interaction effect

[sedki zn]

Dear all,
i hope you are doing good

i've got confused while dealing with the interaction effect
i would appreciate it if you could help me to interpret the following results

( i am trying to investigate the interaction effect (mox) between stock options (Stockoptions) and firm performance (ROE) and their impact on firm R&D.
i would like to study how can ROE moderate the SO/R&D relationship !! )

kind regards
sedki

[sedki zn]

Richard Williams
Dear professor,
i would appreciate your help
kind regards

[Richard Williams]

I am not familiar with the user-written program you are using. Does it not support factor variable notation? If it does, use it instead of computing the interaction yourself.

How are Stockoptions and ROE measured? If one of them is a dichotomy, life is simpler than it is when both are continuous.

[sedki zn]

Dear Richard Williams
thank you for your reply

actually it is a quantile regression approach.
unfortunately factor variables not allowed, so i have generated the new interaction variable.
both stockoptions and ROE are continuous variables

my question is how can i interpret the economic relation

: an increase of ROE will increase the impact of Stockoptions on R&D or will decrease it ??

[Richard Williams]

Here are some generic suggestions for interactions involving continuous variables. I think drawing a graph often helps.

https://www3.nd.edu/~rwilliam/stats2/l55.pdf

[Clyde Schechter]

I am not familiar with -qregpd- either. But if, as seems likely, it is simply a user-written program to do quantile regression in panel data, you can use the official Stata command -xtqreg-, which requires version 14 or later. It might at least be worth checking whether it does the same thing as -qregpd-. If so, you can get the benefits of factor-variable notation and -margins-.

[sedki zn]

Dear Clyde Schechter
thank you professor for you intervention and your valuable recommendations.
Actually my question is how to interpret the results ( signs )
i need to focus only on the interaction variable's sign ( mox) or i need also to consider the 2 other variables' sign

For example here i can say : an increase in ROE will decrease the negative impact of Stockoptions on R&D ( just making the interpretation based on the NEGATIVE sign of "mox") ?

kind regards
sedki

[Clyde Schechter]

I would avoid "decrease the negative impact" because it may confuse readers. If it goes from -1 to -3, is that a decrease or an increase in the negative impact? Plain English is ambiguous in this way. It is also not clear whether the stock options impact is actually negative to start with. That negative coefficient of stock options is the marginal effect of stock options when ROE = 0. I don't know what ROE is and whether it can ever be 0, and whether that is common or unusual if it is possible. But my point is, is that your model explicitly assumes that there is no such thing as "the" effect of stock options. There are infinitely many effects of stockoptions, and they depend on the level of ROE. If we are starting out with a negative ROE, then the starting marginal effect of stock options might well be positive.

Interactions are tricky to interpret, and one-liners are almost guaranteed to be misleading in at least some respect. I think you are much better off calculating the actual marginal effects of stock options at various realistic levels of both stock options and ROE, and presenting those in a table or graph.

[Richard Williams]

I sometimes say thing like "decrease the magnitude of an effect" in the hope that readers get the idea the coefficient goes toward zero, whether it is positive or negative.

I agree. Interactions involving continuous variables hurt my head. I have a hard time visualizing them. Graphs can be very helpful. Or maybe plug in some values, e.g. when ROE = 10, the effect of Stockoptions is 7. When ROE = 20, the effect of Stockoptions is 11; or whatever. I might choose high, medium, and low values of ROE to illustrate the effects.

Again, some examples on how to do this are at

https://www3.nd.edu/~rwilliam/stats2/l55.pdf

[sedki zn]

I would avoid "decrease the negative impact" because it may confuse readers. If it goes from -1 to -3, is that a decrease or an increase in the negative impact? Plain English is ambiguous in this way. It is also not clear whether the stock options impact is actually negative to start with. That negative coefficient of stock options is the marginal effect of stock options when ROE = 0. I don't know what ROE is and whether it can ever be 0, and whether that is common or unusual if it is possible. But my point is, is that your model explicitly assumes that there is no such thing as "the" effect of stock options. There are infinitely many effects of stockoptions, and they depend on the level of ROE. If we are starting out with a negative ROE, then the starting marginal effect of stock options might well be positive.

Interactions are tricky to interpret, and one-liners are almost guaranteed to be misleading in at least some respect. I think you are much better off calculating the actual marginal effects of stock options at various realistic levels of both stock options and ROE, and presenting those in a table or graph.

Dear Professor
thank you for your answer

actually i am trying to study if ROE ( which can not be = 0) moderate the relationship between stock options and R&D at high levels of this latter.
in the main regression ( sotckoptions and R&D ( without interaction) i have got a negative relation).
my supervisor tells me that we should look at the interaction's term SIGN (mox sign). if it is the same as the stockoptions, we can say that ROE amplify the impact of stockoptions on R&D. if we get an opposite sign, we conclude that ROE weakens that impact (either positive or negative impact).
can this be a way to interpret the results ??

best regards
sedki

[Clyde Schechter]

No, I don't think that's right. The coefficient in a non-interaction model is not estimating the same parameter as any of the coefficients in the interaction model. To say that anything in the interaction model does anything to something in the non-interaction model is, I think, inappropriate. It may turn out to be correct on occasion, but then it is often better to be lucky than smart. The interaction coefficient can only be understood in the context of the interaction model as a whole. I stand by my recommendation in the second paragraph of #8.

