3,386 research outputs found
MATS: Inference for potentially Singular and Heteroscedastic MANOVA
In many experiments in the life sciences, several endpoints are recorded per
subject. The analysis of such multivariate data is usually based on MANOVA
models assuming multivariate normality and covariance homogeneity. These
assumptions, however, are often not met in practice. Furthermore, test
statistics should be invariant under scale transformations of the data, since
the endpoints may be measured on different scales. In the context of
high-dimensional data, Srivastava and Kubokawa (2013) proposed such a test
statistic for a specific one-way model, which, however, relies on the
assumption of a common non-singular covariance matrix. We modify and extend
this test statistic to factorial MANOVA designs, incorporating general
heteroscedastic models. In particular, our only distributional assumption is
the existence of the group-wise covariance matrices, which may even be
singular. We base inference on quantiles of resampling distributions, and
derive confidence regions and ellipsoids based on these quantiles. In a
simulation study, we extensively analyze the behavior of these procedures.
Finally, the methods are applied to a data set containing information on the
2016 presidential elections in the USA with unequal and singular empirical
covariance matrices
LIMO EEG: A Toolbox for hierarchical LInear MOdeling of ElectroEncephaloGraphic data
Magnetic- and electric-evoked brain responses have traditionally been analyzed by comparing the peaks or mean amplitudes of signals from selected channels and averaged across trials. More recently, tools have been developed to investigate single trial response variability (e.g., EEGLAB) and to test differences between averaged evoked responses over the entire scalp and time dimensions (e.g., SPM, Fieldtrip). LIMO EEG is a Matlab toolbox (EEGLAB compatible) to analyse evoked responses over all space and time dimensions, while accounting for single trial variability using a simple hierarchical linear modelling of the data. In addition, LIMO EEG provides robust parametric tests, therefore providing a new and complementary tool in the analysis of neural evoked responses
Small sample inference for probabilistic index models
Probabilistic index models may be used to generate classical and new rank tests, with the additional advantage of supplementing them with interpretable effect size measures. The popularity of rank tests for small sample inference makes probabilistic index models also natural candidates for small sample studies. However, at present, inference for such models relies on asymptotic theory that can deliver poor approximations of the sampling distribution if the sample size is rather small. A bias-reduced version of the bootstrap and adjusted jackknife empirical likelihood are explored. It is shown that their application leads to drastic improvements in small sample inference for probabilistic index models, justifying the use of such models for reliable and informative statistical inference in small sample studies
Analysis of variance--why it is more important than ever
Analysis of variance (ANOVA) is an extremely important method in exploratory
and confirmatory data analysis. Unfortunately, in complex problems (e.g.,
split-plot designs), it is not always easy to set up an appropriate ANOVA. We
propose a hierarchical analysis that automatically gives the correct ANOVA
comparisons even in complex scenarios. The inferences for all means and
variances are performed under a model with a separate batch of effects for each
row of the ANOVA table. We connect to classical ANOVA by working with
finite-sample variance components: fixed and random effects models are
characterized by inferences about existing levels of a factor and new levels,
respectively. We also introduce a new graphical display showing inferences
about the standard deviations of each batch of effects. We illustrate with two
examples from our applied data analysis, first illustrating the usefulness of
our hierarchical computations and displays, and second showing how the ideas of
ANOVA are helpful in understanding a previously fit hierarchical model.Comment: This paper discussed in: [math.ST/0508526], [math.ST/0508527],
[math.ST/0508528], [math.ST/0508529]. Rejoinder in [math.ST/0508530
fullfact: an R package for the analysis of genetic and maternal variance components from full factorial mating designs
Full factorial breeding designs are useful for quantifying the amount of additive genetic, nonadditive genetic, and maternal variance that explain phenotypic traits. Such variance estimates are important for examining evolutionary potential. Traditionally, full factorial mating designs have been analyzed using a two-way analysis of variance, which may produce negative variance values and is not suited for unbalanced designs. Mixed-effects models do not produce negative variance values and are suited for unbalanced designs. However, extracting the variance components, calculating significance values, and estimating confidence intervals and/or power values for the components are not straightforward using traditional analytic methods. We introduce fullfact an R package that addresses these issues and facilitates the analysis of full factorial mating designs with mixed-effects models. Here, we summarize the functions of the fullfact package. The observed data functions extract the variance explained by random and fixed effects and provide their significance. We then calculate the additive genetic, nonadditive genetic, and maternal variance components explaining the phenotype. In particular, we integrate nonnormal error structures for estimating these components for nonnormal data types. The resampled data functions are used to produce bootstrap-t confidence intervals, which can then be plotted using a simple function. We explore the fullfact package through a worked example. This package will facilitate the analyses of full factorial mating designs in R, especially for the analysis of binary, proportion, and/or count data types and for the ability to incorporate additional random and fixed effects and power analyses
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