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).
Table 6.1, page 152.
use https://stats.idre.ucla.edu/stat/stata/examples/long/nomocc2, clear
describe
Contains data from https://stats.idre.ucla.edu/stat/stata/examples/long/nomocc2.dta
obs: 337 1982 General Social Survey
vars: 4 15 Jan 2001 15:24
size: 2,696 (99.7% of memory free) (_dta has notes)
-------------------------------------------------------------------------------
storage display value
variable name type format label variable label
-------------------------------------------------------------------------------
occ byte %10.0g occlbl Occupation
white byte %10.0g Race: 1=white 0=nonwhite
ed byte %10.0g Years of education
exper byte %10.0g Years of work experience
-------------------------------------------------------------------------------
Sorted by: occ
sum
Variable | Obs Mean Std. Dev. Min Max
-------------+--------------------------------------------------------
occ | 337 3.397626 1.367913 1 5
white | 337 .9169139 .2764227 0 1
ed | 337 13.09496 2.946427 3 20
exper | 337 20.50148 13.95936 2 66
Table 6.2, page 159.
* Stata 8 code.
mlogit occ white ed exp, basecategory(1)
* Stata 9 code and output.
mlogit occ white ed exp, baseoutcome(1)
Iteration 0: log likelihood = -509.84406
Iteration 1: log likelihood = -437.11493
Iteration 2: log likelihood = -427.50193
Iteration 3: log likelihood = -426.8061
Iteration 4: log likelihood = -426.80048
Iteration 5: log likelihood = -426.80048
Multinomial logistic regression Number of obs = 337
LR chi2(12) = 166.09
Prob > chi2 = 0.0000
Log likelihood = -426.80048 Pseudo R2 = 0.1629
------------------------------------------------------------------------------
occ | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
BlueCol |
white | 1.236504 .7244352 1.71 0.088 -.1833631 2.656371
ed | -.0994247 .1022812 -0.97 0.331 -.2998922 .1010428
exper | .0047212 .0173984 0.27 0.786 -.0293789 .0388214
_cons | .7412336 1.51954 0.49 0.626 -2.23701 3.719477
-------------+----------------------------------------------------------------
Craft |
white | .4723436 .6043097 0.78 0.434 -.7120817 1.656769
ed | .0938154 .097555 0.96 0.336 -.0973888 .2850197
exper | .0276838 .0166737 1.66 0.097 -.004996 .0603636
_cons | -1.091353 1.450218 -0.75 0.452 -3.933728 1.751022
-------------+----------------------------------------------------------------
WhiteCol |
white | 1.571385 .9027216 1.74 0.082 -.1979166 3.340687
ed | .3531577 .1172786 3.01 0.003 .1232959 .5830194
exper | .0345959 .0188294 1.84 0.066 -.002309 .0715007
_cons | -6.238608 1.899094 -3.29 0.001 -9.960764 -2.516453
-------------+----------------------------------------------------------------
Prof |
white | 1.774306 .7550543 2.35 0.019 .2944273 3.254186
ed | .7788519 .1146293 6.79 0.000 .5541826 1.003521
exper | .0356509 .018037 1.98 0.048 .000299 .0710028
_cons | -11.51833 1.849356 -6.23 0.000 -15.143 -7.893659
------------------------------------------------------------------------------
(Outcome occ==Menial is the comparison group)
Table 6.3, page 162.
* Stata 8 code.
quietly mlogit occ white ed exp, basecategory(5)
* Stata 9 code and output.
quietly mlogit occ white ed exp, baseoutcome(5)
mlogtest, lr
**** Likelihood-ratio tests for independent variables
Ho: All coefficients associated with given variable(s) are 0.
occ | chi2 df P>chi2
-------------+-------------------------
white | 8.095 4 0.088
ed | 156.937 4 0.000
exper | 8.561 4 0.073
---------------------------------------
mlogtest, wald
**** Wald tests for independent variables
Ho: All coefficients associated with given variable(s) are 0.
occ | chi2 df P>chi2
-------------+-------------------------
white | 8.149 4 0.086
ed | 84.968 4 0.000
exper | 7.995 4 0.092
---------------------------------------
Page 163, Section 6.5.2.
Wald test.
