Abstract
Assessing the significance of patterns in presence-absence data is an important question in ecological data analysis, e.g., when studying nestedness. Significance testing can be performed with the commonly used fixed-fixed models, which preserve the row and column sums while permuting the data. The manuscript considers the properties of fixed-fixed models and points out how their strict constraints can lead to limited randomizability. The manuscript considers the question of relaxing row and column sun constraints of the fixed-fixed models. The Rasch models are presented as an alternative with relaxed constraints and sound statistical properties. Models are compared on presence-absence data and surprisingly the fixed-fixed models are observed to produce unreasonably optimistic measures of statistical significance, giving interesting insight into practical effects of limited randomizability.
Highlights
Binary presence-absence datasets encode information on species occurrence over different sites
The manuscript considers the properties of fixed-fixed models and points out how their strict constraints can lead to limited randomizability
Models are compared on presence-absence data and surprisingly the fixed-fixed models are observed to produce unreasonably optimistic measures of statistical significance, giving interesting insight into practical effects of limited randomizability
Summary
Binary presence-absence datasets encode information on species occurrence over different sites. The datasets are essentially simple matrices of ones and zeros, but they form the basis for analyses of more complex phenomena, such as correlation between occurrences of taxa [1], nestedness [2, 3] or niches [4]. In the case of presence-absence data, the task of significance testing is often difficult due to the high-level structure of the data matrix, described by the row and column sums. Those sums indicate the number of ones in corresponding rows and columns, and are collectively referred to as margin sums. The distribution of margin sums can often be skewed, which causes problems for typical statistical tests
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