This page shows an example of multinomial logit regression with footnotes
explaining the output. First an example is shown using Stata, and then an
example is shown using Mplus, to help you relate the output you are likely to be
familiar with (Stata) to output that may be new to you (Mplus). We suggest that
you view this page using two web browsers so you can show the page side by side
showing the Stata output in one browser and the corresponding Mplus output in
the other browser.
This example is from the Mplus User’s Guide (example 3.6) and we suggest that
you see the Mplus User’s Guide for more details about this example. We thank the
kind people at Muthén & Muthén for permission to use examples from their manual.
Stata Example
Here is a multinomial logit regression example using Stata with two continuous predictors
x1 and x2 used to predict a binary outcome variable, u1.
infile u1 x1 x3 using https://stats.idre.ucla.edu/wp-content/uploads/2016/02/ex3.6.dat, clear
mlogit u1 x1 x3
Iteration 0: log likelihood = -539.2303
Iteration 1: log likelihood = -446.49742
Iteration 2: log likelihood = -434.20483
Iteration 3: log likelihood = -433.4331
Iteration 4: log likelihood = -433.42628
Iteration 5: log likelihood = -433.42628
Multinomial logistic regression Number of obs = 500
LR chi2(4) = 211.61
Prob > chi2 = 0.0000
Log likelihood = -433.42628 Pseudo R2 = 0.1962
------------------------------------------------------------------------------
u1 | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
0 |
x1 | .7686261C .1567749 4.90 0.000 .461353 1.075899
x3 | 2.259422C .2144306 10.54 0.000 1.839146 2.679699
_cons | -.7488877E .1702198 -4.40 0.000 -1.082512 -.4152631
-------------+----------------------------------------------------------------
1 |
x1 | .2798667D .1131474 2.47 0.013 .0581018 .5016316
x3 | .885101D .1402897 6.31 0.000 .6101382 1.160064
_cons | .2622508E .1198104 2.19 0.029 .0274268 .4970748
------------------------------------------------------------------------------
(u1==2 is the base outcome)
estat ic
------------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+----------------------------------------------------------------
. | 500 -539.2303 -433.4263A 6 878.8526B 904.1402B
------------------------------------------------------------------------------
The output is labeled with superscripts to help you relate the later Mplus
output to this Stata output. To summarize the output, both predictors in this model, x1 and x3, are
significantly related to predicting the comparison of level 0 to level 2 of the
outcome variable, u1. Likewise, x1 and x3, are
significantly related to predicting the comparison of level 1 to level 2 of the
outcome variable, u1. The estat ic command produces fit indices for the
model including the log likelihood for the empty (null) model, the log
likelihood for the model, as well as the AIC and BIC fit indices.
Mplus Example
Here is the same example illustrated in Mplus based on the ex3.6 data file.
TITLE: this is an example of a multinomial logistic regression for an unordered categorical (nominal) dependent variable with two covariates DATA: FILE IS https://stats.idre.ucla.edu/wp-content/uploads/2016/02/ex3.6.dat; VARIABLE: NAMES ARE u1 x1 x3; NOMINAL IS u1; MODEL: u1#1 u1#2 ON x1 x3;
Number of observations 500
Estimator MLR
THE MODEL ESTIMATION TERMINATED NORMALLY
TESTS OF MODEL FIT
Loglikelihood
H0 Value -433.426A
Information Criteria
Number of Free Parameters 6
Akaike (AIC) 878.853B
Bayesian (BIC) 904.140B
Sample-Size Adjusted BIC 885.096
(n* = (n + 2) / 24)
MODEL RESULTS
Estimates S.E. Est./S.E.
U1#1 ON
X1 0.769C 0.165 4.670
X3 2.259C 0.203 11.148
U1#2 ON
X1 0.280D 0.114 2.444
X3 0.885D 0.143 6.200
Intercepts
U1#1 -0.749E 0.158 -4.728
U1#2 0.262E 0.120 2.192
- This is the log likelihood value associated with the model (see the ll(model)
from the estat ic command in Stata. - These are the AIC and BIC values, see the AIC and BIC values from the
estat ic command in Stata. - These are the logit coefficients expressing the relationship between
x1 x3
and u1 in the logit scale. Note that u1 is coded 0, 1, 2 and Mplus
converts those values into groups 1, 2 and 3 respectively. So these
coefficients represent the comparison of u1 for the first
level of u1 (i.e., 0) to the omitted level of u1 (i.e., 2).
These results parallel the results of the Stata mlogit command. - These are the logit coefficients expressing the relationship
between
x1 x3
and u1 in the logit scale. These coefficients represent the
comparison of u1 for the second
level of u1 (i.e., 1) to the omitted level of u1 (i.e., 2).
These results parallel the results of the Stata mlogit command. - These are the intercepts for the model, representing the intercepts
for the first and second levels of u1 (i.e., levels 0 and 1).