## Stata 15 help for bayes_mepoisson

```
[BAYES] bayes: mepoisson -- Bayesian multilevel Poisson regression

Syntax

bayes [, bayesopts] : mepoisson depvar fe_equation [|| re_equation]
[|| re_equation ...] [, options]

where the syntax of fe_equation is

[indepvars] [if] [in] [weight] [, fe_options]

and the syntax of re_equation is one of the following:

for random coefficients and intercepts

levelvar: [varlist] [, re_options]

for a random effect among the values of a factor variable

levelvar: R.varname

levelvar either is a variable identifying the group structure for the
random effects at that level or is _all, representing one group
comprising all observations.

fe_options               Description
-------------------------------------------------------------------------
Model
noconstant             suppress constant term from the fixed-effects
equation
exposure(varname_e)    include ln(varname_e) in model with coefficient
constrained to 1
offset(varname_o)      include varname_o in model with coefficient
constrained to 1
-------------------------------------------------------------------------

re_options               Description
-------------------------------------------------------------------------
Model
covariance(vartype)    variance-covariance structure of the random
effects; only structures independent,
identity, and unstructured supported
noconstant             suppress constant term from the random-effects
equation
-------------------------------------------------------------------------

options                  Description
-------------------------------------------------------------------------
Model
collinear              keep collinear variables

Reporting
irr                    report incidence-rate ratios
notable                suppress coefficient table
nogroup                suppress table summarizing groups
display_options        control spacing, line width, and base and empty
cells

level(#)               set credible level; default is level(95)
-------------------------------------------------------------------------
indepvars may contain factor variables; see fvvarlist.
depvar, indepvars, and varlist may contain time-series operators; see
tsvarlist.
fweights are allowed; see weight.
bayes: mepoisson, level() is equivalent to bayes, clevel(): mepoisson.
For a detailed description of options, see Options in [ME] mepoisson.

bayesopts                       Description
-------------------------------------------------------------------------
Priors
* normalprior(#)                specify standard deviation of default
normal priors for regression
coefficients; default is
normalprior(100)
* igammaprior(# #)              specify shape and scale of default
inverse-gamma prior for variance
components; default is igammaprior(0.01
0.01)
* iwishartprior(# [...])        specify degrees of freedom and,
optionally, scale matrix of default
inverse-Wishart prior for unstructured
random-effects covariance

prior(priorspec)              prior for model parameters; this option
may be repeated
dryrun                        show model summary without estimation

Simulation
mcmcsize(#)                   MCMC sample size; default is
mcmcsize(10000)
burnin(#)                     burn-in period; default is burnin(2500)
thinning(#)                   thinning interval; default is thinning(1)
rseed(#)                      random-number seed
exclude(paramref)             specify model parameters to be excluded
from the simulation results
restubs(restub1 restub2 ...)  specify stubs for random-effects
parameters for all levels

Blocking
* blocksize(#)                  maximum block size; default is
blocksize(50)
block(paramref[, blockopts])  specify a block of model parameters; this
option may be repeated
blocksummary                  display block summary

* noblocking                    do not block parameters by default

Initialization
initial(initspec)             initial values for model parameters
nomleinitial                  suppress the use of maximum likelihood
estimates as starting values
initrandom                    specify random initial values
initsummary                   display initial values used for
simulation
* noisily                       display output from the estimation
command during initialization

scale(#)                      initial multiplier for scale factor;
default is scale(2.38)
covariance(cov)               initial proposal covariance; default is
the identity matrix

Reporting

clevel(#)                     set credible interval level; default is
clevel(95)
hpd                           display HPD credible intervals instead of
the default equal-tailed credible
intervals
* irr                           report incidence-rate ratios
eform[(string)]               report exponentiated coefficients and,
optionally, label as string
remargl                       compute log marginal likelihood
batch(#)                      specify length of block for batch-means
calculations; default is batch(0)
saving(filename[, replace])   save simulation results to filename.dta
nomodelsummary                suppress model summary
nomesummary                   suppress multilevel-structure summary
[no]dots                      suppress dots or display dots every 100
iterations and iteration numbers every
1,000 iterations; default is dots
dots(#[, every(#)])           display dots as simulation is performed
[no]show(paramref)            specify model parameters to be excluded
from or included in the output
showreffects[(reref)]         specify that all or a subset of
random-effects parameters be included
in the output
melabel                       display estimation table using the same
row labels as mepoisson
nogroup                       suppress table summarizing groups
notable                       suppress estimation table
title(string)                 display string as title above the table
of parameter estimates
display_options               control spacing, line width, and base and
empty cells

search(search_options)        control the search for feasible initial
values
corrlag(#)                    specify maximum autocorrelation lag;
default varies
corrtol(#)                    specify autocorrelation tolerance;
default is corrtol(0.01)
-------------------------------------------------------------------------
* Starred options are specific to the bayes prefix; other options are
common between bayes and bayesmh.
Options prior() and block() can be repeated.
priorspec and paramref are defined in [BAYES] bayesmh.
paramref may contain factor variables; see fvvarlist.
See [BAYES] bayesian postestimation for features available after
estimation.
Model parameters are regression coefficients {depvar:indepvars}, random
effects {rename}, and either variance components {rename:sigma2} or, if
option covariance(unstructured) is specified, matrix parameter
{restub:Sigma,matrix}; see Likelihood model in [BAYES] bayes for how
renames and restub are defined.  Use the dryrun option to see the
definitions of model parameters prior to estimation.
For a detailed description of bayesopts, see Options in [BAYES] bayes.

Statistics > Multilevel mixed-effects models > Bayesian regression >
Poisson regression

Description

bayes: mepoisson fits a Bayesian multilevel Poisson regression to a
nonnegative count outcome; see [BAYES] bayes and [ME] mepoisson for
details.

Examples

Setup
. webuse melanoma

Fit Bayesian two-level Poisson regression with random intercepts by
region using default priors
. bayes: mepoisson deaths uv, exposure(expected) || region:

Increase the burn-in period to 5,000 from the default of 2,500; use
standard deviation of 10 of the default normal prior for regression
coefficients; and specify random-number seed for reproducibility
. bayes, burnin(5000) normalprior(10) rseed(123): mepoisson deaths
uv, exposure(expected) || region:

Display incidence-rate ratios instead of coefficients
. bayes, irr

In addition to the main model parameters, display results for regions 1
through 5
. bayes, showreffects({U0[(1/5).region]})

Check MCMC convergence for the main model parameters and the 1st, 10th,
and 15th random effects
. bayesgraph diagnostics _all, showreffects({U0[1 10 15]})

Plot histograms of posterior distributions of the first 12 random effects
on one graph
. bayesgraph histogram {U0[1/12]}, byparm

Display estimation results using mepoisson's parameter labels and compute
log marginal likelihood on replay
. bayes, melabel remargl

Fit Bayesian three-level Poisson regression with random intercepts by
nation and by region nested within nation
. bayes: mepoisson deaths uv, exposure(expected) || nation: ||
region:

Save MCMC results on replay
. bayes, saving(mymcmc)

Stored results

See Stored results in [BAYES] bayesmh.

```