Interpretation of marginal effects in a binary logit model

[Sherry Ahmed]

I’m trying to run a binary logit model to study the commute distance between place of residence and place of work for individuals. I’m reporting the marginal effects. I’m having hard time interpreting the results and I would really appreciate if you can help me with that. I divided commute distance into 2 categories (0 if commute > 0 and <=100 and I called it low) and (1 if commute > 100 and I called it long).

My independent variables are age (25-64 years old), marital status (single as a reference category), educational attainment (having a high school as reference category), presence of kids, homeownership (tenur) and female.

My issue is how I would interpret the results in a binary logit model, for example

1- The age variable came back with a negative sign in the low commute (0-100) does that means that I can conclude that: as people get older, they will commute less in the 0-100 km range? Does that automatically implies that, as people get older they will commute more in the above 100 range or not necessarily?

2- A positive marginal effect for the married variable (reference single): I can say that a married individual will commute more than a single individual in the 0-100 commute. Again, does that imply that a single individual will commute above 100 more than a married one?

3- Female variable: a female will commute more in the 0-100 km patterns compared to male which will imply that males commute more than females in the above 100 pattern.

[Clyde Schechter]

I think your chances of getting a clear and helpful response would be improved by showing the actual -margins- output you are trying to interpret. Copy them (and the immediately preceding commands along with the regression and its output) directly from your Results window or log file directly into the Forum editor, enclosing them between code delimiter so they will be readable here. If you are not familiar with code delimiters, please read Forum FAQ #12 for details.

[Sherry Ahmed]

Thank you for your response. I do not have access to my log file or results windows because, for confidentiality reason, I can only access the data within an office at the university and they do not allow us to take it outside. I will try however, to type what commands I used. Using Stata 16 I have: (pwdist2 is my commute distance between place of residence and place of work; lfpresch is the presence of kids)

gen commutedist = .
replace commutedist = 0 if pwdist2>0 &pwdist 2<= 100 (gave it the name of “low”)
replace commutedist = 1 if pwdist2>100 (gave it the name of “long”)
global ylist low
global xlist age ib(4). education ib(2). marst tenur female lfpresch
logit $ylist $xlist
quietly logit $ylist $xlist
margins, dydx(*)
logistic $ylist $xlist

[Sherry Ahmed]

Age	-0.0031186
	(-2.19)*
Bachelor	-0.0460879
	(-10.68)*
Married	0.076906
	(14.25)*
Children	0.0010119
	(2.1)*
Tenur	-0.1426941
	(-31.39)*
Female	0.0441656
	(15.97)*

[Clyde Schechter]

The first caveat is that this is a non-linear model, so it is important to remember that the marginal effect of any predictor actually depends on the baseline probability of the outcome (low commute) from which you are starting, and hence they vary with the values of the predictor variables themselves. Since you did not use the -at()- option to specify particular values of the predictors you are getting average marginal effects here.

1. So for the age variable, it says that if a person were selected at random from the population your sample comes from, and another person selected at random but exactly 1 year older, the probability that the latter has a low commute is 0.003 (0.3 percentage points) lower than the probability that the former does. Actually, even that is an approximation because age was modeled as continuous. The strictly correct interpretation is that the rate of increase in the probability of low commute as a function of age among the population from which you sampled is -0.3 percentage points per year.

2. If two people are drawn at random from your population, and one is married and the other is not, the married person's probability of a low commute is approximately 0.08 (8 percentage points) higher than that of the unmarried person's.

3. If a man and a woman are drawn at random from your population, the probability that the woman has a low commute is 4.4 percentage points higher than that of the man. (Actually, this is a somewhat technically erroneous result: you entered female in the model as a continuous variable even though it is actually discrete. So Stata calculated the marginal effect as if it were a continuous variable. The real value for a discrete variable would be slightly different, though not by very much. You might consider re-running the whole thing with female entered as a discrete variable (i.female) if you really want a more exactly correct result. But, as I say, the difference will be very small, probably negligible.

I would stick to quantitative statements that spell out the details like this. A shorthand like "older people are less likely to have a shorter commute" leaves too much to the imagination: how much older? how much less likely? how much shorter?

