R/RGWAS.multisnp.interaction.R

In RAINBOWR: Genome-Wide Association Study with SNP-Set Methods

#' Testing multiple SNPs and their interaction with some kernel simultaneously for GWAS
#'
#' @description This function performs SNP-set GWAS (genome-wide association studies),
#' which tests multiple SNPs (single nucleotide polymorphisms) simultaneously. The model of SNP-set GWAS is
#'
#' \deqn{y = X \beta + Q v +  Z _ {c} u _ {c} +  Z _ {r} u _ {r} + \epsilon,}
#'
#' where \eqn{y} is the vector of phenotypic values,
#' \eqn{X \beta} and \eqn{Q v} are the terms of fixed effects,
#' \eqn{Z _ {c} u _ {c}} and \eqn{Z _ {c} u _ {c}} are the term of random effects and \eqn{e} is the vector of residuals.
#' \eqn{X \beta} indicates all of the fixed effects other than population structure, and often this term also plays
#' a role as an intercept. \eqn{Q v} is the term to correct the effect of population structure.
#' \eqn{Z _ {c} u _ {c}} is the term of polygenetic effects, and suppose that \eqn{u _ {c}}
#' follows the multivariate normal distribution whose variance-covariance
#' matrix is the genetic covariance matrix. \eqn{u _ {c} \sim MVN (0, K _ {c} \sigma_{c}^{2})}.
#' \eqn{Z _ {r} u _ {r}} is the term of effects for SNP-set of interest, and suppose that \eqn{u _ {r}}
#' follows the multivariate normal distribution whose variance-covariance
#' matrix is the Gram matrix (linear, exponential, or gaussian kernel)
#' calculated from marker genotype which belong to that SNP-set.
#' Therefore, \eqn{u _ {r} \sim MVN (0, K _ {r} \sigma_{r}^{2})}.
#' Finally, the residual term is assumed to identically and independently follow
#' a normal distribution as shown in the following equation.
#' \eqn{e \sim MVN (0, I \sigma_{e}^{2})}.
#'
#'
#' @param pheno Data frame where the first column is the line name (gid). The remaining columns should be a phenotype to test.
#' @param geno Data frame with the marker names in the first column. The second and third columns contain the chromosome and map position.
#'        Columns 4 and higher contain the marker scores for each line, coded as {-1, 0, 1} = {aa, Aa, AA}.
#' @param ZETA A list of covariance (relationship) matrix (K: \eqn{m \times m}) and its design matrix (Z: \eqn{n \times m}) of random effects.
#' Please set names of list "Z" and "K"! You can use more than one kernel matrix.
#' For example,
#'
#' ZETA = list(A = list(Z = Z.A, K = K.A), D = list(Z = Z.D, K = K.D))
#' \describe{
#' \item{Z.A, Z.D}{Design matrix (\eqn{n \times m}) for the random effects. So, in many cases, you can use the identity matrix.}
#' \item{K.A, K.D}{Different kernels which express some relationships between lines.}
#' }
#' For example, K.A is additive relationship matrix for the covariance between lines, and K.D is dominance relationship matrix.
#' @param interaction.kernel A \eqn{n \times n} Gram (kernel) matrix which may indicate some interaction with SNP-sets to be tested.
#' @param include.interaction.kernel.null Whether or not including `iteraction.kernel` itself into the null and alternative models.
#' @param include.interaction.with.gb.null Whether or not including the interaction term between `iteraction.kernel`
#' and the genetic background (= kinship matrix) into the null and alternative models. By setting this TRUE, you can avoid the false positives caused
#' by epistastis between polygenes, especially you set kinship matrix as `interaction.kernel`.
#' @param package.MM The package name to be used when solving mixed-effects model. We only offer the following three packages:
#' "RAINBOWR", "MM4LMM" and "gaston". Default package is `gaston`.
#' See more details at \code{\link{EM3.general}}.
#' @param covariate A \eqn{n \times 1} vector or a \eqn{n \times p _ 1} matrix. You can insert continuous values, such as other traits or genotype score for special markers.
#' This argument is regarded as one of the fixed effects.
#' @param covariate.factor A \eqn{n \times p _ 2} dataframe. You should assign a factor vector for each column.
#' Then RGWAS changes this argument into model matrix, and this model matrix will be included in the model as fixed effects.
#' @param structure.matrix You can use structure matrix calculated by structure analysis when there are population structure.
#' You should not use this argument with n.PC > 0.
#' @param n.PC Number of principal components to include as fixed effects. Default is 0 (equals K model).
#' @param min.MAF Specifies the minimum minor allele frequency (MAF).
#' If a marker has a MAF less than min.MAF, it is assigned a zero score.
#' @param test.method RGWAS supports only one method to test effects of each SNP-set.
#' \describe{
#' \item{"LR"}{Likelihood-ratio test, relatively slow, but accurate (default).}
#' }
#' @param n.core Setting n.core > 1 will enable parallel execution on a machine with multiple cores.
#' This argument is not valid when `parallel.method = "furrr"`.
#' @param parallel.method Method for parallel computation. We offer three methods, "mclapply", "furrr", and "foreach".
#'
#' When `parallel.method = "mclapply"`, we utilize \code{\link[pbmcapply]{pbmclapply}} function in the `pbmcapply` package
#' with `count = TRUE` and \code{\link[parallel]{mclapply}} function in the `parallel` package with `count = FALSE`.
#'
#' When `parallel.method = "furrr"`, we utilize \code{\link[furrr]{future_map}} function in the `furrr` package.
#' With `count = TRUE`, we also utilize \code{\link[progressr]{progressor}} function in the `progressr` package to show the progress bar,
#' so please install the `progressr` package from github (\url{https://github.com/HenrikBengtsson/progressr}).
#' For `parallel.method = "furrr"`, you can perform multi-thread parallelization by
#' sharing memories, which results in saving your memory, but quite slower compared to `parallel.method = "mclapply"`.
#'
