Summarizing MDMR Results

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Description

summary method for class mdmr

Usage

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## S3 method for class 'mdmr'
summary(object, ...)

Arguments

object

Output from mdmr

...

Further arguments passed to or from other methods.

Value

Calling summary(mdmr.res) produces a data frame comprised of:

Statistic

Value of the corresponding MDMR test statistic

Pseudo R2

Size of the corresponding effect on the distance matrix

p-value

The p-value for each effect.

In addition to the information in the three columns comprising summary(res), the res object also contains:

p.prec

A data.frame reporting the precision of each p-value. If analytic p-values were computed, these are the maximum error bound of the p-values reported by the davies function in CompQuadForm. If permutation p-values were computed, it is the standard error of each permutation p-value.

lambda

A vector of the eigenvalues of G (if return.lambda = T).

nperm

Number of permutations used. Will read NA if analytic p-values were computed

Note that the printed output of summary(res) will truncate p-values to the smallest trustworthy values, but the object returned by summary(res) will contain the p-values as computed. The reason for this truncation differs for analytic and permutation p-values. For an analytic p-value, if the error bound of the Davies algorithm is larger than the p-value, the only conclusion that can be drawn with certainty is that the p-value is smaller than (or equal to) the error bound. For a permutation test, the estimated p-value will be zero if no permuted test statistics are greater than the observed statistic, but the zero p-value is only a product of the finite number of permutations conduted. The only conclusion that can be drawn is that the p-value is smaller than 1/nperm.

Author(s)

Daniel B. McArtor (dmcartor@nd.edu) [aut, cre]

References

Davies, R. B. (1980). The Distribution of a Linear Combination of chi-square Random Variables. Journal of the Royal Statistical Society. Series C (Applied Statistics), 29(3), 323-333.

Duchesne, P., & De Micheaux, P. L. (2010). Computing the distribution of quadratic forms: Further comparisons between the Liu-Tang-Zhang approximation and exact methods. Computational Statistics and Data Analysis, 54(4), 858-862.

McArtor, D. B., Lubke, G. H., & Bergeman, C. S. (second revision under review). Extending multivariate distance matrix regression with an effect size measure and the distribution of the test statistic.

Examples

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# --- The following two approaches yield equivalent results --- #
# Approach 1
data(mdmrdata)
D <- dist(Y.mdmr, method = 'euclidean')
mdmr.res <- mdmr(X = X.mdmr, D = D)
summary(mdmr.res)