zoib
Author: Maarten L. Buis
zoib fits by maximum likelihood a zero-one inflated beta distribution to a distribution of a variable depvar. depvar ranges between 0 and 1: for example, it may be a proportion. zoib will estimate the probabilities of having the value 0 and/or 1 as separate processes. The logic is that we can often think of proportions of 0 or 1 as being qualitatively different and generated through a different process as the other proportions.
This package can be installed by typing in Stata: ssc install zoib
Supporting materials
- Presentation held at the 2010 German Stata Users' meeting on analyzing proportions with betafit, zoib, the fractional logit, dirifit, and fmlogit.
- summary on ssc
- certification script
Example
. use "http://fmwww.bc.edu/repec/bocode/k/k401.dta", clear (source: Papke and Wooldridge 1996)
. replace totemp = totemp / 10000 (4734 real changes made)
. . zoib prate mrate totemp age sole, oneinflate( mrate totemp age sole) robust
Iteration 0: log pseudolikelihood = -1759.3734 Iteration 1: log pseudolikelihood = -1299.8822 Iteration 2: log pseudolikelihood = -1293.69 Iteration 3: log pseudolikelihood = -1293.6594 Iteration 4: log pseudolikelihood = -1293.6594
ML fit of oib Number of obs = 4734 Wald chi2(4) = 136.47 Log pseudolikelihood = -1293.6594 Prob > chi2 = 0.0000
------------------------------------------------------------------------------ | Robust prate | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- proportion | mrate | .1524644 .0466905 3.27 0.001 .0609527 .243976 totemp | -.0265332 .0092522 -2.87 0.004 -.0446673 -.0083992 age | .0216248 .0020206 10.70 0.000 .0176645 .0255852 sole | .0604715 .0376378 1.61 0.108 -.0132972 .1342402 _cons | .8738362 .0354738 24.63 0.000 .8043088 .9433636 -------------+---------------------------------------------------------------- oneinflate | mrate | .7935556 .0653962 12.13 0.000 .6653814 .9217297 totemp | -.1416409 .0354509 -4.00 0.000 -.2111235 -.0721584 age | .020835 .003494 5.96 0.000 .0139869 .0276832 sole | .9044132 .0654829 13.81 0.000 .7760692 1.032757 _cons | -1.472011 .0702084 -20.97 0.000 -1.609617 -1.334405 -------------+---------------------------------------------------------------- ln_phi | _cons | 1.77591 .0358677 49.51 0.000 1.705611 1.84621 ------------------------------------------------------------------------------
. . // effect on total proportion . mfx, predict(pr) at(mean sole = 0)
Marginal effects after zoib y = Proportion (predict, pr) = .85369833 ------------------------------------------------------------------------------ variable | dy/dx Std. Err. z P>|z| [ 95% C.I. ] X ---------+-------------------------------------------------------------------- mrate | .0566366 .00679 8.34 0.000 .043326 .069947 .746335 totemp | -.0100315 .00208 -4.83 0.000 -.014104 -.005959 .462107 age | .0034952 .00031 11.37 0.000 .002893 .004098 13.1398 sole*| .053115 .0047 11.31 0.000 .043908 .062322 0 ------------------------------------------------------------------------------ (*) dy/dx is for discrete change of dummy variable from 0 to 1
. . // effect on probability of having a proportion 1 . mfx, predict(pr1) at(mean sole = 0)
Marginal effects after zoib y = probability of having value 1 (predict, pr1) = .33817515 ------------------------------------------------------------------------------ variable | dy/dx Std. Err. z P>|z| [ 95% C.I. ] X ---------+-------------------------------------------------------------------- mrate | .1776078 .01555 11.42 0.000 .147125 .208091 .746335 totemp | -.031701 .00796 -3.98 0.000 -.047304 -.016098 .462107 age | .0046631 .00078 6.01 0.000 .003143 .006184 13.1398 sole*| .2198069 .01548 14.20 0.000 .189476 .250138 0 ------------------------------------------------------------------------------ (*) dy/dx is for discrete change of dummy variable from 0 to 1
. . // effect on proportion given proportion < 1 . mfx, predict(prcond) at(mean sole = 0)
Marginal effects after zoib y = proportion conditional on not having value 0 or 1 (predict, prcond) = .778942 ------------------------------------------------------------------------------ variable | dy/dx Std. Err. z P>|z| [ 95% C.I. ] X ---------+-------------------------------------------------------------------- mrate | .0262531 .00781 3.36 0.001 .010948 .041558 .746335 totemp | -.0045688 .0016 -2.86 0.004 -.007698 -.001439 .462107 age | .0037236 .00035 10.57 0.000 .003033 .004414 13.1398 sole*| .0102369 .00632 1.62 0.105 -.002149 .022623 0 ------------------------------------------------------------------------------ (*) dy/dx is for discrete change of dummy variable from 0 to 1