Devil in the details: how can we avoid potential pitfalls of CATS regression when our data do not follow a Poisson distribution?

Background Community assembly by trait selection (CATS) allows for the detection of environmental filtering and estimation of the relative role of local and regional (meta-community-level) effects on community composition from trait and abundance data without using environmental data. It has been shown that Poisson regression of abundances against trait data results in the same parameter estimates. Abundance data do not necessarily follow a Poisson distribution, and in these cases, other generalized linear models should be fitted to obtain unbiased parameter estimates. Aims This paper discusses how the original algorithm for calculating the relative role of local and regional effects has to be modified if Poisson model is not appropriate. Results It can be shown that the use of the logarithm of regional relative abundances as an offset is appropriate only if a log-link function is applied. Otherwise, the link function should be applied to the product of local total abundance and regional relative abundances. Since this product may be outside the domain of the link function, the use of log-link is recommended, even if it is not the canonical link. An algorithm is also suggested for calculating the offset when data are zero-inflated. The relative role of local and regional effects is measured by Kullback-Leibler R2. The formula for this measure presented by Shipley (2014) is valid only if the abundances follow a Poisson distribution. Otherwise, slightly different formulas have to be applied. Beyond theoretical considerations, the proposed refinements are illustrated by numerical examples. CATS regression could be a useful tool for community ecologists, but it has to be slightly modified when abundance data do not follow a Poisson distribution. This paper gives detailed instructions on the necessary refinement.

COVID-19 Misinformation in Portuguese-Speaking Countries: Agreement with Content and Associated Factors

In the wake of the COVID-19 pandemic, a complex phenomenon called the “infodemic” has emerged, compromising coping with the pandemic. This study aims to estimate the prevalence of agreement with misinformation about COVID-19 and to identify associated factors. A web survey was carried out in Portuguese-speaking countries in two stages: 1. the identification of misinformation circulating in the included countries; 2. a multicentric online survey with residents of the included countries. The outcome of the study was agreement or disagreement with misinformation about COVID-19. Multivariate analyzes were conducted using the Poisson regression model with robust variance, a logarithmic link function, and 95% confidence intervals. The prevalence of agreement with misinformation about COVID-19 was 63.9%. The following factors increased the prevalence of this outcome: having a religious affiliation (aPR: 1454, 95% CI: 1393–1517), having restrictions on leisure (aPR: 1230, 95% CI: 1127–1342), practicing social isolation (aPR: 1073, 95% CI: 1030–1118), not avoiding agglomeration (aPR: 1060, 95% CI: 1005–1117), not seeking/receiving news from scientific sources (aPR: 1153, 95% CI: 1068–1245), seeking/receiving news from three or more non-scientific sources (aPR: 1114, 95% CI: 1049–1182), and giving credibility to news carried by people from social networks (aPR: 1175, 95% CI: 1104–1251). There was a high prevalence of agreement with misinformation about COVID-19. The quality, similarity, uniformity, and acceptance of the contents indicate a concentration of themes that reflect “homemade”, simple, and easy methods to avoid infection by SARS-CoV-2, compromising decision-making and ability to cope with the disease.

Evaluating Alternatives to Locomotion Scoring for Lameness Detection in Pasture-Based Dairy Cows in New Zealand: Infra-Red Thermography

Lameness in cattle is a complex condition with huge impacts on welfare, and its detection is challenging for the dairy industry. The present study aimed to evaluate the association between foot skin temperature (FST) measured using infrared thermography (IRT) and locomotion scoring (LS) in dairy cattle kept at pasture. Data were collected from a 940-cow dairy farm in New Zealand. Cows were observed at two consecutive afternoon milkings where LS was undertaken at the first milking (4-point scale (0–3), DairyNZ). The next day, cows were thermally imaged from the plantar aspect of the hind feet using a handheld T650sc forward-looking infrared camera (IRT). The association between FST and locomotion score was analysed using a generalised linear model with an identity link function and robust estimators. ROC curves were performed to determine optimal threshold temperature cut-off values by maximising sensitivity and specificity for detecting locomotion score ≥ 2. There was a linear association between individual locomotion scores and FST. For mean temperature (MT), each one-unit locomotion score increase was associated with a 0.944 °C rise in MT. Using MT at a cut-off point of 34.5 °C produced a sensitivity of 80.0% and a specificity of 92.4% for identifying cows with a locomotion score ≥ 2 (lame). Thus, IRT has a substantial potential to be used on-farm for lameness detection. However, automation of the process will likely be necessary for IRT to be used without interfering with farm operations.

