# Questions tagged [zero-inflation]

Excessive 0's in a variable compared to a specified reference distribution. Regression approaches include zero-inflated models and hurdle (2-part) models. For count data, zero-inflated and hurdle models based on Poisson or negative binomial distributions are common (ZIP/ZINB and HP/HNB).

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### Diagnostic plots for count regression

What diagnostic plots (and perhaps formal tests) do you find most informative for regressions where the outcome is a count variable? I'm especially interested in Poisson and negative binomial models, ...
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### What is the difference between zero-inflated and hurdle models?

I wonder if there is a clear-cut difference between the so-called zero-inflated distributions (models) and so-called hurdle-at-zero distributions (models)? The terms occur quite often in the ...
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### Is a “hurdle model” really one model? Or just two separate, sequential models?

Consider a hurdle model predicting count data y from a normal predictor x: ...
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### When to use Poisson vs. geometric vs. negative binomial GLMs for count data?

I'm trying to layout for myself when it's appropriate to use which regression type (geometric, Poisson, negative binomial) with count data, within the GLM framework (only 3 of the 8 GLM distributions ...
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### Dealing with 0,1 values in a beta regression

I have some data in [0,1] which I would like to analyze with a beta regression. Of course something needs to be done to accommodate the 0,1 values. I dislike modifying data to fit a model. also I ...
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### Beta regression of proportion data including 1 and 0

I am trying to produce a model for which I have a response variable which is a proportion between 0 and 1, this includes quite a few 0s and 1s but also many values in between. I am thinking about ...
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### Why exactly can't beta regression deal with 0s and 1s in the response variable?

Beta regression (i.e. GLM with beta distribution and usually the logit link function) is often recommended to deal with response aka dependent variable taking values between 0 and 1, such as fractions,...
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### Zero-inflated negative binomial mixed-effects model in R

Is there such a package that provides for zero-inflated negative binomial mixed-effects model estimation in R? By that I mean: Zero-inflation where you can specify the binomial model for zero ...
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### Fitting custom distributions by MLE

My question relates to fitting custom distributions in R but I feel it has enough of a probability element to remain on CV. I have an interesting set of data which has the following characteristics: ...
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### How to model non-negative zero-inflated continuous data?

I'm currently trying to apply a linear model (family = gaussian) to an indicator of biodiversity that cannot take values lower than zero, is zero-inflated and is ...
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### Can a model for non-negative data with clumping at zeros (Tweedie GLM, zero-inflated GLM, etc.) predict exact zeros?

A Tweedie distribution can model skewed data with a point mass at zero when the parameter $p$ (exponent in the mean-variance relationship) is between 1 and 2. Similarly a zero-inflated (whether ...
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### Zero inflated distributions, what are they really?

I am struggling to understand zero inflated distributions. What are they? What's the point? If I have data with many zeroes, then I could fit a logistic regression first calculate the probability of ...
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### GLM with continuous data piled up at zero

I am trying to run a model to estimate how well catastrophic illnesses such as TB, AIDS etc affect spending on hospitalization. I have "per hospitalization cost" as the dependent variable and various ...
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### Poisson regression assumptions and how to test them in R

I would like to test in what regression fits my data best. My dependent variable is a count, and has a lot of zeros. And I would need some help to determine what model and family to use (poisson or ...
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### Proper use and interpretation of zero-inflated gamma models

Background: I am a biostatistician presently wrestling with a dataset of cellular expression rates. The study exposed a host of cells, collected in groups from various donors, to certain peptides. ...
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### Measure of “deviance” for zero-inflated Poisson or zero-inflated negative binomial?

Scaled deviance, defined as D = 2 * (log-likelihood of saturated model minus log-likelihood of fitted model), is often used as a measure of goodness-of-fit in GLM models. Percent deviance explained, ...
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### Gamma hurdle model for continuous response

I am modelling invertebrate.biomass ~ habitat.type * calendar.day + habitat.type * calendar.day ^ 2, with a random intercept of transect.id (50 transects were repeated 5 times) My response is zero-...
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### GAMM with zero-inflated data

Is it possible to fit a GAMM(Generalized Additive Mixed Model) for zero-inflated data in R? If not, is it possible to fit a GAM(Generalized Additive Model) for zero-inflated data with a negative ...
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### Are a zero-truncated Poisson and basic Poisson nested or non-nested?

I've seen plenty that discusses whether a basic Poisson regression is a nested version of a zero-inflated Poisson regression. For instance this site argues that it is, since the latter includes extra ...
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### How to test/prove data is zero inflated?

I've got a problem that I think should be simple but can't quite figure it out. I'm looking at seed pollination, I have plants (n=36) that flower in clusters, I sample 3 flower clusters from each ...
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### How to get standard errors from R zero-inflated count data regression? [closed]

The following code PredictNew <- predict (glm.fit, newdata = Predict, X1 =X1, Y1= Y1, type = "response", se.fit = TRUE) produces a 3-...
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### Why are there no one-inflated count data models?

