1
$\begingroup$

I have the following model: $$ |X| = B_0 +B_1 \cdot y + B_2 \cdot z , $$ where $z$ and $y$ are normally distributed random variables, and $B_1$ and $B_2$ denote the coefficients.

My dependent variable contains either the positive or negative values of $X$. The positive and negative values of $X$ together are normally distributed, with a mean and median of around zero. For statistical reasons I would like to separately test the positive and negative values. This splits the left and right side of the otherwise normally distributed variable $X$. This clearly violates the normality assumption used for linear regression models. If I want to compare groups I would use a nonparametric type of test, but in this case I want to run the equivalent of a linear regression. Is this possible?

$\endgroup$
12
  • $\begingroup$ The normal distribution is symmetric, so you only need a solution for one case. $\endgroup$
    – emcor
    Commented Jun 25, 2014 at 22:56
  • $\begingroup$ I presume you mean with one case it is either positive or negative. $\endgroup$ Commented Jun 25, 2014 at 23:00
  • 1
    $\begingroup$ It is difficult, if not impossible, to formulate a legitimate statistical model based on this information. Could you please explain the context of this question and the basis for your suppositions about $X$? $\endgroup$
    – whuber
    Commented Jun 26, 2014 at 1:42
  • 1
    $\begingroup$ "For statistical reasons I would like to separately test the positive and negative values" - what are these reasons? I'm afraid you are trying to formulate the problem that you dont need to solve $\endgroup$
    – Aksakal
    Commented Oct 13, 2015 at 15:10
  • 1
    $\begingroup$ Is it possible to restate the model? As it stands it doesn't make a lot of sense since the left side is nonnegative but the right side can be negative. $\endgroup$
    – dsaxton
    Commented Mar 1, 2016 at 13:57

1 Answer 1

1
$\begingroup$

I think you can run a regression with $X_+$ and $X_-$ as independents, long as you assume a linear relationship to $Y$.

The "normality assumption" for linear regression is only regarding the error term assumed normally distributed around the true value.

$\endgroup$
12
  • $\begingroup$ I have tried this, but unfortunately I got results that were insignificant. $\endgroup$ Commented Jun 25, 2014 at 23:21
  • $\begingroup$ It may be the case, that linear regression is the wrong model then. Linear regression assumes a purely linear relationship. You may think of just plotting X vs. Y, to see if their relationship is linear. $\endgroup$
    – emcor
    Commented Jun 25, 2014 at 23:27
  • 4
    $\begingroup$ That doesn't necessarily mean the results are wrong or that the wrong technique was used. $\endgroup$
    – Peter Flom
    Commented Jun 25, 2014 at 23:27
  • 1
    $\begingroup$ By $X_+$ you mean a dummy variable for when $X$ is positive correct? Given the OP's comments, I would suggest a paramterization that includes the interactions with one dummy (you can't include both as the are collinear unless you do not include the intercept). $\endgroup$
    – Andy W
    Commented Jun 25, 2014 at 23:31
  • 1
    $\begingroup$ The relationship between X and y has been established before in prior research and is a linear relation. With regard to z there is also evidence of a linear relationship. I was wondering if the problem was with the separation of positive and negative values. $\endgroup$ Commented Jun 25, 2014 at 23:35

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.