PLUM does -- in part -- what SAS does. It reverses the response 0/1
relationship. Stata and many other software packages parameterize the binary
response of 1 as a success. SAS and PLUM do the reverse. Moreover, PLUM's nloglog
reverses the sign of the standard loglog output, hence the -n- in nloglog. SAS,
following other packages, uses the loglog link.
With respect to priority, I tend to follow GLIM, the software developed by
the founders of GLM methodology. They used the same parameterization for
cloglog as did Fisher when he initially derived it in 1922.
use lbw
gen low0 = 1 if low ==0
replace low0 = 0 if low==1
SUMMARY
glm low *, cloglog = gologit2b low *, nloglog (loglog with
reversed sign)
glm low0 *, cloglog = gologit2b low0 *, nloglog (loglog with
reversed sign)
glm low *, loglog = gologit2b low *, cloglog
glm low0 *, loglog = gologit2b low0 *, cloglog
Joe Hilbe
. glm low age smoke ptl, nolog fam(bin) link(cloglog)
Generalized linear models No. of obs =
189
Optimization : ML Residual df =
185
Scale parameter = 1
Deviance = 222.6159083 (1/df) Deviance =
1.203329
Pearson = 185.6292037 (1/df) Pearson =
1.003401
Variance function: V(u) = u*(1-u) [Bernoulli]
Link function : g(u) = ln(-ln(1-u)) [Complementary log-log]
AIC = 1.22019
Log likelihood = -111.3079541 BIC =
-747.1073
------------------------------------------------------------------------------
| OIM
low | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
age | -.047111 .0274916 -1.71 0.087 -.1009935 .0067715
smoke | .4509498 .2700837 1.67 0.095 -.0784045 .9803041
ptl | .4689538 .191363 2.45 0.014 .0938892 .8440184
_cons | -.2137965 .6398918 -0.33 0.738 -1.467961 1.040368
------------------------------------------------------------------------------
. glm low0 age smoke ptl, nolog fam(bin) link(cloglog)
Generalized linear models No. of obs =
189
Optimization : ML Residual df =
185
Scale parameter = 1
Deviance = 220.0134175 (1/df) Deviance =
1.189262
Pearson = 188.1663766 (1/df) Pearson =
1.017116
Variance function: V(u) = u*(1-u) [Bernoulli]
Link function : g(u) = ln(-ln(1-u)) [Complementary log-log]
AIC = 1.20642
Log likelihood = -110.0067088 BIC =
-749.7098
------------------------------------------------------------------------------
| OIM
low0 | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
age | .0373414 .0190252 1.96 0.050 .0000526 .0746302
smoke | -.3452314 .1994667 -1.73 0.083 -.736179 .0457162
ptl | -.5769123 .2454426 -2.35 0.019 -1.057971 -.0958536
_cons | -.4593313 .453224 -1.01 0.311 -1.347634 .4289715
------------------------------------------------------------------------------
. glm low age smoke ptl, nolog fam(bin) link(loglog)
Generalized linear models No. of obs =
189
Optimization : ML Residual df =
185
Scale parameter = 1
Deviance = 220.0134175 (1/df) Deviance =
1.189262
Pearson = 188.1663766 (1/df) Pearson =
1.017116
Variance function: V(u) = u*(1-u) [Bernoulli]
Link function : g(u) = -ln(-ln(u)) [Log-log]
AIC = 1.20642
Log likelihood = -110.0067088 BIC =
-749.7098
------------------------------------------------------------------------------
| OIM
low | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
age | -.0373414 .0190252 -1.96 0.050 -.0746302 -.0000526
smoke | .3452314 .1994667 1.73 0.083 -.0457162 .736179
ptl | .5769123 .2454426 2.35 0.019 .0958536 1.057971
_cons | .4593313 .453224 1.01 0.311 -.4289715 1.347634
------------------------------------------------------------------------------
glm low0 age smoke ptl, nolog fam(bin) link(loglog)
Generalized linear models No. of obs =
189
Optimization : ML Residual df =
185
Scale parameter = 1
Deviance = 222.6159083 (1/df) Deviance =
1.203329
Pearson = 185.6292037 (1/df) Pearson =
1.003401
Variance function: V(u) = u*(1-u) [Bernoulli]
Link function : g(u) = -ln(-ln(u)) [Log-log]
AIC = 1.22019
Log likelihood = -111.3079541 BIC =
-747.1073
------------------------------------------------------------------------------
| OIM
low0 | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
age | .047111 .0274916 1.71 0.087 -.0067715 .1009935
smoke | -.4509498 .2700837 -1.67 0.095 -.9803041 .0784045
ptl | -.4689538 .191363 -2.45 0.014 -.8440184 -.0938892
_cons | .2137965 .6398918 0.33 0.738 -1.040368 1.467961
