[Clyde Schechter]

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

That's wrong. Increasing a negative effect means it becomes less negative. Thank of the real numbers as a line that extends from negative infinity on the left to positive infinity on the right. Increase means moving to the right: positives become more positive, zero becomes positive, a negative number becomes less negative or may even increase to zero or a positive number. That is the meaning of increase.

But your confusion is natural. Many people think that increasing a negative means making it more negative. That's not correct English usage, but it's common. That's why describing things in this way is a recipe for confusion. Even after it becomes clear in your own mind, the likelihood that other you communicate your results to will misunderstand is high. That's why I think it's better to avoid short summaries like that and speak about specific numbers or show graphs. That leaves no room for misunderstanding.

Re #14: you are getting confused because you are thinking you have two models like this:

Y = B0 + B1 X1
Y = B0 + B1 X1 + B2 X2 + B3 X1*X2

But that's not correct. You are misusing the symbols B0 and B1: the coefficients in those two models do not refer to the same thing. You should think of the models as:

Y = C0 + C1 X1
Y = B0 + B1 X1 + B2 X2 + B3 X1*X2

B1 is not C1, and they do not even estimate the same real world thing. B1 estimates the marginal effect of X1 on Y conditional on X2 = 0. C1 estimates an overall effect of X1 on Y that is independent of X2. This overall effect that C1 estimates does not even exist in the second model. Nothing in the second model corresponds to C1. Nor does anything in the first model correspond to B1. B3 tells you how X2 modifies the marginal effect of X1 in the second model. B3 does not exist in the first model and cannot be interpreted in any way as having anything to do with the C coefficients. You cannot draw any conclusions about the C coefficients from the B coefficients, nor vice versa.

Most important, these models are not alternative valid descriptions of a single reality. They are inconsistent with each other, and if either is correct the other is incorrect, except in the very unusual case where B2 and B3 are zero, or close enough to 0 to ignore. You do not get to choose between these models. At most one of them is a satisfactory description of the data generating process.

[sedki zn]

Dear Clyde Schechter

thank you very much. thank you for your time and your constrictive answers.
now it's clear
again, thank you

Kind regards
SEDKI

[sedki zn]

Dear Clyde Schechter

i hope you are doing good, you and your family

i am back to you to share with you my final results.
studying the moderating role of firm performance (X2) in the relationship between Stock options(X1) and risk taking (Y), i have got the following results:

the interaction term (B3) is NEGATIVE
B1 (coff of X1) is NEGATIVE
B2 is POSITIVE


Interpretation ==>

More the ROE increases, more the negative impact of SO on R&D decreases. More the firm performance (ROE) increases, more negative the impact of CEO stock options on R&D will be.
More the firm performance improves, so the stock price, more the executive risk-aversion increases. Even the impact of CEO stock options on R&D is negative at high level of R&D, confirming the lose-averse attitude of the CEO, this negative impact will be more and more negative by the increase of the firm performance.
"

is it correct ?

(last time we discussed it when B3 is positive, so i would like to know is my interpretation is correct when B3 is negative)

best regards
SEDKI

[Clyde Schechter]

Your presentation is a bit confusing. You state that Y is a measure of risk-taking, but then you talk about impact of your predictor variables on R&D. Are we talking about the same model here? Is R&D what you mean by risk-taking? I don't normally think of it that way. For the sake of discussion, I'll assume that's what you mean.

Here's how to figure out what's going on. We have the model Y = B0 + B1*stock options + B2 * firm performance + B3*stock options*firm performance + error.

More the ROE increases, more the negative impact of SO on R&D decreases. More the firm performance (ROE) increases, more negative the impact of CEO stock options on R&D will be.

Then at any given level of firm performance, the marginal effect of stock options on Y is B1 + B3*firm performance. From a baseline of firm performance = 0, we start out with a marginal effect of stock options being B1, which you say is also negative. So as firm performance increases from 0, the marginal effect of stock options decreases, it becomes even more negative. This agrees with your sentence. Be careful to avoid restating this in terms that imply causation, as you have only observational data, and I see nothing in your study that brings us closer to identifying a causal effect.

More the firm performance improves, so the stock price, more the executive risk-aversion increases. Even the impact of CEO stock options on R&D is negative at high level of R&D, confirming the lose-averse attitude of the CEO, this negative impact will be more and more negative by the increase of the firm performance.

Here you are introducing constructs that are not included in your model, such as risk aversion/loss-aversion. You are proposing an explanation for your first conclusion in terms of things not observed. Consequently the data have nothing to say about whether this is correct or not. If there is a strong theoretical basis for this explanation, you might adopt it, at least tentatively. But otherwise you would need a different study that includes some measure of risk/loss aversion and that includes it as a mediator in the model, and we would have to see what the results of that study are to draw a conclusion about this particular mechanism.