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help spostado
-------------------------------------------------------------------------------------
spostado: SPost ado files for post-estimation interpretation of regression
models for categorical and limited dependent variables.
-------------------------------------------------------------------------------------
Commands by J. Scott Long and Jeremy Freese. These commands will work with
the estimation commands: clogit, cloglog, cnreg, intreg, logit, mlogit,
nbreg, ologit, oprobit, poisson, probit, regress, tobit, zinb,
zip, and in most cases gologit. The commands are:
fitstat computes fit statistics following model estimation.
listcoef lists factor change, percent change coefficients, and
standardized coefficients. The help option provides details on
interpretation.
mlogtest computes a variety of tests useful for the mlogit model.
mlogview opens a dialog plot for constructing discrete change plots
and odds ratio plots for mlogit.
prchange computes the marginal and discrete change coefficients.
prcounts computes predicted rates and probabilities for count models.
prgen computes predicted values for a range of values. These values
can then be plotted.
prtab computes a table of predicted values for given values of the
independent variables.
prvalue computes predicted values for set values of the independent
variables.
-------------------------------------------------------------------------------
Authors: J. Scott Long - jslong@indiana.edu - www.indiana.edu/~jsl650
Jeremy Freese - jfreese@ssc.wisc.edu
use http://www.ats.ucla.edu/stat/stata/webbooks/logistic/hsblog
(highschool and beyond (200 cases))
describe female read math honcomp
storage display value
variable name type format label variable label
-------------------------------------------------------------------------------
female float %9.0g fl
read float %9.0g reading score
math float %9.0g math score
honcomp float %9.0g honors composition
logit honcomp female read math
Iteration 0: log likelihood = -115.64441
Iteration 1: log likelihood = -79.367198
Iteration 2: log likelihood = -75.475342
Iteration 3: log likelihood = -75.211846
Iteration 4: log likelihood = -75.209827
Logit estimates Number of obs = 200
LR chi2(3) = 80.87
Prob > chi2 = 0.0000
Log likelihood = -75.209827 Pseudo R2 = 0.3496
------------------------------------------------------------------------------
honcomp | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
female | 1.154801 .4340856 2.66 0.008 .304009 2.005593
read | .0752424 .027577 2.73 0.006 .0211924 .1292924
math | .1317117 .0324607 4.06 0.000 .06809 .1953335
_cons | -13.12749 1.850769 -7.09 0.000 -16.75493 -9.50005
------------------------------------------------------------------------------
logistic honcomp female read math
Logit estimates Number of obs = 200
LR chi2(3) = 80.87
Prob > chi2 = 0.0000
Log likelihood = -75.209827 Pseudo R2 = 0.3496
------------------------------------------------------------------------------
honcomp | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
female | 3.173393 1.377524 2.66 0.008 1.355281 7.430502
read | 1.078145 .0297321 2.73 0.006 1.021419 1.138023
math | 1.140779 .0370305 4.06 0.000 1.070462 1.215716
------------------------------------------------------------------------------
These results are pretty straight forward but there are other ways of looking at the
coefficients. Let's try the listcoef command with the const option.
listcoef, const
logistic (N=200): Factor Change in Odds
Odds of: 1 vs 0
----------------------------------------------------------------------
honcomp | b z P>|z| e^b e^bStdX SDofX
-------------+--------------------------------------------------------
female | 1.15480 2.660 0.008 3.1734 1.7798 0.4992
read | 0.07524 2.728 0.006 1.0781 2.1629 10.2529
math | 0.13171 4.058 0.000 1.1408 3.4347 9.3684
_cons | -13.12749 -7.093 0.000
----------------------------------------------------------------------
The column labeled 'b' (above) are the logistic regression coefficients. The column 'z' is the
Wald z-test that the coefficient is different from zero and the next column (P>|z|) gives the
p-value for the z-test. The column 'e^b' are e raised to the logistic coefficient power
(exponentiated coefficients) which are the odds ratios. Next comes 'e^bStdX' which gives the
odds ratios for a one standard deviation change in the covariate. Finally, there is a
column giving the standard deviation of the covariate (SDofX).Let's try listcoef again, this time with the std option.