#' When `parallel.method = "foreach"`, we utilize \code{\link[foreach]{foreach}} function in the `foreach` package
#' with the utilization of \code{\link[parallel]{makeCluster}} function in `parallel` package,
#' and \code{\link[doParallel]{registerDoParallel}} function in `doParallel` package.
#' With `count = TRUE`, we also utilize \code{\link[utils]{setTxtProgressBar}} and
#' \code{\link[utils]{txtProgressBar}} functions in the `utils` package to show the progress bar.
#'
#' We recommend that you use the option `parallel.method = "mclapply"`, but for Windows users,
#' this parallelization method is not supported. So, if you are Windows user,
#' we recommend that you use the option `parallel.method = "foreach"`.
#' @param kernel.method It determines how to calculate kernel. There are three methods.
#' \describe{
#' \item{"gaussian"}{It is the default method. Gaussian kernel is calculated by distance matrix.}
#' \item{"exponential"}{When this method is selected, exponential kernel is calculated by distance matrix.}
#' \item{"linear"}{When this method is selected, linear kernel is calculated by NOIA methods for additive GRM.}
#'}
#' So local genomic relation matrix is regarded as kernel.
#' @param kernel.h The hyper parameter for gaussian or exponential kernel.
#' If kernel.h = "tuned", this hyper parameter is calculated as the median of off-diagonals of distance matrix of genotype data.
#' @param haplotype If the number of lines of your data is large (maybe > 100), you should set haplotype = TRUE.
#'             When haplotype = TRUE, haplotype-based kernel will be used for calculating -log10(p).
#'             (So the dimension of this gram matrix will be smaller.)
#'             The result won't be changed, but the time for the calculation will be shorter.
#' @param num.hap When haplotype = TRUE, you can set the number of haplotypes which you expect.
#'           Then similar arrays are considered as the same haplotype, and then make kernel(K.SNP) whose dimension is num.hap x num.hap.
#'           When num.hap = NULL (default), num.hap will be set as the maximum number which reflects the difference between lines.
#' @param test.effect Effect of each marker to test. You can choose "test.effect" from "additive", "dominance" and "additive+dominance".
#' You also can choose more than one effect, for example, test.effect = c("additive", "aditive+dominance")
#' @param window.size.half This argument decides how many SNPs (around the SNP you want to test) are used to calculated K.SNP.
#' More precisely, the number of SNPs will be 2 * window.size.half + 1.
#' @param window.slide This argument determines how often you test markers. If window.slide = 1, every marker will be tested.
#' If you want to perform SNP set by bins, please set window.slide = 2 * window.size.half + 1.
#' @param chi0.mixture RAINBOWR assumes the deviance is considered to follow a x chisq(df = 0) + (1 - a) x chisq(df = r).
#' where r is the degree of freedom.
#' The argument chi0.mixture is a (0 <= a < 1), and default is 0.5.
#' @param gene.set If you have information of gene (or haplotype block), you can use it to perform kernel-based GWAS.
#'            You should assign your gene information to gene.set in the form of a "data.frame" (whose dimension is (the number of gene) x 2).
#'            In the first column, you should assign the gene name. And in the second column, you should assign the names of each marker,
#'            which correspond to the marker names of "geno" argument.
#' @param map.gene.set Genotype map for `gene.set` (list of haplotype blocks).
#' This is a data.frame with the haplotype block (SNP-set, or gene-set) names in the first column.
#' The second and third columns contain the chromosome and map position for each block.
#' The forth column contains the cumulative map position for each block, which can be computed by \code{\link{cumsumPos}} function.
#' If this argument is NULL, the map will be constructed by \code{\link{genesetmap}} function after the SNP-set GWAS.
#' It will take some time, so you can reduce the computational time by assigning this argument beforehand.
#' @param weighting.center In kernel-based GWAS, weights according to the Gaussian distribution (centered on the tested SNP) are taken into account when calculating the kernel if Rainbow = TRUE.
#'           If weighting.center = FALSE, weights are not taken into account.
#' @param weighting.other You can set other weights in addition to weighting.center. The length of this argument should be equal to the number of SNPs.
#'           For example, you can assign SNP effects from the information of gene annotation.
#' @param sig.level Significance level for the threshold. The default is 0.05.
#' @param method.thres Method for detemining threshold of significance. "BH" and "Bonferroni are offered.
#' @param plot.qq If TRUE, draw qq plot.
#' @param plot.Manhattan If TRUE, draw manhattan plot.
#' @param plot.method If this argument = 1, the default manhattan plot will be drawn.
#' If this argument = 2, the manhattan plot with axis based on Position (bp) will be drawn.
#'  Also, this plot's color is changed by all chromosomes.
#' @param plot.col1 This argument determines the color of the manhattan plot.
#'  You should substitute this argument as color vector whose length is 2.
#'  plot.col1[1] for odd chromosomes and plot.col1[2] for even chromosomes
#' @param plot.col2 Color of the manhattan plot. color changes with chromosome and it starts from plot.col2 + 1
#' (so plot.col2 = 1 means color starts from red.)
#' @param plot.type  This argument determines the type of the manhattan plot. See the help page of "plot".
#' @param plot.pch This argument determines the shape of the dot of the manhattan plot. See the help page of "plot".
#' @param saveName When drawing any plot, you can save plots in png format. In saveName, you should substitute the name you want to save.
#' When saveName = NULL, the plot is not saved.
