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Fitting a fractional multinomial logit model by quasi maximum likelihood

fmlogit
depvars
[weight]
[if] [in]
[,
etavar(varlist)
rpr
cluster(clustervar)
constraints(numlist|matname)}
level(#)
nolog
noconstant
maximize_options
]

by ... : may be used with fmlogit; see help
by.

fweights, and pweights are allowed; see help weights.

etavar may contain factor variables; see fvvarlist.

Description

fmlogit fits by quasi maximum likelihood a fractional multinomial logit
model. Each variable in depvarlist ranges between 0 and 1 and all variables in
depvarlist must, for each observation, add up to 1: for example, they may be
proportions. It is a multivariate generalization of the fractional logit model
proposed by Papke and Wooldridge (1996).

Note that cases will be ignored if the one or more of the dependent variables
has a value less zero or more than one or if the dependent variables don't add
up to one.

Also note that fmlogit always implies the vce(robust) option because
the model is fitted using quasi maximum likelihood.

Options

etavar() specifies the explanatory variables. (The name of this
option originates from the symbol commonly used for the linear predictor, the
Greek letter eta.)

rpr reports the estimated coefficients transformed to relative
proportion ratios, i.e., exp(b) rather than b. Standard errors and confidence
intervals are similarly transformed. This option affects how results are
displayed, not how they are estimated.

Relative proportion ratios can be useful when the model contains
interaction terms, as in that case marginal effects as computed by dfmlogit
will no longer be appropriate. Relative proportion ratios for the
interaction terms can still be interpreted as the factor by which the
relative proportion ratio changes, as is discussed in Buis (2010).

cluster(clustervar) specifies that the observations
are independent across groups (clusters) but not necessarily within groups.
clustervar specifies to which group each observation belongs; e.g.,
cluster(personid) in data with repeated observations on individuals. See
[U] 23.14 Obtaining robust variance estimates.

constraints(numlist|matname)} specifies
linear constraint(s) that are to be applied to the model; see help
constraint.

level(#) specifies the confidence level, in percent,
for the confidence intervals of the coefficients; see help level.

nolog suppresses the iteration log.

noconstant suppresses the constant in the eta equations.

maximize_options control the maximization process; see
help maximize. If you are seeing many "(not concave)" messages in the
log, using the difficult option may help convergence.

Example

use http://fmwww.bc.edu/repec/bocode/c/citybudget.dta, clear

gen pol = minorityleft + 2*noleft
label define pol 0 "left parties are majority" ///
1 "left parties are minority" ///
2 "no left party"
label value pol pol
label var pol "political orientation of city government"

fmlogit governing safety education recreation social urbanplanning, ///
eta(i.pol houseval popdens)

margins, dydx(*) predict(outcome(governing))
margins, dydx(*) predict(outcome(safety))
margins, dydx(*) predict(outcome(education))
margins, dydx(*) predict(outcome(recreation))
margins, dydx(*) predict(outcome(social))
margins, dydx(*) predict(outcome(urbanplanning))

(click to run)

Author

Maarten L. Buis, University of Konstanz
maarten.buis@uni.kn

References

Buis, M.L. 2010. Stata tip 87: Interpretation of interactions in non-linear
models. The Stata Journal 10(2): 305-308.

Papke, Leslie E. and Jeffrey M. Wooldridge. 1996.
Econometric Methods for Fractional Response Variables with an Application to
401(k) Plan Participation Rates. Journal of Applied Econometrics 11(6):619-632.

Also see

Online: help for fmlogit postestimation,

If installed: dirifit