Estimation, Testing, and Prediction Regions of the Fixed and Random Effects by Solving the Henderson’s Mixed Model Equations

Witkovský, Viktor

doi:10.2478/v10048-012-0033-6

Cited by 18 publications

(25 citation statements)

References 65 publications

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“…We ran planned comparisons by setting the positive control to the intercept to determine if the sparrowhawk’s behavior or state affected blue tit behavioral response. Our models were fit using REML and t tests used Satterthwaite approximations to estimate degrees of freedom as this is one accepted method for estimating degrees of freedom for mixed models in order to generate p values (Witkovský 2012 ). We did not correct these planned comparisons for multiple tests as it can be argued that as they were orthogonal (all treatments are tested against the negative control), no experiment-wise type I error rate corrections are necessary (Ruxton and Beauchamp 2008 ) and using a method such as a Bonferroni correction could be overly stringent and increase the chance of committing type II errors to the point that we may overlook important differences in blue tit behavior (Rothman 1990 ; Perneger 1998 ; Feise 2002 ).…”

Section: Discussionmentioning

confidence: 99%

Sparrowhawk movement, calling, and presence of dead conspecifics differentially impact blue tit (Cyanistes caeruleus) vocal and behavioral mobbing responses

Carlson

Pargeter

Templeton

2017

Behav Ecol Sociobiol

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Many animals alter their anti-predator behavior in accordance to the threat level of a predator. While much research has examined variation in mobbing responses to different predators, few studies have investigated how anti-predator behavior is affected by changes in a predator’s own state or behavior. We examined the effect of sparrowhawk (Accipiter nisus) behavior on the mobbing response of wild blue tits (Cyanistes caeruleus) using robotic taxidermy sparrowhawks. We manipulated whether the simulated predator moved its head, produced vocalizations, or held a taxidermy blue tit in its talons. When any sparrowhawk model was present, blue tits decreased foraging and increased anti-predator behavior and vocalizations. Additionally, each manipulation of the model predator’s state (moving, vocalizing, or the presence of a dead conspecific) impacted different types of blue tit anti-predator behavior and vocalizations. These results indicate that different components of mobbing vary according to the specific state of a given predator—beyond its presence or absence—and suggest that each might play a different role in the overall mobbing response. Last, our results indicate that using more life-like predator stimuli—those featuring simple head movements and audio playback of vocalizations—changes how prey respond to the predator; these ‘robo-raptor’ models provide a powerful tool to provide increased realism in simulated predator encounters without sacrificing experimental control.Significance statementAnti-predatory behavior is often modulated by the threat level posed by a particular predator. While much research has tested how different types of predators change prey behavior, few experiments have examined how predator behavior affects anti-predatory responses of prey. By experimentally manipulating robotic predators, we show that blue tits not only respond to the presence of a sparrowhawk, by decreasing feeding and increasing anti-predator behavior and vocalizations, but that they vary specific anti-predator behaviors when encountering differently behaving predators (moving, vocalizing, or those with captured prey), suggesting that prey pay attention to their predators’ state and behavior.Electronic supplementary materialThe online version of this article (doi:10.1007/s00265-017-2361-x) contains supplementary material, which is available to authorized users.

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Section: Discussionmentioning

confidence: 99%

Sparrowhawk movement, calling, and presence of dead conspecifics differentially impact blue tit (Cyanistes caeruleus) vocal and behavioral mobbing responses

Carlson

Pargeter

Templeton

2017

Behav Ecol Sociobiol

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“…A detailed mathematical explanation of the LMM and its analysis, which provides a theoretical background for the semantic model proposed below, can be found in Supplementary File 1 and the previous literature cited there [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] .…”

Section: Methodsmentioning

confidence: 99%

Semantic concept schema of the linear mixed model of experimental observations

et al. 2020

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In the information age, smart data modelling and data management can be carried out to address the wealth of data produced in scientific experiments. In this paper, we propose a semantic model for the statistical analysis of datasets by linear mixed models. We tie together disparate statistical concepts in an interdisciplinary context through the application of ontologies, in particular the Statistics Ontology (StatO), to produce FaIR data summaries. We hope to improve the general understanding of statistical modelling and thus contribute to a better description of the statistical conclusions from data analysis, allowing their efficient exploration and automated processing.

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“…The first approach, denoted by FPC-lme, is a two step procedure to fit model (1). We first apply a functional principal component (FPC) analysis (Yao, 2007) to transform model (1) to the space of principal component scores, and then apply Henderson’s mixed model equations (Witkovsky, 2001) to get the best linear unbiased estimator (BLUE) for the fixed effects and get the best linear unbiased predictor (BLUP) for the random effects. The resulting estimates were finally reconstructed in time domain using basis expansion.…”

Section: Simulation Studymentioning

confidence: 99%

A Unified Analysis of Structured Sonar-Terrain Data Using Bayesian Functional Mixed Models

et al. 2017

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Sonar emits pulses of sound and uses the reflected echoes to gain information about target objects. It offers a low cost, complementary sensing modality for small robotic platforms. While existing analytical approaches often assume independence across echoes, real sonar data can have more complicated structures due to device setup or experimental design. In this paper, we consider sonar echo data collected from multiple terrain substrates with a dual-channel sonar head. Our goals are to identify the differential sonar responses to terrains and study the effectiveness of this dual-channel design in discriminating targets. We describe a unified analytical framework that achieves these goals rigorously, simultaneously, and automatically. The analysis was done by treating the echo envelope signals as functional responses and the terrain/channel information as covariates in a functional regression setting. We adopt functional mixed models that facilitate the estimation of terrain and channel effects while capturing the complex hierarchical structure in data. This unified analytical framework incorporates both Gaussian models and robust models. We fit the models using a full Bayesian approach, which enables us to perform multiple inferential tasks under the same modeling framework, including selecting models, estimating the effects of interest, identifying significant local regions, discriminating terrain types, and describing the discriminatory power of local regions. Our analysis of the sonar-terrain data identifies time regions that reflect differential sonar responses to terrains. The discriminant analysis suggests that a multi- or dual-channel design achieves target identification performance comparable with or better than a single-channel design.

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Estimation, Testing, and Prediction Regions of the Fixed and Random Effects by Solving the Henderson’s Mixed Model Equations

Cited by 18 publications

References 65 publications

Sparrowhawk movement, calling, and presence of dead conspecifics differentially impact blue tit (Cyanistes caeruleus) vocal and behavioral mobbing responses

Sparrowhawk movement, calling, and presence of dead conspecifics differentially impact blue tit (Cyanistes caeruleus) vocal and behavioral mobbing responses

Semantic concept schema of the linear mixed model of experimental observations

A Unified Analysis of Structured Sonar-Terrain Data Using Bayesian Functional Mixed Models

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