Stata Zi, models are designed to address this issue by assuming that the zero counts come from a distinct process from the count process. There are two components to a Zero-Inflated model:
- Zero-Inflation Component: This part of the model explains why some observations are “structurally” zero (i.e., they are zero due to a different underlying process). For instance, it could model the likelihood that an individual will have zero events (e.g., zero doctor visits) based on covariates.
- Count Component: This part models the positive counts (non-zero values) using a standard count model, such as Poisson or Negative Binomial regression.
The main idea behind Zero-Inflated models is that there are two processes at play: one generating excess zeros and another generating the counts, once the zero counts are excluded.
Types of Zero-Inflated Models in Stata
Stata offers several ways to model zero-inflated data, with the most common being:
- Zero-Inflated Poisson (ZIP) Model: The Zero-Inflated Poisson model is appropriate when the count data follows a Poisson distribution, but there is an excess of zeros. The ZIP model assumes that the counts are generated by two processes:
- A binary process that determines whether an observation is a structural zero (with probability π).
- A Poisson process that generates counts, but only when the observation is not a structural zero.
- Zero-Inflated Negative Binomial (ZINB) Model: Similar to the ZIP model, the ZINB model also assumes two components (zero-inflation and count), but the count process follows a Negative Binomial distribution instead of a Poisson. The Negative Binomial distribution is often preferred when there is overdispersion (i.e., the variance exceeds the mean), which is common in many real-world count data.
Stata can estimate both Zero-Inflated Poisson and Zero-Inflated Negative Binomial models, and users can select the appropriate model based on the nature of their data.
When to Use Zero-Inflated Models
Zero-inflated models are typically used in situations where:
- The dependent variable is a count, such as the number of occurrences of an event (e.g., number of accidents, number of visits to a doctor, number of purchases made, etc.).
- The dataset contains an excess of zeros that cannot be explained by a simple count model like Poisson regression.
- The zeros may arise from a different mechanism than the positive counts.
Some examples of situations where Zero-Inflated models are useful include:
- Healthcare Data: Patients may visit a doctor several times, but many might visit zero times. The zero visits may be influenced by factors such as access to care or personal health behaviors, while the positive visits are determined by medical needs.
- Ecology and Biology: Species count data, where some locations might have no species present (zero counts), while others have several individuals.
- Economics and Retail: The number of purchases or transactions may have many customers who do not purchase at all (zeros), while others make multiple purchases.
How to Fit a Zero-Inflated Model in Stata
To fit a Zero-Inflated model in Stata, you would typically use the zinb or zip commands, depending on whether you are assuming a Poisson or Negative Binomial distribution for the count part of the model.
Example: Zero-Inflated Poisson Model
Suppose we have a dataset where visits represents the number of doctor visits, and we want to model the relationship between the number of visits and several predictors, such as age and income, using a Zero-Inflated Poisson model.
visits: Dependent variable (the count of doctor visits).age income: Predictor variables for the count process (Poisson distribution).inflate(age): Predictor variable for the zero-inflation process (models the probability of an observation being a structural zero).
Example: Zero-Inflated Negative Binomial Model
To fit a Zero-Inflated Negative Binomial model, you can use the zinb command. Here’s how you might do it:
In this case, the model assumes that the count part follows a Negative Binomial distribution (which is appropriate when the count data exhibits overdispersion).
Interpreting the Results
The output from Stata will include two sets of coefficients: one for the count component and one for the zero-inflation component.
- Count Component: These coefficients are interpreted like those in a typical Poisson or Negative Binomial regression model. For instance, a coefficient for
agetells you how the expected number of visits changes with each year of age, assuming the individual is not in the zero-inflated group. - Zero-Inflation Component: These coefficients explain the likelihood of being in the “zero group.” For example, if the coefficient for
agein the inflation part is positive, it means that older individuals are more likely to have zero doctor visits, compared to younger individuals.
Model Evaluation and Diagnostics
Like any regression model, it’s important to evaluate the fit of a Zero-Inflated model. Some diagnostic tools include:
- Goodness-of-fit tests: Stata provides several tests for goodness-of-fit, such as the likelihood ratio test to compare the Zero-Inflated model against simpler models (e.g., Poisson or Negative Binomial).
- Vuong Test: The Vuong test is specifically designed for comparing Zero-Inflated models (ZIP or ZINB) with standard count models (Poisson or Negative Binomial), helping to determine whether zero inflation is warranted in the data.
- Residuals: You can check residuals from Zero-Inflated models to see if the model is appropriately capturing the data’s characteristics, especially the excess zeros.
Conclusion
Stata’s Zero-Inflated (ZI) models, including the Zero-Inflated Poisson (ZIP) and Zero-Inflated Negative Binomial (ZINB) models, provide powerful tools for handling datasets with an overabundance of zero counts. By modeling the excess zeros separately from the count process, these models offer a more nuanced understanding of the underlying data generation process. Researchers and data analysts working with count data in fields like healthcare, ecology, and economics can benefit from these models to provide more accurate and reliable insights.
By carefully selecting the appropriate ZI model (ZIP or ZINB) and interpreting both the count and zero-inflation components, users can effectively account for the dual nature of their data—leading to better model fit and more informed conclusions.