#' @param main.qq The title of qq plot. If this argument is NULL, trait name is set as the title.
#' @param main.man The title of manhattan plot. If this argument is NULL, trait name is set as the title.
#' @param plot.add.last If saveName is not NULL and this argument is TRUE, then you can add lines or dots to manhattan plots.
#' However, you should also write "dev.off()" after adding something.
#' @param optimizer The function used in the optimization process. We offer "optim", "optimx", and "nlminb" functions.
#' @param return.EMM.res When return.EMM.res = TRUE, the results of equation of mixed models are included in the result of RGWAS.
#' @param thres If thres = TRUE, the threshold of the manhattan plot is included in the result of RGWAS.
#' When return.EMM.res or thres is TRUE, the results will be "list" class.
#' @param skip.check As default, RAINBOWR checks the type of input data and modifies it into the correct format.
#' However, it will take some time, so if you prepare the correct format of input data, you can skip this procedure
#' by setting `skip.check = TRUE`.
#' @param verbose If this argument is TRUE, messages for the current steps will be shown.
#' @param verbose2 If this argument is TRUE, welcome message will be shown.
#' @param count When count is TRUE, you can know how far RGWAS has ended with percent display.
#' @param time When time is TRUE, you can know how much time it took to perform RGWAS.
#'
#'
#' @return
#' \describe{
#' \item{$D}{Dataframe which contains the information of the map you input and the results of RGWAS (-log10(p)) which correspond to the map.
#' If there are more than one test.effects, then multiple lists for each test.effect are returned respectively.}
#' \item{$thres}{A vector which contains the information of threshold determined by FDR = 0.05.}
#' \item{$EMM.res}{This output is a list which contains the information about the results of "EMM" perfomed at first in regular GWAS.
#'  If you want to know details, see the description for the function "EMM1" or "EMM2".}
#' }
#'
#'
#' @details P-value for each SNP-set is calculated by performing the LR test
#' or the score test (Lippert et al., 2014).
#'
#' In the LR test, first, the function solves the multi-kernel mixed model and
#' calaculates the maximum restricted log likelihood.
#' Then it performs the LR test by using the fact that the deviance
#'
#' \deqn{D = 2 \times (LL _ {alt} - LL _ {null})}
#'
#' follows the chi-square distribution.
#'
#' In the score test, the maximization of the likelihood is only performed for the null model.
#' In other words, the function calculates the score statistic
#' without solving the multi-kernel mixed model for each SNP-set.
#' Then it performs the score test by using the fact that the score statistic follows the chi-square distribution.
#'
#'
#' @references
#' Storey, J.D. and Tibshirani, R. (2003) Statistical significance for genomewide studies. Proc Natl Acad Sci. 100(16): 9440-9445.
#'
#' Yu, J. et al. (2006) A unified mixed-model method for association mapping that accounts for multiple levels of relatedness. Nat Genet. 38(2): 203-208.
#'
#' Kang, H.M. et al. (2008) Efficient Control of Population Structure in Model Organism Association Mapping. Genetics. 178(3): 1709-1723.
#'
#' Endelman, J.B. (2011) Ridge Regression and Other Kernels for Genomic Selection with R Package rrBLUP. Plant Genome J. 4(3): 250.
#'
#' Endelman, J.B. and Jannink, J.L. (2012) Shrinkage Estimation of the Realized Relationship Matrix. G3 Genes, Genomes, Genet. 2(11): 1405-1413.
#'
#' Zhou, X. and Stephens, M. (2012) Genome-wide efficient mixed-model analysis for association studies. Nat Genet. 44(7): 821-824.
#'
#' Listgarten, J. et al. (2013) A powerful and efficient set test for genetic markers that handles confounders. Bioinformatics. 29(12): 1526-1533.
#'
#' Lippert, C. et al. (2014) Greater power and computational efficiency for kernel-based association testing of sets of genetic variants. Bioinformatics. 30(22): 3206-3214.
#'
#' @example R/examples/RGWAS.multisnp.interaction_example.R
#'
#'
#'
RGWAS.multisnp.interaction <- function(pheno, geno, ZETA = NULL,
                                       interaction.kernel = NULL,
                                       include.interaction.kernel.null = FALSE,
                                       include.interaction.with.gb.null = FALSE,
                                       package.MM = "gaston",
                                       covariate = NULL, covariate.factor = NULL,
                                       structure.matrix = NULL, n.PC = 0, min.MAF = 0.02,
                                       test.method = "LR", n.core = 1, parallel.method = "mclapply",
                                       kernel.method = "linear", kernel.h = "tuned",
                                       haplotype = TRUE, num.hap = NULL, test.effect = "additive",
                                       window.size.half = 5, window.slide = 1, chi0.mixture = 0.5,
                                       gene.set = NULL, map.gene.set = NULL,
                                       weighting.center = TRUE, weighting.other = NULL,
                                       sig.level = 0.05, method.thres = "BH", plot.qq = TRUE,
                                       plot.Manhattan = TRUE, plot.method = 1,
                                       plot.col1 = c("dark blue", "cornflowerblue"), plot.col2 = 1,
                                       plot.type = "p", plot.pch = 16, saveName = NULL,
                                       main.qq = NULL, main.man = NULL, plot.add.last = FALSE,
                                       return.EMM.res = FALSE, optimizer = "nlminb",
                                       thres = TRUE, skip.check = FALSE, verbose = TRUE,
                                       verbose2 = FALSE, count = TRUE, time = TRUE) {