listcoef, const std
logistic (N=200): Unstandardized and Standardized Estimates
Observed SD: .4424407
Latent SD: 2.1498873
Odds of: 1 vs 0
-------------------------------------------------------------------------------
honcomp | b z P>|z| bStdX bStdY bStdXY SDofX
-------------+-----------------------------------------------------------------
female | 1.15480 2.660 0.008 0.5765 0.5371 0.2682 0.4992
read | 0.07524 2.728 0.006 0.7715 0.0350 0.3588 10.2529
math | 0.13171 4.058 0.000 1.2339 0.0613 0.5740 9.3684
_cons | -13.12749 -7.093 0.000
-------------------------------------------------------------------------------
The columns 'b', 'z' and 'P>|z|' are the same as before. The next column, 'bStdX', gives the amount
of change in the log odds for a one standard deviation change in the covariate.
The column 'bStdY' gives the amount of change, in
standard deviations, in the log odds for a one unit change in the covariate.
The next column, 'bStdXY', gives the amount of change, in standard deviations,
in the log odds for a one standard deviation change in the covariate. Finally, there is a
column giving the standard deviation of the covariate (SDofX).The fitstat command presents a number of indices for model fit.
fitstat
Measures of Fit for logit of honcomp
Log-Lik Intercept Only: -115.644 Log-Lik Full Model: -75.210
D(196): 150.420 LR(3): 80.869
Prob > LR: 0.000
McFadden's R2: 0.350 McFadden's Adj R2: 0.315
Maximum Likelihood R2: 0.333 Cragg & Uhler's R2: 0.485
McKelvey and Zavoina's R2: 0.524 Efron's R2: 0.379
Variance of y*: 6.912 Variance of error: 3.290
Count R2: 0.830 Adj Count R2: 0.358
AIC: 0.792 AIC*n: 158.420
BIC: -888.051 BIC': -64.974
This table contains the log-likelihood for a model with the intercept only
(-115.644) and for the full model (-75.210). These measures are followed by the deviance (150.420)
with degrees of freedom. Deviance in logistic regression is analogous to the sum of squared residuals
in OLS regression. The second line also contains the likelihood ratio chi-square (80.869) with
degrees of freedom (3), which tests whether the model with three covariates predicts better than a
model with intercept only. The p-value for this chi-square (0.000) is on the next line.Next comes a series of pseudo-R2 measures. Unlike OLS regression, logistic regression does not have a single measure that reflects proportion of the variance accounted for. The different R2 measures each have their own interpretation. The item labeled 'Variance of y*' is the variance of the underlying latent dependent variable while 'Variance or error' for logistic regression is p2/3 (which is approximately 3.29).
Finally, there are several information criterion measures including Akaike's Information Criterion (AIC & AIC*n) and Bayesian Information Criterion (BIC & BIC'). These are useful in comparing models with the same response variable but different covariates.Now, let's move on to another program prchange. prchange computes discrete and marginal change for categorical and count regression models.
prchange
logit: Changes in Predicted Probabilities for honcomp
min->max 0->1 -+1/2 -+sd/2 MargEfct
female 0.1539 0.1539 0.1592 0.0789 0.1577
read 0.5079 0.0003 0.0103 0.1058 0.0103
math 0.7731 0.0000 0.0180 0.1703 0.0180
0 1
Pr(y|x) 0.8368 0.1632
female read math
x= .545 52.23 52.645
sd(x)= .49922 10.2529 9.36845
For each covariate, prchange computes the min/max change, a zero/one change, a one unit change,
a one standard deviation change, and the marginal effect (instantaneous change) in the probability.With the fromto option, prchange displays the beginning and ending probabilities in addition to the change in probability.
