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The score test for the two-sample occupancy model

Karavarsamis, N., Guillera-Arroita, G., Huggins, R. M., Morgan, B.J.T. (2020) The score test for the two-sample occupancy model. Australia & New Zealand Journal of Statistics, 62 (1). pp. 95-115. (doi:10.1111/anzs.12288) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:82322)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. (Contact us about this Publication)
Official URL
https://dx.doi.org/10.1111/anzs.12288

Abstract

The score test statistic computed using the observed information is easy to compute numerically. Its large sample distribution under the null hypothesis is well known and is equivalent to that of the score test based on the expected information, the likelihood-ratio test and the Wald test. However, several authors have noted that under the alternative hypothesis this no longer holds and in particular the score statistic computed using the observed information can take negative values. We extend the body of work on the score test to a problem of interest in ecology when studying the occurrence of species. This is the comparison of two zero-inflated binomial random variables from two independent samples under imperfect detection. An analysis of eigenvalues associated with the score test in this setting assists in understanding why using the observed information matrix in the score test can be problematic. We demonstrate through a combination of simulations and theoretical analysis that the power of the score test calculated under the observed information decreases as the populations being compared become more dissimilar. In particular, the score test based on the observed information is inconsistent. Finally, we propose a modified rule that rejects the null hypothesis when the score statistic is computed using the observed information is

negative or is larger than the usual chi-square cut-off. In simulations in our setting this has power that is comparable to the Wald and likelihood ratio tests and consistency is largely restored. Our new test is easy to use and inference is possible. Supplementary material for this article is available online as per journal instructions.

Item Type: Article
DOI/Identification number: 10.1111/anzs.12288
Uncontrolled keywords: eigenvalues; observed information; occupancy modelling; power of hypothesis test; zero-inflation
Subjects: Q Science > QA Mathematics (inc Computing science) > QA276 Mathematical statistics
Q Science > QH Natural history > QH541 Ecology
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Byron Morgan
Date Deposited: 31 Jul 2020 15:51 UTC
Last Modified: 16 Feb 2021 14:14 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/82322 (The current URI for this page, for reference purposes)
Morgan, B.J.T.: https://orcid.org/0000-0002-5465-8006
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