The other thing you need to do is form some judgments about whether these differences are large enough to be of any practical importance. With continuous variables like age, you have to do that with some care, because the marginal effect of age is in units of per year, but the range of ages in your data may be wide, so that even though -.003 per year seems incredibly small, if you are contrasting a 60 year old with a 20 year old, that adds up to a pretty large difference. So spend some time thinking carefully about these issues, and in particular, about how big a difference in probability of a low commute is meaningful in real world terms.

[Sherry Ahmed]

Thank you so much for your detailed explanation. I really appreciate it. Do I have to use i.female in stata even after I generated female = 1 and male = 0?

- I'm still a little confused about the interpretation in case its above 100.

If commuting 0-100 is 1 and commuting above 100 is 0 in the logit model. Would I, for example be able to say that, as you mentioned "So for the age variable, it says that if a person were selected at random from the population your sample comes from, and another person selected at random but exactly 1 year older, the probability that the latter has a low commute is 0.003 (0.3 percentage points) lower than the probability that the former does. Actually, even that is an approximation because age was modeled as continuous. The strictly correct interpretation is that the rate of increase in the probability of low commute as a function of age among the population from which you sampled is -0.3 percentage points per year." but would that imply the opposite too? For example, would I be able to conclude that, for commute above 100 km, as age increase, commuting above 100 km increase? I'm asking this question because when I ran the logit model with the commute above 100 as my dependent variable (instead of the dependent variable that used to be 0-100), the marginal effect of the variable age came negative which confused me so much. I expected that if marginal effect of age (and any other variable) is negative for commuting 0-100 that it must be positive (the opposite sign) for commuting above 100.

I would really appreciate your help.

[Clyde Schechter]

Do I have to use i.female in stata even after I generated female = 1 and male = 0?

Yes, you do. In order for -margins- to work correctly, you must specify i. in front of categorical variables. That is the only way that -margins- will know that it is a discrete variable and treat it accordingly.

but would that imply the opposite too? For example, would I be able to conclude that, for commute above 100 km, as age increase, commuting above 100 km increase? I'm asking this question because when I ran the logit model with the commute above 100 as my dependent variable (instead of the dependent variable that used to be 0-100), the marginal effect of the variable age came negative which confused me so much. I expected that if marginal effect of age (and any other variable) is negative for commuting 0-100 that it must be positive (the opposite sign) for commuting above 100.

If the variable for high commuting is always the exact opposite of the variable for low commuting, i.e. high = 1 when low = 0 and vice versa, then, yes, changing which one you use as the outcome variable should have no effect other than to reverse all the signs of the coefficients. Everything else should stay the same. If that is not what happened then either you did something else different in the two models, perhaps inadvertently and without noticing it, or the variables are not always exact opposites. Perhaps one of them has some missing values where the other doesn't. Try -tab low_commute high_commute, miss- to see if they are, in fact, exact opposites. If you find surprising results there, then you have to go back and fix the data.

If you want more specific help with this, you need to show example data and the code and results from the analyses that are giving you conflicting results. I understand you are working under constraints that make that difficult or impossible. I sympathize--I've been there. But it also isn't possible to do serious troubleshooting of code and results that you can't see.

[Sherry Ahmed]

Thank you for all the information. I will run the regression again and once I'm able to get authorization for data release I will post here.

[Sherry Ahmed]

I just got my data released and attached is one of the example of the average marginal effect results. After I made all the coding corrections, low commuting versus high commuting gave the exact same results with the exception of different sign coefficients. I want to make sure that my interpretation make sense and is correct. For example,

1- Age: I can say something (as you mentioned above): the rate of decrease in the probability of high commute as a function of age among my sample is -0.0002545 percentage points per year. Or to make it easier, I can just say that, as individuals get older, their probability to commute above 100 km is -0.0002545 percentage point per year compared to the probability of commuting less than 100 km (would that still be correct?)

2- Marital status (my reference is being single): I can say that the probability of commuting above 100 km is lower for a married individual compared to a single individual by -0.0109121

3- Educational attainment (my reference is high school degree): an individual with a bachelor degree has a lower probability (-0.0155945 percentage points) to commute above 100 km compared to an individual with a high school degree.

4- lfpresch (having kids): having kids lower the probability to commute above 100 km by -.0018746

5- Homeownership "tenur" (compared to renting): the probability of homeowners to commute above 100 km is 0.0110065 percentage points higher than individuals who are renting their homes.