prchange, fromto
logit: Changes in Predicted Probabilities for honcomp
from: to: dif: from: to: dif: from:
x=min x=max min->max x=0 x=1 0->1 x-1/2
female 0.0942 0.2481 0.1539 0.0942 0.2481 0.1539 0.0987
read 0.0305 0.5385 0.5079 0.0038 0.0041 0.0003 0.1582
math 0.0145 0.7875 0.7731 0.0002 0.0002 0.0000 0.1545
to: dif: from: to: dif:
x+1/2 -+1/2 x-1/2sd x+1/2sd -+sd/2 MargEfct
female 0.2579 0.1592 0.1276 0.2065 0.0789 0.1577
read 0.1685 0.0103 0.1171 0.2230 0.1058 0.0103
math 0.1724 0.0180 0.0952 0.2656 0.1703 0.0180
0 1
Pr(y|x) 0.8368 0.1632
female read math
x= .545 52.23 52.645
sd(x)= .49922 10.2529 9.36845
A great feature of prchange is the ability to display results for specific values of the
covariates. Let's look at the prchange for females with reading scores of 60.
prchange, x(female=1 read=60)
logit: Changes in Predicted Probabilities for honcomp
min->max 0->1 -+1/2 -+sd/2 MargEfct
female 0.2146 0.2146 0.2639 0.1339 0.2697
read 0.6131 0.0005 0.0176 0.1784 0.0176
math 0.8757 0.0001 0.0308 0.2811 0.0308
0 1
Pr(y|x) 0.6281 0.3719
female read math
x= 1 60 52.645
sd(x)= .49922 10.2529 9.36845
The prtab command is used to display the predicted probabilities for different values of the
covariates. Let's look at female first.
prtab female
logit: Predicted probabilities of positive outcome for honcomp
----------------------
female | Prediction
----------+-----------
male | 0.0942
female | 0.2481
----------------------
female read math
x= .545 52.23 52.645
The table gives the probability of males and females being in honcomp 1 with the other
variables (read and math) held at their mean.Next we will try the same thing for the variable read while holding female and math at their mean.
prtab read
logit: Predicted probabilities of positive outcome for honcomp
----------------------
reading |
score | Prediction
----------+-----------
28 | 0.0305
31 | 0.0380
34 | 0.0472
35 | 0.0507
36 | 0.0544
37 | 0.0584
39 | 0.0673
41 | 0.0773
42 | 0.0829
43 | 0.0888
44 | 0.0950
45 | 0.1017
46 | 0.1088
47 | 0.1163
48 | 0.1243
50 | 0.1416
52 | 0.1609
53 | 0.1713
54 | 0.1823
55 | 0.1937
57 | 0.2183
60 | 0.2593
61 | 0.2740
63 | 0.3049
65 | 0.3377
66 | 0.3548
68 | 0.3899
71 | 0.4447
73 | 0.4821
76 | 0.5385
----------------------
female read math
x= .545 52.23 52.645
Now, let's combine female and reading into a single table.
prtab read female
logit: Predicted probabilities of positive outcome for honcomp
--------------------------
reading | female
score | male female
----------+---------------
28 | 0.0165 0.0506
31 | 0.0206 0.0626
34 | 0.0257 0.0772
35 | 0.0277 0.0828
36 | 0.0297 0.0887
37 | 0.0320 0.0949
39 | 0.0370 0.1087
41 | 0.0428 0.1241
42 | 0.0459 0.1326
43 | 0.0494 0.1414
44 | 0.0530 0.1508
45 | 0.0569 0.1607
46 | 0.0611 0.1711
47 | 0.0656 0.1821
48 | 0.0703 0.1936
50 | 0.0808 0.2181
52 | 0.0927 0.2449
53 | 0.0992 0.2591
54 | 0.1062 0.2738
55 | 0.1135 0.2890
57 | 0.1296 0.3208
60 | 0.1572 0.3719
61 | 0.1675 0.3896
63 | 0.1895 0.4259
65 | 0.2137 0.4631
66 | 0.2266 0.4818
68 | 0.2541 0.5194
71 | 0.2992 0.5753
73 | 0.3316 0.6116
76 | 0.3834 0.6637
--------------------------
female read math
x= .545 52.23 52.645
If we wish to add the predicted probabilites to our data we can use the prgen command.