  #### The start of the RGWAS function ####
  start <- Sys.time()


  #### Some settings to perform RGWAS ####
  if (verbose2) {
    welcome_to_RGWAS()
  }

  ### For phenotype ###
  n.sample.pheno <- nrow(pheno)
  n.pheno <- ncol(pheno) - 1
  pheno.ix <- 2:ncol(pheno)
  pheno.names <- colnames(pheno)[2:ncol(pheno)]
  lines.name.pheno <- as.character(pheno[, 1])

  ### For covariate ###
  X0 <- matrix(1, n.sample.pheno, 1)
  colnames(X0) <- "Intercept"
  rownames(X0) <- lines.name.pheno

  if (!is.null(covariate)) {
    covariate <- as.matrix(covariate)
    p1 <- ncol(covariate)
    X0 <- cbind(X0, scale(covariate))
  }

  if (!is.null(covariate.factor)) {
    covariate.factor <- data.frame(covariate.factor)
    p2 <- ncol(covariate.factor)
    for (i in 1:p2) {
      cov.fac.now <- covariate.factor[, i]
      if (length(unique(cov.fac.now)) > 1) {
        model.mat.now <- model.matrix(~ x - 1, data.frame(x = cov.fac.now))
        colnames(model.mat.now) <- paste0("cov.fac.", i, "_", 1:length(unique(cov.fac.now)))
        X0 <- cbind(X0, model.mat.now[, -length(unique(cov.fac.now))])
      }
    }
  }

  if (!is.null(structure.matrix)) {
    structure.matrix <- as.matrix(structure.matrix)
    colnames(structure.matrix) <- paste0("subpop", 1:ncol(structure.matrix))
    X0 <- cbind(X0, structure.matrix)

    n.PC <- 0
  }


  ### For genotype ###
  geno <- geno[order(geno[, 2], geno[, 3]), ]
  lines.name.geno <- colnames(geno)[-c(1:3)]
  M0 <- t(geno[, -c(1:3)])
  map <- geno[, 1:3]
  marker <- as.character(map[, 1])
  chr <- map[, 2]
  if (!is.numeric(chr)) {
    stop("Chromosome numbers should be `numeric` (not `character`) !!")
  }
  chr.tab <- table(chr)
  chr.max <- length(chr.tab)
  chr.cum <- cumsum(chr.tab)
  pos <- as.double(map[, 3])
  cum.pos <- pos
  if (length(chr.tab) != 1) {
    for (i in 1:(chr.max - 1)) {
      cum.pos[(chr.cum[i] + 1):(chr.cum[i + 1])] <- pos[(chr.cum[i] + 1):(chr.cum[i + 1])] + cum.pos[chr.cum[i]]
    }
  }
  n.mark <- ncol(M0)
  rownames(M0) <- lines.name.geno


  ### Match phenotype and genotype ###
  pheno.mat <- as.matrix(pheno[, -1, drop = FALSE])
  rownames(pheno.mat) <- lines.name.pheno

  if (skip.check) {
    pheno.mat.modi <- pheno.mat
    match.modi <- 1:nrow(pheno.mat.modi)
    pheno.match <- pheno[match.modi, ]
    M <- M0
  } else {
    modification.res <- modify.data(pheno.mat = pheno.mat, geno.mat = M0,
                                    pheno.labels = NULL, geno.names = NULL,
                                    map = NULL, return.ZETA = is.null(ZETA),
                                    return.GWAS.format = FALSE)

    pheno.mat.modi <- modification.res$pheno.modi
    match.modi <- match(rownames(pheno.mat.modi), pheno[, 1])
    pheno.match <- pheno[match.modi, ]

