glmtoolbox (version 0.1.12)

zero.excess: Test for zero-excess in Count Regression Models

Description

Allows to assess if the observed number of zeros is significantly higher than expected according to the fitted count regression model (poisson or negative binomial).

Usage

zero.excess(
  object,
  alternative = c("excess", "lack", "both"),
  method = c("boot", "naive"),
  rep = 100,
  verbose = TRUE
)

Value

A matrix with 1 row and the following columns:

Observed	the observed number of zeros,
Expected	the expected number of zeros,
z-value	the value of the statistical test,
p.value	the p-value of the statistical test.

Arguments

object

an object of the class glm, for poisson regression models, or an object of the class overglm, for negative binomial regression models.

alternative

an (optional) character string indicating the alternative hypothesis. There are three options: excess of zeros ("excess"), lack of zeros ("lack"), and both ("both"). As a default, type is set to "excess".

method

an (optional) character string indicating the method to calculate the mean and variance of the difference between observed and estimated expected number of zeros. There are two options: parametric bootstrapping ("boot") and naive ("naive"). As a default, type is set to "boot".

rep

an (optional) positive integer which allows to specify the number of replicates which should be used by the parametric bootstrapping. As a default, rep is set to 100.

verbose

an (optional) logical switch indicating if should the report of results be printed. As a default, verbose is set to TRUE.

Details

According to the formulated count regression model, we have that \(Y_i\sim P(y;\mu_i,\phi)\) for \(i=1,\ldots,n\) are independent variables. Consequently, the expected number of zeros can be estimated by \(P(0;\hat{\mu}_i,\hat{\phi})\) for \(i=1,\ldots,n\), where \(\hat{\mu}_i\) and \(\hat{\phi}\) represent the estimates of \(\mu_i\) and \(\phi\), respectively, obtained from the fitted model. Thus, the statistical test can be defined as the standardized difference between the observed and (estimated) expected number of zeros. The standard normal distribution tends to be the distribution of that statistic when the sample size, \(n\), tends to infinity. In He, Zhang, Ye, and Tang (2019), the above approach is called a naive test since it ignores the sampling variation associated with the estimated model parameters. To correct this, parametric bootstrapping is used to estimate the mean and variance of the difference between the (estimated) expected and observed number of zeros.

References

He Hua, Zhang Hui, Ye Peng, Tang Wan (2019) A test of inflated zeros for Poisson regression models, Statistical Methods in Medical Research 28, 1157-1169.

See Also

overglm, zeroinf

Examples

####### Example 1: Self diagnozed ear infections in swimmers
data(swimmers)
fit1 <- glm(infections ~ frequency + location, family=poisson, data=swimmers)
zero.excess(fit1,rep=50)
fit2 <- overglm(infections ~ frequency + location, family="nb1", data=swimmers)
zero.excess(fit2,rep=50)

####### Example 2: Article production by graduate students in biochemistry PhD programs
bioChemists <- pscl::bioChemists
fit1 <- glm(art ~ fem + kid5 + ment, family=poisson, data=bioChemists)
zero.excess(fit1,rep=50)
fit2 <- overglm(art ~ fem + kid5 + ment, family="nb1", data=bioChemists)
zero.excess(fit2,rep=50)
####### Example 3: Roots Produced by the Columnar Apple Cultivar Trajan
data(Trajan)
fit1 <- glm(roots ~ photoperiod, family=poisson, data=Trajan)
zero.excess(fit1,rep=50)
fit2 <- overglm(roots ~ photoperiod, family="nbf", data=Trajan)
zero.excess(fit2,rep=50)