Let's generate the predicted probabilities for each of the values of reading while holding the
other variables at their mean.
prgen read, gen(nr) from(28) to(76) ncases(49)
logit: Predicted values as read varies from 28 to 76.
female read math
x= .545 52.23 52.645
list nrx nrp0 nrp1 in 1/50
nrx nrp0 nrp1
1. 28 .9694503 .0305497
2. 29 .9671414 .0328586
3. 30 .9646644 .0353356
4. 31 .962008 .037992
5. 32 .9591603 .0408397
6. 33 .9561089 .043891
7. 34 .9528408 .0471592
8. 35 .9493423 .0506578
9. 36 .9455989 .0544011
10. 37 .941596 .058404
11. 38 .9373181 .0626819
12. 39 .9327492 .0672508
13. 40 .9278729 .0721271
14. 41 .9226723 .0773277
15. 42 .9171303 .0828697
16. 43 .9112293 .0887707
17. 44 .9049516 .0950484
18. 45 .8982795 .1017204
19. 46 .8911955 .1088045
20. 47 .8836819 .1163181
21. 48 .8757218 .1242782
22. 49 .8672988 .1327012
23. 50 .8583972 .1416027
24. 51 .8490025 .1509975
25. 52 .8391013 .1608987
26. 53 .8286819 .1713181
27. 54 .8177343 .1822657
28. 55 .8062507 .1937493
29. 56 .7942256 .2057744
30. 57 .7816563 .2183437
31. 58 .768543 .231457
32. 59 .7548891 .2451109
33. 60 .7407016 .2592985
34. 61 .7259908 .2740092
35. 62 .7107713 .2892287
36. 63 .6950616 .3049384
37. 64 .6788841 .3211159
38. 65 .6622654 .3377346
39. 66 .6452361 .3547639
40. 67 .6278306 .3721694
41. 68 .6100873 .3899128
42. 69 .5920476 .4079524
43. 70 .5737565 .4262435
44. 71 .5552613 .4447387
45. 72 .5366117 .4633883
46. 73 .5178592 .4821408
47. 74 .4990562 .5009438
48. 75 .4802559 .5197441
49. 76 .4615113 .5384887
50. . . .
The column 'nrx' gives the values of read, 'nrp0' the probability of being in
honcomp 0,
and 'nrp1' the probability of being in honcomp 1. Note that the column 'nrp1' is the same
as the results from prtab read (above), just with more decimal places.The prvalue command is used to compute the conditional probability being in each of the levels of response variable. In this first example, we will hold all of the covariates at their mean value.
prvalue
logit: Predictions for honcomp
Pr(y=1|x): 0.1632 95% ci: (0.1068,0.2415)
Pr(y=0|x): 0.8368 95% ci: (0.7585,0.8932)
female read math
x= .545 52.23 52.645
Next, let's look at the predicted values for males and females while holding reading and math at
their means.
prvalue, x(female=0)
logit: Predictions for honcomp
Pr(y=1|x): 0.0942 95% ci: (0.0468,0.1805)
Pr(y=0|x): 0.9058 95% ci: (0.8195,0.9532)
female read math
x= 0 52.23 52.645
prvalue, x(female=1)
logit: Predictions for honcomp
Pr(y=1|x): 0.2481 95% ci: (0.1604,0.3630)
Pr(y=0|x): 0.7519 95% ci: (0.6370,0.8396)
female read math
x= 1 52.23 52.645
Now, let's look at the predicted values for males and females when all of the other
variables are held are their maximum values.
