Score Test for Covariates with Fixed Effects in Linear or Logistic Mixed Model
Score Test for association between covariates and phenotype.
score.fixed.linear(x, Y, X = matrix(1, length(Y)), K, ...) score.fixed.logistic(x, Y, X = matrix(1, length(Y)), K, ...)
x |
A matrix of covariates |
Y |
The phenotype vector |
X |
A covariable matrix. The default is a column vector of ones, to include an intercept in the model |
K |
A positive definite matrix or a |
... |
Optional arguments used to fit null model in |
The function score.fixed.linear considers the linear mixed model
Y = X alpha + x beta + omega_1 + ... + omega_k + varepsilon
whereas the score.fixed.logistic function considers the following logistic model
logit(P[Y=1|X,x,omega_1,...,omega_k]) = Xalpha + x beta + omega_1 + ... + omega_k
with omega_j ~ N(0, tau_j K_j) where K_j are Genetic Relationship Matrix (GRM), epsilon ~ N(0, sigma^2 I_n) and fixed effects alpha and beta.
The two functions give score test for
H0 : beta=0 vs H1 : beta !=0.
In this aim, all parameters under null model are estimated with lmm.aireml or logistic.mm.aireml.
A named list of values:
score |
Estimated score |
p |
The corresponding p-value |
log.p |
The logarithm of corresponding p-value |
Hervé Perdry and Claire Dandine-Roulland
# Load data data(AGT) x <- as.bed.matrix(AGT.gen, AGT.fam, AGT.bim) standardize(x) <- "p" # Calculate GRM et its eigen decomposition k <- GRM(x) eig <- eigen(k) eig$values <- round(eig$values, 5) # generate covariate matrix set.seed(1) X <- cbind( rbinom(nrow(x), 1, prob=1/2), rnorm(nrow(x)) ) # simulate quantitative phenotype with polygenic component and covariate effects y <- X %*% c(-1,0.5) + lmm.simu(0.3,1,eigenK=eig)$y t <- score.fixed.linear(X, y, K=k, verbose=FALSE) str(t) # simulate binary phenotype with polygenic component and covariate effects mu <- X %*% c(-1,0.5) + lmm.simu(1, 0, eigenK=eig)$y pi <- 1/(1+exp(-mu)) y <- 1*( runif(length(pi))<pi ) tt <- score.fixed.logistic(X, y, K=k, verbose=FALSE) str(tt)
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