summary.mvlm {MVLM}

Summarizing mvlm Results

Description

summary method for class mvlm

Usage

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

Arguments

object

Output from mvlm

...

Further arguments passed to or from other methods.

Value

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

Statistic

Value of the corresponding test statistic.

Numer DF

Numerator degrees of freedom for each test statistic.

Pseudo R2

Size of the corresponding (omnibus or conditional) effect on the multivariate outcome. Note that the intercept term does not have an estimated effect size.

p-value

The p-value for each (omnibus or conditional) effect.

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

p.prec

A data.frame reporting the precision of each p-value. These are the maximum error bound of the p-values reported by the davies function in CompQuadForm.

y.rsq

A matrix containing in its first row the overall variance explained by the model for variable comprising Y (columns). The remaining rows list the variance of each outcome that is explained by the conditional effect of each predictor.

beta.hat

Estimated regression coefficients.

adj.n

Adjusted sample size used to determine whether or not the asmptotic properties of the model are likely to hold. See McArtor et al. (under review) for more detail.

data

Original input data and the model.matrix used to fit the model.

Note that the printed output of summary(res) will truncate p-values to the smallest trustworthy values, but the object returned by summary(mvlm.res) will contain the p-values as computed. 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.

Author(s)

Daniel B. McArtor ([e-mail]) [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., Grasman, R. P. P. P., Lubke, G. H., & Bergeman, C. S. (under review). A new approach to conducting linear model hypothesis tests with a multivariate outcome.

Examples

data(mvlmdata)

Y <- as.matrix(Y.mvlm)

# Main effects model
mvlm.res <- mvlm(Y ~ Cont + Cat + Ord, data = X.mvlm)
summary(mvlm.res)

# Include two-way interactions
mvlm.res.int <- mvlm(Y ~ .^2, data = X.mvlm)
summary(mvlm.res.int)