mvMORPH (version 1.2.1)

mvqqplot: Quantile-Quantile plots for multivariate models fit with mvgls or mvols

Description

The quantile-quantile plots of the Chi square distribution is used to assess multivariate normality and detect outliers using the squared Mahalanobis distances from the models residuals.

Usage

mvqqplot(object, conf=0.95, ...)

Value

a list with components

squared_dist

the squared Mahalanobis distances (standardized)

chi2q

the chi squared quantiles

Arguments

object

A model fit obtained by the mvgls or mvols function.

conf

Confidence interval for the approximate envelope. Default is 0.95.

...

Graphical options.

Author

J. Clavel

Details

The empirical quantiles of standardized Mahalanobis distances (Caroni 1987) estimated from models fit by mvgls (or mvols) are compared to the quantiles of a Chi square distribution with 'p' degrees of freedom (where 'p' is the number of dimensions) when models are fit by maximum likelihood (method='LL'). For penalized likelihood model fit (regularized covariance), a matching moments method is used to map the standardized Mahalanobis distances to the Chi square distribution (Clavel, in prep.). This last option is experimental and still under development.

References

Caroni, C. 1987. Residuals and Influence in the multivariate linear model. Journal of the Royal Statistical Society 36(4): 365-370.

Clavel, J., Aristide, L., Morlon, H., 2019. A Penalized Likelihood framework for high-dimensional phylogenetic comparative methods and an application to new-world monkeys brain evolution. Systematic Biology 68(1): 93-116.

Clavel, J., Morlon, H. 2020. Reliable phylogenetic regressions for multivariate comparative data: illustration with the MANOVA and application to the effect of diet on mandible morphology in phyllostomid bats. Systematic Biology 69(5): 927-943.

See Also

mvgls, mvols, manova.gls

Examples

# \donttest{
data(phyllostomid)

# Fit a linear model by PL
fit <- mvgls(mandible~grp1, data=phyllostomid, phyllostomid$tree, model="lambda", method="PL") 

# QQ plots
mvqqplot(fit, lty=2, conf=0.99)
# }