fmlogit: module fitting a fractional multinomial logit model by quasi-maximum likelihood
Author: Maarten L. Buis
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
Supporting material
- Presentation held at the 2010 German Stata Users' meeting on analyzing proportions with betafit, zoib, the fractional logit, dirifit, and fmlogit.
- summary on ssc.
- helpfiles:
- Announcement of fmlogit on statalist.
- Short text explaining the relationship between the likelihood function used in mlogit and the quasi-liklihood function used in 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