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

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

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

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

Generalized Linear Models Parameter Estimates Note identical to REGRESSION output

Generalized Linear Models Goodness-of-fit Note output gives log likelihood and AIC = 2835 (AIC = -2x-1409.6 +2x7= 2835) Footnote explains smaller AIC is ‘better’

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 -1409.6 7 2835.6 2 Non-significant variables removed -1413.6 4 2837.2 Change is 1.6

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

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

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

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

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

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 -1423.1 2852.2 - 2 +Adherence -1418.0 2844.1 8.1 3 +Age -1413.6 2837.2 6.9 4

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

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

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

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

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

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

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

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: 279-87.

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 1288-1347

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?