marginal effect in STATA logit

[Paola Ancona]

I run a logistic regression in which the Y is coded 1 if the company financed an acquisition through stock and 0 if the company financed it through cash. The dependend variables are: Fraud: is dummy coded 0 if the company didn't make a fraud and 1 otherwise; Leverage, roa and cash: are continous variable expressed in percentage I calculated the average marginal effect (margins, dydx) but I have some problems in interpreting them since they are expressed in percentage. The margin of cash is equal to -0.72. This means that 1 unit increase of cash produces an deacrese of 72% in the probability of Y=1, on average. This doesn't really make sense in economics. I wonder if could say that an increase of 10% in the variable cash is equal to a decrease of 7.2% in the probability of Y=1. It must be a stupid question but I want to be sure I correcly interpret results

[Marcos Almeida]

Hello Paola,

Welcome to the Stata Forum.

I kindly suggest to type the commands and present the output, as recommend in the FAQ.

This is surely the best way to increase the odds of getting insightful advice.

[Paola Ancona]

Sorry, I am new on this forum. I run a logistic regression and now I have problems in interpreting the average marginal effects, regardless of the pvalues.
Y (the dependent variable) is 1 if the acquisition was financed through stock, 0 if it's financed by cash.

logit y fraud leverage roa cash

fraud is a dummy variable equal to 1 is there was a fraud and 0 otherwise.
the variable leverage, roa and cash are in percentage.
In particular levarage, roa and cash are equal to total liabilities, net income and cash all scaled by total assets (respectively)
1 point increase in cash should produce a decrease of -33% in the probability that Y equals 1, on average. In economics this doesn't make that much change. I wonder if it's statistically correct saying that a 10% increase in cash produces a decrease of 3.3% in the probability that Y equals 1.

margins, dydx( leverage roa cash frode)

Average marginal effects Number of obs = 121
Model VCE : OIM

Expression : Pr(y), predict()
dy/dx w.r.t. : frode leverage roa cash


------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
fraud | .2592051 .0822552 3.15 0.002 .0979878 .4204224
leverage | -.2366726 .2178692 -1.09 0.277 -.6636883 .1903431
roa | -.4065535 .5190355 -0.78 0.433 -1.423844 .6107374
cash | -.3311004 .3332147 -0.99 0.320 -.9841891 .3219884
------------------------------------------------------------------------------

[Weiwen Ng]

...
Y (the dependent variable) is 1 if the acquisition was financed through stock, 0 if it's financed by cash.

logit y fraud leverage roa cash

fraud is a dummy variable equal to 1 is there was a fraud and 0 otherwise.
the variable leverage, roa and cash are in percentage.
In particular levarage, roa and cash are equal to total liabilities, net income and cash all scaled by total assets (respectively)
1 point increase in cash should produce a decrease of -33% in the probability that Y equals 1, on average. In economics this doesn't make that much change. I wonder if it's statistically correct saying that a 10% increase in cash produces a decrease of 3.3% in the probability that Y equals 1.

margins, dydx( leverage roa cash frode)

Average marginal effects Number of obs = 121
Model VCE : OIM

Expression : Pr(y), predict()
dy/dx w.r.t. : frode leverage roa cash
...

I am not sure what you mean when you say that this doesn't make that much change (referring to a 1 point increase in cash is associated with a 33% lower probability of Y = 1). Are you saying that the effect is too big? In particular, you said that you coded cash in percent. Did you mean that cash takes values of 0 to 100, or 0 to 1? If it's the latter, then the approximate size of the marginal effect does seem to make sense - this is the marginal effect of going from cash as 0% of total assets to 100% of total assets. I don't work in your field, but I wouldn't immediately think that effect is too big. If cash is coded as 0-100, though, then no, a marginal effect of 33% for a 1 percentage point change in cash seems like it would be too big. However, unless there are errors in your data, I suspect that cash was coded as 0-1.

Also, because this is a nonlinear model, the marginal effect depends on how much change in the independent variable you are making. Say you requested the

,OR

option to give you odds ratios, and say you had coded cash (as a percent of assets) in 10% units like I recommended (so, cash is now equal to 0 to 10). Say you had an OR of 1.5. That means that for each 1 unit change, the odds of Y = 1 are multiplied by 1.5. That's a non-linear change. So, a 10% increase in cash is not associated with a 3.3 percentage point decrease in the probability of Y=1.

[Paola Ancona]

I am not sure what you mean when you say that this doesn't make that much change (referring to a 1 point increase in cash is associated with a 33% lower probability of Y = 1). Are you saying that the effect is too big? In particular, you said that you coded cash in percent. Did you mean that cash takes values of 0 to 100, or 0 to 1? If it's the latter, then the approximate size of the marginal effect does seem to make sense - this is the marginal effect of going from cash as 0% of total assets to 100% of total assets. I don't work in your field, but I wouldn't immediately think that effect is too big. If cash is coded as 0-100, though, then no, a marginal effect of 33% for a 1 percentage point change in cash seems like it would be too big. However, unless there are errors in your data, I suspect that cash was coded as 0-1.

Also, because this is a nonlinear model, the marginal effect depends on how much change in the independent variable you are making. Say you requested the

,OR

option to give you odds ratios, and say you had coded cash (as a percent of assets) in 10% units like I recommended (so, cash is now equal to 0 to 10). Say you had an OR of 1.5. That means that for each 1 unit change, the odds of Y = 1 are multiplied by 1.5. That's a non-linear change. So, a 10% increase in cash is not associated with a 3.3 percentage point decrease in the probability of Y=1.

Thank you for your reply. I didn't want to use OR because it also tells me if the event Y=1 is less likely or more likely. I wanted to use average marginal effect in order to quantify the effect of the probability after 1 unit increase in a generic independent variable, on average. When I say that the variables are percentage I mean that generally they goes from 0 to 1.
In particular, in the sample:

1. Roa goes from -1 to +1
2. leverage goes from 0 to 1.4
3. cash from 0 to 1

Since a change from 0 to 100% cash doesn't make that much sense, I would know if I could say that a 10% increase in cash produces a 3.3% increase in probability of the event Y=1. From what I understood I cannot tell that. Is there another way to get this kind of output on STATA?

[Richard Williams]

Paola, first off, your Stata output would be far easier to read if you used code tags. See pt. 12 of the FAQ.

Second, when it comes to interpreting effects of continuous variables, I am a big fan of Patrick Royston's mcp command (marginscontplot). My summary of what it does is at

http://www3.nd.edu/~rwilliam/stats3/Margins03.pdf

His complete article is at

http://www.stata-journal.com/article...article=gr0056

Third, if cash goes from 0 to 1, then a 1 point increase in cash is a 100% increase, right? If so, then I agree with Weiwen. a 100% increase in one thing producing a 33% decrease in something else doesn't seem so odd to me. For your purposes it might make more sense to code cash on a 0 to 100 scale.