Score test for zero inflation in Poisson data
zero.test.Rd
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.
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
Examples
# synthetic tests
zero.test(rpois(100, 1))
#> Score test for zero inflation
#>
#> Chi-square = 0.15113
#> df = 1
#> pvalue: 0.69746
zero.test(rpois(100, 5))
#> Score test for zero inflation
#>
#> Chi-square = 0.00949
#> df = 1
#> pvalue: 0.92239
# add some extra zeros
zero.test(c(rep(0, 20), rpois(100, 5)))
#> Score test for zero inflation
#>
#> Chi-square = 194.79356
#> 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