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In Bayesian analysis, we seek a balance between prior information in a form of expert knowledge
or belief and evidence from data at hand. Achieving the right balance is one of the difficulties in
Bayesian modeling and inference. In general, we should not allow the prior information to overwhelm
the evidence from the data, especially when we have a large data sample. A famous theoretical
result, the Bernstein–von Mises theorem, states that in large data samples, the posterior distribution is
independent of the prior distribution and, therefore, Bayesian and likelihood-based inferences should
yield essentially the same results. On the other hand, we need a strong enough prior to support weak
evidence that usually comes from insufficient data. It is always good practice to perform sensitivity
analysis to check the dependence of the results on the choice of a prior.

Posterior / Likelihood Prior
If the posterior distribution can be derived in a closed form, we may proceed directly to the
inference stage of Bayesian analysis. Unfortunately, except for some special models, the posterior
distribution is rarely available explicitly and needs to be estimated via simulations. MCMC sampling
can be used to simulate potentially very complex posterior models with an arbitrary level of precision.
MCMC methods for simulating Bayesian models are often demanding in terms of specifying an efficient
sampling algorithm and verifying the convergence of the algorithm to the desired posterior distribution.
Inference is the next step of Bayesian analysis. If MCMC sampling is used for approximating the
posterior distribution, the convergence of MCMC must be established before proceeding to inference.
Point and interval estimators are either derived from the theoretical posterior distribution or estimated
from a sample simulated from the posterior distribution. Many Bayesian estimators, such as posterior

Multiple-group IRT models in Stata
IRT models explore the relationship between a latent (unobserved) trait and items that measure aspects of the trait. This often arises in standardized testing where the trait of interest is ability, such as mathematical ability. A set of items (test questions) is designed, and the responses measure this unobserved trait. Researchers in education, psychology, and health frequently fit IRT models.
Stata’s irt commands fit 1-, 2-, and 3-parameter logistic models. They also fit graded response, nominal response, partial credit, and rating scale models, and any combination of them. And after fitting a model, irtgraph graphs item-characteristic curves, test characteristic curves, item information functions, and test information functions.
New in Stata 16, the irt commands allow comparisons across groups. Take any of the existing irt commands, add a group(varname) option, and fit the corresponding multiple-group model. For instance, type
. irt 2pl item1-item10, group(female)
and fit a two-group 2PL model.
Group-specific means and variances of the latent trait will be estimated. Group-specific difficulty and discrimination parameters can also be estimated for one or more items. With constraints, you can specify exactly which parameters are allowed to vary and which parameters are constrained to be equal across groups.
You can even use likelihood-ratio tests to compare models with and without constraints to perform an IRT model-based test of differential item functioning.

Stata 16版本更新22条新功能。比以往的版本更强大,更值得您拥有。
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