Xtlogit interaction term continuous and discrete

[Wessel van Luijk]

Hello everyone,

I have some trouble interpreting my xtlogit results in Stata 13.0. The xtlogit regression looks as follows:

xtlogit turnover_observation c.investment_return##c.board_size tenure fundingratio assets///
if interim==0, or nolog

Turnover_observation = equals one when there is a turnover observation, equals zero when there is no turnover observation
Investment_return = benchmark-adjusted investment return
Board_size = number of board members
Tenure = amount of years employed
Funding ratio = assets/discounted value of liabilities
Assets = natural logarithm of the amount of assets under management

My question concerns the interaction between investment return and board size. I want to interpret the odds ratio of the interation term as the ratio by which the odds ratio of investment return changes when one member is added to the board. Do I achieve this by running the regression listed above? And if so, will I be able to get the marginal effect of a one-unit change in board size on the predicted probability of a turnover with respect to the investment returns?

I am in doubt, since board size actually is a discrete variable and I should therefore use i.board_size. However, in that case Stata returns the odds ratio of the interaction term per specified board size.

Thanks in advance.

Best,

Wessel

[Clyde Schechter]

I want to interpret the odds ratio of the interation term as the ratio by which the odds ratio of investment return changes when one member is added to the board. Do I achieve this by running the regression listed above?

Yes.

And if so, will I be able to get the marginal effect of a one-unit change in board size on the predicted probability of a turnover with respect to the investment returns?

No. There is no such thing as "the" marginal effect of anything in a non-linear model. The effect of a one-unit change in board size on predicted probability of a turnover will depend on the board size before the one unit change, and also on the current level of investment returns, and also on all the other variables in the model! You can get specific marginal effects where you specify the values of some variables, and average (marginalize) over the others. You can also get an average marginal effect. For the latter, the code is simple:

margins, dydx(board_size)

For the former, you need to use the -at- (perhaps combined with -atmeans-) options of the -margins- command to specify variable values.

If you are not familiar with Stata's -margins- command, I highly recommend Richard Williams' Stata Journal article http://www.stata-journal.com/sjpdf.h...iclenum=st0260 as an introduction. It covers the most basic functions and applications in a particularly clear way. After that, read the -margins- section in Stata's PDF manual to learn some of the more advanced aspects.

[Wessel van Luijk]

Thank you very much for your quick reply Mr. Schechter! This is very helpful.

[Wessel van Luijk]

Dear mr. Schechter,

I have a question regarding your answer.

You recommended me to use the following code:

margins, dydx(board_size)

So this, in combination with the -at/atmeans- option will provide me with the marginal effects for a one-unit increase in the board size at a specific value of board size. However, what I am looking for is the marginal effect of the interaction term. I want to know by how much the marginal effects of investment return changes in case of one-unit increase in board size at the mean value of investment return.

I have tried to run the following code to achieve this:

margins board_size if interim==0, dydx(investment_return) at((mean)investment_return) predict(pu0)

However, Stata returns the following error: 'board_size' not found in list of covariates

My guess is that this does not work since board_size is a continuous variable. It will have to produce the marginal effects at each possible value of board_size. Is it possible to get the marginal effects of the interaction term in another way?

Thanks in advance.

Best,

Wessel

[Clyde Schechter]

However, what I am looking for is the marginal effect of the interaction term.

There is no such thing.

I want to know by how much the marginal effects of investment return changes in case of one-unit increase in board size at the mean value of investment return.

This is not the marginal effect of the interaction term, nor of anything else. If board size were a truly continuous variable, it would be a second partial derivative of the outcome with respect to board size. Since board size is actually discrete (though treated as "continuous," by which we really mean linear, in the model), it is actually a mixed second difference-derivative.

In any case, you have underspecified it, because it depends on the "starting value" of board size. Let's say you want to use 10 as your starting value for board size. Then you could do this:

margins, dydx(investment_return) at(board_size = (10 11)) at((mean) investment_return), pwcompare effects predict(pu0)

The contrast between the results for board_size = 10 and board_size = 11 will be the difference in the marginal effect of investment return that you are looking for.

I also think that for most audiences, this difference in marginal effect will be somewhat difficult to understand. I think that a clearer approach would be to calculate the marginal effect of investment return at a range of board sizes, and graph that. So, say that interesting range of board sizes is from 10 to 20, I'd do something like this:

margins, dydx(investment_return) at(board_size = (10(1)20)) at((mean) investment_return), predict(pu0)
marginsplot, xdimension(board_size)

I think the graph will make it easier for most people to see what you're talking about.

[Umar Ahmed]

Hi there. I am trying to use the margins after xtlogit and I have tried to use your code in the above section. However, I get the following error after the first line:
invalid 'predict'

[Clyde Schechter]

Sorry, there is a typo in the code. There should not be a comma before the -predict-.