fmlogit: module fitting a fractional multinomial logit model by quasi-maximum likelihood

Description

fmlogit fits by quasi maximum likelihood a fractional multinomial logit model. It models a set of dependent variables that each must range between 0 and 1 and must always, 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)

This package can be installed by typing in Stata: ssc install fmlogit

Reference

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.

Example

```
. use http://fmwww.bc.edu/repec/bocode/c/citybudget.dta, clear
(Spending on different categories by Dutch cities in 2005)

. fmlogit governing safety education recreation social urbanplanning, ///
>     eta(minorityleft noleft houseval popdens)

Iteration 0:   log pseudolikelihood = -677.06246
Iteration 1:   log pseudolikelihood = -673.14922
Iteration 2:   log pseudolikelihood = -673.12025
Iteration 3:   log pseudolikelihood = -673.12025

ML fit of fractional multinomial logit            Number of obs   =        392
Wald chi2(20)   =     275.23
Log pseudolikelihood = -673.12025                 Prob > chi2     =     0.0000

------------------------------------------------------------------------------
|               Robust
|      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
eta_safety   |
minorityleft |   .1893638   .0596067     3.18   0.001     .0725368    .3061908
noleft |    .082542   .0616854     1.34   0.181    -.0383592    .2034432
houseval |  -.1400078   .0558587    -2.51   0.012    -.2494889   -.0305266
popdens |   .0115814   .0212536     0.54   0.586    -.0300748    .0532377
_cons |     .74898    .092535     8.09   0.000     .5676147    .9303453
-------------+----------------------------------------------------------------
eta_educat~n |
minorityleft |   .0387367   .1181969     0.33   0.743    -.1929249    .2703983
noleft |  -.3648018   .1185739    -3.08   0.002    -.5972024   -.1324013
houseval |  -.6371485   .1248264    -5.10   0.000    -.8818037   -.3924933
popdens |   .0927616   .0374607     2.48   0.013     .0193399    .1661832
_cons |   1.215266   .1979107     6.14   0.000     .8273682    1.603164
-------------+----------------------------------------------------------------
eta_recrea~n |
minorityleft |   .2226632    .071707     3.11   0.002     .0821201    .3632062
noleft |   .0138519   .0757628     0.18   0.855    -.1346405    .1623443
houseval |  -.2308754   .0705698    -3.27   0.001    -.3691897   -.0925611
popdens |   .0720411   .0256728     2.81   0.005     .0217234    .1223588
_cons |   .4208606   .1160496     3.63   0.000     .1934076    .6483136
-------------+----------------------------------------------------------------
eta_social   |
minorityleft |    .136064   .0895568     1.52   0.129    -.0394641     .311592
noleft |  -.1467066   .0928848    -1.58   0.114    -.3287575    .0353442
houseval |  -.6208166   .0934095    -6.65   0.000    -.8038958   -.4377373
popdens |    .198176   .0273592     7.24   0.000     .1445529     .251799
_cons |   1.706708   .1595395    10.70   0.000     1.394016      2.0194
-------------+----------------------------------------------------------------
eta_urbanp~g |
minorityleft |   .2344396   .1064104     2.20   0.028     .0258791    .4430001
noleft |   .0302175   .1141221     0.26   0.791    -.1934578    .2538928
houseval |  -.1785858   .0862281    -2.07   0.038    -.3475897   -.0095819
popdens |   .1604767   .0417837     3.84   0.000     .0785822    .2423713
_cons |   .9818296   .1534122     6.40   0.000     .6811473    1.282512
------------------------------------------------------------------------------

. dfmlogit, at(minorityleft 0 noleft 0 )
-------------------------------------------------------------------------------
discrete      |  Min --> Max                +-SD/2                  +-1/2
change        |  coef.     se            coef.     se            coef.     se
--------------+----------------------------------------------------------------
governing     |
minorityleft | -.014    .0066
noleft | .0056    .0072
houseval | .1038    .0254         .0129     .0027        .0329     .0069
popdens |-.0529    .0085        -.0101     .0021       -.0108     .0022
--------------+----------------------------------------------------------------
safety        |
minorityleft | .0062    .0064
noleft | .0251    .0068
houseval | .0849    .0181          .013     .0025        .0331     .0064
popdens |-.0847    .0106        -.0157     .0024       -.0167     .0025
--------------+----------------------------------------------------------------
education     |
minorityleft | -.015    .0107
noleft |-.0369    .0104
houseval |-.1074    .0322        -.0163     .0058       -.0416     .0148
popdens |-.0205    .0189        -.0022     .0034       -.0023     .0036
--------------+----------------------------------------------------------------
recreation    |
minorityleft |  .008    .0043
noleft |  .008    .0045
houseval | .0224    .0128         .0046     .0016        .0117     .0042
popdens |-.0279    .0077         -.004     .0014       -.0042     .0015
--------------+----------------------------------------------------------------
social        |
minorityleft |-.0044    .0111
noleft |-.0221    .0111
houseval |-.1873    .0306        -.0281     .0053       -.0716     .0136
popdens | .1303    .0271          .021     .0035        .0223     .0037
--------------+----------------------------------------------------------------
urbanplann~g  |
minorityleft | .0192     .014
noleft | .0203    .0153
houseval | .0836     .042         .0139     .0056        .0356     .0144
popdens | .0558     .038         .0109     .0057        .0116     .0061
-------------------------------------------------------------------------------

--------------------------------
Marginal      |    MFX at x
Effects       |  coef.     se
--------------+-----------------
governing     |
houseval |  .033    .0066
popdens |-.0108    .0024
--------------+-----------------
safety        |
houseval | .0333    .0062
popdens |-.0167    .0026
--------------+-----------------
education     |
houseval |-.0418    .0124
popdens |-.0023    .0036
--------------+-----------------
recreation    |
houseval | .0117    .0041
popdens |-.0042    .0015
--------------+-----------------
social        |
houseval |-.0719    .0121
popdens | .0223    .0036
--------------+-----------------
urbanplann~g  |
houseval | .0358    .0141
popdens | .0116     .006
--------------------------------

E(governing|x) =     .0983
E(safety|x) =        .1704
E(education|x) =     .1385
E(recreation|x) =    .1125
E(social|x) =        .2519
E(urbanplann~g|x) =  .2283

x   mean     sd    min    max
minorityleft      0  .4337  .4962      0      1
noleft      0  .3878  .4879      0      1
houseval  1.483  1.483  .3902    .72   3.63
popdens  .7839  .7839  .9408   .025  5.711

[do-file]```