How to use dirifit command to estimate Dirichlet Distribution followed by xtreg command

[Ijaz Ahmad]

Hello, everyone; I have state-level panel data comprising 50 US states from 2005 to 2022. This dataset has three dependent variables: proportions of state financial support for student financial aid (stfinaid), general appropriations to colleges (st_approp), and amount given to colleges through grants and contracts (st_gnc). In each observation, the sum of the three dependent variables is equal to 1 (i.e., the state's total support for higher education).

I have five independent variables, including economic freedom (econfree), performance-based funding (pbf), total private college enrollment (totenpvt), legislative professionalism(lp), and 18 to 24 years population (pop18to24). Here, I have shown data for only 20 states over three years, from 2005 to 2007.

input float state_code str16 state float(year stfinaid st_approp st_gnc) byte(econfree pbf) float(totenpvt lp pop18to24)
 1 "Alabama"     2005 .0027806354 .9358705  .06134879 15 0  .1133934  1391.457 .09278798
 1 "Alabama"     2006  .003616355 .9166794   .0797042 15 0 .11134716  1347.974 .10012633
 1 "Alabama"     2007  .004488028 .9158435  .07966851 19 0 .11545899  1310.644  .0988165
 2 "Alaska"      2005  .003598831 .9458614  .05053981 50 0 .05233803 31820.635 .10380942
 2 "Alaska"      2006  .005195576 .9386975  .05610693 50 0 .04863795  30826.24 .11153745
 2 "Alaska"      2007  .005223306 .9440607  .05071598 49 0 .04885167 29972.557 .11783993
 3 "Arizona"     2005 .0017848266 .9509934  .04722178  9 0 .42074955  31804.73 .09478752
 3 "Arizona"     2006  .001637462 .9458956  .05246696 10 0  .4220104  30810.83 .09504667
 3 "Arizona"     2007  .013068232 .9319074  .05502433 23 0  .4767367  29957.58  .0934529
 4 "Arkansas"    2005   .03502926 .8499562   .1150146 20 0 .12129366 18641.549 .09323022
 4 "Arkansas"    2006   .05072419 .8271005   .1221753 27 0 .12407328  18507.04  .0962374
 4 "Arkansas"    2007   .05081435 .8363829  .11280274 28 0  .1249116  18430.15 .09577229
 5 "California"  2005    .0967054 .8101667   .0931279 47 0 .18180065 146937.86 .09423756
 5 "California"  2006   .09781416 .8062217  .09596422 48 0  .1778098 143769.77 .10404783
 5 "California"  2007   .09043077  .814012   .0955573 47 0 .17103037  141172.6   .104993
 7 "Connecticut" 2005    .0445298 .8618568   .0936135 22 0   .390592 37105.523 .07755974
 7 "Connecticut" 2006   .09396895 .7652938  .14073719 20 0  .3971299 35945.973 .09114106
 7 "Connecticut" 2007    .0981563 .8147151   .0871286 16 0 .39596415 34950.508 .09242217
 8 "Delaware"    2005     .279817  .720183          0 20 0 .26220223  52722.97 .08801141
 8 "Delaware"    2006    .2442309 .7557691          0 24 0 .26384702  52497.16 .09775084
 8 "Delaware"    2007    .2699953 .7300047          0 25 0 .26482868  52425.76 .09852052
 9 "Florida"     2005   .12571846 .7605692  .11371229  8 0 .26735812   39644.6 .08542374
 9 "Florida"     2006   .12880301 .7484795  .12271743  9 0 .27512524  39098.95  .0890446
 9 "Florida"     2007   .12326452 .7558233  .12091216  5 0 .26255676  38690.21 .08878798
10 "Georgia"     2005   .18537527 .7707725  .04385226  9 0  .2177975  21897.56  .0948061
10 "Georgia"     2006    .1699736 .7814682  .04855823 10 0 .22506984 21738.326 .10075523
10 "Georgia"     2007   .15584846 .8030966  .04105493 11 0  .2222179  21646.85  .0988006
11 "Hawaii"      2005  .003246772 .7296168  .26713642 41 0  .2584165  45321.74 .08938278
11 "Hawaii"      2006 .0029226656 .7151033  .28197408 42 0 .25823155  44996.66 .09742995
11 "Hawaii"      2007    .0557091 .6658583  .27843264 40 0  .2480887  44811.54 .09654056
12 "Idaho"       2005  .002497227 .8981326  .09937017 25 0  .2352762 20734.035 .10437335
12 "Idaho"       2006  .018277815 .8768147   .1049075 23 0  .2489217 20387.785 .10429639
12 "Idaho"       2007  .003464603 .9025261  .09400925 21 0 .24122456 20116.514   .097008
13 "Illinois"    2005   .17399083 .7223806  .10362858 30 0  .3488443  76356.54 .09074374
13 "Illinois"    2006    .1770583 .7130849  .10985686 29 0  .3495486  73970.39 .10048753
13 "Illinois"    2007   .19683643 .6862172  .11694638 26 0  .3534841  71921.91 .10110097
14 "Indiana"     2005    .1698264 .7522808   .0778928 24 0 .27712247 15372.287  .0892171
14 "Indiana"     2006   .17823847 .7556606 .066100955 22 0 .26734152 14891.902  .0987039
14 "Indiana"     2007    .1974633 .7440481  .05848865 21 1  .2713091 14479.496  .0969948
15 "Iowa"        2005   .06994651 .8920375  .03801601 26 0  .3512102  28333.43 .09348233
15 "Iowa"        2006   .06840197 .8917735  .03982456 26 0  .3721157  29771.31 .10581154
15 "Iowa"        2007   .06721614 .8842185   .0485653 29 0  .4014491  31205.81 .10103154
16 "Kansas"      2005           0   .91526  .08474001 19 0 .12486912  9144.682 .09965537
16 "Kansas"      2006   .02644302 .9120745  .06148242 18 1  .1314589  9926.249 .10789251
16 "Kansas"      2007   .02323154 .9194295  .05733893 15 1 .13658047   9526.51 .10409413
17 "Kentucky"    2005   .12144458 .7006003   .1779551 32 0 .19527414 36645.793  .0903548
17 "Kentucky"    2006   .12359276 .7051803  .17122693 35 0  .1974737  43220.35 .09342703
17 "Kentucky"    2007   .12877673 .6927116   .1785117 34 0  .2010008 35242.355 .09336825
18 "Louisiana"   2005    .0897527 .7123476  .19789965 31 0 .10370991  22263.31 .10416546
18 "Louisiana"   2006   .08985943 .7173808   .1927598 31 0 .16277775 21567.584 .10827381
18 "Louisiana"   2007   .08359338 .7452673  .17113927 27 0  .1593327 20970.305 .10990626
19 "Maine"       2005   .04767591 .7851633   .1671608 45 0 .28623357 15086.044  .0840697
19 "Maine"       2006   .04401449 .7899513   .1660342 46 0 .28843805  11230.55 .08805712
19 "Maine"       2007  .001734564 .8271238  .17114164 46 0  .2904433 15868.778 .08754053
20 "Maryland"    2005   .06930555 .7868726  .14382194  6 0 .19694246  53670.49 .08789802
20 "Maryland"    2006   .06586162 .7839794  .15015897 14 0  .1981001  53918.96 .09546102
20 "Maryland"    2007    .0683832 .7931583  .13845849 10 0 .18998453  54298.11 .09723168
end

