interaction effects

[lisa bäcker]

Hello,

I need some help with my regression:

Deposit AGE INCOME JOB (INCOME*CRISIS)

Crisis is a dummy variable which can be 1 (crisis) or zero otherwise.
I need to center my variable income on the interaction term because of multicollinearity

Deposit AGE INCOME JOB (INCOME-AVERAGE_INCOME) * CRISIS

1. First I started running the regression without the interaction term and income is significant. When I included the interaction effect, it is not significant any more. Is this logical?
2. When I need to center the interaction term. How does it change my interpretation?
3 how can I include the interaction effect without multiplying the terms (is this correct: c.INCOME#CRISIS ?)
4 if my regression is transformed with the natural logarithm, do I calculate the average income using the geometrical average or the arithmetic average?

Thanks for your help.
Kind regard
Lisa

[Carlo Lazzaro]

Lisa:
you may want to try:

quietly sum INCOME
g ctrd_INCOME=INCOME-r(mean)

.

As far as interaction is concerned, you can try:

c.ctrd_INCOME##i.CRISIS

Centering INCOME around the mean changes the interpretation of your coefficient insofar now the reference is the average INCOME.
If your regression is log-transformed, it would be better to center INCOME after logging has been made.
To reply helpfully to your other queries, please post what you typed and what Stata gave you back (as per FAQ). Thanks.

[lisa bäcker]

Hello

so even if I want to center a variable which is transformed ny the logarithm, I use the arithmetic mean (r(mean)) and not the geometric mean (r(mean_g))?


My two regressions are

regress  Deposit ASSET WEALTH INCOME AGE  CRISIS  , vce(cluster id)
regress  Deposit ASSET INCOME AGE  CRISIS  INCOME_CRISIS ASSET_CRISIS WEALTH_CRISIS, vce(cluster id)

the interaction variables are centered.

and I get the following output:

I am wondering why my variable income gets insignificant?!

How do I Interpret the interaction effcts? (Remember that they are centered)

Thank you very much!
Kind regards,
Lisa

[lisa bäcker]

sorry, I forgot WEALTH in my regression:
So ist this Output for the interaction regression:

[Clyde Schechter]

The coefficient of INCOME represents two different things in the two models, and there is no reason to be surprised that one might be statistically significant and the other not. (Notice, though, that once you corrected the model to include the WEALTH main effect, you do happen to end up with a statistically significant value for INCOME--but it need not have worked out that way.)

In the model without interaction, the coefficient of INCOME represents the expected change in Deposit for a unit increase in INCOME. This is a single, effect that you expect to apply regardless of the value of CRISIS.

When you go to the interaction model, you are specifying that THERE IS NO SUCH THING as THE effect of INCOME on Deposit. You are asserting, by your very use of the interaction model, that there is one effect of INCOME on Deposit when CRISIS = 0, and another, different effect of INCOME in Deposit when CRISIS = 1. What your model results say in #r is that the effect of INCOME is 0.0005941 Deposit/Unit INCOME when CRISIS = 0, and (0.0005941+0.0005942) Deposit/Unit INCOME when CRISIS = 1. So the presence of CRISIS nearly doubles the effect of INCOME.

The centering of INCOME has no effect on the interpretation of either the INCOME or the INTERACTION term coefficients. It does, however, change the interpretation of the CRISIS variable. When you use the uncentered version of INCOME, the meaning of the CRISIS coefficient is that it is the expected difference between Deposit when CRISIS = 1 and Deposit when CRISIS = 0, conditional on INCOME = 0. Now, I don't know exactly what these variables are, but just from the name, I'm guessing that INCOME = 0 is rare or non-existent in your data, and maybe even in principle impossible for your population. So the coefficient of CRISIS is at best awkward to explain, and at worst meaningless here. When you center income, the coefficient of CRISIS has a different interpretation. It means the expected difference in Deposit when CRISIS = 1 and Deposit when CRISIS = 0 conditional on INCOME = average INCOME. So it is the effect of CRISIS on entities with average INCOME. That is probably a useful, and easily understood number.

FInally, completely as an aside, I find working with coefficients that have multiple zeroes after the decimal point bothersome. Things would be a bit easier to read and grasp if you were to rescale your asset income and wealth variables by a factor of 1,000 or 10,000, and your age variable by a factor of 10.

[lisa bäcker]

You can not imagine how much you helped me with your message!
Thank you very much!!

[lisa bäcker]

Just one last question. If my interaction effects are insignificant:
How do I interprete this? Can I say, that the effect of income does not change in times of crisis or normal times?
Or would you still interprete it like you have done it before?

[Maarten Buis]

You fail to reject the hypothesis that the effect of income does not change in times of crisis or normal times. This is not the same thing as saying that the effects are the same. It is a difference between absence of evidence (the former, correct, interpretion) and evidence of absence (the latter interpretation). Especially with interaction effects, where statistical power tends to be low, you should be careful not to confuse the two.

[lisa bäcker]

That sounds reasonable, thanks.

But do I need to make a joint test of significance to test the interaction variables?
Do it need to make it for each variable like:

test WEALTH WEALTH_CRISIS

or do I need to make it for all interaction variables, to test the impact of this variables in times of crisis

test WEALTH_CRISIS ASSET_CRISIS INCOME_CRISIS

Thanks in advance.
Kind regards,
Lisa

[Maarten Buis]

That depends on the exact null hypothesis you want to test. If you want to know if the effect of wealth differs depending on whether one is in a crisis or not, then a test of the null hypothesis that just the interaction effect equals 0 is enough.

[lisa bäcker]

so if my interaction variable INCOME_CRISIS is not significant, I fail to reject the hypothesis that the effect of income does not change in times of crisis or normal times. If it is significant I can say that INCOME is an important variable for Deposits in times of crisis, true?

And if I want to know if all interaction variables at once are significant I test:

  test WEATH_CRISIS INCOME_CRISIS ASSET_CRISIS

Is this all right?

thank you very much!

[Maarten Buis]

Almost, except that signficant and important are not synomyms in statistics.