    M <- modification.res$geno.modi
  }


  n.line <- nrow(M)
  X <- as.matrix(X0[match.modi, ])


  if (is.null(ZETA)) {
    if (skip.check) {
      K.A <- calcGRM(M)
      Z.A <- design.Z(pheno.labels = pheno.match[, 1],
                      geno.names = rownames(K.A))
      ZETA <- list(A = list(Z = Z.A,
                            K = K.A))
    } else {
      ZETA <- modification.res$ZETA
    }
  } else {
    ZETA.check <- any(unlist(lapply(ZETA, function(x) {
      (is.null(rownames(x$Z))) | (is.null(colnames(x$Z)))
    })))

    if (ZETA.check) {
      stop("No row names or column names for design matrix Z!!
           Please fill them with row : line (variety) names for phenotypes.
           and column : line (variety) names for genotypes.")
    }

    ZETA <- lapply(ZETA, function(x) {
      Z.match.pheno.no <- match(rownames(pheno.mat.modi), rownames(x$Z))
      Z.match.geno.no <- match(rownames(M), rownames(x$Z))

      Z.modi <- x$Z[Z.match.pheno.no, Z.match.geno.no]
      K.modi <- x$K[Z.match.geno.no, Z.match.geno.no]

      return(list(Z = Z.modi, K = K.modi))
    })
  }
  K.A <- ZETA[[1]]$K
  Z.A <- ZETA[[1]]$Z



  ### For interacton.kernel ###
  if (is.null(interaction.kernel)) {
    Z.A.sp <- as(object = Z.A, Class = "sparseMatrix")
    Z.A.t.sp <- as(object = t(Z.A), Class = "sparseMatrix")

    interaction.kernel <- as.matrix(Z.A.sp %*% K.A %*% Z.A.t.sp)

    if (include.interaction.kernel.null) {
      include.interaction.kernel.null <- FALSE
      message(paste0("`include.interaction.kernel.null` is set as `FALSE`",
                     " because genomic relationship matrix is set as `interaction.kernel`!"))
    }

    if (!include.interaction.with.gb.null) {
      include.interaction.with.gb.null <- TRUE
      message(paste0("`include.interaction.with.gb.null` is set as `TRUE`",
                     " because genomic relationship matrix is set as `interaction.kernel`!"))
    }
  } else {
    stopifnot(nrow(interaction.kernel) == ncol(interaction.kernel))
    stopifnot(nrow(interaction.kernel) == nrow(pheno.mat))
    if (is.null(rownames(interaction.kernel))) {
      rownames(interaction.kernel) <- colnames(interaction.kernel) <-
        rownames(pheno.mat)
    } else {
      stopifnot(all(rownames(interaction.kernel) == colnames(interaction.kernel)))
      stopifnot(all(rownames(interaction.kernel) == rownames(pheno.mat)))
    }

    interaction.kernel <- interaction.kernel[match.modi, match.modi]
  }


  ### For covariates (again) ###
  if (n.PC > 0) {
    eigen.K.A <- eigen(K.A)
    eig.K.vec <- eigen.K.A$vectors

    PC.part <- Z.A %*% eig.K.vec[, 1:n.PC]
    colnames(PC.part) <- paste0("n.PC_", 1:n.PC)

    X <- cbind(X, PC.part)
  }
  X <- make.full(X)


  ### Some settings ###
  trait.names <- colnames(pheno)[pheno.ix]
  if (is.null(gene.set)) {
    n.scores.each <- (chr.tab + (window.slide - 1)) %/% window.slide
    n.scores <- sum(n.scores.each)
  } else {
    gene.set <- gene.set[gene.set$marker %in% geno$marker, ]
    n.scores <- length(unique(gene.set[, 1]))
  }
  if ((kernel.method == "linear") & (length(test.effect) >= 2)) {
    all.scores <- rep(list(matrix(0, nrow = n.scores, ncol = n.pheno)), length(test.effect))
    names(all.scores) <- test.effect

    for (test.effect.no in 1:length(test.effect)) {
      colnames(all.scores[[test.effect.no]]) <- trait.names
    }
    thresholds <- matrix(NA, nrow = length(test.effect), ncol = n.pheno)
    rownames(thresholds) <- test.effect
    colnames(thresholds) <- trait.names
  } else {
    all.scores <- matrix(0, nrow = n.scores, ncol = n.pheno)
    colnames(all.scores) <- trait.names
    thresholds <- matrix(NA, nrow = 1, ncol = n.pheno)
    rownames(thresholds) <- kernel.method
    colnames(thresholds) <- trait.names
  }

  if (n.pheno == 0) {
    stop("No phenotypes.")
  }



  ##### START RGWAS for each phenotype #####
  for (pheno.no in 1:n.pheno) {
    trait.name <- trait.names[pheno.no]
    if (verbose) {
      print(paste("GWAS for trait:", trait.name))
    }
    y0 <- pheno.match[, pheno.ix[pheno.no]]
    not.NA <- which(!is.na(y0))
    y <- y0[not.NA]

    n <- length(y)

