MLOGIT reporting and interpreting interactions between binary and continuous variables

[Barbora Sedova]

Dear all,

I am running a panel data multinomial logit model, where I regress a categorical variable on households’ migration decision (0=no migration, 1=rural migration, 2=urban migration, 3=international migration) on interactions of temperature and precipitation continuous variables with a binary variable agriculture (1=agricultural dependence). Additionally, I control for some other household-specific characteristics (educ, income, assets …):
mlogit migr c.temp##i.agriculture c.precip##i.agriculture c.educ c.income i.assets, cluster(State)

I would like to report the marginal effects for each outcome category. Now, I know that it gets tricky with the interaction terms. What I am doing right now is that for instance for the outcome category 1, I estimate the marginal effects in the following manner:

margins, dydx(temp precip ) at(Agriculture=(0 1)) predict(outcome(1)) post

If I understand this correctly, the coefficients give me marginal probability that a household migrates to another rural area if temperature and precipitation change by one unit separately for agricultural and non-agricultural households. Is this a correct interpretation?

What I would like to show, however, is whether the marginal probability of migrating to lets say a rural area is significantly different for agricultural and non-agricultural households, in other words whether the two marginal probabilities are significantly different. Is this also a valid approach to report the results ? Or is the previous approach a better one? Additionally, I would like the outcome table also to include the marginal effects of the additional controls. How do Isay this in the command?

I have tried to go through a lot of posts and literature (also here in Statalist) but still I am not really sure.
Could you please help me?
I would be super grateful.

Thank you!

Best,

Barbora

[Clyde Schechter]

If I understand this correctly, the coefficients give me marginal probability that a household migrates to another rural area if temperature and precipitation change by one unit separately for agricultural and non-agricultural households. Is this a correct interpretation?

Basically, yes. I would choose my words a bit differently because the term marginal probability can mean a few different things. So for clarity, I would say it as "the coefficients give the rate of change in probability of migrating to another rural area for agricultural and non-agricultural households per unit change in temperature and precipitation." By the way, you can simplify the code for this a little bit:

margins Agriculture, dydx(temp precip ) predict(outcome(1)) post

What I would like to show, however, is whether the marginal probability of migrating to lets say a rural area is significantly different for agricultural and non-agricultural households, in other words whether the two marginal probabilities are significantly different.

Since you specified the -post- option here, you can do this using -lincom- or -test- the same way you could compare coefficients immediately after a regression.

Is this also a valid approach to report the results ? Or is the previous approach a better one?

Well, the American Statistical Association recommends abandoning the use of significance testing. https://www.tandfonline.com/doi/full...5.2019.1583913. It would be consistent with this position to apply -lincom- as suggested above and report the difference in those incremental probabilities along with its standard error or 95% CI, and the p-value if you wish.

How do Isay this in the command?

It's probably something like this:

lincom _b[temp:1.Agriculture] - _b[temp:2.Agriculture]
lincom _b[precip:1.Agriculture] - _b[precip:2.Agriculture]

If that's not it exactly, re-run the -mlogit- and then re-run the -margins- command, this time adding the -coefl- option. The output will now show you the exact expressions for the coefficients that you need to use in your -lincom-.

[Barbora Sedova]

Dear Clyde,

thanks a lot. This is exactly what I wanted. However, I would like to reportone more additional thing. In addition to the difference in the response coefficients of the agricultural and non-agricultural households and their standard errors, I would like to report the stars (or p-values) indicating whether the difference in responses is significant. How can I best implement this?

Thank you very much.

Best,

Barbora