Education 231C

Applied Categorical & Nonnormal Data Analysis

Zero-truncated Count Models

In this unit we will encounter the opposite situation from the zero-inflated models, we will look at data that have no zeros, the so called zero-truncated models. If one tries to use standard poisson or negative binomial analysis with these kinds of data the procedures try to fit the models by including probabilities for zero values. One should be able to produce more accurate models by using a probability model that does not include the zero values.

We will illustrate zero-truncated count models examining length of hospital stay (los) from the 1997 MedPar dataset. Length of stay does not and cannot have any zero values. Length of stay begins with a value of one and grows from there.

Stata 9 introduced two new commands ztp for zero-truncated poisson and ztnb for zero-truncated negative binomial. We will use both of these commands in this unit.

Note: The commands trpois0 and trnbin0 ado's and the medpar dataset were taken from a Stata Technical article (STB-47, January 1999) by Joseph Hilbe of Arizona State University can be used with Stata 8 and below.

Looking at the Data

The response variable in this example is length of hospital stay. With length of hospital stay, regardless of how little time is spent in the hospital, patients are credited as having at least one day.

Tricking Stata

Its clear from the nbvargr that neither the poisson and negative binomial distributions fit the observed data very well. Also, the negative binomial distribution expects that there will be some (approximately 40) zero values.

We will run standard poisson and negative binomial regressions and then we will trick Stata by subtracting one from the value of length of stay and rerunning these models.

The negative binomial regression with the trick is only slightly better and the poisson regression with the trick is actually worse.

Zero-truncated Poisson

We will begin the zero-truncated models with a zero-truncated poisson regression even though it is unlikely that a poisson distribution will be appropriate for these data since the mean and variance of los are nowhere near equal.

Zero-truncated Negative Binomial

The zero-truncated models provided only a slight improvement over the negative binomial with the subtraction trick and also slightly better for than the standrad poisson regression.

In the final analysis, the predicted counts 't seem to match the observed counts only moderately well. This may be due, in part, to the fact that there are only eight different covariate patterns among the predictors, one of which, was not significant.

Categorical Data Analysis Course

Phil Ender 6dec05