What does inflate mean in a ZINB model?

[KI student]

I am not sure what variable (predictor) to put in inflate( ) as I do not really understand the purpose if it?

The command desc is as follows:

Zero-inflated negative binomial model of y on x1 and x2 with inflation modeled using x3

zinb y x1 x2, inflate(x3)



Thanks in advance!

[Clyde Schechter]

Zero-inflation is used when the distribution of an outcome variable that you might otherwise analyze with a Poisson or negative binomial regression exhibits a large spike of zero values beyond what can be accommodated by the shape of the Poisson (or neg bin) distribution. In the zero-inflated commands, Stata will actually fit two separate regression models. The first will be a logistic regression model to predict which observations get a zero value for the dependent variable, and then the second equation is a Poisson (or, in your situation, negative binomial) regression model for the rest of the observations. In effect, it models your data as a mixture of two populations. One population is just going to have zero dependent variable, and the other follows a negative binomial model. The logistic equation assigns to each observation the probability it belongs in the former, and the negative binomial equation models the distribution for the latter.

The -inflate()- option in the -zinb- and -zip- commands allows you to specify variables as predictors of being in that 0-dependent variable component of the mix. As for what they should be, that derives from your understanding of what distinguishes the observations that contribute to the zero spike in the distribution from the ones that are just a plain-old neg-bin or Poisson distribution. That's a substantive question that only you, or colleagues in your discipline who are familiar with what you are studying can answer. By the way, sometimes you don't have to specify anything for -inflate()-: in that case you are modeling a constant probability for all observations to be part of the zero-spike.

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[Federico Tedeschi]

By the way, sometimes you don't have to specify anything for -inflate()-: in that case you are modeling a constant probability for all observations to be part of the zero-spike.

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In such case, I actually get the error message: "option inflate() required". However I get the desidered result through "inflate(_cons)".

[Clyde Schechter]

Thank you for pointing that out. You are correct; I phrased my response loosely. I meant to say the -inflate()- option is required, but you don't have to specify any variables in it--you can specify _cons only if that is appropriate.