# Covariates considered moderator or control variables?

Are covariates considered moderator variables or control variables? To elaborate on my question, I'm conducting a research study which has:

1. variables that are supposed to affect the dependent variable but that I don't consider in any analysis (e.g., daytime the experiment done)

2. variables that are used as exclusion criteria, so that some subjects are removed (filtered) from the analysis (e.g., having medical condition)

3. variables that are supposed to influence the dependent variable and which I therefore include as covariates in my model (e.g., a GLM or MANCOVA).

What would you call each of these three kinds of variables?

• In general, the difference between a moderator and a control is semantic. If the effect is moderated by a given effect, then the estimates are also controlled by that effect. Usually "control" implies that it is included in the model to reduce/remove confounding of the variable of interest. There is nothing mathematically different about the variable of interest. Aug 6 '13 at 4:19
• @ACD Thanks, but could you elaborate on the semantic difference ? I just want this to know how to describe kind of my variables in my thesis. Aug 6 '13 at 4:26
• Say you are running y = a +bx + e. x is the variable of interest. it is confounded by z. That means that z is a moderating variable. if you run y = a + b1x + b2z + e, then you are controlling for z as a moderating variable. Aug 6 '13 at 6:34
• I disagree with @ACD. A moderator is a variable that interacts with the predictor of interest and in this way influences the predictor's relationship with the DV. In a purely statistical sense (that is, ignoring any notions of causality), moderation is synonymous with interaction. A covariate or "control variable," on the other hand, does not interact with the predictor of interest. So, no, the difference between a moderator and a control variable is not merely semantic. The z variable from @ACD's previous comment would be a covariate and not a moderator, since there is no interaction. Aug 9 '13 at 3:22
• ^I don't disagree. Either way, what we've got here is an example of why it is dangerous to rely on metaphor and other linguistic constructs for mathematical concepts. Aug 9 '13 at 3:55

## 1 Answer

A control variable (confounder, potential omitted variable) is a variable you include in the model because you suspect it is confounding the main relationship you are interested in (so it is suspected to be related to both the main independent variable (explanatory variable, predictor, treatment) of interest and to the dependent (outcome) variable.

A moderator is a variable which changes the effect of the main independent variable on the outcome variable, so it interacts with the main independent variable.

A mediating variable is a variable that translates fully or partially the effect of the main independent variable on the outcome.

A covariate is in my opinion unspecified and could refer to either of these.

A variable that is suspected to be related with the outcome variable but not with the main independent variable of interest is a covariate but not a control variable (as it does not control for anything).

A variable that is suspected to be related to the main independent variable of interest but not to the outcome would be an instrumental variable.

To come back to your concrete questions:

1. since you don't use them it matters little what you called them - alternative predictors (causal factors), unmodelled effects, etc are all options

2. definitely no controls or covariates, these are just sample selection criteria

3. see above

• +1. Clear, complete, and to the point. Welcome to our site!
– whuber
Feb 4 '14 at 15:55
• +1, However, I wouldn't call "a variable you include" an "omitted variable". Would you mind tweaking that? Feb 4 '14 at 16:47
• @gung Good catch. Yes, that phrase could be confusing. I read "potential omitted variable" in the sense of "if you were to leave it out, it would cause an 'omitted variable' error" (and therefore, by implication, you should include it in the model).
– whuber
Feb 4 '14 at 18:12
• yeah, I added 'potential' later. The underlying problem being addressed is usually referred to as 'omitted variable bias' so often one speaks of 'omitted variables' while they are, in fact, 'variables included to avoid an omitted variable bias'. Feb 4 '14 at 19:06