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In my nonexperimental data, when running regression, I faced the Simpson Paradox. Simplistically speaking, Pearl,2014 said:

Simpson’s paradox refers to a phenomena whereby the association between a pair of variables (X, Y ) reverses sign upon conditioning of a third variable, Z, regardless of the value taken by Z.

I use the sample of this topic to describe:

Imagine

You run a linear regression with four numeric predictors (IV1, ..., IV4)

When only IV1 is included as a predictor the standardised beta is +.20

When you also include IV2 to IV4 the sign of the standardised regression coefficient of IV1 flips to -.25 (i.e., it's become negative).

In my case, I use OLS to run the panel data, my method is:

inventory_turnover = b1pt + b2firmsize + b3lnGDP .

pt is a binary variable, representing for treatment group. When I run this regression using fixed-effect model (controlled for firm and year), b1 is positive. But when I add another variable called gross margin to the independent groups (because Gaur,2005 said that gross margin affects inventory turnover), b1 become negative I have a look through the comments and have not found any approach or instruction to deal with Simpson Paradox in linear regression with nonexperimental data.

I am wondering if there is any way to deal with this problem, for example, spotting multicollinearity,... I saw a comment in this topic mention about the residualization approach but I do not know how to spot the variable IV1 in this case.

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  • $\begingroup$ Could you clarify what you mean by "deal with"? Are you looking for models, simplifications, interpretations, transformations, ...? $\endgroup$
    – whuber ♦
    Commented Apr 28, 2021 at 14:38
  • $\begingroup$ Hi @whuber, I am looking for the instructions and transformations to address Simpson's paradox in nonexperimental data $\endgroup$
    – Phil Nguyen
    Commented Apr 28, 2021 at 20:16
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    $\begingroup$ Unfortunately your question remains vague: could you explain what you mean by "address"? After all, Simpson's Paradox merely describes a characteristic of your data. What, if anything, to do about that depends on many other things I am hoping you will articulate for us, such as the objectives of your regression and the range of statistical models you are considering. $\endgroup$
    – whuber ♦
    Commented Apr 28, 2021 at 20:32
  • $\begingroup$ Hi @whuber, sorry for the unclear explanation. Could you please tell me what is the "range of statistical models" mean, please? In my case, I use OLS to run the panel data, my method is: inventory_turnover = b1*pt + b2*firmsize + b3*lnGDP . pt is a binary variable, representing for treatment group. When I run this regression using fixed effect model (controlled for firm and year), b1 is positive. But when I add another variable called gross margin to the independent groups, b1 become negative. Please let me know if there is any thing need to be clarified. $\endgroup$
    – Phil Nguyen
    Commented Apr 28, 2021 at 21:06
  • $\begingroup$ "When I add another variable" means you are looking at a second model. The set of models you are looking at (or willing to consider) is an important consideration. So far, you haven't given us any information about why you are considering this second model or what role evaluating two or models is intended to play in your overall analysis. $\endgroup$
    – whuber ♦
    Commented Apr 28, 2021 at 22:00

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Simpson's paradox merely describes two conditional association relationships between variables in the data that are in opposite directions. Unless there is some broader objective in your analysis, there is nothing you need to do to "deal with" this other than noting that it occurs. The operative question if you are doing some analysis from this data is which of the two results is of interest; the marginal or the conditional result? So, the question here is, do you wish to infer the statistical association between variables conditional on "gross margin" or unconditional on this variable?

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    $\begingroup$ Thank you for your response, @Ben, because gross margin affects inventory turnover as in literature(Gaur,2005, Management Science). Therefore, I want to infer the statistical association between variables conditional on "gross margin". $\endgroup$
    – Phil Nguyen
    Commented Apr 28, 2021 at 22:43

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