How to Use Generalized Additive Models in SAS Viya

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The procedure PROC GAMMOD and the Generalized Additive Model (GAM) node in SAS Model Studio build generalized additive models. GAMs are able to fit non-normal, non-linear models.  This makes them quite useful!  This post will show you how easy they are to use in SAS Model Studio.

Example Use Case:

• Number of births per area
• Predict number of births to determine need for hospitals, pediatricians, teachers, etc.
• Inputs can include population totals, proportion female, proportion child-bearing age, income levels, education levels, access to birth control, etc.

GAMs versus GLMs versus Linear Regression

Recall the assumptions of ordinary least squares simple linear regression models:

• Linearity
• Normality
• IID
• Homoscedasticity

Linearity: The relationship between the outcome and the features is linear in the parameters

From Brian Gaines https://blogs.sas.com/content/subconsciousmusings/2022/03/24/accuracy-versus-interpretability-with-g...

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Normality: Errors follow a normal distribution

IID errors: Error terms are independent and identically distributed.

Homoscedasticity: Equal variance. 

In most cases we do not have normality. We may have other distributions such as Poisson, negative binomial, Gamma, Tweedie, etc. But not to worry. In these cases we can use generalized linear models (GLMs) or generalized additive models (GAMs). Generalized Linear Models (GLMs) assume linearity, but generalized additive models (GAMs) do not.  GAMs accomplish this using spline terms to generalize linear models’ assumption of linearity.  Thus GAMs are even more generalized than GLMs!

Another perk of GAMs is that they have less bias than GLMs. However, as the number of observations increases, GAMs tend to converge more slowly than GLMs.

PROC GAMMOD versus PROC GAMPL

PROC GAMMOD (SAS Viya) is very similar to PROC GAMPL (SAS/STAT SAS 9 high performance) in features, options and results. PROC GAMMOD does provide additional functionality by supporting:

• BY processing
• Creation of an analytic store for scoring

The link function also differs between the procedures. PROC GAMMOD uses a log link for both the Gamma and Inverse Gaussian distributions. PROC GAMPL uses the reciprocal for a Gamma distribution and the reciprocal square for Inverse Gaussian distributions, as shown in the table below.

PROC GAMMOD versus PROC GAM

PROC GAM (SAS/STAT SAS 9) supports Gaussian (normal), binomial, Poisson, Gamma and inverse Gaussian distributions. PROC GAMMOD (SAS Viya) supports all of these PLUS negative binomial and Tweedie distributions. In addition, PROC GAMMOD and PROC GAM work very differently. Do not expect results to be similar. See some of the differences detailed in the table below.

Source: https://go.documentation.sas.com/doc/en/pgmsascdc/default/casstat/casstat_gammod_overview02.htm

The Generalized Additive Model node became available in SAS Model Studio in 2020.1.4. GAM is now included in the Advanced Template for an Interval Target in SAS Model Studio.

Defaults for the GAM node are:

• Selection Method: Boosting
• Interval target probability distribution: Normal
• Interval target link function: Identity
• Binary target link function: Logit
• Degrees of freedom: 4
• Class input order: Formatted
• Class input coding: GLM

as shown in the screen capture below.

Other distributions available are Gamma, inverse Gaussian, negative binomial, Poisson and Tweedie.

The default boosting options are:

• Maximum number of iterations: 500
• Learning rate: 0.1
  
  

By default, smoothing plots are displayed as individual plots (up to 10 plots) and grouped as one report.

If you automatically generate a pipeline in SAS Model Studio, if will consider a GAM model.

You can, in fact, force it to include a GAM model in the pipeline, if you so desire.

Here is the resulting pipeline for my data (HEART data) when I forced it to include GAM.

With my data the GAM model did better than Forest or Linear Regression. However, Gradient Boosting and the Ensemble model did better than GAM.

Summary

Generalized additive models are useful when you have neither linearity nor normality.  SAS Model Studio makes it very easy to add a GAM model using the GAM node. SAS Model Studio now includes GAM in its Advanced Template with an Interval Target.  SAS Model Studio also considers GAM in its automatically generated pipeline if you have an interval target.

Because it is so easy to add a GAM model in SAS Model Studio, you can always include a GAM to see if it outperforms your other models.

For More Information

• SAS Viya Platform Programming Documentation
• Accuracy versus interpretability? With generalized additive models (GAMs), you can have both

Find more articles from SAS Global Enablement and Learning here.