Multilinear tools: Tools for the Multilinear Regression

Description

The functions perform various tasks required by the multilinear regression model.

Usage

formulaMultilinear(nloc=2, max.level=2, max.dom=2, 
		e.unique=FALSE)
reconstructLinearEffects(noia.multilinear)
startingValues(phen, genZ, reference="noia", max.level=2, 
	max.dom=2, fast=FALSE, e.unique=FALSE, start.algo="linear", 
	bilinear.steps=NULL, ...) 
startingValuesReg(reg, max.level=2, max.dom=2, e.unique=FALSE, 
	nloc=NULL)
startingValuesNothing(nloc, max.level=2, max.dom=2, 
	e.unique=FALSE)
startingValuesLinear(noia.linear, max.level=2, max.dom=2, 
	e.unique=FALSE, e.init=TRUE)
startingValuesMultilinear(noia.multilinear, max.level=2, 
	max.dom=2, e.unique=FALSE)
bilinearStep(form, X, phen, marginal, interactions, ...)

Arguments

nloc

Number of loci.

max.level

Maximum order of interactions.

max.dom

Maximum order for dominance.

e.unique

Whether a single interaction term is used for all pairs.

e.init

Whether starting values for epistatic effects should be calculated (if FALSE, all epistatic effects are set to 0).

phen

Vector of phenotypes.

genZ

The matrix of individual genotypic probabilities in the population.

reference

The reference point from which the regression is performed.

fast

Use of the "fast" algorithm.

start.algo

Algorithm used to compute the starting values. Can be "linear", "multilinear", "subset" or "bilinear".

bilinear.steps

Number of calls of the bilinearStep function. Ignored if start.algo is not "bilinear".

noia.multilinear

Object of class "noia.multilinear" provided by multilinearRegression.

noia.linear

Object of class "noia.linear" provided by linearRegression.

reg

Object of class "noia.linear" or "noia.multilinear".

form

A multilinear formula as returned by formulaMultilinear.

The product between a Z matrix and a S matrix. Can be provided directly by genZ2X.

marginal

A list of marginal effects.

interactions

A list of interaction effects. Should be complementary to marginal, together accounting for all genetic effects.

...

Extra parameters to the non-linear regression function nls.

Details

Because of the way the non-linear regression function nls works, the multilinear formula has to follow a specific form, with specific names for parameters. formulaMultilinear provides this formula. reconstructLinearEffects generates a vector of genetic effects, including general interaction effects (e.g. Additive by Additive etc) from the result of a multilinear regression. This is necessary for further computation of the Genotype-to-Phenotype map. Finally, startingValues provide a vector of starting values for the multilinear regression, from the result of a linear regression (through the function startingValuesLinear) or a simplier multilinear regression (through StartingValuesMultilinear). startingValuesNothing generates a list of starting values and sets all of them to 0. Starting values are necessary to ensure the convergence of the non-linearRegression (nls).

References

Hansen TF, Wagner G. (2001) Modeling genetic architecture: A multilinear theory of gene interactions. Theoretical Population Biology 59:61-86.

Le Rouzic A, Alvarez-Castro JM. (2008). Estimation of genetic effects and genotype-phenotype maps. Evolutionary Bioinformatics, 4.

Examples

Run this code

set.seed(123456789)

map <- c(0.25, -0.75, -0.75, -0.75, 2.25, 2.25, -0.75, 2.25, 2.25)
pop <- simulatePop(map, N=500, sigmaE=0.2, type="F2")

linear <- linearRegression(phen=pop$phen, gen=pop[2:3])
multilinear <- multilinearRegression(phen=pop$phen, 
	gen=cbind(pop$Loc1, pop$Loc2))

formulaMultilinear(nloc=2)
startingValuesReg(linear)
reconstructLinearEffects(multilinear)