 |
|
Scott Long's postestimation commands on Logistic Rregression
We know the logistic regression model is linear in the log odds
ln (o) = b0 + b1 X1 + b2 X2 + ...
To ask STATA to run a logistic regression, we may use either logit or,
logistic command.
. logit (coefficients of the independent variables measured in logged odds)
e.g. . logit depvar indep_var1 indep_var2 indep_var3
. logistic (presents the coefficients in odds ratios)
The odds coefficients can be obtained also with the logit command by using the
option or after the command, thus:
. logit depvar indep_var1 indep_var2 indep_var3, or = . logistic depvar indep_var1
indep_var2 indep_var3
Our difficulty is not getting the coefficients or odds ratios, rather, how to interpreting them:
Option 1: interpreting coefficients: difficult.
Option 2: interpreting odds ratios: not very difficult, but easy to be misleading,since odds ratios
do not equal to probability.For example, if 20% of female students smoke, and 40% of male students
smoke, the odd ratios of male and female students smoking is,if you interpret this result as
“male students are 2.67 times more likely to be a smoker than female students” would be wrong,
Since the probability of male students smoking is 40%, and 20% for female students,thus “male
students are only twice more likely to be a smoker than female students.”
Option 3: Interpreting probability: would be much easier. When dealing with probabilities, one of the
most useful commands is:
. prchange
(Authors: J.Scott Long and Jeremy Freese;www.indiana.edu/~jslsoc/spost.htm;spostsup@indiana.edu)
(if you see “unrecognized command: prchange” after you enter command, this means since prchang
is not built-in Stata routine, you need to install this user-written add-on program. You can put
command:
.findit prchange
And click the first link under “Web resources from Stata and other users:
spost9_ado from http://www.indiana.edu/~jslsoc/stata
Distribution-date: 04Jun2007 / spost9_ado Stata 9 commands for the
post-estimation interpretation of / regression models. Use package
spostado.pkg for Stata 8. / Based on Long & Freese - Regression Models for
Categorical Dependent / Variables Using Stata. Second Edition. / Support
And then click: (click here to install)
("prchange computes discrete and marginal change for regression models for
categorical and count variables. Marginal change is the partial derivative
of the predicted probability or predicted rate with respect to the
independent variables. Discrete change is the difference in the predicted
value as one independent variable changes values while all others are held
constant at specified values.")
Example: data from Jay’s Transitions Study Young Adult Wave II:
Dependent variable ciga : Have you ever smoked more than 10 cigarettes in a
single day? (1=yes, 0=no).
Independent variables: race (1=non-Hispanic white; 0= other race).
. use http://cdph.fsu.edu/people/minxing/transyt2_s.dta
. logistic ciga race
Logistic regression Number of obs = 1204
LR chi2(1) = 23.96
Prob > chi2 = 0.0000
Log likelihood = -686.17107 Pseudo R2 = 0.0172
------------------------------------------------------------------------------
ciga | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
race | 2.010997 .2837647 4.95 0.000 1.52511 2.651682
------------------------------------------------------------------------------
. prchange
logistic: Changes in Probabilities for ciga
min->max 0->1 -+1/2 -+sd/2 MargEfct
race 0.1448 0.1448 0.1348 0.0595 0.1353
0 1
Pr(y|x) 0.7375 0.2625
race
x= .262458
sd(x)= .440153
Note 1: from Odds Ratio Table: very often people might interpret as: Whites are about
TWICE more likely to smoked more than 10 cigarettes in a single day THAN other race
people. However, if we look Probabilities Table, we find the probability only increase
14.48 percent for whites, it is far less than twice.
Note 2: Probability Table: the first column shows the change in the probabilities when
the independent variable varies from its minimum to its maximum. The second shows the
change when the independent variable varies from 0 to 1. This is the most useful when
analysing dummy variables. The third and fourth columns show the change in
probabilities when the independent variable varies one unit in real value or in
standard deviations, respectively. The last column presents the marginal changes of
the independent variable. All this values are calculated at the predicted probability
when the independent variables take their mean values, which are listed just below
this table.
How about if you want to know the predicted probabilities of positive outcome for your
dependent variable for specific population?
For example, if you want to know the predicted probabilities of ever smoking 10 cigarettes in a single
day for white female, you may use command:prtab
. prtab race sex
logistic: Predicted probabilities of positive outcome for ciga
--------------------------
1=non-his |
panic |
white;0=o |0=female,1=male
thers | 0 1
----------+---------------
0 | 0.2101 0.2445
1 | 0.3472 0.3930
--------------------------
race sex
x= .26245847 .54734219
this Table teels us, for example, for white female students, the predicted probability of positive
outcome is around .347
prtab is able to present a one- to four-way table of the predicted values (probabilities, rate) for
different combinations of values of independent variable.
How to make plots showing the predicted probabilities change when one independent variable
varies over a specified range while the others are held in a specific value?
For example, if you want to make plots showing how the predicted probabilities of dependent
variable (ciga) change when the frequency of church/synagogue services attendance varies from 1
(never) to 5 (more than once a week) while race and sex are held in a specific value (e.g. white male,
white female, other male, and other female)?
Firstly, you need to compute predicted values by using command: prgen
use http://cdph.fsu.edu/people/minxing/transyt2_s.dta
logistic ciga race sex church
prgen church, from(1) to(5) gen(prg1) x(sex=0 race=0)
prgen church, from(1) to(5) gen(prg2) x(sex=1 race=0)
prgen church, from(1) to(5) gen(prg3) x(sex=0 race=1)
prgen church, from(1) to(5) gen(prg4) x(sex=1 race=1)
Then, you may use graphical command to create plots:
twoway connected prg1p1 prg2p1 prg3p1 prg4p1 prg1x, msym(O D S T)
prtab is able to present a one- to four-way table of the predicted values (probabilities, rate) for
different combinations of values of independent variable.
NOTE: prchange, prtab, prgen work with many regression models such as: logit, mlogit, mprobit,
nbreg, ologit, oprobit, probit, etc.. more information are available from
http://www.indiana.edu/~jslsoc/spost.htm
back to previous page
|
|
|