prvalue, x(female=0) rest(max)
logit: Predictions for honcomp
Pr(y=1|x): 0.9220 95% ci: (0.7812,0.9751)
Pr(y=0|x): 0.0780 95% ci: (0.0249,0.2188)
female read math
x= 0 76 75
prvalue, x(female=1) rest(max)
logit: Predictions for honcomp
Pr(y=1|x): 0.9740 95% ci: (0.9097,0.9929)
Pr(y=0|x): 0.0260 95% ci: (0.0071,0.0903)
female read math
x= 1 76 75
mlogit prog female read math
Iteration 0: log likelihood = -204.09667
Iteration 1: log likelihood = -177.18429
Iteration 2: log likelihood = -175.51578
Iteration 3: log likelihood = -175.46792
Iteration 4: log likelihood = -175.46786
Multinomial regression Number of obs = 200
LR chi2(6) = 57.26
Prob > chi2 = 0.0000
Log likelihood = -175.46786 Pseudo R2 = 0.1403
------------------------------------------------------------------------------
prog | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
general |
female | -.1565038 .3793112 -0.41 0.680 -.8999401 .5869325
read | -.0332741 .0247308 -1.35 0.178 -.0817457 .0151975
math | -.06964 .0280339 -2.48 0.013 -.1245854 -.0146946
_cons | 4.707234 1.332392 3.53 0.000 2.095794 7.318675
-------------+----------------------------------------------------------------
vocation |
female | -.1843515 .3973611 -0.46 0.643 -.963165 .5944619
read | -.0572131 .0265751 -2.15 0.031 -.1092994 -.0051268
math | -.1180523 .0309737 -3.81 0.000 -.1787597 -.0573449
_cons | 8.303956 1.491516 5.57 0.000 5.380637 11.22727
------------------------------------------------------------------------------
(Outcome prog==academic is the comparison group)
Next, we will use listcoef, fitstat, and prchange on the mlogit.
listcoef
mlogit (N=200): Factor Change in the Odds of prog
Variable: female (sd= .49922)
Odds comparing|
Group 1 vs Group 2| b z P>|z| e^b e^bStdX
------------------+---------------------------------------------
general -vocation | 0.02785 0.066 0.947 1.0282 1.0140
general -academic | -0.15650 -0.413 0.680 0.8551 0.9248
vocation-general | -0.02785 -0.066 0.947 0.9725 0.9862
vocation-academic | -0.18435 -0.464 0.643 0.8316 0.9121
academic-general | 0.15650 0.413 0.680 1.1694 1.0813
academic-vocation | 0.18435 0.464 0.643 1.2024 1.0964
----------------------------------------------------------------
Variable: read (sd= 10.2529)
Odds comparing|
Group 1 vs Group 2| b z P>|z| e^b e^bStdX
------------------+---------------------------------------------
general -vocation | 0.02394 0.846 0.397 1.0242 1.2782
general -academic | -0.03327 -1.345 0.178 0.9673 0.7109
vocation-general | -0.02394 -0.846 0.397 0.9763 0.7824
vocation-academic | -0.05721 -2.153 0.031 0.9444 0.5562
academic-general | 0.03327 1.345 0.178 1.0338 1.4066
academic-vocation | 0.05721 2.153 0.031 1.0589 1.7979
----------------------------------------------------------------
Variable: math (sd= 9.36845)
Odds comparing|
Group 1 vs Group 2| b z P>|z| e^b e^bStdX
------------------+---------------------------------------------
general -vocation | 0.04841 1.470 0.142 1.0496 1.5739
general -academic | -0.06964 -2.484 0.013 0.9327 0.5208
vocation-general | -0.04841 -1.470 0.142 0.9527 0.6354
vocation-academic | -0.11805 -3.811 0.000 0.8886 0.3309
academic-general | 0.06964 2.484 0.013 1.0721 1.9202
academic-vocation | 0.11805 3.811 0.000 1.1253 3.0221
----------------------------------------------------------------
fitstat
Measures of Fit for mlogit of prog