6- Female: the probability of females commuting above 100 km is -0.0718827 compared to males.


Will the above interpretations be right? These are the marginal effects results so the only variable that I will say "per unit" is the age (per year) because its continuous (unlike all the other variables in my results), right?

I would really appreciate your help
Thank you so much

[Clyde Schechter]

I'm sorry, but I do not download or open attachments from people I don't know, especially not Microsoft Word documents, which can contain active malware. Please copy and paste the contents of your document directly into the forum editor and I'll try to comment on them.

[Sherry Ahmed]

Sorry about that, I copied and pasted it below. Thank you

Age	-0.0002545
Married	-0.0101921
Bachelor degree	-0.0155945
Presence of children	-0.0018746
Home ownership	0.0110065
Female	-0.0718827

[Clyde Schechter]

1- Age: I can say something (as you mentioned above): the rate of decrease in the probability of high commute as a function of age among my sample is -0.0002545 percentage points per year. Or to make it easier, I can just say that, as individuals get older, their probability to commute above 100 km is -0.0002545 percentage point per year compared to the probability of commuting less than 100 km (would that still be correct?)

The first is correct. The second is not; I don't even understand what the second is supposed to mean.

2- Marital status (my reference is being single): I can say that the probability of commuting above 100 km is lower for a married individual compared to a single individual by -0.0109121

Correct.

3- Educational attainment (my reference is high school degree): an individual with a bachelor degree has a lower probability (-0.0155945 percentage points) to commute above 100 km compared to an individual with a high school degree.

Correct.

4- lfpresch (having kids): having kids lower the probability to commute above 100 km by -.0018746

Probably incorrect. As worded, this is a causality claim. Want to commute less--have children and your chances will get better. Stated that way, the implausibility of the claim is obvious--your wording makes it less blatantly wrong, but it still leans in the direction of an unsupportable causality claim. No, unless this data comes from some bizarre trial where people where randomized to have more chlildren or not, you can't make this claim. What you can say is that those who have children have a lower probability of commuting over 100km than those who don't. Whether that's causal or due to other circumstances cannot be discerned from these results.

5- Homeownership "tenur" (compared to renting): the probability of homeowners to commute above 100 km is 0.0110065 percentage points higher than individuals who are renting their homes.

Correct.

6- Female: the probability of females commuting above 100 km is -0.0718827 compared to males.

I think I know what you mean by this, but the syntax is awkward at best and the end result is either uninterpretable or incorrect. Compared to a male, the probability a female commuest above 100 km is lower by 0.0718827.

Finally, when you do report these results, don't report them to 6+ decimal places. I don't know what data these results came from, but I doubt that you have the sample size, nor the precision of data that would be required to support a claim of that level of precision in your results. This is a study of humans, and even if it comes from a very large survey, it is unlikely you can justify more than 3 decimal places, and perhaps only 1 or 2.

[Sherry Ahmed]

Thank you so much. Will it be better if my interpretations used the "more likely" versus " less likely" wording. For example, a female is less likely to commute above 100km compared to a male (-0.07 percentage points)?

One more question, will I need to mention that (vice versa is correct too) or by definition, the logit model means that anyways?

[Clyde Schechter]

Will it be better if my interpretations used the "more likely" versus " less likely" wording.

I think that's a matter of what you want to emphasize. Either way it means the same thing. For age, bachelors degree, and having children, the only possible transitions in real life are forward: you can't get younger, once you have a bachelors degree you can't unhave it, and you can't unhave children. So it probably makes sense for these to speak of the decrease in probability per year of increasing age, or the decrease in probability associated with having a bachelors degree, or with having children. As for gender, that is in most circumstances, unchanging, so I think either way is fine unless there is something in the context of your research or of who you will be presenting it to that would make you want to emphasize one perspective over the other. Home ownership and marriage are mostly one-way transitions, but they do go the other way sometimes in normal life circumstances. So, again, either direction of comparison probably makes equal sense, again unless there is some contextual reason to think otherwise.

One more question, will I need to mention that (vice versa is correct too) or by definition, the logit model means that anyways?

Well, that depends on how much your target audience understands about logit models.

[Sherry Ahmed]

Perfect. Thank you so much. I really appreciate your help