score.variance.linear/score.variance.logistic {gaston}

Variance Component Test in Linear or Logistic Mixed Model

Description

Test if a variance component is significaly different from 0 using score test in a Linear or Logistic Mixed Model.

Usage

 
score.variance.linear(K0, Y, X = matrix(1, length(Y)), K, acc_davies=1e-10, ...)
score.variance.logistic(K0, Y, X = matrix(1, length(Y)), K, acc_davies=1e-10, ...)

Arguments

K0

A positive definite matrix

Y

The phenotype vector

X

A covariate matrix. The default is a column vector of ones, to include an intercept in the model

K

A positive definite matrix or a list of such matrices

acc_davies

Accuracy in Davies method used to compute p-value

...

Optional arguments used to fit null model with lmm.aireml of logistic.mm.aireml function.

Details

In score.variance.linear, we consider the linear mixed model

Y = X\alpha + \gamma + \omega_1 + \ldots + \omega_k + \varepsilon

or, in score.variance.logistic, we consider the following logistic model

\mbox{logit}(P[Y=1|X,x,\omega_1,\ldots,\omega_k]) = X\alpha + \gamma + \omega_1 + \ldots + \omega_k

with \gamma\sim N(0,\kappa K_0)\gamma, \omega_j \sim N(0,\tau_j K_j) , \varepsilon \sim N(0,\sigma^2 I_n) . K_0 and K_j are Genetic Relationship Matrix (GRM).

score.variance.linear and score.variance.logistic functions permit to test

H_0 : \kappa=0 \mbox{ vs } H_1 : \kappa>0

with, for linear mixed model, the score

Q = Y'P_OK_0P_0Y/2

or, for logistic mixed model, the score

Q = (Y-\pi_0)'K_0(Y-\pi_0)/2

where P_0 is the last matrix P computed in the optimization process for null model and \pi_0 the vector of fitted values under null logistic model.

The associated p-value is computed with Davies method.

In this aim, all parameters under null model are estimated with lmm.aireml or logistic.mm.aireml. The p-value corresponding to the estimated score is computed using Davies method implemented in 'CompQuadForm' R package.

Value

A named list of values:

score

Estimated score

p

The corresponding p-value

Author(s)

Hervé Perdry and Claire Dandine-Roulland

References

Davies R.B. (1980) Algorithm AS 155: The Distribution of a Linear Combination of chi-2 Random Variables, Journal of the Royal Statistical Society. Series C (Applied Statistics), 323-333

See Also

lmm.aireml, logistic.mm.aireml

Examples

# Load data
data(AGT)
x <- as.bed.matrix(AGT.gen, AGT.fam, AGT.bim)
standardize(x) <- "p"

# Calculate GRM et its eigen decomposition
K0 <- GRM(x)
eig <- eigen(K0)
eig$values <- round(eig$values, 5)

# generate an other positive matrix (to play the role of the second GRM)
set.seed(1)
R <- random.pm(nrow(x))


# simulate quantitative phenotype with two polygenic components
y <- lmm.simu(0.1,1,eigenK=eig)$y + lmm.simu(0.2,0,eigenK=R$eigen)$y

t <- score.variance.linear(K0, y, K=R$K, verbose=FALSE)
str(t)


# simulate binary phenotype with two polygenic components
mu <- lmm.simu(0.1,0.5,eigenK=eig)$y + lmm.simu(0.2,0,eigenK=R$eigen)$y
pi <- 1/(1+exp(-mu))
y <- 1*(runif(length(pi))<pi)

tt <- score.variance.logistic(K0, y, K=R$K, verbose=FALSE)
str(tt)