Log-Lik Intercept Only: -204.097 Log-Lik Full Model: -175.468
D(192): 350.936 LR(6): 57.258
Prob > LR: 0.000
McFadden's R2: 0.140 McFadden's Adj R2: 0.101
Maximum Likelihood R2: 0.249 Cragg & Uhler's R2: 0.286
Count R2: 0.600 Adj Count R2: 0.158
AIC: 1.835 AIC*n: 366.936
BIC: -666.341 BIC': -25.468
prchange
mlogit: Changes in Predicted Probabilities for prog
female
Avg|Chg| general vocation academic
0->1 .02790104 -.02005389 -.02179766 .04185158
read
Avg|Chg| general vocation academic
Min->Max .3214145 -.13366224 -.34845948 .48212177
-+1/2 .00725731 -.00335795 -.00752802 .01088595
-+sd/2 .0741224 -.03413837 -.07704523 .11118361
MargEfct .0217727 -.0033582 -.00752815 .01088635
math
Avg|Chg| general vocation academic
Min->Max .49183498 -.1889001 -.54885237 .73775247
-+1/2 .01506265 -.00711139 -.01548259 .02259398
-+sd/2 .13917912 -.06468265 -.14408605 .20876867
MargEfct .04519518 -.00711382 -.01548377 .02259759
general vocation academic
Pr(y|x) .25057834 .20160662 .54781502
female read math
x= .545 52.23 52.645
sd(x)= .49922 10.2529 9.36845
The mlogtest command computes a variety of tests for multinomial logit models. The user
selects the tests they want by specifying the appropriate options. For each
independent variable, mlogtest can perform either a likelihood-ratio or
Wald test of the null hypothesis that the coefficients of the variable equal
zero across all equations. We will use mlogtest with the all option.
mlogtest, all
**** Likelihood-ratio tests for independent variables
Ho: All coefficients associated with given variable(s) are 0.
prog | chi2 df P>chi2
-------------+-------------------------
female | 0.275 2 0.872
read | 5.121 2 0.077
math | 17.874 2 0.000
---------------------------------------
**** Wald tests for independent variables
Ho: All coefficients associated with given variable(s) are 0.
prog | chi2 df P>chi2
-------------+-------------------------
female | 0.274 2 0.872
read | 4.928 2 0.085
math | 15.780 2 0.000
---------------------------------------
**** Hausman tests of IIA assumption
Ho: Odds(Outcome-J vs Outcome-K) are independent of other alternatives.
Omitted | chi2 df P>chi2 evidence
---------+------------------------------------
general | -21.017 4 --- for Ho
vocation | 0.630 4 0.960 for Ho
----------------------------------------------
Note: If chi2<0, the estimated model does not
meet asymptotic assumptions of the test.
**** Small-Hsiao tests of IIA assumption
Ho: Odds(Outcome-J vs Outcome-K) are independent of other alternatives.
Omitted | lnL(full) lnL(omit) chi2 df P>chi2 evidence
---------+---------------------------------------------------------
general | -41.797 -39.076 5.442 4 0.245 for Ho
vocation | -46.130 -44.449 3.364 4 0.499 for Ho
-------------------------------------------------------------------
**** Wald tests for combining outcome categories
Ho: All coefficients except intercepts associated with given pair
of outcomes are 0 (i.e., categories can be collapsed).
Categories tested | chi2 df P>chi2
------------------+------------------------
general-vocation | 5.716 3 0.126
general-academic | 17.157 3 0.001
vocation-academic | 35.665 3 0.000
-------------------------------------------
**** LR tests for combining outcome categories
Ho: All coefficients except intercepts associated with given pair
of outcomes are 0 (i.e., categories can be collapsed).
