Nonparametric methods for unbalanced multivariate data and many factor levels

Harrar, Solomon W.; Bathke, Arne C.

doi:10.1016/j.jmva.2008.01.005

Cited by 45 publications

(29 citation statements)

References 21 publications

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“…Our asymptotic framework is that the replication sizes are fixed but the number of levels of one of the factors is large. It was shown in Harrar and Bathke (2008) that the distributions of the test statistics are sensitive to non-normality when the covariances and sample sizes per treatment are not constant. The underlying cause of this problem appears to be the weighting scheme in pulling the data together to get estimates of the within and between variabilities.…”

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confidence: 99%

“…More motivations for this type of asymptotics in agriculture, health sciences, and other disciplines are found in Boos and Brownie (1995), Akritas and Arnold (2000), Bathke (2002Bathke ( , 2004, Harrar and Gupta (2007), in univariate settings, and Gupta et al (2006Gupta et al ( , 2008, Bathke and Harrar (2008), and Harrar and Bathke (2008) in the multivariate setting. Whereas Gupta et al (2006Gupta et al ( , 2008 are restricted to the equal covariance case, Bathke and Harrar (2008) and Harrar and Bathke (2008) consider the single factor nonparametric situation.…”

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confidence: 99%

“…Whereas Gupta et al (2006Gupta et al ( , 2008 are restricted to the equal covariance case, Bathke and Harrar (2008) and Harrar and Bathke (2008) consider the single factor nonparametric situation. For a recent treatise on high-dimensional multivariate approximations, see also Fujikoshi et al (2010).…”

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A modified two-factor multivariate analysis of variance: asymptotics and small sample approximations

Harrar

Bathke

2010

Ann Inst Stat Math

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In this paper, we present results for testing main, simple and interaction effects in heteroscedastic two factor MANOVA models. In particular, we suggest modifications to the MANOVA sum of squares and cross product matrices to account for heteroscedasticity. Based on these modified matrices, we define some multivariate test statistics and derive their asymptotic distributions under non-normality for the null as well as non-null cases. Derivation of these results relies on the perturbation method and limit theorems for independently distributed random matrices. Based on the asymptotic distributions, we devise small sample approximations for the quantiles of the null distributions. The numerical accuracy of the large sample as well as small sample approximations are favorable. A real data set from a Smoking Cessation Trial is analyzed to illustrate the application of the methods.

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A modified two-factor multivariate analysis of variance: asymptotics and small sample approximations

Harrar

Bathke

2010

Ann Inst Stat Math

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“…The simulation results show that they yield conservative test decisions if the data follow distributions with a positive skew. In this case or for other non-normal distributions, non-parametric procedures -like those of Munzel and Brunner [22]; Bathke and Harrar [23]; Harrar and Bathke [24,25] -should be used instead. Note that these procedures do not provide multiplicity-adjusted p-values or SCIs for each contrast-endpoint combination as they use ANOVA-type χ 2 or F statistics, respectively.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Multiple Contrast Tests for Multiple Endpoints in the Presence of Heteroscedasticity

Hasler

2014

The International Journal of Biostatistics

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This article describes an extension of multiple contrast tests to the case of multiple, correlated endpoints. These endpoints are assumed to be normally distributed with different scales and variances. Unlike in previous articles, the covariance matrices are also assumed to be unequal for the treatment groups. Approximate multivariate t-distributions are used to obtain multiplicity-adjusted p-values and quantiles for test decisions or simultaneous confidence intervals. Simulation results show that this approach controls the family-wise error type I over both the comparisons and the endpoints in an admissible range. The approach will be applied to a semi-synthetic example data set of a randomized, placebo-controlled phase IIb dose-finding study of a novel anti-muscarinic agent for five continuous endpoints. A related R package is available.

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“…The package is available from the Comprehensive R Archive Network (CRAN) at http://CRAN.R-project. org/package=npmv, and the underlying methodology is based on the nonparametric approach to multivariate inference presented in , Harrar and Bathke (2008a), Harrar and Bathke (2008b), Bathke, Harrar, and Madden (2008), Ahmad (2009), andLiu, Bathke, andHarrar (2011). One major achievement in the recent methodology development is that no parametric assumptions such as multivariate normality have to be made.…”

Section: Introductionmentioning

confidence: 99%

Nonparametric Inference for Multivariate Data: The R Package npmv

Burchett¹,

Ellis²,

Harrar³

et al. 2017

J. Stat. Soft.

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146

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We introduce the R package npmv that performs nonparametric inference for the comparison of multivariate data samples and provides the results in easy-to-understand, but statistically correct, language. Unlike in classical multivariate analysis of variance, multivariate normality is not required for the data. In fact, the different response variables may even be measured on different scales (binary, ordinal, quantitative). p values are calculated for overall tests (permutation tests and F approximations), and, using multiple testing algorithms which control the familywise error rate, significant subsets of response variables and factor levels are identified. The package may be used for low-or highdimensional data with small or with large sample sizes and many or few factor levels.

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Nonparametric methods for unbalanced multivariate data and many factor levels

Cited by 45 publications

References 21 publications

A modified two-factor multivariate analysis of variance: asymptotics and small sample approximations

A modified two-factor multivariate analysis of variance: asymptotics and small sample approximations

Multiple Contrast Tests for Multiple Endpoints in the Presence of Heteroscedasticity

Nonparametric Inference for Multivariate Data: The R Package npmv

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