Hypothesis Tests for Multivariate Linear Models Using the car Package

Fox, John; Friendly, Michael; Weisberg, Sanford

doi:10.32614/rj-2013-004

Cited by 560 publications

(518 citation statements)

References 17 publications

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“…Mixed models were analyzed using R package lme4 (Bates et al ). We report tests of coefficients using Wald χ 2 statistics from Type II ANOVAs that assess effects after accounting for all other non‐interaction effects using R package car (Fox #8954). For treatments with significant ( p < 0.05) Wald χ 2 tests for the treatment as a whole, we show results of Tukey multiple comparisons on the graphs using letters that indicate which treatment levels differ significantly from each other.…”

Section: Methodsmentioning

confidence: 99%

Increased light availability due to forestry mowing of invasive European buckthorn promotes its regeneration

Anfang

Schuster

Wragg

2020

Restoration Ecology

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The invasive shrub Rhamnus cathartica L. (common buckthorn) dominates the understory of many temperate forests of eastern North America. Common buckthorn outcompetes native understory species for light, forming monospecific stands that suppress plant and animal diversity. Removing common buckthorn is a common management priority within its invasive range. In recent years, forestry mowing has become popular in removing common buckthorn. This control method removes a midstory of common buckthorn, increasing light availability to the lower understory (which could favor buckthorn regeneration) and creating a layer of mulch on the forest floor (which could suppress buckthorn regeneration). Here we investigate whether and how increased light availability and increased ground cover (mulch) resulting from forestry mowing affects buckthorn regeneration from the seed bank. We evaluated buckthorn germination, survival, and early growth in response to a factorial combination of shading treatments and buckthorn mulch depth treatments in an oak forest in Minnesota, U.S.A. Increased light availability increased buckthorn seedling survival and growth, whereas increased mulch depth did not significantly affect the number of buckthorn establishing from seed over one growing season and winter. Thus, removing buckthorn by forestry mowing (or any other method) is likely to facilitate buckthorn reestablishment by increasing light availability at the ground.

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Section: Methodsmentioning

confidence: 99%

Increased light availability due to forestry mowing of invasive European buckthorn promotes its regeneration

Anfang

Schuster

Wragg

2020

Restoration Ecology

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“…Finally, when modelling the number of discrete looks within a trial (a count response), we used a Poisson distribution. Across analyses, graphs showing predicted effects and confidence intervals (CIs) from these models were calculated using the effects package in R (Fox et al, 2016). …”

Section: Methodsmentioning

confidence: 99%

Tolerant Barbary macaques maintain juvenile levels of social attention in old age, but despotic rhesus macaques do not

Rosati

Santos

2017

Animal Behaviour

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Complex social life is thought to be a major driver of complex cognition in primates, but few studies have directly tested the relationship between a given primate species’ social system and their social cognitive skills. We experimentally compared life span patterns of a foundational social cognitive skill (following another’s gaze) in tolerant Barbary macaques, Macaca sylvanus, and despotic rhesus macaques, Macaca mulatta. Semi-free-ranging monkeys (N = 80 individuals from each species) followed gaze more in test trials where an actor looked up compared to control trials. However, species differed in ontogenetic trajectories: both exhibited high rates of gaze following as juveniles, but rhesus monkeys exhibited declines in social attention with age, whereas Barbary macaques did not. This pattern indicates that developmental patterns of social attention vary with social tolerance, and that diversity in social behaviour can lead to differences in social cognition across primates.

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“…Once the associated R in Eq. (4) is constructed, under the sphericity assumption its SS term and the corresponding SS term for errors can be obtained (Fox et al, 2013) as tr ( H ( R T R ) −1 ) and tr ( E ( R T R ) −1 ). Under alternative coding schemes that render an orthonormal transformation matrix R , unique portions of variance among the transformed response variables can be captured, and the SS terms simplify to tr ( H ) and tr ( E ).…”

Section: Univariate Testing (Uvt) Under the Mvm Platformmentioning

confidence: 99%

“…The two correction methods above, UVT-SC and HT, adopted at the voxel level in , are similar to statistical packages such as car in R (Fox et al, 2013), in IBM SPSS Statistics (IBM Corp., 2012) and REPEATED statement in of SAS (SAS Institute Inc., 2011) except that contingent schemes are adopted here. In addition, instead of directly adjusting the degrees of freedom for sphericity correction, we opt to keep the original degrees of freedom (constant across the brain) but change the F -value to match the adjusted p -value, and this allows us to simplify the bookkeeping and visualization of the output.…”

Section: Implementation Of Mvm In Afnimentioning

confidence: 99%

Applications of multivariate modeling to neuroimaging group analysis: A comprehensive alternative to univariate general linear model

et al. 2014

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All neuroimaging packages can handle group analysis with t-tests or general linear modeling (GLM). However, they are quite hamstrung when there are multiple within-subject factors or when quantitative covariates are involved in the presence of a within-subject factor. In addition, sphericity is typically assumed for the variance–covariance structure when there are more than two levels in a within-subject factor. To overcome such limitations in the traditional AN(C)OVA and GLM, we adopt a multivariate modeling (MVM) approach to analyzing neuroimaging data at the group level with the following advantages: a) there is no limit on the number of factors as long as sample sizes are deemed appropriate; b) quantitative covariates can be analyzed together with within- subject factors; c) when a within-subject factor is involved, three testing methodologies are provided: traditional univariate testing (UVT)with sphericity assumption (UVT-UC) and with correction when the assumption is violated (UVT-SC), and within-subject multivariate testing (MVT-WS); d) to correct for sphericity violation at the voxel level, we propose a hybrid testing (HT) approach that achieves equal or higher power via combining traditional sphericity correction methods (Greenhouse–Geisser and Huynh–Feldt) with MVT-WS.

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Hypothesis Tests for Multivariate Linear Models Using the car Package

Abstract: The multivariate linear model is

Cited by 560 publications

References 17 publications

Increased light availability due to forestry mowing of invasive European buckthorn promotes its regeneration

Increased light availability due to forestry mowing of invasive European buckthorn promotes its regeneration

Tolerant Barbary macaques maintain juvenile levels of social attention in old age, but despotic rhesus macaques do not

Applications of multivariate modeling to neuroimaging group analysis: A comprehensive alternative to univariate general linear model

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