* Stata 8 code.
quietly mlogit occ white ed exp, basecategory(5)
* Stata 9 code and output.
quietly mlogit occ white ed exp, baseoutcome(5)
test[4]
( 1) [WhiteCol]white = 0
( 2) [WhiteCol]ed = 0
( 3) [WhiteCol]exper = 0
chi2( 3) = 22.20
Prob > chi2 = 0.0001
NOTE: You can also use mlogtest, combine for combining all possible combinations of the dependent variable.
LR test.
quietly mlogit occ white ed exp
est store a
constraint define 999 [4]
* Stata 8 code.
quietly mlogit occ white ed exp, basecategory(5) constraint(999)
* Stata 9 code and output.
quietly mlogit occ white ed exp, baseoutcome(5) constraint(999)
est store b
lrtest a b, stats
likelihood-ratio test LR chi2(3) = 26.74
(Assumption: b nested in a) Prob > chi2 = 0.0000
------------------------------------------------------------------------------
Model | nobs ll(null) ll(model) df AIC BIC
-------------+----------------------------------------------------------------
b | 337 -509.8441 -440.1682 13 906.3365 955.9976
a | 337 -509.8441 -426.8005 16 885.601 946.7223
------------------------------------------------------------------------------
NOTE: You can also use mlogtest, lrcomb for combining all possible combinations of the dependent variable after running the full model. In the book, J. Scott Long uses the binary logistic regression for the LR test for combining outcomes. The results obtained from this approach are consistent with the book (the next command), but not with the lrtest and mlogtest, lrcomb in the previous commands.
use https://stats.idre.ucla.edu/stat/stata/examples/long/nomocc2 if (occ >= 4), clear
(1982 General Social Survey)
gen prof = (occ == 5)
logit prof white ed exp
Iteration 0: log likelihood = -88.928674
Iteration 1: log likelihood = -77.752675
Iteration 2: log likelihood = -77.231101
Iteration 3: log likelihood = -77.225873
Iteration 4: log likelihood = -77.225872
Logit estimates Number of obs = 153
LR chi2(3) = 23.41
Prob > chi2 = 0.0000
Log likelihood = -77.225872 Pseudo R2 = 0.1316
------------------------------------------------------------------------------
prof | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
white | -.1886257 .8999111 -0.21 0.834 -1.952419 1.575168
ed | .3756717 .0894349 4.20 0.000 .2003824 .5509609
exper | .0014674 .0145408 0.10 0.920 -.0270321 .0299669
_cons | -4.214093 1.619653 -2.60 0.009 -7.388554 -1.039633
------------------------------------------------------------------------------
Table 6.4, page 167.
use https://stats.idre.ucla.edu/stat/stata/examples/long/nomocc2.dta, clear
(1982 General Social Survey)
quietly mlogit occ white ed exp, basecategory(5)
prchange
mlogit: Changes in Predicted Probabilities for occ
white
Avg|Chg| Menial BlueCol Craft WhiteCol Prof
0->1 .11623582 -.13085523 .04981799 -.15973434 .07971004 .1610615
ed
Avg|Chg| Menial BlueCol Craft WhiteCol Prof
Min->Max .39242268 -.13017954 -.70077323 -.15010394 .02425591 .95680079
-+1/2 .05855425 -.02559762 -.06831616 -.05247185 .01250795 .13387768
-+sd/2 .1640657 -.07129153 -.19310513 -.14576758 .03064777 .37951647
MargEfct .05894859 -.02579097 -.06870635 -.05287415 .01282041 .13455107
exper
Avg|Chg| Menial BlueCol Craft WhiteCol Prof
Min->Max .12193559 -.11536534 -.18947365 .03115708 .09478889 .17889298
-+1/2 .00233425 -.00226997 -.00356567 .00105992 .0016944 .00308132
-+sd/2 .03253578 -.03167491 -.04966453 .01479983 .02360725 .04293236
MargEfct .00233427 -.00226997 -.00356571 .00105992 .00169442 .00308134
Menial BlueCol Craft WhiteCol Prof
Pr(y|x) .09426806 .18419114 .29411051 .16112968 .26630062
white ed exper
x= .916914 13.095 20.5015
sd(x)= .276423 2.94643 13.9594
Figure 6.1, page 168.
