Note: This chapter uses a suite of commands, called spost, written by J. Scott Long and Jeremy Freese. The commands must be downloaded prior to their use, and this can be done by typing search spost in the Stata command line (see How can I use the search command to search for programs and get additional help? for more information about using search).
Figure 8.2, page 220.
use https://stats.idre.ucla.edu/stat/stata/examples/long/couart2.dta, clear
poisson art
Iteration 0: log likelihood = -1742.5735
Iteration 1: log likelihood = -1742.5735
Poisson regression Number of obs = 915
LR chi2(0) = 0.00
Prob > chi2 = .
Log likelihood = -1742.5735 Pseudo R2 = 0.0000
------------------------------------------------------------------------------
art | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_cons | .5264408 .0254082 20.72 0.000 .4766416 .57624
------------------------------------------------------------------------------
prcounts psn, plot max(9) /*prcounts is from spostado */
label var psnobeq "Observed Proportion"
label var psnpreq "Poisson Prediction"
label var psnval "# of articles"
graph twoway (scatter psnobeq psnpreq psnval, connect (l l) xlabel(0(1)9) ytitle("Probability"))
Table 8.1, page 227.
gen lnart = ln(art + .5)
label var lnart "Log of (Art + .5)"
describe
Contains data from https://stats.idre.ucla.edu/stat/stata/examples/long/couart2.dta
obs: 915 Academic Biochemists / S Long
vars: 34 30 Jan 2001 10:49
size: 114,375 (89.0% of memory free) (_dta has notes)
-------------------------------------------------------------------------------
storage display value
variable name type format label variable label
-------------------------------------------------------------------------------
art byte %9.0g Articles in last 3 yrs of PhD
fem byte %9.0g sexlbl Gender: 1=female 0=male
mar byte %9.0g marlbl Married: 1=yes 0=no
kid5 byte %9.0g Number of children < 6
phd float %9.0g PhD prestige
ment byte %9.0g Article by mentor in last 3 yrs
psnrate float %9.0g Predicted rate from poisson
psnpr0 float %9.0g Pr(y=0) from poisson
psnpr1 float %9.0g Pr(y=1) from poisson
psnpr2 float %9.0g Pr(y=2) from poisson
psnpr3 float %9.0g Pr(y=3) from poisson
psnpr4 float %9.0g Pr(y=4) from poisson
psnpr5 float %9.0g Pr(y=5) from poisson
psnpr6 float %9.0g Pr(y=6) from poisson
psnpr7 float %9.0g Pr(y=7) from poisson
psnpr8 float %9.0g Pr(y=8) from poisson
psnpr9 float %9.0g Pr(y=9) from poisson
psncu0 float %9.0g Pr(y=0) from poisson
psncu1 float %9.0g Pr(y<=1) from poisson
psncu2 float %9.0g Pr(y<=2) from poisson
psncu3 float %9.0g Pr(y<=3) from poisson
psncu4 float %9.0g Pr(y<=4) from poisson
psncu5 float %9.0g Pr(y<=5) from poisson
psncu6 float %9.0g Pr(y<=6) from poisson
psncu7 float %9.0g Pr(y<=7) from poisson
psncu8 float %9.0g Pr(y<=8) from poisson
psncu9 float %9.0g Pr(y<=9) from poisson
psnprgt float %9.0g Pr(y>9) from poisson
psnval float %9.0g # of articles
psnobeq float %9.0g Poisson Prediction
psnpreq float %9.0g Predicted Pr(y=k) from poisson
psnoble float %9.0g Observed Pr(y<=k) from poisson
psnprle float %9.0g Predicted Pr(y<=k) from poisson
lnart float %9.0g Log of (Art + .5)
-------------------------------------------------------------------------------
Sorted by: art
Note: dataset has changed since last saved
sum
Variable | Obs Mean Std. Dev. Min Max
-------------+--------------------------------------------------------
art | 915 1.692896 1.926069 0 19
fem | 915 .4601093 .4986788 0 1
mar | 915 .6622951 .473186 0 1
kid5 | 915 .495082 .76488 0 3
phd | 915 3.103109 .9842491 .755 4.62
-------------+--------------------------------------------------------
ment | 915 8.767213 9.483916 0 77
psnrate | 915 1.692896 0 1.692896 1.692896
