An adjusted coefficient of determination (R2 ) for generalized linear mixed models in one go

The coefficient of determination (R2 ) is a common measure of goodness of fit for linear models. Various proposals have been made for extension of this measure to generalized linear and mixed models. When the model has random effects or correlated residual effects, the observed responses are correlated. This paper proposes a new coefficient of determination for this setting that accounts for any such correlation. A key advantage of the proposed method is that it only requires the fit of the model under consideration, with no need to also fit a null model. Also, the approach entails a bias correction in the estimator assessing the variance explained by fixed effects. Three examples are used to illustrate new measure. A simulation shows that the proposed estimator of the new coefficient of determination has only minimal bias.

A coefficient of determination (R2 ) for generalized linear mixed models

Extensions of linear models are very commonly used in the analysis of biological data. Whereas goodness of fit measures such as the coefficient of determination (R² ) or the adjusted R² are well established for linear models, it is not obvious how such measures should be defined for generalized linear and mixed models. There are by now several proposals but no consensus has yet emerged as to the best unified approach in these settings. In particular, it is an open question how to best account for heteroscedasticity and for covariance among observations present in residual error or induced by random effects. This paper proposes a new approach that addresses this issue and is universally applicable for arbitrary variance-covariance structures including spatial models and repeated measures. It is exemplified using three biological examples.

Exploration Feeding and Higher Space Allocation Improve Welfare of Growing-Finishing Pigs

Simple Summary

A lack of exploration materials in pig pens can result in damaging behavior towards pen mates. The objective of our study was to reduce skin and tail lesions by frequently providing small amounts of feed on the floor and by providing more space per pig. Both the so-called “exploration feeding” and the additional space resulted in fewer skin lesions. Finally, this can lead to a more welfare-friendly pig husbandry.

Abstract

Lack of environmental enrichment and high stocking densities in growing-finishing pigs can lead to adverse social behaviors directed to pen mates, resulting in skin lesions, lameness, and tail biting. The objective of the study was to improve animal welfare and prevent biting behavior in an experiment with a 2 × 2 × 2 factorial design on exploration feeding, stocking density, and sex. We kept 550 pigs in 69 pens from 63 days to 171 days of life. Pigs were supplemented with or without exploration feeding, kept in groups of seven (1.0 m²/pig) or nine animals (0.8 m²/pig) and separated per sex. Exploration feeding provided small amounts of feed periodically on the solid floor. Skin lesion scores were significantly lower in pens with exploration feeding (p = 0.028, p < 0.001, p < 0.001 for front, middle, and hind body), in pens with high compared to low space allowance (p = 0.005, p = 0.006, p < 0.001 for front, middle and hind body), and in pens with females compared to males (p < 0.001, p = 0.005, p < 0.001 for front, middle and hind body). Males with exploration feeding had fewer front skin lesions than females with exploration feeding (p = 0.022). Pigs with 1.0 m² compared to 0.8 m² per pig had a higher daily gain of 27 g per pig per day (p = 0.04) and males compared to females had a higher daily gain of 39 g per pig per day (p = 0.01). These results indicate that exploration feeding might contribute to the development of a more welfare-friendly pig husbandry with intact tails in the near future.

Multinomial logit random effects models

This article presents a general approach for logit random effects modelling of clustered ordinal and nominal responses. We review multinomial logit random effects models in a unified form as multivariate generalized linear mixed models. Maximum likelihood estimation utilizes adaptive Gauss-Hermite quadrature within a quasi-Newton maximization algorithm. For cases in which this is computationally infeasible, we generalize a Monte Carlo EM algorithm. We also generalize a pseudo-likelihood approach that is simpler but provides poorer approximations for the likelihood. Besides the usual normality structure for random effects, we also present a semi-parametric approach treating the random effects in a non-parametric manner. An example comparing reviews of movie critics uses adjacent-categories logit models and a related baseline-category logit model.

Expert opinion as 'validation' of risk assessment applied to calf welfare

BACKGROUND

Recently, a Risk Assessment methodology was applied to animal welfare issues in a report of the European Food Safety Authority (EFSA) on intensively housed calves.

METHODS

Because this is a new and potentially influential approach to derive conclusions on animal welfare issues, a so-called semantic-modelling type 'validation' study was conducted by asking expert scientists, who had been involved or quoted in the report, to give welfare scores for housing systems and for welfare hazards.

RESULTS

Kendall's coefficient of concordance among experts (n = 24) was highly significant (P < 0.001), but low (0.29 and 0.18 for housing systems and hazards respectively). Overall correlations with EFSA scores were significant only for experts with a veterinary or mixed (veterinary and applied ethological) background. Significant differences in welfare scores were found between housing systems, between hazards, and between experts with different backgrounds. For example, veterinarians gave higher overall welfare scores for housing systems than ethologists did, probably reflecting a difference in their perception of animal welfare. Systems with the lowest scores were veal calves kept individually in so-called "baby boxes" (veal crates) or in small groups, and feedlots. A suckler herd on pasture was rated as the best for calf welfare. The main hazards were related to underfeeding, inadequate colostrum intake, poor stockperson education, insufficient space, inadequate roughage, iron deficiency, inadequate ventilation, poor floor conditions and no bedding. Points for improvement of the Risk Assessment applied to animal welfare include linking information, reporting uncertainty and transparency about underlying values.

CONCLUSION

The study provides novel information on expert opinion in relation to calf welfare and shows that Risk Assessment applied to animal welfare can benefit from a semantic modelling approach.

Multilevel Grouped Regression for Analyzing Self-reported Health in Relation to Environmental Factors: the Model and its Application

A method for modeling the relationship of polychotomous health ratings with predictors such as area characteristics, the distance to a source of environmental contamination, or exposure to environmental pollutants is presented. The model combines elements of grouped regression and multilevel analysis. The statistical model describes the entire response distribution as a function of the predictors so that any measure that summarizes this distribution can be calculated from the model. With the model, polychotomous health ratings can be used, and there is no need for a priori dichotomizing such variables which would lead to loss of information. It is described how, according to the model, various measures describing the response distribution are related to the exposure, and the confidence and tolerance intervals for these relationships are presented. Specific attention is given to the incorporation of random factors in the model. The application that here serves as an example, concerns annoyance from transportation noise. Exposure-response relationships obtained with the described method of modeling are presented for aircraft, road traffic, and railway noise.