R/scan_multi_onechr.R
scan_multi_oneqtl.RdThe function first discards individuals with one or more missing phenotypes or missing covariates. It then infers variance components, Vg and Ve. Both Vg and Ve are d by d covariance matrices. It uses an expectation maximization algorithm, as implemented in the `gemma2` R package. `gemma2` R package is an R implementation of the GEMMA algorithm for multivariate variance component estimation (Zhou & Stephens 2014 Nature methods). Note that variance components are fitted on a model that uses the d-variate phenotype but contains no genetic information. This model does, however, use the specified covariates (after dropping dependent columns in the covariates matrix). These inferred covariance matrices, \(\hat{Vg}\) and \(\hat{Ve}\), are then used in subsequent model fitting via generalized least squares. Generalized least squares model fitting is applied to every marker on every chromosome. For a single marker, we fit the model: $$vec(Y) = Xvec(B) + vec(G) + vec(E)$$ where $$G \sim MN(0, K, \hat{Vg})$$ and $$E \sim MN(0, I, \hat{Ve})$$ where \(MN\) denotes the matrix-variate normal distribution with three parameters: mean matrix, covariance among rows, and covariance among columns. \(vec\) denotes the vectorization operation, ie, stacking by columns. \(K\) is a kinship matrix, typically calculated by leave-one-chromosome-out methods. \(Y\) is the n by d phenotypes matrix. \(X\) is a block-diagonal nd by fd matrix consisting of d blocks each of dimension n by f. Each n by f block (on the diagonal) contains a matrix of founder allele probabilities for the n subjects at a single marker. The off-diagonal blocks have only zero entries. The log-likelihood is returned for each model. The outputted object is a tibble with d + 1 columns. The first d columns specify the markers used in the corresponding model fit, while the last column specifies the log-likelihood value at that d-tuple of markers.
scan_multi_oneqtl( probs_list, pheno, kinship_list = NULL, addcovar = NULL, cores = 1 )
| probs_list | an list of arrays of founder allele probabilities |
|---|---|
| pheno | a matrix of phenotypes |
| kinship_list | a list of kinship matrices, one for each chromosome |
| addcovar | a matrix, n subjects by c additive covariates |
| cores | number of cores for parallelization via parallel::mclapply() |
a tibble with d + 1 columns. First d columns indicate the genetic data (by listing the marker ids) used in the design matrix; last is log10 likelihood
Knott SA, Haley CS (2000) Multitrait least squares for quantitative trait loci detection. Genetics 156: 899–911.
Jiang C, Zeng ZB (1995) Multiple trait analysis of genetic mapping for quantitative trait loci. Genetics 140: 1111-1127.
Zhou X, Stephens M (2014) Efficient multivariate linear mixed model algorithms for genome-wide association studies. Nature methods 11:407-409.
Broman KW, Gatti DM, Simecek P, Furlotte NA, Prins P, Sen S, Yandell BS, Churchill GA (2019) R/qtl2: software for mapping quantitative trait loci with high-dimensional data and multi-parent populations. GENETICS https://www.genetics.org/content/211/2/495.
# read data n <- 50 pheno <- matrix(rnorm(2 * n), ncol = 2) rownames(pheno) <- paste0("s", 1:n) colnames(pheno) <- paste0("tr", 1:2) probs <- array(dim = c(n, 2, 5)) probs[ , 1, ] <- rbinom(n * 5, size = 1, prob = 0.2) probs[ , 2, ] <- 1 - probs[ , 1, ] rownames(probs) <- paste0("s", 1:n) colnames(probs) <- LETTERS[1:2] dimnames(probs)[[3]] <- paste0("m", 1:5) scan_multi_oneqtl(probs_list = list(probs, probs), pheno = pheno, cores = 1)#> [[1]] #> # A tibble: 5 x 4 #> Var1 Var2 log10lik null_log10lik #> <chr> <chr> <dbl> <dbl> #> 1 m1 m1 -60.0 -60.7 #> 2 m2 m2 -60.5 -60.7 #> 3 m3 m3 -60.2 -60.7 #> 4 m4 m4 -60.5 -60.7 #> 5 m5 m5 -60.3 -60.7 #> #> [[2]] #> # A tibble: 5 x 4 #> Var1 Var2 log10lik null_log10lik #> <chr> <chr> <dbl> <dbl> #> 1 m1 m1 -60.0 -60.7 #> 2 m2 m2 -60.5 -60.7 #> 3 m3 m3 -60.2 -60.7 #> 4 m4 m4 -60.5 -60.7 #> 5 m5 m5 -60.3 -60.7 #>