psnpr0 | 915 .1839859 0 .1839859 .1839859
psnpr1 | 915 .311469 0 .311469 .311469
psnpr2 | 915 .2636423 0 .2636423 .2636423
-------------+--------------------------------------------------------
psnpr3 | 915 .148773 0 .148773 .148773
psnpr4 | 915 .0629643 0 .0629643 .0629643
psnpr5 | 915 .0213184 0 .0213184 .0213184
psnpr6 | 915 .006015 0 .006015 .006015
psnpr7 | 915 .0014547 0 .0014547 .0014547
-------------+--------------------------------------------------------
psnpr8 | 915 .0003078 0 .0003078 .0003078
psnpr9 | 915 .0000579 0 .0000579 .0000579
psncu0 | 915 .1839859 0 .1839859 .1839859
psncu1 | 915 .4954549 0 .4954549 .4954549
psncu2 | 915 .7590972 0 .7590972 .7590972
-------------+--------------------------------------------------------
psncu3 | 915 .9078703 0 .9078703 .9078703
psncu4 | 915 .9708346 0 .9708346 .9708346
psncu5 | 915 .992153 0 .992153 .992153
psncu6 | 915 .9981681 0 .9981681 .9981681
psncu7 | 915 .9996227 0 .9996227 .9996227
-------------+--------------------------------------------------------
psncu8 | 915 .9999305 0 .9999305 .9999305
psncu9 | 915 .9999884 0 .9999884 .9999884
psnprgt | 915 .0000116 0 .0000116 .0000116
psnval | 10 4.5 3.02765 0 9
psnobeq | 10 .0993443 .1139905 .0010929 .3005464
-------------+--------------------------------------------------------
psnpreq | 10 .0999988 .1187734 .0000579 .311469
psnoble | 10 .8328962 .2308122 .3005464 .9934426
psnprle | 10 .8307106 .2791442 .1839859 .9999884
lnart | 915 .4399161 .8566493 -.6931472 2.970414
Table 8.2 , page 228.
quietly reg lnart fem mar kid5 phd ment
listcoef
regress (N=915): Unstandardized and Standardized Estimates
Observed SD: .8566493
SD of Error: .81457396
-------------------------------------------------------------------------------
lnart | b t P>|t| bStdX bStdY bStdXY SDofX
-------------+-----------------------------------------------------------------
fem | -0.13457 -2.349 0.019 -0.0671 -0.1571 -0.0783 0.4987
mar | 0.13283 2.043 0.041 0.0629 0.1551 0.0734 0.4732
kid5 | -0.13315 -3.275 0.001 -0.1018 -0.1554 -0.1189 0.7649
phd | 0.02550 0.896 0.371 0.0251 0.0298 0.0293 0.9842
ment | 0.02542 8.607 0.000 0.2411 0.0297 0.2814 9.4839
-------------------------------------------------------------------------------
quietly poisson art fem mar kid5 phd ment
listcoef
poisson (N=915): Factor Change in Expected Count
Observed SD: 1.926069
----------------------------------------------------------------------
art | b z P>|z| e^b e^bStdX SDofX
-------------+--------------------------------------------------------
fem | -0.22459 -4.112 0.000 0.7988 0.8940 0.4987
mar | 0.15524 2.529 0.011 1.1679 1.0762 0.4732
kid5 | -0.18488 -4.607 0.000 0.8312 0.8681 0.7649
phd | 0.01282 0.486 0.627 1.0129 1.0127 0.9842
ment | 0.02554 12.733 0.000 1.0259 1.2741 9.4839
----------------------------------------------------------------------
quietly nbreg art fem mar kid5 phd ment
listcoef
nbreg (N=915): Factor Change in Expected Count
Observed SD: 1.926069
----------------------------------------------------------------------
art | b z P>|z| e^b e^bStdX SDofX
-------------+--------------------------------------------------------
fem | -0.21642 -2.978 0.003 0.8054 0.8977 0.4987
mar | 0.15049 1.833 0.067 1.1624 1.0738 0.4732
kid5 | -0.17642 -3.325 0.001 0.8383 0.8738 0.7649
phd | 0.01527 0.424 0.672 1.0154 1.0151 0.9842
ment | 0.02908 8.381 0.000 1.0295 1.3176 9.4839
-------------+--------------------------------------------------------
ln alpha | -0.81730
alpha | 0.44162 SE(alpha) = 0.05297
----------------------------------------------------------------------
LR test of alpha=0: 180.20 Prob>=LRX2 = 0.000
----------------------------------------------------------------------
Figure 8.4, page 229.
