Analysis of Proportions in the Presence of over-/under-Dispersion

Testing the homogeneity of proportions for clustered binary data without knowing the correlation structure

“…For p = 2, we use the simulation configurations from Table 1 of Paul [7] with m 1 = 27, n i = 12, 7, 6, 6,7,8,10,7,8,6,11,7,8,9,2,7,9,7,11,10,4,8,10,12,8,7,8, and m 2 = 19, n i = 5, 11, 7, 9, 12, 8, 6, 7, 6, 4, 6, 9, 6, 7, 5, 9, 2, 6, 9. For p = 3, we use m 1 = 27, m 2 = 19 with the same cluster sizes as those for p = 2. In addition, we add m 3 = 32 and join the sizes of the control and the treatment groups from the data in Section 3 of Williams [13] to form n i = 13, 12, 9, 9, 8, 8, 13, 12, 10, 10, 9, 13, 5, 7, 10, 10, 12, 11, 10, 9, 11, 10, 10, 9, 9, 5, 9, 7, 10, 6, 10, 7. Paul and Islam [8] parameterized the correlation ρ as θ/(1 + θ) to express the beta-binomial distribution in a more compact form.…”

“…In many applications, presumed models or the parametric assumptions underlying the models may not be justified. Getting satisfactory parameter estimations can sometimes be problematic that makes the models less appealing [4,8].…”

“…Paul and Islam [8] proposed a statistic, C Q , based on quasi-likelihood for the analysis of proportions in the presence of over/under dispersion. They found that C Q holds the nominal level well and has some advantage in power over some other statistics in some situations.…”

Analysis of the Binary Littermate Data in the One‐Way Layout

“…;f f I fixed to get a new estimate,p p I: . Paul and Islam (1995) derived the CðaÞ statistic for testing the equality of the probabilities of several groups in the presence of a common dispersion parameter, which means that f 1 ¼ . .…”

The generalized linear model and extensions: a review and some biological and environmental applications

“…Inference for the parameters φ and ρ can be made using Q + (z i , φ, ρ) (see Paul and Islam, 1995). In a manner described in Subsection 3.1 a hierarchical likelihood can be obtained for the binomial data.…”