marginal effect multinomial logit - beginner question

[natalia malancu]

hi guys!


one other question. when one computes the marginal effect of a continous variable one of the outcomes of a mlogit (margins, dydx (age) predict (outcome(1)) does the interpretation still account for the reference category?

say the value is 0.025

is the intepretation: one additional year = a 2.5 percentage points higher probability of outcome 1 or one additional year = a 2.5 percentage points higher probability of outcome 1 and not outcome 0 (which was the reference in the model).
if the latter is correct, then does it makes sense to compute the marginal effect for outcome 0? if so, what would then be the reference for it?
i'm inclined to believe the first interpretation is correct and not the latter.

thanks

[Richard Williams]

I like Long & Freese's spost13 commands (findit spost13_ado) but I especially like them for commands like mlogit where you otherwise have to do all these predict commands for each outcome. An example:

. webuse nhanes2f, clear

. quietly mlogit health i.female c.age

. mchange

mlogit: Changes in Pr(y) | Number of obs = 10335

Expression: Pr(health), predict(outcome())

             |      poor       fair    average       good  excellent 
-------------+-------------------------------------------------------
female       |                                                       
      1 vs 0 |    -0.015      0.026      0.021      0.008     -0.040 
     p-value |     0.002      0.000      0.016      0.340      0.000 
age          |                                                       
          +1 |     0.003      0.005      0.001     -0.003     -0.006 
     p-value |     0.000      0.000      0.000      0.000      0.000 
         +SD |     0.073      0.082     -0.003     -0.064     -0.088 
     p-value |     0.000      0.000      0.527      0.000      0.000 
    Marginal |     0.003      0.005      0.001     -0.003     -0.006 
     p-value |     0.000      0.000      0.000      0.000      0.000 

Average predictions

             |      poor       fair    average       good  excellent 
-------------+-------------------------------------------------------
  Pr(y|base) |     0.071      0.162      0.284      0.251      0.233 


.

Notice that as you sum across categories, the sum is 0. i.e. increases in the explanatory variable will increase the likelihood of being in some categories while reducing the likelihood of being in others.

I find marginal effects much easier to interpret for categorical variables than I do for continuous variables. .025 would be the instantaneous rate of change, which may or may not correspond very well to the effect of a 1 unit change. I do my best to explain this at http://www3.nd.edu/~rwilliam/xsoc73994/Margins02.pdf, but you may want to look at the sources I cite or other sources that cover the topic.

I highly recommend Long & Freese's book: http://www.stata.com/bookstore/regre...ent-variables/

[natalia malancu]

hi richard!

i am very familiar with you previous explanations, but this ones

what is an instantaneous rate of change exactly? i have never heard or read term before.

any chance to help me out with y axis as well.

[natalia malancu]

more importantly how would you phrase the effect in instantaneous rate of change language... i previous the change is still measured in percentage points...so one would say that instantaneous rate of change would be on average of 2.5 percentage points

[Richard Williams]

Again see this handout and/or some of the sources it cites: http://www3.nd.edu/~rwilliam/xsoc73994/Margins02.pdf

Also check out commands like mcp and combomarginsplot, available from SSC.

[natalia malancu]

thank you. your notes helped a lot (especially the additional explanation). will definitely look into purchasing the book.

[Rashad Jafarov]

Again see this handout and/or some of the sources it cites: http://www3.nd.edu/~rwilliam/xsoc73994/Margins02.pdf

Also check out commands like mcp and combomarginsplot, available from SSC.

Hi Richard,

You mention to use mcp command with mlogit. However I gave it a try, and seems like predict syntax is not compatible with it. I have run the following codes;

mlogit borrow $xxxxlist $xxxlist $xxlist $xlist, rrr nolog base(0)
mcp age, predict(outcome(1)) show
mcp age, predict(outcome(2)) show
mcp age, predict(outcome(3)) show



Is there something I am missing here?
Best regards,
Rashad

[Richard Williams]

I don't have Stata handy, but check out the margopts option.

[Richard Williams]

Ok, you could do something like this:

webuse nhanes2f, clear
mlogit health i.female i.black weight
mcp weight, margopts(predict(outcome(#1))) var1(20) plotopts(name(Poor))
mcp weight, margopts(predict(outcome(#2))) var1(20) plotopts(name(Fair))
mcp weight, margopts(predict(outcome(#3))) var1(20) plotopts(name(Average))
mcp weight, margopts(predict(outcome(#4))) var1(20) plotopts(name(Good))
mcp weight, margopts(predict(outcome(#5))) var1(20) plotopts(name(Excellent))

Personally though, I would probably try to use something like combomarginsplot. Or else Long & Freese's spost13 commands (findit spost13_ado), including mtable and mgen. The use of the spost13 commands is illustrated in Appendix A of

http://www3.nd.edu/~rwilliam/xsoc73994/Mlogit1.pdf

[Rashad Jafarov]

Thank you Richard!! Yes I figured it out too. Do you mean using combomarginsplot to combine mcp outputs?

By the way, very grateful for all these notes you have made available online, very illustrative and helpful. Many thanks!!
Another question. Are you familiar with reporting of adjusted risk ratios adovocated by Norton, Miller & Kleinman (2013). Their view is adjusted odds ratios in mlogit estiamtions are far off the true estimates.

Ref: Norton, E. C., Miller, M. M., & Kleinman, L. C. (2013). Computing adjusted risk ratios and risk differences in Stata. Stata J, 13(3), 492-509.

[Richard Williams]

I haven't tried it but I suppose you could combine mcp outputs. mcp is basically a shell for margins so you could use margins too.

Glad you find the notes helpful.

Not familiar with the Norton et al article. You might start a new thread on it.

[Maria Franco]

hi guys!


one other question. when one computes the marginal effect of a continous variable one of the outcomes of a mlogit (margins, dydx (age) predict (outcome(1)) does the interpretation still account for the reference category?

say the value is 0.025

is the intepretation: one additional year = a 2.5 percentage points higher probability of outcome 1 or one additional year = a 2.5 percentage points higher probability of outcome 1 and not outcome 0 (which was the reference in the model).
if the latter is correct, then does it makes sense to compute the marginal effect for outcome 0? if so, what would then be the reference for it?
i'm inclined to believe the first interpretation is correct and not the latter.

thanks

Hi everyone,

I have checked the suggested notes, but I still have the same doubt as Natalia regarding whether it makes sense to compute the marginal effects for outcome 0 (reference group). Using Stata 14's margins command, I get by default the marginal effects also for outcome 0, but I'm not clear how to interpret it. I am modelling the decision to migrate where 0 is "Did not move", 1 "Move for studies", 2 "Move for work" and 3 "Move for marriage". In this case, I want to know the instantaneous rate of change of the individual's age on the probability of getting each outcome. For the case of outcome 0 (my base category), would it be correct to interpret the marginal effect 0.025 as "one additional year is associated with 2.5 percentage points higher probability of not moving"?
Thanks in advance.
Maria