Categories tested | chi2 df P>chi2
------------------+------------------------
general-vocation | 6.035 3 0.110
general-academic | 20.262 3 0.000
vocation-academic | 52.127 3 0.000
------------------------------------------
use http://www.ats.ucla.edu/stat/stata/notes/lahigh
poisson daysabs gender langnce
Iteration 0: log likelihood = -1549.8567
Iteration 1: log likelihood = -1549.8567
Poisson regression Number of obs = 316
LR chi2(2) = 171.50
Prob > chi2 = 0.0000
Log likelihood = -1549.8567 Pseudo R2 = 0.0524
------------------------------------------------------------------------------
daysabs | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
gender | -.4093528 .0482192 -8.49 0.000 -.5038606 -.3148449
langnce | -.01467 .0012934 -11.34 0.000 -.0172051 -.0121349
_cons | 3.056329 .1005107 30.41 0.000 2.859332 3.253327
------------------------------------------------------------------------------
fitstat
Measures of Fit for poisson of daysabs
Log-Lik Intercept Only: -1635.608 Log-Lik Full Model: -1549.857
D(313): 3099.713 LR(2): 171.503
Prob > LR: 0.000
McFadden's R2: 0.052 McFadden's Adj R2: 0.051
Maximum Likelihood R2: 0.419 Cragg & Uhler's R2: 0.419
AIC: 9.828 AIC*n: 3105.713
BIC: 1298.166 BIC': -159.991
nbreg daysabs gender langnce
Fitting comparison Poisson model:
Iteration 0: log likelihood = -1549.8567
Iteration 1: log likelihood = -1549.8567
Fitting constant-only model:
Iteration 0: log likelihood = -897.78991
Iteration 1: log likelihood = -891.24455
Iteration 2: log likelihood = -891.24271
Iteration 3: log likelihood = -891.24271
Fitting full model:
Iteration 0: log likelihood = -881.55269
Iteration 1: log likelihood = -880.9306
Iteration 2: log likelihood = -880.9274
Iteration 3: log likelihood = -880.9274
Negative binomial regression Number of obs = 316
LR chi2(2) = 20.63
Prob > chi2 = 0.0000
Log likelihood = -880.9274 Pseudo R2 = 0.0116
------------------------------------------------------------------------------
daysabs | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
gender | -.4312069 .1396913 -3.09 0.002 -.7049968 -.1574169
langnce | -.0156493 .0039485 -3.96 0.000 -.0233882 -.0079104
_cons | 3.134647 .3187701 9.83 0.000 2.509869 3.759425
-------------+----------------------------------------------------------------
/lnalpha | .25394 .095509 .0667457 .4411342
-------------+----------------------------------------------------------------
alpha | 1.289094 .1231201 1.069024 1.554469
------------------------------------------------------------------------------
Likelihood ratio test of alpha=0: chibar2(01) = 1337.86 Prob>=chibar2 = 0.000
fitstat
Measures of Fit for nbreg of daysabs
Log-Lik Intercept Only: -891.243 Log-Lik Full Model: -880.927
D(312): 1761.855 LR(2): 20.631
Prob > LR: 0.000
McFadden's R2: 0.012 McFadden's Adj R2: 0.007
Maximum Likelihood R2: 0.063 Cragg & Uhler's R2: 0.063
AIC: 5.601 AIC*n: 1769.855
BIC: -33.937 BIC': -9.119
It is clear from the fitstat results and the likelihood ratio test that alpha=0 that the
negative binomial regression model fits much better than the poisson regression model, so we
will keep working the nbreg model.Let's start with the listcoef and prchange commands.
