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The title of my question says pretty much what I'm struggling to understand: What is the difference between a Zero-inflated negative binomial (ZINB) regression and a Heckman-two-step regression model? I get that the ZINB is for count data and the Heckit model usually goes with censored data. I still don't understand the difference. Both account for an overinflation of 0 and allow the calculation for the probability of getting a 0 on the dependent variable.

Are there advantages and disadvantages (especially when dealing with development aid data)?

I would greatly appreciate any explanation!

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  • $\begingroup$ can you provide a link to a description of the Heckmann-two-step regression model? I only find sources that refer to the Heckman Two-Step Correction for Selection Bias which is quite obviously something else than a negative-binomial regression. $\endgroup$ – LuckyPal Dec 10 '19 at 13:02
  • $\begingroup$ Its also known as Heckit model -> its a generalization of a Tobit model if I understood that correctly. $\endgroup$ – H.Stevens Dec 10 '19 at 13:04
  • $\begingroup$ Never heard of "Heckit". But to the question, the Heckman two-stage model, which uses a logistic or probit binary model in the first stage, allows for arbitrary clumping at zero. Zero-inflated single models can only inflate P(zero) so much. $\endgroup$ – Frank Harrell Dec 10 '19 at 13:30
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Basically, the Heckit model is supposed to model data that is zero-inflated due to sample bias while the distribution of the population is not zero-inflated, while the zero-inflated negative binomial regression is used if the true distribution of the population is actually zero-inflated. As a conclusion, the Heckit model and the zero-inflated negative binomial regression are not alternatives to each other but suitable for completely different situations.

The following two citations nicely wrap this up:

Theoretically the standard Tobit model is applicable only if the underlying dependent variable contains negative values that have been censored to zero in the empirical realization of the variable. In practice, though, the Tobit modelis routinely employed when the values of the observed dependent variable are exclusively nonnegative and are clustered at zero, irrespective of whether any censoring has occurred. The Heckit model has emerged as the de facto default alternative to Tobit when values cluster at zero due to selection bias rather than censoring, but applications of the Heckit model have proven problematic as well.

Sigelman, L., & Zeng, L. (1999). Analyzing Censored and Sample-Selected Data with Tobit and Heckit Models. Political Analysis, 8(2), 167-182. doi:10.1093/oxfordjournals.pan.a029811

The zero-inflated negative binomial (ZINB) regression is used for count data that exhibit overdispersion and excess zeros. The data distribution combines the negative binomial distribution and the logit distribution. The possible values of Y are the nonnegative integers: 0, 1, 2, 3, and so on.

From the NCSS Statistical Software (Developers of PASS Sample Size) Chapter 328. Link.

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