I want to transform my dependent variables to Dirichlet Distribution using STATA’s ‘dirifit’ command. I have already read STATA’s help and Maarten Buis’s two presentations (2006 and 2010) on analyzing proportions, but I am still unsure how to use the ‘dirifit’ command. After using ‘dirifit’ command, I will apply fixed effects using the ‘xtreg’ command.

Could someone kindly guide me on how to use ‘dirifit’ command followed by ‘xtreg’ command? I have been using 'xtreg' but I don't how to use after 'dirifit.'

Thank you,
Ijaz

[Nick Cox]

Sorry, but I don't follow even in very broad terms what you want to do.

dirifit from SSC is about modelling a set of outcomes in terms of predictors. (I am listed as an author but that is a courteous gesture from Maarten Buis who started from a different command with a related but different purpose.)

I wouldn't describe it as being about transformation of dependent variables to a Dirichlet distribution. There isn't any transformation.

More importantly, xtreg has quite different flavour, as it focuses on single outcomes.

These commands could be complementary for your purposes but I can't understand any sense in which one should be run before another, let alone being a prerequisite.

[Ijaz Ahmad]

Thank you, Nick. I am sorry for my ambiguous question. I want to model my outcome variables in terms of predictors. Then, I will use 'xtreg' on each predictor. I intend to do so because, in another state-level study, the researcher used the 'dirifit' command before independently performing fixed-effects analysis using STATA's 'areg' command on his three outcome variables measured as proportions. My apologies if I am still vague.
Thank you,
Ijaz

[Nick Cox]

I don't think your question is ambiguous. It's just unclear to me how two separate commands are to be linked in any sense.

Even here, I wonder whether you mean apply xtreg to each outcome (not each predictor). Unfortunately, much of the point is that a set of proportions is a multivariate outcome.

I imagine that Maarten Buis will join the discussion at some point. He's not only the lead author of dirifit but also immensely more experienced than I am with these analyses.

[Maarten Buis]

This looks like panel data, and dirifit (or fmlogit) are not made for that case. Unfortunately, I cannot help you further.

[Ijaz Ahmad]

Thank you, Nick and Maarten. In the following article, the author uses a 'dirifit' on panel data and cites your reference. Subsidizing Institutions vs. Outputs vs. Individuals: States’ Choices for Financing Public Postsecondary Education | Journal of Public Administration Research and Theory | Oxford Academic (oup.com).