Dear all,
I was wondering if you could suggest me sources to read about variance, more specifically variance and r-squared in mediation and moderation.
I have significant interactions among variables, a significant model, but with low variance. So the model is not very "fit"... Anyway, the relations among variables I was testing are significant.
Do you have any source to interpret and comment this issue?
Thank you
You can use the penalized least square method , see my papers
1- Article comparison between Huber Lasso and Huber Elastic Net estimat...
2- Article comparison between some of the robust penalized estimators u...
Hi Giulia,
first, it is important to distinguish whether are interested in the effect of one or several independent variable(s) or whether you are interested in statistically predict as much of the dependent variable. R2 and "fit" is more relevant in that latter case. As you are testing hypotheses about the effects of the independent variable(s), the R2 is irrelevant in the first place - however.....
....a low R2 indicates that there are many influential variables not included in the model. Instead, they are represented in the error term. That has two implications
a) it increases the standard errors of the included predictors
b) it MAY bias the effects of the contained predictors if the excluded variables not only cause the dependent variable but also the independent variable (that is, act as confounders). This is the typical omitted variable problem that you find in any regression text (although regression text do a poor job when they label these excluded variables such as no explanation under which conditions this is problematic, is given.
As you say that your variables are significant, aspect #a may not be so relevant (beyond that you get larger confidence intervals) but #b may be relevant. Hence, think about such confounding variables and include them (if your data set contains further variables).
HTH
Holger
you can take a look to these two simple examples
http://orsp.kean.edu/documents/Moderation_Meditation.pdf
https://us.sagepub.com/sites/default/files/upm-binaries/47569_ch_15.pdf
hope that help
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