[Meng Yu]

Thank you for your reply again. If I use -pwcompare- command, I guess the reference group will be respondents who did not invest regardless of sex. I assume I will get just one coefficient indicating the difference in marginal effect between men and women.

(If this was a linear model, were you saying I could simply subtract the two coefficients in the regression output?)

[Clyde Schechter]

If I use -pwcompare- command, I guess the reference group will be respondents who did not invest regardless of sex.

First, let me be clear, I am not suggesting you use the -pwcompare- command. (There is such a command; it is related, but different.) I am suggesting you use the -pwcompare- option in the -margins- command. Second, such a comparison has no "reference group" at all. It is, instead, as you say in your next sentence: one coefficient indicating the difference in marginal effect between men and women.

(If this was a linear model, were you saying I could simply subtract the two coefficients in the regression output?)

No, and I don't even understand what two coefficients in the regression output you are talking about. If you have a sex variable that covers male and female, then there will be only one coefficient in the regression output: one sex will be omitted, and the coefficient of the other will be the difference in outcome level, not marginal effect, between the two sexes. I was not referring to that. I was saying that if it was a linear model, and you had a sex#invest term in the model, you could look at the sex#invest term to compare the marginal effects of invest for men and women.

[Meng Yu]

I used

margins sex, dydx (invest) pwcompare

and obtained a table like:

	Contrast dy/dx	s.e.	95% CI
0.invest	(base outcome)
1.invest female vs male	0.003	0.003	-.002 .009

Since the CI includes 0, does that mean the result is not statistically significant?

[Meng Yu]

When testing another variable between male and female using the command

margins sex, dydx (donate) pwcompare (effects)

I got the result like:

	Contrast dy/dx	s.e	z	P>|z|	95% CI
0.donate
1.donate Female vs Male	-.067	.02	-3.43	0.001	-.11 -.03

Does this mean the result is significant at 99% CI? Can I interpret the result as donating makes women happier (supposing having mental health problems is my outcome variable) by 6.7 percentage points? Thank you.

[Clyde Schechter]

Well, you have likely read enough of my posts here to know that I do not endorse the use of significance testing (except in a few unusual contexts, none of which applies here.) But if you insist on, or are being forced into, using it, then regarding #48, the results are "not statistically significant" at the .05 level, and in #49, they are "significant" at the .001 level. The output there does not show the 99% CI, but given that you have "significance" at the .001 level, it is safe to conclude that the 99% CI would exclude 0. Nevertheless, even the ardent supporters of significance testing would not speak of results as being "significant at 99%CI." That is a conflation of two related, but distinct, concepts: a significance level and a confidence interval.

Can I interpret the result as donating makes women happier (supposing having mental health problems is my outcome variable) by 6.7 percentage points?

No, for several reasons. First, unless this is a randomized trial, it is wrong to speak in causal terms. Second, happiness and having fewer mental health problems are hardly the same thing at all. Third, speaking in terms of percentage points difference in the outcome is only appropriate if the outcome itself is a percentage--which may be the case, but you haven't said so, or if you have, it is so far back in the history of this long thread that I cannot find it.

Let me take you literally that your outcome variable is "having mental health problems," and that the underlying analysis here is a logistic or probit regression, so that -margins- is reporting effects on the probability of having mental health problems. I also assume that your sex variable is coded 1 = female, 0 = male, not the other way around. If those assumptions are accurate, it would be accurate to say that the difference in probability of mental health problems associated with donating is 0.067 (6.7 percentage points) less among women than it is among men.

[Meng Yu]

I agree with everything you said. Thank you.

I conducted logistic regression for panel data. I thought a marginal effects testing after such a regression always gives you percentage points if the predictor is categorical. But if the predictor is continuous, then it gives you the rate of change in the probability. In this case, if we used amount of donation, then the result would be interpreted as the difference in the rate of change of the probabilities of having mental problems is … Is that right?

[Clyde Schechter]

I thought a marginal effects testing after such a regression always gives you percentage points if the predictor is categorical.

No, that's only true if the outcome variable is itself a percentage. If the outcome variable is, say, a continuous variable in a linear regression, then the marginal effect would be the expected difference in outcome associated with a unit difference in the predictor.

But if the predictor is continuous, then it gives you the rate of change in the probability.

Same thing: if the outcome is a probability, then you are right. Otherwise, no.

In this case, if we used amount of donation, then the result would be interpreted as the difference in the rate of change of the probabilities of having mental problems is … Is that right?

Yes, that's right.

[Meng Yu]

If the outcome variable is dichotomous and the predictor variable is continuous, and the marginal effect is 0.45 (p<0.05), can I say "a one unit increase in the predictor is associated with an increase in the likelihood of (whatever 1 stands for in the outcome), with a rate of change in probability of 0.45?"

I believe if the marginal effect is negative, then the increase in the predictor will be associated with a decrease in the likelihood of the outcome. Is that right?

Thank you.

[Clyde Schechter]

can I say "a one unit increase in the predictor is associated with an increase in the likelihood of (whatever 1 stands for in the outcome), with a rate of change in probability of 0.45?"

Not quite. The rate of difference of probability (of whatever 1 stands for in the outcome) associated with differences in the predictor is 0.45 per (whatever the unit of the predictor is).

I believe if the marginal effect is negative, then the increase in the predictor will be associated with a decrease in the likelihood of the outcome. Is that right?

Yes.

[Meng Yu]

The rate of difference of probability (of whatever 1 stands for in the outcome) associated with differences in the predictor is 0.45 per (whatever the unit of the predictor is).

The predictor is a score ranging from 0 to 1. So the unit would be how they measure the score; it could be 0.01 or 0.001. How do I know by just looking at the data? What if the data don't show all the numbers after the decimal point?

Does what you wrote mean "difference of probability of (whatever 1 stands for in the outcome)" divided by "differences in the predictor?" Can I say "The rate of increase in the probability of having mental health problems associated with increase in the score is 0.45 per unit of the score?"

Thank you.

[Clyde Schechter]

Can I say "The rate of increase in the probability of having mental health problems associated with increase in the score is 0.45 per unit of the score?"

Yes!

[Meng Yu]

Thank you very much!

If you don't mind, I also want to know how people find out about the unit of a continuous variable. In theory, the unit can be infinitely small.

[Clyde Schechter]

Well, somewhere in the paper or presentation, there should be a table with descriptive statistics for all of the variables involved, and that table should mention the unit for any continuous variable that is not dimensionless. Now, sometimes that will be skipped if the dimension is conventionally known. For example, in a medical study of adults, probably nobody will bother to mention that the unit for age is years--everybody understands that. But otherwise, it would be mentioned in "Table 1" where descriptive statistics are given.

[Meng Yu]

This is my own research. I took a look at the data yesterday and found there are ten digits after the decimal point. I am trying to get in contact with the people who created this variable to find out about the unit.

I wonder how the change in unit, say from 0.001 to 0.01, affects the regression coefficient.

[Clyde Schechter]

If the original unit is 0.001 and you change it units of .01, then the magnitude of the variable will go down by a factor of 10. (E.g. 1000 of the original units = 1, which = 100 of the original units). If the magnitude of the variable goes down by a factor of 10, its regression coefficient, assuming every other variable is left as is, will go up by a factor of 10.