**[R] poisson postestimation** -- Postestimation tools for poisson

__Postestimation commands__

The following postestimation command is of special interest after
**poisson**:

Command Description
-------------------------------------------------------------------------
**estat gof** goodness-of-fit test
-------------------------------------------------------------------------
**estat gof** is not appropriate after the **svy** prefix.

The following standard postestimation commands are also available:

Command Description
-------------------------------------------------------------------------
**contrast** contrasts and ANOVA-style joint tests of estimates
**estat ic** Akaike's and Schwarz's Bayesian information criteria
(AIC and BIC)
**estat summarize** summary statistics for the estimation sample
**estat vce** variance-covariance matrix of the estimators (VCE)
**estat** (svy) postestimation statistics for survey data
**estimates** cataloging estimation results
* **forecast** dynamic forecasts and simulations
* **hausman** Hausman's specification test
**lincom** point estimates, standard errors, testing, and
inference for linear combinations of coefficients
**linktest** link test for model specification
* **lrtest** likelihood-ratio test
**margins** marginal means, predictive margins, marginal effects,
and average marginal effects
**marginsplot** graph the results from margins (profile plots,
interaction plots, etc.)
**nlcom** point estimates, standard errors, testing, and
inference for nonlinear combinations of coefficients
**predict** predictions, residuals, influence statistics, and
other diagnostic measures
**predictnl** point estimates, standard errors, testing, and
inference for generalized predictions
**pwcompare** pairwise comparisons of estimates
**suest** seemingly unrelated estimation
**test** Wald tests of simple and composite linear hypotheses
**testnl** Wald tests of nonlinear hypotheses
-------------------------------------------------------------------------
* **forecast**, **hausman**, and **lrtest** are not appropriate with **svy** estimation
results. **forecast** is also not appropriate with **mi** estimation results.

__Syntax for predict__

**predict** [*type*] *newvar* [*if*] [*in*] [**,** *statistic* __nooff__**set**]

*statistic* Description
-------------------------------------------------------------------------
Main
**n** number of events; the default
**ir** incidence rate
**pr(***n***)** probability Pr(y = n)
**pr(***a***,***b***)** probability Pr(a __<__ y __<__ b)
**xb** linear prediction
**stdp** standard error of the linear prediction
__sc__**ore** first derivative of the log likelihood with respect to
xb
-------------------------------------------------------------------------
These statistics are available both in and out of sample; type **predict**
*...* **if e(sample)** *...* if wanted only for the estimation sample.

__Menu for predict__

**Statistics > Postestimation**

__Description for predict__

**predict** creates a new variable containing predictions such as numbers of
events, incidence rates, probabilities, linear predictions, standard
errors, and equation-level scores.

__Options for predict__

+------+
----+ Main +-------------------------------------------------------------

**n**, the default, calculates the predicted number of events, which is
exp(xb) if neither **offset()** nor **exposure()** was specified when the
model was fit;
exp(xb + offset) if **offset()** was specified; or
exp(xb)*exposure if **exposure()** was specified.

**ir** calculates the incidence rate exp(xb), which is the predicted number
of events when exposure is 1. Specifying **ir** is equivalent to
specifying **n** when neither **offset()** nor **exposure()** was specified when
the model was fit.

**pr(***n***)** calculates the probability Pr(y = n), where n is a nonnegative
integer that may be specified as a number or a variable.

**pr(***a***,***b***)** calculates the probability Pr(a __<__ y __<__ b), where a and b are
nonnegative integers that may be specified as numbers or variables;

b missing (b __>__ .) means plus infinity;
**pr(20,.)** calculates Pr(y __>__ 20);
**pr(20,***b***)** calculates Pr(y __>__ 20) in observations for which b __>__ .
and calculates Pr(20 __<__ y __<__ b) elsewhere.

**pr(.,***b***)** produces a syntax error. A missing value in an observation
of the variable *a* causes a missing value in that observation for
**pr(***a***,***b***)**.

**xb** calculates the linear prediction, which is xb if neither **offset()** nor
**exposure()** was specified; xb + offset if **offset()** was specified; or
xb + ln(exposure) if **exposure()** was specified; see **nooffset** below.

**stdp** calculates the standard error of the linear prediction.

**score** calculates the equation-level score, the derivative of the log
likelihood with respect to the linear prediction.

**nooffset** is relevant only if you specified **offset()** or **exposure()** when
you fit the model. It modifies the calculations made by **predict** so
that they ignore the offset or exposure variable; the linear
prediction is treated as xb rather than xb + offset or xb +
ln(exposure). Specifying **predict** ...**,** **nooffset** is equivalent to
specifying **predict** ...**,** **ir**.

__Syntax for margins__

**margins** [*marginlist*] [**,** *options*]

**margins** [*marginlist*] **,** __pr__**edict(***statistic *...**)** [__pr__**edict(***statistic *...**)**
...] [*options*]

*statistic* Description
-------------------------------------------------------------------------
**n** number of events; the default
**ir** incidence rate
**pr(***n***)** probability Pr(y = n)
**pr(***a***,***b***)** probability Pr(a __<__ y __<__ b)
**xb** linear prediction
**stdp** not allowed with **margins**
__sc__**ore** not allowed with **margins**
-------------------------------------------------------------------------

Statistics not allowed with **margins** are functions of stochastic
quantities other than **e(b)**.

For the full syntax, see **[R] margins**.

__Menu for margins__

**Statistics > Postestimation**

__Description for margins__

**margins** estimates margins of response for numbers of events, incidence
rates, probabilities, and linear predictions.

__Syntax for estat__

**estat gof**

__Menu for estat__

**Statistics > Postestimation**

__Description for estat__

**estat gof** performs a goodness-of-fit test of the model. Both the
deviance statistic and the Pearson statistic are reported. If the tests
are significant, the Poisson regression model is inappropriate. Then you
could try a negative binomial model; see **[R] nbreg**.

__Examples__

Setup
**. webuse dollhill3**
**. poisson deaths i.smokes i.agecat, exp(pyears)**

Predict incidence rate
**. predict deathrate, ir**

Estimate incidence rates and standard errors
**. margins agecat#smokes, predict(ir)**

Plot estimates and confidence intervals
**. marginsplot**

Goodness-of-fit tests
**. estat gof**

__Stored results__

**estat gof** after **poisson** stores the following in **r()**:

Scalars
**r(df)** degrees of freedom (Pearson and deviance)
**r(chi2_p)** chi-squared (Pearson)
**r(chi2_d)** chi-squared (deviance)
**r(p_p)** p-value for chi-squared test (Pearson)
**r(p_d)** p-value for chi-squared test (deviance)