Effect of adding covariates to regression model

#1
What is the impact of adding a larger number of covariates to a multivariable regression model? I think I read it has some impact on power, or precision or some other effect?

Also, if one of the variables in the model is categorical, like income, classifying people into four income quartiles, what is the impact on power/precision etc. of increasing the number of categories of the variable (using quintiles instead of quartiles)?

Thanks!
 

hlsmith

Not a robit
#2
The more covariates or covariate groupings the fewer degrees of freedom - and models can become oversaturated and overfitted.

Adding more terms makes the conditional subgroups more sparse and I believe can impact precision.

Though, also if terms are multi-collinear, having a bunch of collinear variables in the model also impacts precision (increases standard error estimates).
 
#5
The more covariates or covariate groupings the fewer degrees of freedom - and models can become oversaturated and overfitted.

Adding more terms makes the conditional subgroups more sparse and I believe can impact precision.

Though, also if terms are multi-collinear, having a bunch of collinear variables in the model also impacts precision (increases standard error estimates).
And I think there is a loss of power i.e. when you dichotomize a continuous variable, there is definitely a loss of power, so I assume when you make further categories within the variable, there's a further loss of power.

Also a good point above about multiple comparisons.