    X.now <- X[not.NA, , drop = FALSE]
    ZETA.now <- lapply(ZETA, function(x) list(Z = x$Z[not.NA, ], K = x$K))

    if (is.diag(x = Z.A)) {
      M.now <- M[not.NA, , drop = FALSE]
    } else {
      Z.A.nonNA.sp <- as(object = Z.A[not.NA, ], Class = "sparseMatrix")
      which.one.Z.A <- apply(Z.A.nonNA.sp == 1, 1, which)
      overlap.Z.A <- is.list(which.one.Z.A)
      if (!overlap.Z.A) {
        M.now <- M[which.one.Z.A, ]
      } else {
        M.now <- as.matrix(Z.A.nonNA.sp %*% M)
      }
    }

    interaction.kernel.now <- interaction.kernel[not.NA, not.NA]

    if (include.interaction.kernel.null) {
      ZETA.now <- c(ZETA.now,
                    list(kernel = list(Z = design.Z(pheno.labels = rownames(X.now),
                                                    geno.names = rownames(interaction.kernel.now)),
                                       K = interaction.kernel.now)))
    }

    if (include.interaction.with.gb.null) {
      Z.A.nonNA.sp <- as(object = Z.A[not.NA, ], Class = "sparseMatrix")
      Z.A.nonNA.t.sp <- as(object = t(Z.A[not.NA, ]), Class = "sparseMatrix")
      ZKZt.now <- as.matrix(Z.A.nonNA.sp %*% K.A %*% Z.A.nonNA.t.sp)
      ZETA.now <- c(ZETA.now,
                    list(kernelxGb = list(Z = design.Z(pheno.labels = rownames(X.now),
                                                       geno.names = rownames(interaction.kernel.now)),
                                          K = interaction.kernel.now * ZKZt.now)))
    }

    p <- ncol(X.now)
    m <- ncol(Z.A)



    #### Calculate LL for the null hypothesis at first ####
    spI <- diag(n)
    S <- spI - tcrossprod(X.now %*% solve(crossprod(X.now)), X.now)

    EMM.res0 <- EM3.general(y = y, X0 = X.now, ZETA = ZETA.now,
                            package = package.MM,
                            n.core = n.core,
                            REML = TRUE, pred = FALSE,
                            return.u.always = FALSE,
                            return.u.each = FALSE,
                            return.Hinv = FALSE)
    weights <- EMM.res0$weights

    ZKZt.list <- NULL
    ZKZt <- matrix(0, nrow = n, ncol = n)
    for (ZKZt.no in 1:length(ZETA)) {
      Z.now <- ZETA.now[[ZKZt.no]]$Z
      K.now <- ZETA.now[[ZKZt.no]]$K
      ZKZt.now <- tcrossprod(Z.now %*% K.now, Z.now)
      ZKZt.weighted <- ZKZt.now * weights[ZKZt.no]

      ZKZt.list <- c(ZKZt.list, list(ZKZt.weighted))
      ZKZt <- ZKZt + ZKZt.weighted
    }

    if (test.method == "LR") {
      LL0 <- EMM.res0$LL

      spectral.res <- spectralG.cpp(ZETA = ZETA.now, X = X.now, weights = weights,
                                    return.G = TRUE, return.SGS = TRUE, spectral.method = "eigen")
      eigen.G <- spectral.res[[1]]
      eigen.SGS <- spectral.res[[2]]
    } else {
      stop("We only support 'LR' (likelihood-ratio test) method for `test.method`!")
      # if (test.method == "score") {
      #   LL0 <- EMM.res0$LL
      #   Vu <- EMM.res0$Vu
      #   Ve <- EMM.res0$Ve
      #
      #   Gu <- tcrossprod(ZKZt)
      #   Ge <- diag(n)
      #   V0 <- Vu * Gu + Ve * Ge
      #
      #
      #   P0 <- MASS::ginv(S %*% V0 %*% S)
      # } else {
      #   stop("We only support 'LR' (likelihood-ratio test) and 'score' (score test)!")
      # }
    }





