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I am wanting to determine whether components of Friendship Quality (measured by a scale) are related to a reduction in fear (multiple DVs). By components I mean that the Friendship scale I'm using is made up of 6 subscales. I have already conducted a 2 x 2 multivariate analysis of covariance as I wanted to see whether hand-holding caused a reduction in fear (friendship quality overall was the covariate). However, my supervisor agreed that it would be worthwhile to follow up with linear regression because it tells me exactly which friendship subscale relates to exactly which DV, which the MANCOVA doesn't do. I have a small sample size (38), so if I include the individual 6 subscales as covariates I would have 8 in total which is too many.

I understand that for multiple regression there should be no multicollinearity between the IVs, however that is inherent in the fact that the subscales all relate to friendship quality! Indeed, the bivariate correlations are all very high. VIFs are also over 10 for two of the subscales.

My question is - is it wrong to do several linear regressions - one for each DV and IV together. I feel like the answer is no ... and in that case, what model can I use? Preferably in SPSS! I had originally planned to do several multiple regressions because I can only use one DV at a time, but the data violate all the other assumptions too, apart from approximate normality, linearity and homoscedasticity of residuals - so likely that I'll need a non-parametric test too.

Please be gentle, I have a very limited understanding of regression models as they weren't really covered that thoroughly in the stats units I've done :( Any help would be greatly appreciated!

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It isn't exactly wrong to do separate regressions, but if you do it that way, then you are not controlling for the effects of other variables, which is presumably what you wanted to do with the multiple regression.

There are other solutions to collinearity, including:

  • Ridge regression, where you accept a small amount of bias in order to reduce the variance of the estimators
  • Partial least squares regression, where you form a linear combination of the independent variables to get the best regression possible
  • Principal component regression, where you form a linear combination of the independent variables to capture the most variance
  • Getting more data

As for other assumptions being violated, you could ask separate questions giving some details as to the problems.

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  • $\begingroup$ Thanks Peter, yes I do want to control for the other variables because I want to know which aspect/s of friendship quality (i.e., which of the 6 subscale items) relate to fear reduction, rather than friendship quality as a whole. Multiple regression would be perfect if not for the multicollinearity issue. To be clear, I am keeping the MANCOVA, I just want a model that can now further clarify the relationship between fear reduction (because of hand-holding) and the 6 aspects that make up friendship quality (e.g., is intimacy most related, or is it trust). $\endgroup$ – Tash Aug 29 '17 at 13:28
  • $\begingroup$ It's too late to collect more data unfortunately, but will look into your suggestions about the other models. Just had a quick skim over PLS, which looks promising - I can do it in SPSS, and it has no hard assumptions?! Thanks very much for your help Peter, this gives me a direction to go in now. $\endgroup$ – Tash Aug 29 '17 at 13:30
  • $\begingroup$ I don't know SPSS at all. For more on PLS see e.g. tqmp.org/RegularArticles/vol11-2/p052/p052.pdf $\endgroup$ – Peter Flom - Reinstate Monica Aug 29 '17 at 13:35

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