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Frequentist inference is based on the sampling distributions of estimators of parameters and provides
parameter point estimates and their standard errors as well as confidence intervals. The exact sampling
distributions are rarely known and are often approximated by a large-sample normal distribution.
Bayesian inference is based on the posterior distribution of the parameters and provides summaries of
this distribution including posterior means and their MCMC standard errors (MCSE) as well as credible
intervals. Although exact posterior distributions are known only in a number of cases, general posterior
distributions can be estimated via, for example, Markov chain Monte Carlo (MCMC) sampling without
any large-sample approximation.
Frequentist confidence intervals do not have straightforward probabilistic interpretations as do
Bayesian credible intervals. For example, the interpretation of a 95% confidence interval is that if
we repeat the same experiment many times and compute confidence intervals for each experiment,
then 95% of those intervals will contain the true value of the parameter. For any given confidence
interval, the probability that the true value is in that interval is either zero or one, and we do not
know which. We may only infer that any given confidence interval provides a plausible range for the
true value of the parameter. A 95% Bayesian credible interval, on the other hand, provides a range
for a parameter such that the probability that the parameter lies in that range is 95%.

summarize shows that the new variable has a mean of approximately zero; 10��9 is the precision of
a float and is close enough to zero for all practical purposes. If we wanted, we could have typed
egen double stdage = std(age), making stdage a double-precision variable, and the mean would
have been 10��16. In any case, summarize also shows that the standard deviation is 1. correlate
shows that the new variable and the original variable are perfectly correlated.

In Stata 16, we introduce a new, unified suite of commands for modeling choice data. We have added new commands for summarizing choice data. We renamed and improved existing commands for fitting choice models. We even added a new command for fitting mixed logit models for panel data. And we document them together in the new Choice Models Reference Manual.
And here’s the best part: margins now works after fitting choice models. This means you can now easily interpret the results of your choice models. While the coefficients estimated in choice models are often almost uninterpretable, margins allows you to ask and answer very specific questions based on your results. Say that you are modeling choice of transportation. You can answer questions such as
• What proportion of travelers are expected to choose air travel?
• How does the probability of traveling by car change for each additional $10,000 in income?
• If wait times at the airport increase by 30 minutes, how does this affect the choice of each mode of transportation?
What else is new? You now cmset your data before fitting a choice model. For instance,
. cmset personid transportmethod
Then, you use cmsummarize, cmchoiceset, cmtab, and cmsample to explore, summarize, and look for potential problems in your data.
And you use cm estimation commands to fit one of the following choice models:
• cmclogit conditional logit (McFadden’s choice) model
• cmmixlogit mixed logit model
• cmxtmixlogit panel-data mixed logit model
• cmmprobit multinomial probit model
• cmroprobit rank-ordered probit model
• cmrologit rank-ordered logit model
Unlike the others, cmxtmixlogit is not renamed and improved. It is completely new in Stata 16, and

Stata 16 Feature highlights:
1. Lasso
2. Reporting
3. Meta-analysis
4. Choice models
5. Python integration
6. New in Bayesian analysis—Multiple chains, predictions, and more
7. Panel-data ERMs
8. Import data from SAS and SPSS
9. Nonparametric series regression
10. Multiple datasets in memory
11. Sample-size analysis for confidence intervals
12. Nonlinear DSGE models
13. Multiple-group IRT models
14. xtheckman
15. Multiple-dose pharmacokinetic modeling
16. Heteroskedastic ordered probit models
17. Graph sizes in printer points, centimeters, and inches
18. Numerical integration
19. Linear programming
20. Stata in Korean
21. Mac interface now supports Dark Mode and native tabbed windows
22. Do-file Editor—Autocompletion and more syntax highlighting
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