    #### Calculating the value of -log10(p) for each SNPs ####
    if ((n.core > 1) & requireNamespace("parallel", quietly = TRUE)) {
      if (test.method == "LR") {
        scores <- score.calc.LR.int.MC(M.now = M.now, y = y, X.now = X.now, ZETA.now = ZETA.now,
                                       interaction.kernel = interaction.kernel.now,
                                       package.MM = package.MM, LL0 = LL0, eigen.SGS = eigen.SGS,
                                       eigen.G = eigen.G, n.core = n.core,
                                       parallel.method = parallel.method, map = map,
                                       kernel.method = kernel.method, kernel.h = kernel.h,
                                       haplotype = haplotype, num.hap = num.hap,
                                       test.effect = test.effect, window.size.half = window.size.half,
                                       window.slide = window.slide, chi0.mixture = chi0.mixture,
                                       optimizer = optimizer, weighting.center = weighting.center,
                                       weighting.other = weighting.other, gene.set = gene.set,
                                       min.MAF = min.MAF, count = count)
      } else {
        stop("We only support 'LR' (likelihood-ratio test) method for `test.method`!")
        # scores <- score.calc.score.MC(M.now = M.now, y = y, X.now = X.now, ZETA.now = ZETA.now,
        #                               LL0 = LL0, Gu = Gu, Ge = Ge, P0 = P0, n.core = n.core,
        #                               parallel.method = parallel.method, map = map,
        #                               kernel.method = kernel.method, kernel.h = kernel.h, haplotype = haplotype,
        #                               num.hap = num.hap, test.effect = test.effect, window.size.half = window.size.half,
        #                               window.slide = window.slide, chi0.mixture = chi0.mixture,
        #                               weighting.center = weighting.center, weighting.other = weighting.other,
        #                               gene.set = gene.set, min.MAF = min.MAF, count = count)
      }
    } else {
      if (test.method == "LR") {
        scores <- score.calc.LR.int(M.now = M.now, y = y, X.now = X.now, ZETA.now = ZETA.now,
                                    interaction.kernel = interaction.kernel.now,
                                    package.MM = package.MM, LL0 = LL0, eigen.SGS = eigen.SGS,
                                    eigen.G = eigen.G, n.core = n.core, map = map, optimizer = optimizer,
                                    kernel.method = kernel.method, kernel.h = kernel.h, haplotype = haplotype,
                                    num.hap = num.hap, test.effect = test.effect, window.size.half = window.size.half,
                                    window.slide = window.slide, chi0.mixture = chi0.mixture,
                                    weighting.center = weighting.center, weighting.other = weighting.other,
                                    gene.set = gene.set, min.MAF = min.MAF, count = count)
      } else {
        stop("We only support 'LR' (likelihood-ratio test) method for `test.method`!")
        # scores <- score.calc.score(M.now = M.now, y = y, X.now = X.now, ZETA.now = ZETA.now,
        #                            LL0 = LL0, Gu = Gu, Ge = Ge, P0 = P0, map = map,
        #                            kernel.method = kernel.method, kernel.h = kernel.h, haplotype = haplotype,
        #                            num.hap = num.hap, test.effect = test.effect, window.size.half = window.size.half,
        #                            window.slide = window.slide, chi0.mixture = chi0.mixture,
        #                            weighting.center = weighting.center, weighting.other = weighting.other,
        #                            gene.set = gene.set, min.MAF = min.MAF, count = count)
      }
    }

    if (is.null(gene.set)) {
      window.centers <- as.numeric(rownames(scores))
      map2 <- map[window.centers, ]
    } else {
      if (verbose) {
        print("Now generating map for gene set. Please wait.")
      }

      if (is.null(map.gene.set)) {
        map20 <- genesetmap(map = map, gene.set = gene.set, cumulative = TRUE)
      } else {
        if (ncol(map.gene.set) == 3) {
          cum.pos.set.mean <- cumsumPos(map = map.gene.set)
          map20 <- cbind(map.gene.set, cum.pos = cum.pos.set.mean)
        } else if (ncol(map.gene.set) == 4) {
          map20 <- map.gene.set
        } else {
          stop("`map.gene.set` should contain 3 or 4 columns; marker, chr, pos (& cum.pos).")
        }

        stopifnot(nrow(map.gene.set) == length(unique(gene.set[, 1])))
      }
      map2 <- map20[, 1:3]
      cum.pos.set.mean <- c(map20[, 4])
    }

    if ((kernel.method == "linear") & (length(test.effect) >= 2)) {
      for (test.effect.no in 1:length(test.effect)) {
        if (plot.qq) {
          if (verbose) {
            print("Now Plotting (Q-Q plot). Please Wait.")
          }
          if (is.null(saveName)) {
            if (length(grep("RStudio", names(dev.cur()))) == 0) {
              if (dev.cur() == dev.next()) {
                dev.new()
              } else {
                dev.set(dev.next())
              }
            }
            qq(scores[, test.effect.no])
            if (is.null(main.qq)) {
              title(main = paste(trait.name, test.effect[test.effect.no]))
            } else {
              title(main = main.qq)
            }
          } else {
            png(paste0(saveName, trait.name, "_qq_kernel_", test.effect[test.effect.no], ".png"))
            qq(scores[, test.effect.no])
            if (is.null(main.qq)) {
              title(main = paste(trait.name, test.effect[test.effect.no]))
            } else {
              title(main = main.qq)
            }
            dev.off()
          }
        }


