`I should like to make you aware of two statistical commands that Kit
``was kind enough to place on the SSC website for me. One was placed
``several weeks ago, the other yesterday.
` TPOISSON - truncated Poisson regression

` Program allows one to left or right truncate the response of a
``Poisson model, or truncation can be
`` made to both sides in the same model. Full Stata maximum
``likelihood options are available; eg survey,
` bootstrap, etc
CPOISSONE - censored Poisson (econometric parameterization)

` Program allows both left and right censoring of a Poisson model,
``or censoring can be made to both
`` sides in the same model. I differentiated between two types of
``censored Poisson models in my
`` book, "Negative Binomial Regression" (2007, Cambridge University
``Press).
`

` In the mid 1990s I wrote a censored Poisson as a SAS macro
``(still published on the SAS Library site),
`` then a year later Dean Judson and I wrote a censored Poisson for
``the Stata Technical Bulletin. I later
`` revised it, and did so again in 2005. That version of a censored
``Poisson let any observation value be
`` censored, and was parameterized as censoring occurs in survival
``models. This differs from the
`` parameterization that has been common in econometric literature,
``where censoring occurs only at the
`` tails of the response distribution. That is, left censoring,
``like left truncation, can occur at time=3, with
`` all observations below 3 being censored. Likewise for right
``censoring; all values over a specified cut
`` point are censored. It is similar to truncation, except that it
``differs on how censored observations are
`` valued. In econometric censoring, censored values are recorded
``as the value of the cut point.
`` In truncation, the truncated values are dropped from
``contributing to the model, but the LL function is
` adjusted to still sum to 1.

`The previous survival parameterization of censored Poisson is on the
``SSC site as CPOISSON. The econometric parameterization of censored
``Poisson is CPOISSONE, and truncated Poisson is TPOISSON. I am planning
``to prepare econometric parameterized censored negative binomial and
``truncated negative binomial commands next. I already have a survival
``censored negative binomial on SSC called CENSORNB, posted in 2005.
`
Joseph Hilbe
hilbe@asu.edu
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