# TRANSFORMATION OF IVS and DVs with reflection - multiple linear regression

13 messages
Open this post in threaded view
|

## TRANSFORMATION OF IVS and DVs with reflection - multiple linear regression

 This post was updated on . I had a dataset with 7 IVs and the DV : wanted to use linear multiple linear regression. The DV was very far from normal (according to usual tests). Very strong negative skew so I used reflection and SQRT transformation and (to pleasant surprise) the Dv then passed normality tests (p>.05). This was good but I noticed that the direction of the relationship between one of the IVs and the DV had changed - e.g. what had been a strongly positive beta (0.9) had become approx -.0.9. So I am wondering is it 'usual' to also transform the IVs when using this sort of transformation on the DV? Some other assumptions of MLR were met - no issues with multicollinearity, heteroscascidicty BTW I realise logistic regression would have been an option but there is a small N (45) and larger samples are generally recommended with logistic. Initial experiments with this gave a very large exp (B) for one IV but yet was still not sig... I am not a statistician -  I am a mixed methods researcher with some experience in quantitative research so highly technical answers may well blow over my head... Any help appreciated though Thanks
Open this post in threaded view
|

## Re: TRANSFORMATION OF IVS and DVs with reflection - multiple linear regression

 or possibly one just allows for the reversal in interpretation - i.e. if you did reflection + SQRT transformation of the  DV, and the IV bow shows a negative relationship with DV (e.g. beta -.07) then one owuld interpret that as meaning that ''in reality'' the relationship is positive (beta .07)?
Open this post in threaded view
|

## Re: TRANSFORMATION OF IVS and DVs with reflection - multiple linear regression

 In reply to this post by researcher The normality assumption applies to the error terms, not the dependent variable.  So while transformations of the dependent variable may be appropriate, that does not follow from its nonnormality.Second, you say that logistic regression would have been appropriate, but logistic is for a dichotomous variable, which would, of course, have a nonnormal distribution.  If that is what you have, then the transformations described do not make sense, and avoiding logistic or other similar methods is probably the wrong strategy.On Mon, Nov 14, 2016 at 6:46 AM, researcher wrote:I had a dataset with 7 IVs and the DV : wanted to use linear multiple linear regression. The DV was very far from normal (accordion to usual tests). Very positive skew so I used reflection and SQRT transformation and (to pleasant surprise) the Dv then passed normality tests (p>.05). This was good but I noticed that the direction of the relationship between one of the IVs and the DV had changed - e.g. what had been a strongly positive beta (0.9) had become approx -.0.9. So I am wondering is it 'usual' to also transform the IVs when using this sort of transformation on the DV? Some other assumptions of MLR were met - no issues with multicollinearity, heteroscascidicty BTW I realise logistic regression would have been an option but there is a small N (45) and larger samples are generally recommended with logistic. Initial experiments with this gave a very large exp (B) for one IV but yet was still not sig... I am not a statistician -  I am a mixed methods researcher with some experience in quantitative research so highly technical answers may well blow over my head... Any hekp appreciated though Thanks -- View this message in context: http://spssx-discussion.1045642.n5.nabble.com/TRANSFORMATION-OF-IVS-and-DVs-with-reflection-multiple-linear-regression-tp5733454.html Sent from the SPSSX Discussion mailing list archive at Nabble.com. ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD -- Jon K Peck[hidden email] ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD
Open this post in threaded view
|

## Re: TRANSFORMATION OF IVS and DVs with reflection - multiple linear regression

 Hi Jon Thanks for that. On logistic - yes I am aware of the need for  a dichotmous Dv and recoded the DV appropriately to get that, when I was exploring the option of logistic regression,   However what I am interested in is how, in multiple linear regression,  to interpret the beta of IVs when the DV (continous)  has been transformed through reflection and SQRT. Thank you
Open this post in threaded view
|