------------------------------------------------------------------------------
. gologit2b low age smoke ptl, nolog link(cloglog)
Generalized Ordered Cloglog Estimates Number of obs =
189
LR chi2(3) = 14.66
Prob > chi2 = 0.0021
Log likelihood = -110.00671 Pseudo R2 =
0.0625
------------------------------------------------------------------------------
low | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
age | -.0373414 .0190252 -1.96 0.050 -.0746302 -.0000526
smoke | .3452314 .1994667 1.73 0.083 -.0457162 .736179
ptl | .5769123 .2454426 2.35 0.019 .0958536 1.057971
_cons | .4593313 .453224 1.01 0.311 -.4289715 1.347634
------------------------------------------------------------------------------
. gologit2b low age smoke ptl, nolog link(nloglog)
Generalized Ordered Nloglog Estimates Number of obs =
189
LR chi2(3) = 12.06
Prob > chi2 = 0.0072
Log likelihood = -111.30795 Pseudo R2 =
0.0514
------------------------------------------------------------------------------
low | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
age | -.047111 .0274916 -1.71 0.087 -.1009935 .0067716
smoke | .4509498 .2700837 1.67 0.095 -.0784045 .9803041
ptl | .4689538 .191363 2.45 0.014 .0938892 .8440184
_cons | -.2137968 .6398918 -0.33 0.738 -1.467962 1.040368
------------------------------------------------------------------------------
. . gologit2b low0 age smoke ptl, nolog link(cloglog)
Generalized Ordered Cloglog Estimates Number of obs =
189
LR chi2(3) = 12.06
Prob > chi2 = 0.0072
Log likelihood = -111.30795 Pseudo R2 =
0.0514
------------------------------------------------------------------------------
low0 | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
age | .047111 .0274916 1.71 0.087 -.0067716 .1009935
smoke | -.4509498 .2700837 -1.67 0.095 -.9803041 .0784045
ptl | -.4689538 .191363 -2.45 0.014 -.8440183 -.0938892
_cons | .2137967 .6398917 0.33 0.738 -1.040368 1.467961
------------------------------------------------------------------------------
. gologit2b low0 age smoke ptl, nolog link(nloglog)
Generalized Ordered Nloglog Estimates Number of obs =
189
LR chi2(3) = 14.66
Prob > chi2 = 0.0021
Log likelihood = -110.00671 Pseudo R2 =
0.0625
------------------------------------------------------------------------------
low0 | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
age | .0373414 .0190252 1.96 0.050 .0000526 .0746302
smoke | -.3452314 .1994667 -1.73 0.083 -.736179 .0457162
ptl | -.5769123 .2454426 -2.35 0.019 -1.057971 -.0958536
_cons | -.4593313 .453224 -1.01 0.311 -1.347634 .4289715
------------------------------------------------------------------------------
.
One last thing - here are examples of how to clone what spss does in
PLUM, including its test of parallel lines. i.e. this gives you
ordered logit, ordered probit, etc. I can send you the corresponding
SPSS output if you want.
webuse nhanes2f, clear
* Logit link (default)
gologit2c health female black age, pl lrf link(l) store(logit_pl)
quietly gologit2c health female black age, npl lrf link(l) store(logit_npl)
* Clone SPSS's test of parallel lines
lrtest logit_pl logit_npl
* Probit link
gologit2c health female black age, pl lrf link(p) store(probit_pl)
quietly gologit2c health female black age, npl lrf link(p) store(probit_npl)
* Clone SPSS's test of parallel lines
lrtest probit_pl probit_npl
* SPSS's cloglog, which Stata calls loglog
gologit2c health female black age, pl lrf link(c) store(cloglog_pl)
quietly gologit2c health female black age, npl lrf link(c) store(cloglog_npl)
lrtest cloglog_pl cloglog_npl
* SPSS's nloglog, which Stata calls cloglog
gologit2c health female black age, pl lrf link(n) store(nloglog_pl)
quietly gologit2c health female black age, npl lrf link(n) store(nloglog_npl)
lrtest nloglog_pl nloglog_npl
-------------------------------------------
Richard Williams, Notre Dame Dept of Sociology
OFFICE: (574)631-6668, (574)631-6463
FAX: (574)288-4373
HOME: (574)289-5227
EMAIL: [email protected]
WWW (personal): http://www.nd.edu/~rwilliam
WWW (department): http://www.nd.edu/~soc
*
* For searches and help try:
* http://www.stata.com/support/faqs/res/findit.html
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/
