For my master's thesis I'm exploring the relationship between attitude towards the advertismenent (Aad), brand types (boutiques and high street) and willingness to recommend (willing or not). Therefore, I need to run two regression analyses:

  • A bivariate regression (Aad = B0 + B1Brandtype + e)

  • A multiple regression (Willingness to recommend = B0 + B1Aad + B2BrandType + B3Aad*BrandType + e

Note that the Aad data are sentiment scores derived from Instagram comments (ranging from -0,9 to 0,9, where the negative values indicate a negative attitude towards the ad). The variables willingness and brand type are dummy coded.

However, when I run the two regressions, none of the assumptions are met... (normality, linearity, homoscedasticity). So my question is: would it make sense to log-transform the variable Aad for the assumptions to be met? However, one problem is that I'm dealing with negative values and so I need to add +100 for instance and then log-transform; however, if I transform those I wouldn't be able to recognize the negative attitude anymore? So then I can only say whether it has a relationship or not, but not which brand types significantly receives more positive attitudes? Right?

Histogram Aad enter image description here

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    $\begingroup$ It's unlikely that log transformation would help here, even with extra constant, if only for the reason you give. Plot log x over the range [99.1, 100.9] to see one reason. I think we need information on the data to give more specific advice. How big is your dataset? Can you show a histogram for aad? $\endgroup$ – Nick Cox Apr 6 at 16:38
  • $\begingroup$ Hi nick, thank you very much for your response. I've added my two histograms in my question above. I have a sample size of 2631. So following the CLT the assumption of normality would be met. However, then i still have the other assumptions who are not met. $\endgroup$ – Renée Stalman Apr 6 at 17:23
  • $\begingroup$ Sorry, but as specified, I wanted to see a histogram for aad, namely the original outcome. The residuals don't give any kind of clear signal about whether the original variable should be transformed. Curious: what is this? SPSS? $\endgroup$ – Nick Cox Apr 6 at 17:48
  • $\begingroup$ Here the original histogram for Aad. Yes this is SPSS! $\endgroup$ – Renée Stalman Apr 6 at 17:57
  • $\begingroup$ OK. I don't think transforming that is either necessary or likely to be helpful. Your regression for willingness to recommend should perhaps be a logit regression. $\endgroup$ – Nick Cox Apr 6 at 18:52

Rather than transforming the DV just to meet assumptions (and using a somewhat arbitrary transformation of log(DV + 100) ) I suggest using a method that does not rely on the assumptions on the errors. Two possibilities are robust regression and quantile regression.

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