## Re: TRANSFORMATION OF IVS and DVs with reflection - multiple linear regression

Open this post in threaded view
|

## Re: TRANSFORMATION OF IVS and DVs with reflection - multiple linear regression

 No I really didn't mean ordinal logistic regression . And I am not sure that it matters for the purposes of this question, what the variables were? My question is about how, in multiple linear regression,  to interpret the beta values of IVs when the DV has been transformed using refection and SQRT.
Open this post in threaded view
|

## Re: TRANSFORMATION OF IVS and DVs with reflection - multiple linear regression

 In reply to this post by researcher Ok.  What I am suggesting is that you go back to the original formulation and assess the  normality issue by looking at residuals, not at the dependent variable.  The residual histogram and the other plots available from the regression, particularly residuals vs fitted values, would be the place to start.On Mon, Nov 14, 2016 at 7:30 AM, researcher wrote:Hi Jon Thanks for that. On logistic - yes I am aware of the need for  a dichotmous Dv and recoded the DV appropriately to get that, when I was exploring the option of logistic regression, However what I am interested in is how, in multiple linear regression,  to interpret the beta of IVs when the DV (continous)  has been transformed through reflection and SQRT. Thank you -- View this message in context: http://spssx-discussion.1045642.n5.nabble.com/TRANSFORMATION-OF-IVS-and-DVs-with-reflection-multiple-linear-regression-tp5733454p5733457.html Sent from the SPSSX Discussion mailing list archive at Nabble.com. ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD -- Jon K Peck[hidden email] ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD
Open this post in threaded view
|

## Re: TRANSFORMATION OF IVS and DVs with reflection - multiple linear regression

 In reply to this post by researcher So you  originally had (say) something like a 0-100 score like a class grade, where a high score meant knowledge.  After you reversed it, a high score meant "error-score".  You can either talk about (1) a high correlation between knowledge and a predictor; or (2) a high negative correlation between errors and the predictor, if you insist on not-omitting the sign of the prediction in your statement.  One simple solution might be to take one more step in your transformation:  reverse the scoring of the transformed variable by taking one more step.  "A better-distributed test score than the usual score was created as follows.  To avoid confusion, it runs from 0 to 10 instead of 0-100.  This 0-to-10 score was computed by subtracting the square-root of the error score from 10, preserving the original notion that a high score is good." Most people would probably not bother with that.  They would toss in a comment, "You see negative r's with the test score because the transformed version runs in the opposite direction. -- Rich Ulrich From: SPSSX(r) Discussion <[hidden email]> on behalf of researcher <[hidden email]> Sent: Monday, November 14, 2016 9:48 AM To: [hidden email] Subject: Re: TRANSFORMATION OF IVS and DVs with reflection - multiple linear regression   No I really didn't mean ordinal logistic regression . And I am not sure that it matters for the purposes of this question, what the variables were? My question is about how, in multiple linear regression,  to interpret the beta values of IVs when the DV has been transformed using refection and SQRT. -- View this message in context: http://spssx-discussion.1045642.n5.nabble.com/TRANSFORMATION-OF-IVS-and-DVs-with-reflection-multiple-linear-regression-tp5733454p5733460.html Sent from the SPSSX Discussion mailing list archive at Nabble.com. ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD
Open this post in threaded view
|

## Re: TRANSFORMATION OF IVS and DVs with reflection - multiple linear regression

 In reply to this post by Jon Peck Thanks Jon. I am afraid I do not have time to do that in this case. The cruder answer to this problem, as I have found through further reading, is either a) interpret in reverse (i.e. a negative relationship of IV and DV, where the DV has been reflected should actually be understood as a positive relationship) b) re-reflection Thanks for your help
Open this post in threaded view
|

## Re: TRANSFORMATION OF IVS and DVs with reflection - multiple linear regression

 In reply to this post by Rich Ulrich Thanks Rich - I didn't see your message till now. Yes I came to that conclusion in the end too, but the re-reflection might be worth it in this case rather than trying to explain to the audience that they have to think it  the other way round...and t shoudl only take a few minutes ot do in SPSS. Thanks for the post - useful to know I was on the right track
Open this post in threaded view
|