What is the difference between adding a random effect to a GAM by adding it to the model as a factorial explanatory variable, compared to adding it as a random effect to a GAMM? Would it be wrong?
I am aware that when adding the mixed-effects part to the model, it is because I want to include some sort of random effect. However, this could perhaps be done in the GAM by simply adding categorical data as an explanatory variable.
In my specific case, I am trying to look at a continuous response variable with time as an explanatory variable, but I have multiple observations from different individuals which needs to be taken into account.
Usually a random effect is an UN- explained difference - that is a latent variable rather than an observed one - that is differences to be explained. Usually the term mixed means that the model has a fixed part (that models the averages) and the random part which is more than a single 'error' term which captures unexplained variance around the means
This software fits GAMMs
https://stat.ethz.ch/R-manual/R-devel/library/mgcv/html/gamm.html
and also see this R interface to BayesX
https://cran.r-project.org/web/packages/R2BayesX/R2BayesX.pdf
Thank you for your answer, I cannot see the file, but I suppose it is the documentation for R2BayesX? This looks nice, I will definitively try it out!
The reason I want to include the different individuals is because I believe they will have subtle differences which could have different unknown effects on the response variable. Possibly causing a shift in the response variable between individuals, but not changing the relationship with the explanatory variable. So in this case I suppose I should add them as random effects.
Hi Lea,
If you have multiple observations within individuals you should add the "individuals" as random effects to account for the differences within individuals, that's correct.
However, in the SAS program a random effect is inserted on a separated line on PROC MIXED, basically you cite the class of the random effect, but the random effect itself is not inside the model line command. For example:
------------------------------------------------------------------
Proc Mixed data=your data;
Class var1 var2 "individuals";
model Outcome = var1 var2 var3(continuous);
Random "individuals";
Repeated / subject = "individuals" type=cs;
Lsmeans "var1, 2 or 3" / adjust=smm;
-------------------------------------------------------------------
So basically in SAS if you uses PROC GLM (including the random variable “individuals” as a categorical variable) besides PROC MIXED in order to account for these random effect, your results will be different (and the PROC GLM results in this case is wrong), so I guess that the same will happen to your results if you do this in any other statistical program.
Find attached a SAS result file with the same data but with different models: proc glm (with the random variable as a categorical inside the model) and the results from the proc mixed, when the random variable is truly inserted as a random variable.
Best regards.
Thank you Marcel!
Very nice of you to make an example. I will go with the GAMM then!
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