Asymmetric effects in regression models

Modeling
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1

Hello All,

Recently I have come across this statement " In his 1987 book Making It Count , Stanley Lieberson devoted a whole chapter to arguing against the nearly universal presumption that causal effects are symmetric. What he meant is that for both theorists and data analysts, there is usually an implicit assumption that if a one-unit increase in variable X produces a change of B units in variable Y , then a one-unit decrease in X will result in a change of – B units in Y".

Also he persuasively argued that there are strong reasons to suspect that many social and psychological phenomena do not work this way. Is the increase in happiness when a person gets married exactly matched by the decrease in happiness when that same person gets divorced? Is the effect of imprisonment on physical health cancelled out by the effect of release from prison? Does a 10 per cent increase in income have the same effect on savings as a 10 per cent decrease in income (in the opposite direction)?

So basically as I understand the coefficient when X goes up will be different from when X goes down. So for a single explanatory variable, there will be two coefficients.

Does anybody know if there exists any methodology in Bayesian literature that could estimate this?

Thanks in advance,

Antony

2

Goes up relative to what? You’d have to define x relative to something, then you have lots of options for encoding different influences of positive deviations and negative deviations. The most trivial would be, assuming x has been defined with a reference at zero, create two contrasts, one with the positive values and zeroes for the negatives, one with the negative values and zeroes for the positives. Then, assuming a generally-positive-but-non-strictly-linear effect of x, associate each contrast with a positive-bounded and negative-bounded coefficient for the positive contrast and negative contrast, respectively. This you can get a positive linear relationship on either side of zero but with possibly different slopes.

3

Mike, thanks for the suggestion, but it is just too high level for me to understand what you are trying to say. Nevertheless, Thank you!
Does anyone else have any suggestions or links to a Bayesian paper or something?

Cheers
Antony