Interaction of inverted U-shaped curve (xtgee regression): Interpretation of output &Graphs. Special quesiton to "_cons"

[Anna Wagner]

Dear Statalists,

I hope you can help me with the following:

1)
I run a regression with an DV, IV, IV², Controls. My output was the following :

Variable names:
Name of independent variable:	IV
Unstandardised Regression Coefficients:
Independent variable:	0.0023
Independent variable squared:	-0.0023
Intercept / Constant:	-0.0002
Means / SDs of IV:
Mean:	0.002072
SD:	1.008405

DV as Marketing Intensity (in % of sales) and IV as Market Orientation.
All relevant values (IV, IV²) significant.
(Please see the graph attached - I know "why" it is below the 0-line (because of _cons <0) , but what does it mean? How do I interpret this graph?
Values of DV: Mean .0296782 and Std. Dev. .0585483.


2) Secondly, I run the same regression (xtgee) with a moderator included: DV, IV², c.IV##Moderator c.IV²#Moderator, Controls

Variable names:
Name of independent variable:	IV
Name of moderator:	Moderator
Unstandardised Regression Coefficients:
Independent variable:	0.0024
Independent variable squared:	-0.0024
Moderator:	0.0055
Interaction - IV x Moderator:	0.0013
Interaction - IV squared x Moderator:	-0.0013
Intercept / Constant:	-0.0002
Means / SDs of variables:
Mean of independent variable:	0.002072
SD of independent variable:	1.008405
Mean of moderator:	0.022643
SD of moderator:	0.9990515

All relevant values (IV, IV², Moderator, Interaction_IV, Interaction_IV²) are significant.

The graph is moving pretty much: in low : stays below the 0-line; in high : is steeper and above 0-line. (please see graphic 2 attached).
Also here it would be awesome to get some hints of you how this could be and if there is a chance to interpret?



3) Does the constant term ("_cons") need to be significant as well? On what does its value depend in general? What is its meaning?


Thank you very much for your thoughts and ideas on this. I appreciate your support and wish you a nice day!
Best,
Anna

[Carlo Lazzaro]

Anna:
the first recommendation focuses on reporting what you typed and what Stata gave you back (as per FAQ): this approach is usually better than trying to summarize what you did.
As per your post, you ran two quite different regression models; by the way, you included an interaction in -xtgee- , that you did not consider in -regression-; perhaps, this may contribute to explain why you got different results (and graphs).
Usually, _cons is, in general, not that relevant.

[Clyde Schechter]

I echo Carlo's important points: you need to show the exact code that produced your results, and the actual results from Stata's results window. Do all this by copy/pasting into a code block (see FAQ #12 for how to use code delimiters) so it is easily readable here.

It would probably help to also post an example of your data. Please use the -dataex- command for that. (-ssc install dataex-, -help dataex- for instructions).

That said, based on what you say it appears that something is deeply wrong here. You state that your dependent variable is a "DV as Marketing Intensity (in % of sales)". Now, I don't know what that jargon means (this is an inter-disciplinary forum and it is usually wise not to explain things in simple English that people with no background in your discipline can understand), but if it is a percentage of something, it will typically be >= 0. Although a regression model can predict negative values for variables that are always positive, when your model predicts impossible values of your dependent variable across most of the data, as the graphs you show suggest it does, then the model is probably poorly specified and in need of substantial revision. That's why it's all the more important to see the actual code and actual results and some example data.

I should also note that your graphs are really difficult to understand, as the horizontal axes contain no information. What is the relationship being shown here? What values of whatever variable is on that horizontal axis are being exhibited? From context, I would guess that the horizontal axis is for the variable you refer to as IV, but the range of values being shown remains a mystery. Are those values typical of the values in the data, or are they some extrapolations beyond the data?

Lots of questions. Not enough information for answers yet.

[Anna Wagner]

Carlo,

thank you very much for your reply.
And I am sorry – I wasn’t aware of the reporting way. I will try to make it better this time:
Please find attached the model.

I ran the same model in 1) and 2) - one time without moderation, but with IV and IV². The other time with IV and IV² but also with the moderation variable and the two interactions (one with IV and one with IV²) - is this procedure not the right one to do?

I wonder, why the graphs are below that line of zero - I have difficulties to explain it.

Thank you and best wishes!
Anna

[Carlo Lazzaro]

Anna:
thanks for acting on FAQ requirements about posting what you typed and what Stata gave you back.
I would take a step aside, though. You seem to have too many predictors in your regression models when contrasted against the number of groups. I would check whether the results are still "weird" with a more parsimonious set of predictors.
I reciprocate best wishes.

[Anna Wagner]

Carlo:
Thank you for this hint - means, I should try to leave the "controls" (dummy variables) for the (panel-) years ("dyear") and the industries ("dsic") out and run the xtgee again? - Is this proceeding in line with the xtgee formatting? Do you know this?
Thank you,
Anna

[Carlo Lazzaro]

Anna:
reading once more the output of your regression models:
- the most effiìcient way to deal with dummies is via -fvvarlist-;
- taht said, I would also check if they are different from zero via a xtgee postestimation- command, such as -testparm-.

[Maarten Buis]

You may also be interested in this: http://maartenbuis.nl/wp/inter_quadr/inter_quadr.html