gencovtest {biotools}

Testing Genetic Covariance

Description

gencovtest() tests genetic covariance components from a MANOVA model. Two different approaches can be used: (I) a test statistic that takes into account the genetic and environmental effects and (II) a test statistic that only considers the genetic information. The first type refers to tests based on the mean cross-products ratio, whose distribution is obtained via Monte Carlo simulation of Wishart matrices. The second way of testing genetic covariance refers to tests based upon an adaptation of Wilks' and Pillai's statistics for evaluating independence of two sets of variables. All these tests are described by Silva (2015).

Usage

## S3 method for class 'manova'
gencovtest(obj, geneticFactor, gcov = NULL, 
	residualFactor = NULL, adjNrep = 1, 
	test = c("MCPR", "Wilks", "Pillai"), 
	nsim = 9999, 
	alternative = c("two.sided", "less", "greater"))
## S3 method for class 'gencovtest'
print(x, digits = 4, ...)
## S3 method for class 'gencovtest'
plot(x, var1, var2, ...)

Arguments

obj

an object of class "manova".

geneticFactor

a character indicating the genetic factor from which to test covariance components. It must be declared as a factor in the manova object.

gcov

optional; a matrix containing estimates of genetic covariances to be tested. If NULL (default), an estimate is obtained via method of moments.

residualFactor

optional; a character indicating a source in the manova model to be used as error term. If NULL (default), the usual term "Residuals" will be used.

adjNrep

a correction index for dealing with unbalanced data. See details.

test

a character indicating the test. It must be on of the following: "MCPR" - the empirical type-I test based on Mean Cross-Products Ratios via Wishart simulation, "Wilks" - a type-II test based on the partial Wilks' Lambda, "Pillai" - a type-II test based on the partial Pillai's statistic.

nsim

the number of Monte Carlo simulations. Used only if test = "MCPR".

alternative

the type of alternative hypothesis. Used only if test = "MCPR". So far, only the option "two.sided" is implemented.

x

an object of class "gencovtest".

digits

the number of digits to be displayed by the print method.

var1

a character of integer indicating one of the two response variable or its position.

var2

a character of integer indicating one of the two response variable or its position.

...

further arguments.

Details

The genetic covariance matrix is currently estimated via method of moments, following the equation:

G = (Mg - Me) / (nrep * adjNrep)

where Mg and Me are the matrices of mean cross-products associated with the genetic factor and the residuals, respectively; nrep is the number of replications, calculated as the ratio between the total number of observations and the number of levels of the genetic factor; adjNrep is supposed to adjust nrep, specially when estimating G from unbalanced data.

Value

An object of class gencovtest, a list of

gcov

a p-dimensional square matrix containing estimates of the genetic covariances.

gcor

a p-dimensional square matrix containing estimates of the genetic correlations.

test

the test (as input).

statistics

a p-dimensional square matrix containing the test statistics. If test = "MCPR" the mean cross-products ratios are computed; if test = "Wilks" the Wilks' Lambda is; and test = "Pillai" results on Pillai's Tn.

p.values

a p-dimensional square matrix containing the associated p-values.

alternative

the type of alternative hypothesis (as input).

X2

a p-dimensional square matrix containing the Chi-square (D.f. = 1) approximation for Wilks's and Pillai's statistics. Stored only if one of these two tests is chosen.

simRatio

an array consisting of nsim p-dimensional matrices containing the simulated mean cross-products ratios.

dfg

the number of degrees of freedom associated with the genetic factor.

dfe

the number of degrees of freedom associated with the residual term.

Warning

When using the MCPR test, be aware that dfg should be equal or greater than the number of variables (p). Otherwise the simulation of Wishart matrices may not be done.

A collinearity diagnosis is carried out using the condition number (CN), for the inferences may be affected by the quality of G. Thus, if CN > 100, a warning message is displayed.

Author(s)

Anderson Rodrigo da Silva <[e-mail]>

References

Silva, A.R. (2015) On Testing Genetic Covariance. LAP Lambert Academic Publishing. ISBN 3659716553

See Also

manova

Examples

# MANOVA
data(maize)
M <- manova(cbind(NKPR, ED, CD, PH) ~ family + env, data = maize)
summary(M)

# Example 1 - MCPR
t1 <- gencovtest(obj = M, geneticFactor = "family")
print(t1)
plot(t1, "ED", "PH")

# Example 2 - Pillai
t2 <- gencovtest(obj = M, geneticFactor = "family", test = "Pillai")
print(t2)
plot(t2, "ED", "PH")

# End (not run)