# Should I tick the variable which I want to control, namely a covariate, as nuisance?

Hello! I'm working on a paper recently and I want to use Bayesian analysis to analyze my data. I have one continuous independent variable A, one dichotomy independent variable B, and a continuous dependent variable C. Therefore I used the Bayesian Linear Regression. Before the regression analysis, I first checked whether some personal characters (X, Y, Z...) differ among the experimental conditions, and found participants in different conditions did differ on X and Y. So I want to take X and Y as covariates in the later analysis for controlling them.

My question is should I tick X and Y as nuisance in the model? And Why?

Thanks in advance for your help!

## Comments

Hi Shuang,

Well, statistically this is a tricky issue. I personally do not like the term "controlling for", because it suggests something that is impossible without an experimental setup. But in general, yes, you can do a "hierarchical regression" (I don't like that term either :-)): you first enter the variables that you are not interested in but could be relevant. These are the nuisance variables. So you depart not from the model without any variables, but from the model that includes the nuisance terms. Then you add the variables you really care about, and you see whether this add anything to what you already had. Short answer: yes, make them nuisance variables. This way you'll do a Bayesian version of hierarchical regression.

Ironically, hierarchical regression is not possible (without some extra work) in the

classicallinear regression in JASP, but we are fixing that as we speak.Cheers,

E.J.

Hi E.J.!

Thank you for your quick response. It clarifies my mind on the nuisance variables. While there is still a question foggy in my mind: when I use JASP to conduct a Bayesian analysis, do I have some criteria for the nuisance? Now I understand if I get variables which I am not interested but could be relevant, then I should regard it as nuisance. Besides this, are there other situations in which I also should set up nuisance? I personally feel this maybe a "stupid" question but forgive me as I'm fairly a freshman in Bayesian

Another question is regarding hierarchical regression in JASP. Since it's not possible at this moment, am I wrong to conduct the Bayesian linear regression as I did in the attached image? Can I say that in this regression analysis, I controlled (sorry for this word ) X and Y, then look at the main effects and interaction? If I'm correct with this, then I think the results should be similar if I use a Bayesian ANCOVA, as I did in the attached image 2, but unfortunately, I got different BF1 and BF inclusion from the two analysis.

Looking forward to your help and thanks again!

Shuang

Hi Shuang,

Maybe the term "nuisance" is confusing. In the next version of JASP, we are replacing it with "include in null model" or something similar. The question when to do this is a substantive one, and the considerations are the same as for classical hierarchical regression.

As to the topic of classical hierarchical regression, we hope to include it in the next JASP version. With respect to the relation between regression and ANCOVA, the ANCOVA respects the fact that one of the predictor variables is a factor. So the models are slightly different.

Cheers,

E.J.