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Using Zero-inflated Models to Analyze Environmental Data Sets with Many Zeroes

Source: OAI

ABSTRACT L’analisi di dati di conteggio pu`o essere talvolta complessa a causa di un numero di zeri superiore a quello atteso sotto il modello Poissoniano, che rappresenta l’assunzione standard per la modellazione di questo tipo di dati. Obbiettivo primario della comunicazione `e quello di impiegare modelli alternativi a quello di Poisson, che contemplino la possibilit`a di trattare esplicitamente questo eccesso di zeri, per valutare eventuali differenze in termini di bont`a di adattamento e di stima dei parametri regressivi.Vengono discussi modelli Zero Inflated Posson (ZIP), Zero Inflated Negative Binomial (ZINB) e Hurdle Poisson (HP) e applicati a due insiemi di dati ambientali reali con un elevato numero di zeri.

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    ABSTRACT: Zero-inflated Poisson (ZIP) regression is a model for count data with excess zeros. It assumes that with probability p the only possible observation is 0, and with probability 1 – p, a Poisson(λ) random variable is observed. For example, when manufacturing equipment is properly aligned, defects may be nearly impossible. But when it is misaligned, defects may occur according to a Poisson(λ) distribution. Both the probability p of the perfect, zero defect state and the mean number of defects λ in the imperfect state may depend on covariates. Sometimes p and λ are unrelated; other times p is a simple function of λ such as p = l/(1 + λ) for an unknown constant T. In either case, ZIP regression models are easy to fit. The maximum likelihood estimates (MLE's) are approximately normal in large samples, and confidence intervals can be constructed by inverting likelihood ratio tests or using the approximate normality of the MLE's. Simulations suggest that the confidence intervals based on likelihood ratio tests are better, however. Finally, ZIP regression models are not only easy to interpret, but they can also lead to more refined data analyses. For example, in an experiment concerning soldering defects on printed wiring boards, two sets of conditions gave about the same mean number of defects, but the perfect state was more likely under one set of conditions and the mean number of defects in the imperfect state was smaller under the other set of conditions; that is, ZIP regression can show not only which conditions give lower mean number of defects but also why the means are lower.
    Technometrics 02/1992; 34(1):1-14. DOI:10.1080/00401706.1992.10485228 · 1.79 Impact Factor

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