Reverse engineering of metacognition

The human ability to introspect on thoughts, perceptions or actions – metacognitive ability – has become a focal topic of both cognitive basic and clinical research. At the same time it has become increasingly clear that currently available quantitative tools are limited in their ability to make unconfounded inferences about metacognition. As a step forward, the present work introduces a comprehensive framework and model of metacognition that allows for inferences about metacognitive noise and metacognitive biases during the readout of type 1 decision values or at the confidence reporting stage. The model assumes that confidence results from a continuous but noisy and potentially biased transformation of decision values, described by a confidence link function. A canonical set of metacognitive noise distributions is introduced which differ, amongst others, in their predictions about metacognitive sign flips of type 1 decision values. Successful recovery of model parameters is demonstrated and the model is validated on an empirical data set. In particular, it is shown that metacognitive noise and bias parameters correlate with conventional behavioral measures. Crucially, in contrast to these conventional measures, metacognitive noise parameters inferred from the model are shown to be independent of type 1 performance. This work is accompanied by a toolbox (ReMeta) that allows researchers to estimate key parameters of metacognition in confidence datasets.

Partially Linear Generalized Single Index Models for Functional Data (PLGSIMF)

Single-index models are potentially important tools for multivariate non-parametric regression analysis. They generalize linear regression models by replacing the linear combination α0⊤X with a non-parametric component η0α0⊤X, where η0(·) is an unknown univariate link function. In this article, we generalize these models to have a functional component, replacing the generalized partially linear single index models η0α0⊤X+β0⊤Z , where α is a vector in IRd, η0(·) and β0(·) are unknown functions that are to be estimated. We propose estimates of the unknown parameter α0, the unknown functions β0(·) and η0(·) and establish their asymptotic distributions, and furthermore, a simulation study is carried out to evaluate the models and the effectiveness of the proposed estimation methodology.

Modeling Proportion Data with Inflation by Using a Power-Skew-Normal/Logit Mixture Model

Rate or proportion data are modeled by using a regression model. The considered regression model can be used for studying phenomena with a response on the (0, 1), [0, 1), (0, 1], or [0, 1] intervals. To connect the response variable with the linear predictor in the regression model, we use a logit link function, which guarantees that the obtained prediction ranges between zero and one in the cases inflated at zero or one (or both). The model is complemented with the assumption that the errors follow a power-skew-normal distribution, resulting in a very flexible model, and with a non-singular information matrix, constituting an advantage over other existing models in the literature. To explain the probability of point mass at the values zero and/or one (inflated part), we used a polytomic logistic model with covariates. The results of two illustrations showed that the proposed model is a better alternative compared to widely known models in the literature.

Behaviour of the Monotone Single Index Model Under Repeated Measurements

The generalized linear model is an important method in the statistical toolkit. The isotonic single index model can be thought of as a further generalization whereby the link function is assumed to be monotone non-decreasing as opposed to known and fixed. Such a shape constraint is quite natural in many statistical problems, and is fulfilled by the usual generalized linear models. In this paper we consider inference in this model in the setting where repeated measurements of predictor values and associated responses are observed. This setting is encountered in medical studies and is very different from the one considered in the classical monotone single index model studied in the literature. Here, we use nonparametric maximum likelihood estimation to infer the unknown regression vector and link function. We present a detailed study of finite and asymptotic properties of this estimator and propose goodness-of-fit tests for the model. Through an extended simulation study, we show that the model has competitive predictive performance. We illustrate our estimation approach using a Leukemia data set.

Binomial GLMs

GLMs with a binomial distribution are designed for the analysis of binomial counts (how many times something occurred relative to the total number of possible times it could have occurred). A logistic link function constrains predictions to be above zero and below the maximum using the S-shaped logistic curve. Overdispersion can be diagnosed and dealt with using a quasi-maximum likelihood extension to GLM analysis.