listcoef
nbreg (N=316): Factor Change in Expected Count
Observed SD: 7.4490028
----------------------------------------------------------------------
daysabs | b z P>|z| e^b e^bStdX SDofX
-------------+--------------------------------------------------------
gender | -0.43121 -3.087 0.002 0.6497 0.8058 0.5006
langnce | -0.01565 -3.963 0.000 0.9845 0.7552 17.9392
-------------+--------------------------------------------------------
ln alpha | 0.25394
alpha | 1.28909 SE(alpha) = 0.12312
----------------------------------------------------------------------
LR test of alpha=0: 1337.86 Prob>=LRX2 = 0.000
----------------------------------------------------------------------
prchange
nbreg: Changes in Predicted Rate for daysabs
min->max 0->1 -+1/2 -+sd/2 MargEfct
gender -2.3892 -3.6772 -2.4022 -1.1957 -2.3837
langnce -9.3413 -0.1879 -0.0865 -1.5570 -0.0865
exp(xb): 5.5280
gender langnce
x= 1.48734 50.0638
sd(x)= .500633 17.9392
Next, we will try the prcount command. prcounts computes the predicted
rate and probabilities of counts from 0 through the specified maximum count based on the last estimates
from the count models poisson, nbreg, zip, zinb. We will include the plot option so that we can plot
the observed counts versus the counts predicted by the negative binomial regression.prcounts nb, plot
summ nbrate-nbprgt
Variable | Obs Mean Std. Dev. Min Max
-------------+-----------------------------------------------------
nbrate | 316 5.826237 1.952521 2.060741 14.69753
nbpr0 | 316 .2007168 .0438959 .0980942 .3657711
nbpr1 | 316 .1346654 .0235343 .0722805 .2061429
nbpr2 | 316 .1036036 .0138286 .0609582 .1329723
nbpr3 | 316 .0832123 .0079426 .0535737 .0936423
nbpr4 | 316 .068304 .0043128 .0480348 .072282
nbpr5 | 316 .056829 .0025965 .0425366 .0588553
nbpr6 | 316 .0477302 .0026664 .0297483 .0496365
nbpr7 | 316 .0403748 .0033407 .0209201 .042915
nbpr8 | 316 .0343472 .0039261 .0147727 .0377968
nbpr9 | 316 .0293571 .0043162 .0104651 .0337698
nbcu0 | 316 .2007168 .0438959 .0980942 .3657711
nbcu1 | 316 .3353822 .0673746 .1703747 .571914
nbcu2 | 316 .4389857 .0810372 .2313329 .7048863
nbcu3 | 316 .5221981 .0886133 .2849067 .7942708
nbcu4 | 316 .590502 .0921422 .3329415 .855569
nbcu5 | 316 .647331 .0929128 .3765217 .8981056
nbcu6 | 316 .6950612 .0917955 .4163698 .9278539
nbcu7 | 316 .7354359 .0893983 .4530075 .948774
nbcu8 | 316 .7697832 .0861544 .4868328 .9635468
nbcu9 | 316 .7991402 .0823758 .5181618 .9740119
nbprgt | 316 .2008598 .0823758 .0259881 .4818382
list daysabs nbrate in 1/30
daysabs nbrate
1. 0 7.965481
2. 4 4.220754
3. 9 14.69753
4. 7 4.852018
5. 2 5.112275
6. 1 7.821788
7. 0 4.19794
8. 18 9.475632
9. 3 7.422179
10. 3 6.660331
11. 3 5.352007
12. 23 6.884264
13. 0 4.852018
14. 3 5.112275
15. 17 3.46986
16. 4 5.634378
17. 0 7.297377
18. 1 5.466737
19. 3 7.359331
20. 3 8.193631
21. 2 4.919608
22. 0 3.171716
23. 2 5.352007
24. 0 6.120268
25. 3 9.7476
26. 3 6.715691
27. 19 5.959813
28. 8 8.193631
29. 34 9.010157
30. 13 7.683804
graph nbpreq nbobeq nbval, c(ll)
The graph of the observed and predicted counts backs up our contention that the negative
binomial regression provides a good fit.
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