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Re: st: Multinomial logit model with selection

From   Stas Kolenikov <>
Subject   Re: st: Multinomial logit model with selection
Date   Fri, 2 Mar 2012 13:08:43 -0500


cleanup issues in your post:

1. there is no -selmlog- in Stata world, as we know it. -findit
selmlog- returns a reference to -svyselmlog- on SSC. If a package is
not downloadable, it is nearly as good as non-existent. Without
knowing what -selmlog- produces, it is impossible to say how to
interpret its output.

2. References to the papers would be helpful. Especially if coupled
with links to full text or to RePEc, at least.

I can answer your question 2: I don't think any of the interpretation
changes. You are doing corrections in a different way, that's all.
What you called DMF(1) is more flexible, although not so internally
consistent compared to DMF(0), but as far as I can recall
Bourguignon's paper, it worked in a greater variety of settings.

On Fri, Mar 2, 2012 at 11:45 AM, T.Randazzo <> wrote:
> Dear Stata List,
> I am trying to analyze how receiving remittances can affect the household expenditure behaviour in Senegal.
> I have four types of household (HH_type)
> HH_type:
> 1.       HH who do not receive remittances
> 2.       HH who receive remittances from national migrants
> 3.       HH who receive remittances from international migrants
> 4.       HH who receive remittances both from national and international migrants
> I would like to investigate if differences exist in some specific expenditure (food, durable goods, education, health...)
> The Model that I am trying to apply is a Multinomial logit model with selection as presented by Dubin and McFadden (1984) and revisited by Bourguignon, Fournier and Gurdand (2007).
> The original DMF’s model [DMF(0)] is based on two assumptions: linearity assumption between the error term in the outcome equation and the error term in the choice equation; correlation coefficients between the two error terms sum up to zero.
> The DMF’ model [DMF(1)] proposed by Bourguignon et al (2007) relaxes the second assumption
> I am using the Selmlog command in Stata10.
> When I consider DMF(0) I end up with 3 Mills’ ratio (M-1).
> When I apply DMF(1) I end up with 4 Mills’ ratio
> 1)   How can I test if the restriction on the correlation parameters is correct?
> 2)   Passing from 3 to 4 Mills’ ratios how does the interpretation of that relevant coefficients change?
> Model DMF(1):
> Gen health1= health
> Replace health1=. if HH_type !=1
> selmlog health1 varlist, select (HH_type= varlist_m) dmf(1)bootstrap(100) gen(rh1_1)
> Gen health2= health
> Replace health2=. if HH_type !=2
> selmlog health2 varlist, select (HH_type= varlist_m) dmf(1)bootstrap(100) gen(rh1_1)
> Considering expenditure on health, I have found that for HH_type=1 rh1_1, rh1_2 and rh1_4 are insignificant while rh1_3 is significant. For HH_type=2 only rh2_2 is significant.
> 3)  How should I interpret those results?
>  I tried to compare the results obtained from the command selmlog with the following prestige:
> a)   run a mlogit where the dependent variable is HH_type
> b)  calculate the mills ratios
> predict p1, outcome(1)
> predict p2, outcome(2)
> predict p3, outcome(3)
> predict p4, outcome(4)
> gen trnsp1=(p1*ln(p1))/(1-p1)
> gen trnsp2=(p2*ln(p2))/(1-p2)
> gen trnsp3=(p3*ln(p3))/(1-p3)
> gen trnsp4=(p4*ln(p3))/(1-p4)
> gen mills1= 4* ln(p1)+ trnsp2 + trnsp3 + trnsp4
> gen mills2= 4* ln(p2)+ trnsp1 + trnsp3 + trnsp4
> gen mills3= 4* ln(p3)+ trnsp1 + trnsp2 + trnsp4
> gen mills4= 4* ln(p4)+ trnsp1 + trnsp2 + trnsp3
> c)  Add the Mills’ ratios to the second step equation (we are considering expenditure on health)
> reg health1 varlist mills1 mills2 mills3 mills4
> reg health2 varlist mills1 mills2 mills3 mills4
> reg health3 varlist mills1 mills2 mills3 mills4
> reg health4 varlist mills1 mills2 mills3 mills4
> 4)  Does this prestige correspond to the one performed using the selmlog command? If it is, why don’t I get the same outcomes?
> Your help to understand the model better would be very appreciate,
> Sincerely,
> Teresa Randazzo
> PhD candidate, University of Kent
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Stas Kolenikov, also found at
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