I am working on zero-inflated count data models using the pscl package. I am just wondering why there is no development of models for one-inflated count data models!...
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### Exact difference between two-part models (e.g., Cragg) and Tobit type 2 models (e.g., Heckman)

I want to run a regression where the DV is the amount of funding (in USD) obtained by startups. Naturally the DV contains a lot of zero's (~55%) and has a continuous distribution for y>0. In general ...
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### “Zero-inflated” predictors in regression?

I know that zero-inflated models (e.g. zero-inflated Poisson or negative binomial models) can be used for dependent variables. I also know that in general there are no assumptions for the independent ...
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### Simulate from a zero-inflated poisson distribution

I am trying to simulate from observed data that I have fit to a zero-inflated poisson regression model. I fit the data in R using zeroinfl() from the package pscl, but I am having trouble figuring out ...
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### Zero inflated models - “true zero” vs. “excess zero”

I am trying to decide if zero inflated poisson is appropriate for my data vs. a Poisson hurdle model. In background reading between the two I've run across a statement saying that a zero inflated ...
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### How to test for Zero-Inflation in a dataset?

I have a dataset which seems to have a lot of zeroes. I have already fit a poisson regression model as well as a negative binomial model. I would like to fit zero-inflated and hurdle models as well. ...
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### Experimental design & questions on use of generalized linear models

I have an ecological experiment for which I need to analyze bird count data. Here is the set up: 2 treatments (open/control), 3 regions. Not quite a full 3x2 factorial because in 2 regions there are ...
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### Fitting a model to a variable with many zeros and few but large values in right tail [duplicate]

I would like to fit a model to a dependent variable distributed like the one below (see picture). The distribution is a count of people (with specific characteristics) in various districts. This ...
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### Zero-inflated negative binomial models: why not use two separate models?

Zero-inflated negative binomial models have two components: a count component (negative binomial regression part) and a zero component (logistic regression part). Why not just run two separate ...
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### Zero-inflated two-part models for semi-continuous data

I am trying to study predictors of companies' pollution output of some specific chemicals. The data I am using have many 0's (i.e., the company did not pollute at all with those chemicals) and then ...
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### Zero-inflated Poisson regression Vuong test: Raw, AIC- or BIC-corrected results

I'm analyzing count data for a set of ten species and found that for the five species with highest detection rate, the zero-inflated poisson (ZIP) regression fits the data significantly better than ...
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### Use loess regression with many zero values

I have measuments of vegetation coverage on Y plotted against surface height (and hence flooding frequency) on X. The vegetation often has two herb layers, which are estimated seperately. If only one ...
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### Interpretation of $\theta$ in negative binomial regression

First off, a very similar question has been asked before. But the answers to this question did not explain what high/low values of theta mean. Here's my crack at trying to figure out what high/low ...
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### Explanatory variables with many zeros

I am trying to fit a linear model to a price response variable. Many of the predictor variables consist of mainly zeros. For example, one possible predictor variable is "drill holes". Not many parts ...
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### When to use zero-inflated poisson regression and negative binomial distribution

I have a fairly simple dataset looking at the relationship between the first nesting date of a bird in a given year (Date) and the birds overall fledgling production from that year (Fledge; count data ...
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### Interpreting random effects in zero-inflated models

For context, I have a longitudinal study measuring counts of bacterial sequences in human stool collected during a dietary intervention. Initially, I was going model the change in each bacterium (...
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### Interpret zero-inflated negative binomial regression

I am trying to estimate a zero-inflated negative binomial model with 11 predictor variables and the number of reported crimes as a response variable. The model seems to work OK, but I'm uncertain on ...
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I have been working on a baseball model to predict success at the major league level using minor league statistics. After posting multiple threads on this site (1, 2, 3) and receiving valuable ...
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### Zero-inflation on steroids: choose among Poisson, negative binomial and zero-inflated regressions

I am struggling to fit alternative count models into my data. I guess my problem is just too many zeros. This is my data ...
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### Fitting a probability distribution to zero inflated data in R

I am trying to learn how to fit a probability distribution to a vector of data, using the program R, but there are a lot of potential probability distributions to use! So my question is, how do I ...
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### Zero inflated beta regression using gamlss for vegetation cover data

My goal is to analyse vegetation cover data. The way the data collection works is that you throw a quadrat (0.5m x 0.5m) in a sample plot and estimate the percent cover of the target species. Here is ...
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### Enormous SEs in zero-inflated negative binomial regression

I have overdispersed count data where the outcome is events (occurrence of a rare disease) and the covariate of interest is season. The unit of analysis is the number of events occurring in a country-...