suppressing constant term in xtlogit regression

[sadegh javaheri]

Hi Statalist Community,

I am using logistic regression to predict and explain the probability of a firm being distressed in a panel dataset. since my dependent variable (Type) is dichotomous (Distressed coded as 1, Not-Distressed coded as 0) I am using xtlogit command. However, when i use nonconstant option, I end up with much more significant results as opposed to when the constant is included.

I understand that in the normal multivariate regression context, unless there is absolute certainty that the constant term does not capture any effect we should not drop it, however, I have difficulty to understand the meaning of the constant term in the logistic regression context. in other words, a firm can either be financially distressed or not and the coefficient for each of the independent variables reflect the impact of that variable on the likelihood of the firm being distressed (category coded as 1), so what does the coefficient of constant term (which is statistically significant) mean and under what circumstances will it be appropriate to drop the constant?


Many Thanks,
Sadegh



***********xtlogit with constant

***********xtlogit without constant

[Clyde Schechter]

The constant term in a logistic regression equals the logarithm of the odds of the outcome when all of the independent variables are zero.

The coefficients of all the independent variables then specify the logarithms of the odds ratios associated with unit values of those variables.

If you omit the constant from a logistic regression, you are imposing the constraint that the probability of the outcome is 50% when all the independent variables are zero. I suppose there must be situations where that is a reasonable assumption, but I have yet to encounter one in a decades-long career.

[sadegh javaheri]

Thanks very much dear Mr. Schechter for your helpful comment.
I have one more question now, in the first instance when constant term is included and it is significant with coefficient of -3.74, how should i interpret this result?

Best,
Sadegh

[Clyde Schechter]

It means that, conditional on the independent variables all being zero, the probability of the outcome is significantly different from 0.5. In fact, your estimated probability of outcome when all independent variables are zero is invlogit(-3.74) = 0.023... If the probability of the outcome with all independent variables equal to zero is of interest in your situation, then you should report this result. If, as is more common, nobody cares about that probability, you should just ignore it.

[sadegh javaheri]

Here I ran the xtlogit command with only the dependent variable and no independent variable: and the coefficient of -2.59, based on what i found on the web, should be the logarithm of the odd ratio, log(p/(1-p))=-2.59 and p should be the overall probability of being distressed (coded as 1). when working out p=exp(-2.59)/(1+exp(-2.59))=0.069=6.9%
however, when looking at the raw data, the probability of firm being distressed is 0.1277=12.77%


*******xtlogit Type

*******tab Type

[Clyde Schechter]

First, remember that invlogit(_cons) is the probability of outcome conditional on all independent variables being zero. That includes the random effects! Calculating the overall probability of the outcome in the data does not get you the same thing: that is the population averaged probability of distress, integrated over the random effects.

As you see they do not turn out to be equal, and, due to the non-linearity of the model, there is no reason to expect that they would.

[sadegh javaheri]

I understand it now! Thank you very much again, I really appreciate your help dear Clyde.

Best,
Sadegh

[Jojo Melchi]

Good morning everyone,
I am trying to evaluate the impact of macroeconomic variables (X_t) from 2002q1 to 2007q2 on the probability of firms to be distressed (Y_it takes value 1 if distressed or 0 elsewhere) during the financial crisis (2002q2 to 2008q4).
How should I specify the xtlogit model in stata?
Thank you in advance for your help