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The negative binomial model was selected because omphalocele is a relatively rare event; 72.4% of the region-, residentiand, age-specificific number of cases was 0 in a given month.
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A binomial model was used for the probability of encountering terns, and a negative binomial was used for the number of terns if encountered.
The beta binomial model was used to account for over-dispersion.
In particular, random parameter negative binomial model was used to investigate pedestrian crashes.
By Vuong test, zero-inflated negative binomial regression model was not significantly better than negative binomial model (z = 1.14, p = 0.128), thus negative binomial model was chosen.
If ' q' is the selection probability for a sample, then the probability of selecting m i samples under the binomial model is as follows: The individual z-scores computed previously that pass the cutoffs are all treated equally (in q).
It is precisely because the binomial model is unable to fit overdispersed binomial data that the application of the beta-binomial is necessary.
Due to survival being binary data, the binomial distribution was selected with a logit link function, and models were fitted using the Laplace approximation.
We used a generalized linear model (GLM) with a negative binomial distribution in SAS (PROC GLM); because of overdispersion in the number of anthrax cases (ratio of the mean/variance was > 1) a negative binomial distribution was selected over a Poisson distribution.
(The glm model with Poisson distribution was selected after comparing different models, including negative binomial regression, using the Akaike information criterion).
A binomial distribution statistical testing method was selected and a significance level of 0.1 was applied.
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