TRANSFORMATION OF IVS and DVs with reflection - multiple linear regression

[researcher]

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

[researcher]

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)?

[Jon Peck]

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 <[hidden email]> 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





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[researcher]

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

[Bruce Weaver]

Re the normality assumption applying to the errors, HEAR, HEAR!  ;-)  

Perhaps the OP meant ordinal logistic regression?  

To the OP:  Please tell us what the variables are.  And please note that with n = 45 and 7 explanatory variables, you have a recipe for severe over-fitting, regardless of what type of model it is.  See Mike Babyak's nice article on over-fitting for more info about that.

  https://people.duke.edu/~mababyak/papers/babyakregression.pdf

HTH.

Jon Peck wrote

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 <[hidden email]> 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
>



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Jon K Peck
[hidden email]

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[researcher]

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.

[Jon Peck]

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 <[hidden email]> 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




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[Rich Ulrich]

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.

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[researcher]

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

[researcher]

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

[Bruce Weaver]

Okay.  Did you mean binary logistic regression?  I ask, because you haven't actually said so.  You've only said it was not ordinal logistic regression.  It could be you meant multinomial logistic regression.  My point is that you're being rather stingy with information about the problem.

I asked what the variables actually are because knowing what they are might be helpful to someone who is trying to help you.  E.g., some types of variables suggest certain transformations.  Depending on what the variables are, someone might have suggested something other than taking square roots and reflecting.  

HTH.

researcher wrote

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.

[researcher]

Bruce I appreciate your help but if you read my posts it is clear that I am asking about multiple linear regression and only mentioned logistic in passing (as something that I had considered but rejected). I agree I  could have said more about the variables etc but time was short, on a deadline, and I did not think it was that relevant for the problem. I do appreciate the expertise available in this group but in this case was just after a 'quick and dirty' solution for want of a better term.  

[Rudobeck, Emil (LLU)]

As a side note, consider that transformation might not be necessary. Many people jump to non-parametric tests or transformations right away, but regression is actually robust to violations of normality and even if normality is violated, the regression coefficients will remain unbiased (but not the significance). The issue with normality can also be overcome with bootstrapping. There are additional options like robust regression (through the R plug-in).

As far as interpretation of coefficients is concerned, you can back-transform your coefficients after most types of transformations. The caveat is that you can't back-transform SEs, only CIs.

This is a helpful paper about assumptions of regression: Williams MN, Grajales CAG, Kurkiewicz D (2013) Assumptions of multiple regression: correcting two misconceptions. Practical Assessment, Research & Evaluation 18:2.

http://pareonline.net/getvn.asp?v=18&n=11
________________________________________
From: SPSSX(r) Discussion [[hidden email]] on behalf of researcher [[hidden email]]
Sent: Monday, November 14, 2016 3:48 PM
To: [hidden email]
Subject: Re: TRANSFORMATION OF IVS and DVs with reflection - multiple linear regression

Bruce I appreciate your help but if you read my posts it is clear that I am
asking about multiple linear regression and only mentioned logistic in
passing (as something that I had considered but rejected). I agree I  could
have said more about the variables etc but time was short, on a deadline,
and I did not think it was that relevant for the problem. I do appreciate
the expertise available in this group but in this case was just after a
'quick and dirty' solution for want of a better term.

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