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 x3Iteration 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 | .7686261.1567749 4.90 0.000 .461353 1.075899 x3 | 2.259422^{C}.2144306 10.54 0.000 1.839146 2.679699 _cons | -.7488877^{C}.1702198 -4.40 0.000 -1.082512 -.4152631 -------------+---------------------------------------------------------------- 1 | x1 | .2798667^{E}.1131474 2.47 0.013 .0581018 .5016316 x3 | .885101^{D}.1402897 6.31 0.000 .6101382 1.160064 _cons | .2622508^{D}.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 -433.4263^{E}6 878.8526^{A}904.1402^{B}------------------------------------------------------------------------------^{B}

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 -433.426Information Criteria Number of Free Parameters 6 Akaike (AIC) 878.853^{A}Bayesian (BIC) 904.140^{B}Sample-Size Adjusted BIC 885.096 (n* = (n + 2) / 24) MODEL RESULTS Estimates S.E. Est./S.E. U1#1 ON X1 0.769^{B}0.165 4.670 X3 2.259^{C}0.203 11.148 U1#2 ON X1 0.280^{C}0.114 2.444 X3 0.885^{D}0.143 6.200 Intercepts U1#1 -0.749^{D}0.158 -4.728 U1#2 0.262^{E}0.120 2.192^{E}

- 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).