[sedki zn]

No, I don't think that's right. The coefficient in a non-interaction model is not estimating the same parameter as any of the coefficients in the interaction model. To say that anything in the interaction model does anything to something in the non-interaction model is, I think, inappropriate. It may turn out to be correct on occasion, but then it is often better to be lucky than smart. The interaction coefficient can only be understood in the context of the interaction model as a whole. I stand by my recommendation in the second paragraph of #8.

Dear professor

thank you
it's really tricky,
following i have got this recommendation :

"Let’s consider the following regression model, conceptually identical with your example:
Y = B0 + B1X1+ B2X2 + B3X1*X2

The interactive effect between X1 and X2 on Y corresponds to the B3 slope. If B3 is reliable (or "statistically significant”), it means that the effect of X2 on Y depends on the level of X1 (or otherwise, but it’s exactly the same, the effect of X1 on Y depends on the level of X2).

Now, to answer your question :
If B3 is positive (the interactive effect is positive), then it means that the more positive X2 is, the more positive becomes the effect of X1 on Y (or alternatively, the more negative X2 is, the more negative effect of X1 on Y becomes).

Conversely, if B3 is negative, then the more positive X2 is, the more negative the effect of X1 on Y becomes (or alternatively, the more negative X2 is, the more positive effect of X1 on Y becomes).
Once again, it’s totally up to you, which variable among X1 and X2 is “the independent variable”, and which one is the “moderator”. Put it differently, the reasoning here applies both if you consider the effects at high/low levels of X1, or high/low levels of X2."

is it a correct ?
kind regards

[Clyde Schechter]

It's more or less correct.

I would disagree with a few small details. First, I am a strong supporter of the American Statistical Association's recommendation that the concept of statistical significance be abandoned. See https://www.tandfonline.com/doi/full...5.2019.1583913 for the "executive summary" and https://www.tandfonline.com/toc/utas20/73/sup1 for all 43 supporting articles. Or https://www.nature.com/articles/d41586-019-00857-9 for the tl;dr. Consequently, I would not equate "reliable" with "statistically significant." In fact, I would not even attempt to say that an interaction effect "does" or "does not" exist. Rather I would ask the question: how big is it? In particular, is it big enough to be important in real world terms? Or not. Statistical significance has nothing to say about that. The confidence intervals do.

Be that as it may, the use of the phrases "more positive" and "more negative" are not quite right. Suppose B3 is positive. Then as B1 increases (whether starting from a positive value and becoming more positive, or starting from a negative value and becoming positive, or just less negative) then the effect of X2 on Y increases. If the "starting" effect of X2 is positive, then, yes, it becomes more positive But if the starting effect of X2 is negative, it will become less negative, and if X2 is large enough, it will turn positive. So the correct language speaks of increasing and decreasing, not in terms of positivity and negativity. "If B3 is positive, then increasing values of X1 are associated with increasing marginal effects of X2" would be a strictly accurate description.

Nevertheless, I think that attempting to summarize effects in an interaction model this way are often unhelpful to the audience of your work. That is why I recommend using the -margins- command to get the marginal effects at representative values of the variables and then show them in a table or graph that makes the associations clear.

[sedki zn]

Dear Clyde Schechter

thank you very much professor.

it starts to be clear in my mind now
just one more thing if you do not mind
if in the main regression ( without interaction) i get positive impact of X1 (independent var) on Y and with interaction that effect turns to be negative, does this change the interpretation ?

for example:
without interaction: stock options impact on R&D is negative
with interaction: it turns to be positive and the interaction turn is negative. the interpretation remains the say as you mentioned ( we do not pay attention to the X1 change of signs ? ( Suppose B3 is negative. Then as B1 increases then the effect of X2 on Y decreases).

Concerning graphs and marginal effect, i'm using quantile regression and i'm not aware of the right method

Best regards
SEDKI

[sedki zn]

Dear professor,

here you say " Then as B1 increases then the effect of X2 on Y increases ......if the starting effect of X2 is negative, it will become less negative"


i have got confused with the this. means B3 is positive, B2 negative ==> more B3 increases more the impact of X2 on Y increase ( which means X2 goes to be less negative ??)
( i thought positive interaction increases the effect ( either positive or negative , so here increases the negative effect ( more negative and not less negative)

as i know, increasing a positive effect means it will be more positive and increasing a negative effect it will be more negative ( not less negative as you mentioned) . please correct me if i'm wrong. i am getting confused

best regards
SEDKI