Zero-Truncated Count Regression

Zero-truncated count regression models counts that can only be observed when at least one event occurred, rescaling the Poisson or negative binomial probabilities by the probability of a nonzero count.

영절단 횟수 회귀는 사건이 한 번 이상 일어난 경우에만 관측되는 횟수를, 0이 아닐 확률로 포아송·음이항 확률을 나눠 모형화합니다.

My count data come only from people who had at least one visit; how should I model the number of visits?

방문 경험이 있는 사람만 조사해서 방문 횟수에 0이 없는데, 어떤 회귀모형을 써야 하나요?

A zero-truncated model uses P(Y = y | Y > 0) = f(y) / (1 - f(0)), so the regression describes the underlying event rate even though zeros were never recorded. Exponentiated coefficients are incidence-rate ratios for the untruncated mean, and a negative binomial version handles overdispersion.

When to use Zero-Truncated Count Regression

• Zeros are impossible by design, such as length of hospital stay or number of items bought by buyers.
• Ordinary Poisson regression would be biased because the sample excludes zero counts.
• You need to check whether a truncated negative binomial is needed for overdispersion.

When to use something else

• The data contain zeros; use Poisson, negative binomial, hurdle or zero-inflated models.
• The outcome is continuous and positive; use a gamma or log-normal regression.

Assumptions and requirements

• Counts are positive integers and zeros are unobservable, not merely rare.
• Independent observations with a log-linear mean.
• Equidispersion for the Poisson version (checked against the negative binomial).

What the analysis reports

• Coefficients with incidence-rate ratios and 95% CIs
• Log-likelihood, AIC and BIC
• Pearson dispersion and a boundary likelihood-ratio test for overdispersion
• Negative binomial dispersion parameter alpha when requested

How to report it

A zero-truncated Poisson regression of [outcome] (N = [value], AIC = [value]) showed that [predictor] had an incidence-rate ratio of [value], 95% CI [[value], [value]], p = [value].

Related methods

• Poisson Regression
• Hurdle and Two-Part Models
• Negative Binomial Regression

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