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Generalized linear latent variable models (GLLVMs) are a class of methods for analyzing multi-response data which has gained considerable popularity in recent years, e.g., in the analysis of multivariate abundance data in ecology. One of the main features of GLLVMs is their capacity to handle a variety of responses types, such as (overdispersed) counts, binomial and (semi-)continuous responses, and proportions data. On the other hand, the inclusion of unobserved latent variables poses a major computational challenge, as the resulting marginal likelihood function involves an intractable integral for non-normally distributed responses. This has spurred research into a number of approximation methods to overcome this integral, with a recent and particularly computationally scalable one being that of variational approximations (VA). However, research into the use of VA for GLLVMs has been hampered by the fact that fully closed-form variational lower bounds have only been obtained for certain combinations of response distributions and link functions. In this article, we propose an extended variational approximations (EVA) approach which widens the set of VA-applicable GLLVMs dramatically. EVA draws inspiration from the underlying idea behind the Laplace approximation: by replacing the complete-data likelihood function with its second order Taylor approximation about the mean of the variational distribution, we can obtain a fully closed-form approximation to the marginal likelihood of the GLLVM for any response type and link function. Through simulation studies and an application to a species community of testate amoebae, we demonstrate how EVA results in a “universal” approach to fitting GLLVMs, which remains competitive in terms of estimation and inferential performance relative to both standard VA (where any intractable integrals are either overcome through reparametrization or quadrature) and a Laplace approximation approach, while being computationally more scalable than both methods in practice. [ABSTRACT FROM AUTHOR]

As most ecosystems, peatlands have been heavily exploited for different human purposes. For example, in Finland the majority is under forestry, agriculture or peat mining use. Peatlands play an important role in carbon storage, water cycle, and are a unique habitat for rare organisms. Such properties highlight their environmental importance and the need for their restoration. To monitor the success of peatland restoration sensitive indicators are needed. Here we test whether testate amoebae can be used as a reliable bioindicator for assessing peatland condition. To qualify as reliable indicators, responses in testate amoebae community structure to ecological changes must be stronger than random spatial and temporal variation. In this study, we simultaneously assessed differences between the effects of seasonality, intermediate scale spatial variation and land uses on living testate amoebae assemblages in natural, forested and restored peatlands. We expected the effects of seasonality on testate amoebae communities to be less pronounced than those of land use and within site variation. On average, natural sites harboured the highest richness and density, while the lowest numbers were found at forestry sites. Despite small changes observed in taxa dominance and differences in TA community structure between seasons and years at some sites, spatial heterogeneity, temperature, pH, nor water table depth seemed to significantly affect testate amoebae communities. Instead, observed differences were related to type of land use, which explained 75% of the community variation. Our results showed that testate amoebae community monitoring is a useful tool to evaluate impacts of human land use on boreal peatlands. [ABSTRACT FROM AUTHOR]

In this paper we consider generalized linear latent variable models that can handle overdispersed counts and continuous but non-negative data. Such data are common in ecological studies when modelling multivariate abundances or biomass. By extending the standard generalized linear modelling framework to include latent variables, we can account for any covariation between species not accounted for by the predictors, notably species interactions and correlations driven by missing covariates. We show how estimation and inference for the considered models can be performed efficiently using the Laplace approximation method and use simulations to study the finite-sample properties of the resulting estimates. In the overdispersed count data case, the Laplace-approximated estimates perform similarly to the estimates based on variational approximation method, which is another method that provides a closed form approximation of the likelihood. In the biomass data case, we show that ignoring the correlation between taxa affects the regression estimates unfavourably. To illustrate how our methods can be used in unconstrained ordination and in making inference on environmental variables, we apply them to two ecological datasets: abundances of bacterial species in three arctic locations in Europe and abundances of coral reef species in Indonesia. Supplementary materials accompanying this paper appear on-line. [ABSTRACT FROM AUTHOR]

Background: End-stage renal disease (ESRD) leads to the need for dialysis and renal transplantation (Tx). Peritoneal dialysis (PD) of young children is normally performed at home by the parents and affects the whole family. We studied the coping of families with a young child with ESRD by interviewing the parents of 19 children. Methods: The spousal and parent-child relationships were assessed by using the Psychosocial Assessment of Childhood Experiences (PACE) and the Brief Measure of Expressed Emotion, respectively. A control group of 22 families with a healthy child was used for the parent-child relationship evaluation. Results: The spousal relationship at the start of PD was good or fairly good in most of the families and remained good in half of the families following renal Tx. Lack of support from close relatives and renal Tx were associated with a poorer relationship quality. Almost all parents expressed much or fairly much emotional warmth towards the child throughout the study, but there was a trend towards increased criticism over time. No differences in the degree of expressed warmth or criticism were noted between the index parents and controls. Conclusions: Overall, the study families appeared to cope well despite the serious illness of their child and the demands of the treatments. [ABSTRACT FROM AUTHOR]

Classical univariate measures of asymmetry such as Pearson’s (mean-median)/σ or (mean-mode)/σ often measure the standardized distance between two separate location parameters and have been widely used in assessing univariate normality. Similarly, measures of univariate kurtosis are often just ratios of two scale measures. The classical standardized fourth moment and the ratio of the mean deviation to the standard deviation serve as examples. In this paper we consider tests of multinormality which are based on the Mahalanobis distance between two multivariate location vector estimates or on the (matrix) distance between two scatter matrix estimates, respectively. Asymptotic theory is developed to provide approximate null distributions as well as to consider asymptotic efficiencies. Limiting Pitman efficiencies for contiguous sequences of contaminated normal distributions are calculated and the efficiencies are compared to those of the classical tests by Mardia. Simulations are used to compare finite sample efficiencies. The theory is also illustrated by an example. [ABSTRACT FROM AUTHOR]