A tale of two logits, compositional data analysis and zero observations

The application of compositional data analysis through log ratio trans- formations corresponds to a multinomial logit model for the shares themselves. This model is characterized by the property of Independence of Irrelevant Alter- natives (IIA). IIA states that the odds ratio in this case the ratio of shares is invariant to the addition or deletion of outcomes to the problem. It is exactly this invariance of the ratio that underlies the commonly used zero replacement procedure in compositional data analysis. In this paper we investigate using the nested logit model that does not embody IIA and an associated zero replacement procedure and compare its performance with that of the more usual approach of using the multinomial logit model. Our comparisons exploit a data set that com- bines voting data by electoral division with corresponding census data for each division for the 2001 Federal election in Australia

Intrinsic test of independence in contingency tables

A condition needed for testing nested hypotheses from a Bayesian viewpoint is that the prior for the alternative model concentrates mass around the small, or null, model. For testing independence in contingency tables, the intrinsic priors satisfy this requirement. Further, the degree of concentration of the priors is controlled by a discrete parameter m, the training sample size, which plays an important role in the resulting answer regardless of the sample size. In this paper we study robustness of the tests of independence in contingency tables with respect to the intrinsic priors with different degree of concentration around the null, and compare with other “robust” results by Good and Crook. Consistency of the intrinsic Bayesian tests is established. We also discuss conditioning issues and sampling schemes, and argue that conditioning should be on either one margin or the table total, but not on both margins. Examples using real are simulated data are given

Primary succession in man-made wetlands: biodiversity, structure and dynamics of macrofaunal assemblages

Man-made wetlands are often created to compensate for the loss or degradation of natural wetlands, but little is known about the processes taking place in these artificial environments, especially at the community level. Throughout this thesis, we have assessed the phenomena of primary succession over different time (short-, mid- and long-term) and spatial scales (local, regional, interregional levels), applying different approaches (taxonomic and functional) and subject groups (invertebrates and amphibians). Our main findings regarding time scales show a 3-phase successional pattern in Mediterranean man-made wetlands’ communities, where at the short term (1 year) colonization processes dominate; at mid term perspectives (2 to 7 years) succession signs begin to be conspicuous, and later on (≥ 10 years) parameters such as species richness reach an asymptote. At that moment, some biological strategies dominate, and biodiversity surrogates indicate that communities are indistinct between man-made and natural wetlands. Regarding spatial effects, we corroborated that both local and regional factors affect the establishing communities. Particularly, the low hydrological stability of the Mediterranean region has enhanced biological traits favoring resilience and resistance to disturbances when comparing Mediterranean and cold temperate aquatic communities. Even within the Mediterranean region, low levels of hydrological stability have significant effects on the successional dynamics. In these cases, local communities are highly nested within regional natural ones, and so are not able to make net contributions to regional richness. We also showed the influence of the regional pool of recruiters over local communities, both in the case of invertebrates and amphibians. Especially for the latter group, man-made Mediterranean temporary ponds (MTPs) can play an important role in their conservation.