        if (plot.Manhattan) {
          if (verbose) {
            print("Now Plotting (Manhattan plot). Please Wait.")
          }
          if (is.null(saveName)) {
            if (length(grep("RStudio", names(dev.cur()))) == 0) {
              if (dev.cur() == dev.next()) {
                dev.new()
              }
              else {
                dev.set(dev.next())
              }
            }
            if (plot.method == 1) {
              manhattan(input = cbind(map2, scores[, test.effect.no]), sig.level = sig.level, method.thres = method.thres, plot.col1 = plot.col1,
                        plot.type = plot.type, plot.pch = plot.pch)
            } else {
              manhattan2(input = cbind(map2, scores[, test.effect.no]), sig.level = sig.level, method.thres = method.thres, plot.col2 = plot.col2,
                         plot.type = plot.type, plot.pch = plot.pch, cum.pos = cum.pos.set.mean)
            }
            if (is.null(main.man)) {
              title(main = paste(trait.name, test.effect[test.effect.no]))
            } else {
              title(main = main.man)
            }
          } else {
            png(paste0(saveName, trait.name, "_manhattan_kernel", test.effect[test.effect.no], ".png"), width = 800)
            if (plot.method == 1) {
              manhattan(input = cbind(map2, scores[, test.effect.no]), sig.level = sig.level, method.thres = method.thres, plot.col1 = plot.col1,
                        plot.type = plot.type, plot.pch = plot.pch)
            } else {
              manhattan2(input = cbind(map2, scores[, test.effect.no]), sig.level = sig.level, method.thres = method.thres, plot.col2 = plot.col2,
                         plot.type = plot.type, plot.pch = plot.pch, cum.pos = cum.pos.set.mean)
            }
            if (is.null(main.man)) {
              title(main = paste(trait.name, test.effect[test.effect.no]))
            } else {
              title(main = main.man)
            }
            if (!(plot.add.last & (pheno.no == n.pheno))) {
              dev.off()
            }
          }
        }
        all.scores[[test.effect.no]][, pheno.no] <- scores[, test.effect.no]
        threshold <- try(CalcThreshold(cbind(map2, scores[, test.effect.no]), sig.level = sig.level, method = method.thres), silent = TRUE)
        if ("try-error" %in% class(threshold)) {
          threshold <- NA
        }
        thresholds[test.effect.no, pheno.no] <- threshold

      }
    } else {
      if (plot.qq) {
        if (verbose) {
          print("Now Plotting (Q-Q plot). Please Wait.")
        }
        if (is.null(saveName)) {
          if (length(grep("RStudio", names(dev.cur()))) == 0) {
            if (dev.cur() == dev.next()) {
              dev.new()
            }
            else {
              dev.set(dev.next())
            }
          }
          qq(scores)
          if (is.null(main.qq)) {
            title(main = trait.name)
          } else {
            title(main = main.qq)
          }
        } else {
          png(paste0(saveName, trait.name, "_qq_kernel.png"))
          qq(scores)
          if (is.null(main.qq)) {
            title(main = trait.name)
          } else {
            title(main = main.qq)
          }
          dev.off()
        }
      }


      if (plot.Manhattan) {
        if (verbose) {
          print("Now Plotting (Manhattan plot). Please Wait.")
        }
        if (is.null(saveName)) {
          if (length(grep("RStudio", names(dev.cur()))) == 0) {
            if (dev.cur() == dev.next()) {
              dev.new()
            }
            else {
              dev.set(dev.next())
            }
          }
          if (plot.method == 1) {
            manhattan(input = cbind(map2, scores), sig.level = sig.level, method.thres = method.thres, plot.col1 = plot.col1,
                      plot.type = plot.type, plot.pch = plot.pch)
          } else {
            manhattan2(input = cbind(map2, scores), sig.level = sig.level, method.thres = method.thres, plot.col2 = plot.col2,
                       plot.type = plot.type, plot.pch = plot.pch, cum.pos = cum.pos.set.mean)
          }
          if (is.null(main.man)) {
            title(main = trait.name)
          } else {
            title(main = main.man)
          }
        } else {
          png(paste0(saveName, trait.name, "_manhattan_kernel.png"), width = 800)
          if (plot.method == 1) {
            manhattan(input = cbind(map2, scores), sig.level = sig.level, method.thres = method.thres, plot.col1 = plot.col1,
                      plot.type = plot.type, plot.pch = plot.pch)
          } else {
            manhattan2(input = cbind(map2, scores), sig.level = sig.level, method.thres = method.thres, plot.col2 = plot.col2,
                       plot.type = plot.type, plot.pch = plot.pch, cum.pos = cum.pos.set.mean)
          }
          if (is.null(main.man)) {
            title(main = trait.name)
          } else {
            title(main = main.man)
          }
          if (!(plot.add.last & (pheno.no == n.pheno))) {
            dev.off()
          }
        }
      }
      all.scores[, pheno.no] <- scores
      threshold <- try(CalcThreshold(cbind(map2, scores), sig.level = sig.level, method = method.thres), silent = TRUE)
      if ("try-error" %in% class(threshold)) {
        threshold <- NA
      }
      thresholds[, pheno.no] <- threshold
    }
  }

  if ((kernel.method == "linear") & (length(test.effect) >= 2)) {
    res.Data <- lapply(all.scores, function(x) {
      cbind(map2, x)
    })
  } else {
    res.Data <- cbind(map2, all.scores)
  }




  if (thres) {
    end <- Sys.time()

    if (time) {
      print(end - start)
    }

    if (return.EMM.res) {
      return(list(D = res.Data, thres = thresholds,
                  EMM.res = EMM.res0))
    } else {
      return(list(D = res.Data, thres = thresholds))
    }
  } else {
    end <- Sys.time()

    if (time) {
      print(end - start)
    }

    if (return.EMM.res) {
      return(list(D = res.Data, EMM.res = EMM.res0))
    } else {
      return(res.Data)
    }
  }
}