Why using an interaction term inversly changes the results (p-value) for the interacted variable?

[Mehrzad Baktash]

I am use a probit model, and use 2 interaction terms in my regression. There seems to be a problem, as I get different results when I use an inversly coded variable.

The variable 'religionimportance' is coded inversly: 1:Very important 2: Important 3: Not important 4: Not important at all
So the interaction terms are also generated using the inversly coded variable 'religionimportance'
Using it this way, I get these results:

	Robust
alc	Coef.	Std. Err.	z	P>z	[95% Conf.	Interval]
shorttermcon	.1118843	.201347	0.56	0.578	-.2827486	.5065173
longtermcon	.5218077	.2038899	2.56	0.010	.1221908	.9214246
religionimportancexshort	.0156052	.07104	0.22	0.826	-.1236306	.1548411
religionimportancexlong	-.122903	.0712793	-1.72	0.085	-.2626078	.0168018
religionimportance	.2761201	.0229579	12.03	0.000	.2311235	.3211167
_cons	.1510165	.0642998	2.35	0.019	.0249911	.2770419

shorttermcon: short term consequences
longtermcon: long term consequences
religionimportancexshort: (shorttermcon * religionimportance)
religionimportancexlong: (longtermcon * religionimportance)

Furthermore, when I use 'religionimportance' the other way round, I generate a new variable 'religionimp', that is: 1:Not important at all 2: Not important 3: Important 4: Very important
with the interaction terms generated using the new 'religionimp' variable.
Then the results are changing for the shorttermcon & longtermcon, also the p-values. (I was expecting that only the sign of the coefficient would change)
Here are the results when I use the new variable 'religionimp' instead of inversly coded 'religionimportance' variable:

	Robust
alc	Coef.	Std. Err.	z	P>z	[95% Conf.	Interval]
shorttermcon	.1899104	.1762609	1.08	0.281	-.1555546	.5353754
longtermcon	-.0927071	.1743547	-0.53	0.595	-.434436	.2490218
religionimpxshort	-.0156052	.07104	-0.22	0.826	-.1548411	.1236306
religionimpxlong	.122903	.0712793	1.72	0.085	-.0168018	.2626078
religionimp	-.2761201	.0229579	-12.03	0.000	-.3211167	-.2311235
_cons	1.531617	.0580889	26.37	0.000	1.417765	1.645469

As expected, the coefficients of the variables 'religionimp', 'religionimpxshort' and 'religionimpxlong' only change their signs. Also, the p-values and z statistics remain the same. However, the main variables 'shorttermcon' and 'longtermcon' have totally new coefficients and are now not significant at all.

Could you please show me the way to solve this problem? Or could you please explain why this problem arises? What should I do in this case? Which regression should I proceed with?

Thank you very much in advance!

Best regards,
Mehrzad Baktash

[daniel klein]

The coefficients for the 'main variables' are conditional on the interacted predictor being 0. In your example, the coefficient for shorttermcon is conditional on religionimp == 0. If you change the direction of religionimp, you change the meaning of 0, too. Note that you do not even observe 0 in your dataset, so interpreting the conditional main effects* is tricky either way.

Technically, it is usually better to use factor-variable notation to create your interactions. See

help fvvarlist

* no claims of causal relationship implied

[Mehrzad Baktash]

Thanks for your answer, but I still have one unanswered question, as I would like to know why does the p-value changes when we use the religionimp variable inversly?

For religionimportance variable (inversly coded one) we get significant result but for religionimp variable the results are insignificant.

I also tried using (0,1, 2, 3) instead of (1, 2, 3, 4), but they give the same results after calculating the coefficients of both main variable and the interaction term.

[Maarten Buis]

No, your question was answered in #2: The main effect is the effect when the other variable equals 0, so when 0 means something else you change the meaning of the main effect.

[Mehrzad Baktash]

Dear Mr. Daniel Klein and Mr. Maarten Buis,

Thank you very much, now I totally understand the problem. That was very helpful.

Best regards,
Mehrzad Baktash