Score test for zero inflation in Poisson data

Carries out a simple score test (van den Broek, 1995) for excess zeros in an otherwise Poisson distribution of counts. It gives a $\chi^2_1$ statistic on one degree of freedom.

Usage

zero.test(x)

Arguments

x: A vector of non-negative counts, or a one-way frequency table of such counts.

Details

The test first calculates the rate estimate from the mean, $\hat{\lambda} = \bar{x}$. The number of observed zeros, $n_0$ is then compared with the expected number, $n \hat{p_0}$, where $\hat{p}_0=\exp[-\hat{\lambda}]$. Then the test statistic is calculated by the formula: $$\frac{(n_0 - n\hat{p}_0)^2}{n\hat{p}_0(1-\hat{p}_0) - n\bar{x}\hat{p}_0^2}$$ This test statistic has a $\chi^2_1$ distribution.

Value

Returns invisibly a list of three elements:

statistic: Description of 'comp1'
df: Description of 'comp2'
pvalue: Upper tail p-value

References

The original R code came from a Stackexchange question, https://stats.stackexchange.com/questions/118322/how-to-test-for-zero-inflation-in-a-dataset

Van den Broek, J. (1995). A Score Test for Zero Inflation in a Poisson Distribution. Biometrics, 51(2), 738-743. https://www.jstor.org/stable/2532959

Yang, Zhao, James W. Hardin, and Cheryl L. Addy (2010). Score Tests for Zero-Inflation in Overdispersed Count Data. Communications in Statistics - Theory and Methods 39 (11) 2008-2030. doi:10.1080/03610920902948228

Author

Michael Friendly

Examples

# synthetic tests
zero.test(rpois(100, 1))
#> Score test for zero inflation
#> 
#>  	Chi-square = 0.195 
#>  	df = 1
#>  	pvalue: 0.65879 
zero.test(rpois(100, 5))
#> Score test for zero inflation
#> 
#>  	Chi-square = 0.05324 
#>  	df = 1
#>  	pvalue: 0.81752 
# add some extra zeros
zero.test(c(rep(0, 20), rpois(100, 5)))
#> Score test for zero inflation
#> 
#>  	Chi-square = 207.29743 
#>  	df = 1
#>  	pvalue: < 2.22e-16 

# Articles by Phd candidates
data(PhdPubs, package="vcdExtra")
zero.test(PhdPubs$articles)
#> Score test for zero inflation
#> 
#>  	Chi-square = 133.91825 
#>  	df = 1
#>  	pvalue: < 2.22e-16 

phd.tab <- table(PhdPubs$articles)
zero.test(phd.tab)
#> Score test for zero inflation
#> 
#>  	Chi-square = 133.91825 
#>  	df = 1
#>  	pvalue: < 2.22e-16