quietly poisson art fem mar kid5 phd ment
prcounts psm, plot max(9)
label var psmpreq "PRM"
label var psmobeq "Observed"
label var psmval "# of articles"
quietly nbreg art fem mar kid5 phd ment
prcounts nbm, plot max(9)
label var nbmpreq "NBM"
graph twoway (scatter psmobeq psmpreq nbmpreq psmval, connect(l l l) xlabel(0(1)9) ytitle("Probability"))
Figure 8.8, page 238.
quietly poisson art fem mar kid5 phd ment
prgen ment, from(0) to(50) rest(mean) gen(pm) n(11)
poisson: Predicted values as ment varies from 0 to 50.
fem mar kid5 phd ment
x= .46010929 .66229508 .49508197 3.1031093 8.7672131
label var pmp0 "PRM"
quietly nbreg art fem mar kid5 phd ment
prgen ment, from(0) to(50) rest(mean) gen(nb) n(11)
nbreg: Predicted values as ment varies from 0 to 50.
fem mar kid5 phd ment
x= .46010929 .66229508 .49508197 3.1031093 8.7672131
label var nbp0 "NBM"
graph twoway (scatter pmp0 nbp0 nbx, c(l l l) xtitle("Mentor's Articles") ///
ytitle("Pr(Zero Articles)") msymbol(Sh Oh))
Table 8.3, page 246.
zip art fem mar kid5 phd ment, inflate(fem mar kid5 phd ment) nolog
Zero-inflated poisson regression Number of obs = 915
Nonzero obs = 640
Zero obs = 275
Inflation model = logit LR chi2(5) = 78.56
Log likelihood = -1604.773 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
art | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
art |
fem | -.2091446 .0634047 -3.30 0.001 -.3334155 -.0848737
mar | .103751 .071111 1.46 0.145 -.035624 .243126
kid5 | -.1433196 .0474293 -3.02 0.003 -.2362793 -.0503599
phd | -.0061662 .0310086 -0.20 0.842 -.066942 .0546096
ment | .0180977 .0022948 7.89 0.000 .0135999 .0225955
_cons | .640839 .1213072 5.28 0.000 .4030814 .8785967
-------------+----------------------------------------------------------------
inflate |
fem | .1097465 .2800813 0.39 0.695 -.4392028 .6586958
mar | -.3540107 .3176103 -1.11 0.265 -.9765155 .2684941
kid5 | .2171001 .196481 1.10 0.269 -.1679956 .6021958
phd | .0012702 .1452639 0.01 0.993 -.2834418 .2859821
ment | -.134111 .0452461 -2.96 0.003 -.2227918 -.0454302
_cons | -.5770618 .5093853 -1.13 0.257 -1.575439 .421315
------------------------------------------------------------------------------
zinb art fem mar kid5 phd ment, inflate(fem mar kid5 phd ment) nolog
Zero-inflated negative binomial regression Number of obs = 915
Nonzero obs = 640
Zero obs = 275
Inflation model = logit LR chi2(5) = 67.97
Log likelihood = -1549.991 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
art | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
art |
fem | -.1955068 .0755926 -2.59 0.010 -.3436655 -.0473481
mar | .0975826 .084452 1.16 0.248 -.0679402 .2631054
kid5 | -.1517325 .054206 -2.80 0.005 -.2579744 -.0454906
phd | -.0007001 .0362696 -0.02 0.985 -.0717872 .0703869
ment | .0247862 .0034924 7.10 0.000 .0179412 .0316312
_cons | .4167466 .1435962 2.90 0.004 .1353032 .69819
-------------+----------------------------------------------------------------
inflate |
fem | .6359328 .8489175 0.75 0.454 -1.027915 2.299781
mar | -1.499469 .9386701 -1.60 0.110 -3.339228 .3402909
kid5 | .6284274 .4427825 1.42 0.156 -.2394105 1.496265
phd | -.0377153 .3080086 -0.12 0.903 -.641401 .5659705
ment | -.8822932 .3162276 -2.79 0.005 -1.502088 -.2624984
_cons | -.1916865 1.322821 -0.14 0.885 -2.784368 2.400995
-------------+----------------------------------------------------------------
/lnalpha | -.9763565 .1354679 -7.21 0.000 -1.241869 -.7108443
-------------+----------------------------------------------------------------
alpha | .3766811 .0510282 .288844 .4912293
------------------------------------------------------------------------------