How to compare beta coefficients from different (transformed) DVs but same predictors?

04 October 2019 5 5K Report

Hello everybody,

I have a dataset with 8 predictors (dimensions of brand image) that I regress on 4 different DVs (Differentiation, Relevance, Esteem and Knowledge). One DV at a time.

In order for those linear regressions to meet assumptions, I had to square-root transform the DVs Differentiation (sqrt(Yd)) and power-transform Knowledge with 2.5 (Yk^2.5) (although I am debating quadratic to be more "simple")

Now I want to compare the effect of the 8 predictors on the different DVs, such as "Classic image is influencing Relevance the strongest, followed by Knowledge,..."

The standardized beta coefficients (z scores) shown here have been calculated from the transformed models of sqrt(Yd) and Yk^2.5 and normal models for Relevance and Esteem.

I have read that I can back-transform sqrt(Yd) and Yk^2.5, but that I must never back-transform betas. How do I make the standardized betas comparable? Even if I put Yd^2, how does that influence my interpretation here?

Honestly, I am confused. Can I compare them anyway because they are standardized scores?

Thank you all in advance!

PS: I am using R

David Eugene Booth

This looks suspiciously like SPSS. It makes no sense comparing regression coefficients from regressions with different DVs. I suggest that you post a new question asking how to do what you want to do. Best regards, David Booth

Sandra Koch

David Eugene Booth , thank you for your answer. I don't understand why it doesn't make sense to compare them. The four DVs combined build another value, but I don't want to go into theory here. If my 8 predictors are the same, and the DVs are measured the same way (before their transformation), then why wouldn't I be able to compare impacts of predictors?

It's not SPSS, I just built a nice table in Word, as the R output isn't very pretty.

Best regards, Sandra

David Eugene Booth

Sandra, would you expect to compare regression coefficients if the DVs were both income but one is in pounds and the other in dollars. Units have to be the same on both sides of the equation. Keep track of your units and this should be clear. D. Booth

Sandra Koch

David Eugene Booth That's a good comparison. So, hypothetically thinking, if I never had to transform the DVs because they fit well, could I compare them then? They're all measured in percentage of buyer's agreement. So the unit and scale is the same for all DVs and the predictors are the same anyway.

Sorry if my understanding is a bit slow, regressions are not my strong suit.

David Eugene Booth

Sandra, very good question. My initial thought is that you are correct. If you make a transformation of course then the units change. It might be interesting to see exactly what that difference is. Best regards, David

How to compare beta coefficients from different (transformed) DVs but same predictors?

How to compare two groups with only two measurements?

Binary Logistic Generalized Linear Mixed model in SPSS. Is it doable?

Enhanced Yellow Fluorescent Protein (Aequorea victoria) DNA sequence?

What kind of fluid could I use for a pitfall trap that also does not invalidate molecular testing?

What's the best way to measure growth rates in House sparrow chicks from day 2 to day 10?

Logistical regression using SPSS for a dichotomous dependent variable, with an independent variable of 1, 2, 5 and 10 seconds?

Do we need to write protocol for a second study of a systematic review that has been registered and published?

How to increase a model accuracy ?

What is the production process of CaFe ferroalloys?

1. What is the impact of having different scales in a survey? and how can we solve this problem before and after data collection (Literature)?