zero.test: Score test for zero inflation in Poisson data

In vcdExtra: 'vcd' Extensions and Additions

Score test for zero inflation in Poisson data

Description

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

Author(s)

Michael Friendly

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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/03610920902948228")}

Examples

# synthetic tests
zero.test(rpois(100, 1))
zero.test(rpois(100, 5))
# add some extra zeros
zero.test(c(rep(0, 20), rpois(100, 5)))

# Articles by Phd candidates
data(PhdPubs, package="vcdExtra")
zero.test(PhdPubs$articles)

phd.tab <- table(PhdPubs$articles)
zero.test(phd.tab)

vcdExtra documentation built on Aug. 22, 2023, 9:11 a.m.