This page shows an example of 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 3.5) 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.

**Example Using Stata**

Here is a 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/ex3.5.dat, clear

tabulate u1u1 | Freq. Percent Cum. ------------+----------------------------------- 0 | 327 65.4065.40 1 | 173 34.60^{A}100.00 ------------+----------------------------------- Total | 500 100.00^{A}

A. These are the percent of cases with 0 and 1 on the variable **u1**

logit u1 x1 x3Iteration 0: log likelihood = -322.46763 Iteration 1: log likelihood = -216.57883 Iteration 2: log likelihood = -203.79479 Iteration 3: log likelihood = -202.63515 Iteration 4: log likelihood = -202.61995 Iteration 5: log likelihood = -202.61995 Logistic regression Number of obs = 500 LR chi2(2) = 239.70 Prob > chi2 = 0.0000 Log likelihood = -202.61995 Pseudo R2 = 0.3717 ------------------------------------------------------------------------------ u1 | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- x1 | 1.071767.1428573 7.50 0.000 .791772 1.351762 x3 | 1.838588^{E}.1794923 10.24 0.000 1.486789 2.190386 _cons | -1.025842^{E}.1369173 -7.49 0.000 -1.294195 -.7574886 ------------------------------------------------------------------------------^{D}

logit , orLogistic regression Number of obs = 500 LR chi2(2) = 239.70 Prob > chi2 = 0.0000 Log likelihood = -202.61995 Pseudo R2 = 0.3717 ------------------------------------------------------------------------------ u1 | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- x1 | 2.920536.4172198 7.50 0.000 2.207304 3.864229 x3 | 6.287652^{F}1.128585 10.24 0.000 4.422872 8.938663 ------------------------------------------------------------------------------^{F}

estat ic------------------------------------------------------------------------------ Model | Obs ll(null) ll(model)df AIC^{B}BIC^{C}-------------+---------------------------------------------------------------- . | 500 -322.4676 -202.6199 3 411.2399 423.8837 ------------------------------------------------------------------------------^{C}

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** x2, **are
significantly related to the outcome variable, **u1**. The coefficients from
the **logit** output can be exponentiated to obtain odds ratios, as shown in
the output from the **logit, or** command. For a one unit increase in **x1**,
the odds of **u1** equaling 1 (as compared to **u1** equaling 0) increases
by a factor of 2.92. 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 #1**

Here is the same example illustrated in Mplus based on the https://stats.idre.ucla.edu/wp-content/uploads/2016/02/ex3.5.dat data file.

TITLE: this is an example of a logistic regression for a categorical observed dependent variable with two covariates DATA: FILE = https://stats.idre.ucla.edu/wp-content/uploads/2016/02/ex3.5.dat; VARIABLE: NAMES = u1 x1 x3; CATEGORICAL = u1; ANALYSIS: ESTIMATOR = ML; ! need to use estimator = ml to make this a logistic model; MODEL: u1 ON x1 x3;SUMMARY OF ANALYSIS Number of observations 500 Estimator MLR <some output was omitted to save space> SUMMARY OF CATEGORICAL DATA PROPORTIONS U1 Category 1 0.654Category 2 0.346^{A}TESTS OF MODEL FIT Loglikelihood H0 Value -202.620^{A}Information Criteria Number of Free Parameters 3 Akaike (AIC) 411.240^{B}Bayesian (BIC) 423.884^{C}Sample-Size Adjusted BIC 414.362 (n* = (n + 2) / 24)^{C}

MODEL RESULTS Estimates S.E. Est./S.E. U1 ON X1 1.072^{D}0.143 7.502 X3 1.839^{D}0.179 10.243 Thresholds U1$1 1.026^{E}0.137 7.492 LOGISTIC REGRESSION ODDS RATIO RESULTS U1 ON X1 2.921^{F}X3 6.288^{F}

- These are the percent of cases with 0 and 1 on the variable
**u1**, see output of**tabulate**command from Stata - 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 x2**and**u1**in the logit scale, corresponding to the results of the Stata**logit**command. This is followed by the S.E. column (standard error) and the estimate divided by the standard error (Est./S.E). This final column is used for assessing significance by treating this like a Z test. - A logit model can incorporate either an intercept or a threshold in the
model. Mplus uses a threshold (which Stata uses for ordinal models and calls
them cutpoints). If you replaced the Stata
**logit**command with**ologit**you would get the same threshold value as shown in Mplus. - These are the exponentiated logit coefficients, aka the odds ratios. These
correspond to the values shown by the
**logit, or**command in Stata.

**Mplus Example #2**

Here is another version of this example in Mplus. Note that by using**
estimator=ml; **(maximum likelihood) the results are shown in a logit metric.
Had we specified something like **estimator=wls; **(weighted least squares)
then the results would be shown in a probit scale. Because this analysis does
not use the **type=logistic **option (unlike example #1), the format of the
output is somewhat different (notably omitting odds ratios from the output).

TITLE: this is an example of a logistic regression for a categorical observed dependent variable with two covariates. DATA: FILE = https://stats.idre.ucla.edu/wp-content/uploads/2016/02/ex3.5.dat; VARIABLE: NAMES = u1 x1 x3; CATEGORICAL = u1; ! note using Maximum Likelihood produces results in Logit scale ! using GLS produces results in Probit scale analysis: estimator=ml; MODEL: u1 ON x1 x3;SUMMARY OF ANALYSIS Number of observations 500 Estimator ML <some output omitted to save space> SUMMARY OF CATEGORICAL DATA PROPORTIONS U1 Category 1 0.654Category 2 0.346^{A}THE MODEL ESTIMATION TERMINATED NORMALLY TESTS OF MODEL FIT Loglikelihood H0 Value -202.620^{A}Information Criteria Number of Free Parameters 3 Akaike (AIC) 411.240^{B}Bayesian (BIC) 423.884^{C}Sample-Size Adjusted BIC 414.362 (n* = (n + 2) / 24) MODEL RESULTS Estimates S.E. Est./S.E. U1 ON X1 1.072^{C}0.143 7.503 X3 1.839^{E}0.179 10.245 Thresholds U1$1 1.026^{E}0.137 7.493^{D}

- These are the percent of cases with 0 and 1 on the variable
**u1**, see output of**tabulate**command from Stata - 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. - A logit model can incorporate either an intercept or a threshold in the
model. Mplus uses a threshold (which Stata uses for ordinal models and calls
them cutpoints). If you replaced the Stata
**logit**command with**ologit**you would get the same threshold value as shown in Mplus. - These are the logit coefficients expressing the relationship between
**x1 x2**and**u1**in the logit scale, corresponding to the results of the Stata**logit**command. You would need to exponentiate these values to convert them into odds ratios. This is followed by the S.E. column (standard error) and the estimate divided by the standard error (Est./S.E). This final column is used for assessing significance by treating this like a Z test.