* Stata 8 code.
quietly mlogit occ white ed exp, basecategory(5)
* Stata 9 code and output.
quietly mlogit occ white ed exp, baseoutcome(5)
prchange
mlogit: Changes in Predicted Probabilities for occ
white
Avg|Chg| Menial BlueCol Craft WhiteCol Prof
0->1 .11623582 -.13085523 .04981799 -.15973434 .07971004 .1610615
ed
Avg|Chg| Menial BlueCol Craft WhiteCol Prof
Min->Max .39242268 -.13017954 -.70077323 -.15010394 .02425591 .95680079
-+1/2 .05855425 -.02559762 -.06831616 -.05247185 .01250795 .13387768
-+sd/2 .1640657 -.07129153 -.19310513 -.14576758 .03064777 .37951647
MargEfct .05894859 -.02579097 -.06870635 -.05287415 .01282041 .13455107
exper
Avg|Chg| Menial BlueCol Craft WhiteCol Prof
Min->Max .12193559 -.11536534 -.18947365 .03115708 .09478889 .17889298
-+1/2 .00233425 -.00226997 -.00356567 .00105992 .0016944 .00308132
-+sd/2 .03253578 -.03167491 -.04966453 .01479983 .02360725 .04293236
MargEfct .00233427 -.00226997 -.00356571 .00105992 .00169442 .00308134
Menial BlueCol Craft WhiteCol Prof
Pr(y|x) .09426806 .18419114 .29411051 .16112968 .26630062
white ed exper
x= .916914 13.095 20.5015
sd(x)= .276423 2.94643 13.9594
NOTE: You can either type mlogview for a window for the multinomial logit plots or use the mlogplot command.
mlogplot white ed exper, std(0ss) p(.1) min(-.25) max(.5) dc ntics(4)
Table 6.5, page 170.
* Stata 8 code.
quietly mlogit occ white ed exp, basecategory(5)
* Stata 9 code and output.
quietly mlogit occ white ed exp, baseoutcome(5)
listcoef white
mlogit (N=337): Factor Change in the Odds of occ
Variable: white (sd=.27642268)
Odds comparing|
Group 1 vs Group 2| b z P>|z| e^b e^bStdX
------------------+---------------------------------------------
Menial -BlueCol | -1.23650 -1.707 0.088 0.2904 0.7105
Menial -Craft | -0.47234 -0.782 0.434 0.6235 0.8776
Menial -WhiteCol | -1.57139 -1.741 0.082 0.2078 0.6477
Menial -Prof | -1.77431 -2.350 0.019 0.1696 0.6123
BlueCol -Menial | 1.23650 1.707 0.088 3.4436 1.4075
BlueCol -Craft | 0.76416 1.208 0.227 2.1472 1.2352
BlueCol -WhiteCol | -0.33488 -0.359 0.720 0.7154 0.9116
BlueCol -Prof | -0.53780 -0.673 0.501 0.5840 0.8619
Craft -Menial | 0.47234 0.782 0.434 1.6037 1.1395
Craft -BlueCol | -0.76416 -1.208 0.227 0.4657 0.8096
Craft -WhiteCol | -1.09904 -1.343 0.179 0.3332 0.7380
Craft -Prof | -1.30196 -2.011 0.044 0.2720 0.6978
WhiteCol-Menial | 1.57139 1.741 0.082 4.8133 1.5440
WhiteCol-BlueCol | 0.33488 0.359 0.720 1.3978 1.0970
WhiteCol-Craft | 1.09904 1.343 0.179 3.0013 1.3550
WhiteCol-Prof | -0.20292 -0.233 0.815 0.8163 0.9455
Prof -Menial | 1.77431 2.350 0.019 5.8962 1.6331
Prof -BlueCol | 0.53780 0.673 0.501 1.7122 1.1603
Prof -Craft | 1.30196 2.011 0.044 3.6765 1.4332
Prof -WhiteCol | 0.20292 0.233 0.815 1.2250 1.0577
----------------------------------------------------------------
Tables 6.6 and 6.7 and Figures 6.2-6.6 where constructed using hypothetical data and therefore are not reproduced. The graphs can be generated by typing mlogview after the mlogit model and prchange commands or with the mlogplot command.