using forward and backward elimination. Are the results the same? Add other factors than those considered in the presentation such as BMI, smoking. Remember the goal is to assess the association of APOE with LDL response.
Try fitting multiple regression models for Min Chol achieved. Is the model similar to that found for Min LDL Chol?