tests/testthat/test-fitabn_mle.R

In abn: Modelling Multivariate Data with Additive Bayesian Networks

test_that("Test fitAbn.mle() with real Gaussian nodes", {
  suppressMessages({
    if(.Platform$OS.type == "unix") {
      capture.output({
        # Gaussian
        df <- airquality[complete.cases(airquality), ]

        dist <- list(Ozone="gaussian", Solar.R="gaussian", Wind="gaussian", Temp="gaussian", Month="gaussian", Day="gaussian")
        names(dist) <- colnames(df)

        d <- matrix(data=0, nrow=6, ncol=6)
        d[1, ] <- c(0, 1, 1, 1, 1, 1)
        colnames(d) <- rownames(d) <- names(dist)

        m1 <- fitAbn(method = "mle", dag=d, data.df=df, data.dists=dist, centre=FALSE)
        m2 <- lm(df[, 1] ~ as.matrix(df[, 2:6]))

        expect_equal(unname(m1$coef[[1]]), unname(t(coef(summary.lm(object=m2))[, 1])))
        expect_equal(unname(m1$Stderror[[1]]), unname(t(coef(summary.lm(object=m2))[, 2])))

        ## test centre
        m1 <- fitAbn(method = "mle", dag=d, data.df=df, data.dists=dist, centre=TRUE)
        m3 <- fitAbn(method = "mle", dag=d, data.df=df, data.dists=dist)
        d[1, ] <- c(0, 1, 0, 0, 0, 0)
        m2 <- fitAbn(method = "mle", dag=d, data.df=df, data.dists=dist)
        m4 <- cor(df[, 1:6])
      },
      file = "/dev/null")
      expect_equal(m1, m3)
      expect_equal(unname(m2$coef[[1]])[2], m4[1, 2])
    } else {
      skip("fitAbn.mle() is tested mainly on Unix-like systems")
    }
  })
})

test_that("Test fitAbn.mle() with simulated Gaussian nodes", {
  suppressMessages({
    if(.Platform$OS.type == "unix") {
      capture.output({
        # Gaussian
        N <- 1000
        mydists <- list(a="gaussian",
                        b="gaussian",
                        c="gaussian")
        a <- rnorm(n = N, mean = 0, sd = 1)
        b <- 1 + 2*rnorm(n = N, mean = 5, sd = 1)
        c <- 2 + 1*a + 2*b + rnorm(n = N, mean = 2, sd = 1)
        mydf <- data.frame("a" = a,
                           "b" = b,
                           "c" = c)
        mycache.mle <- buildScoreCache(data.df = mydf,
                                       data.dists = mydists,
                                       method = "mle",
                                       max.parents = 2)
        mydag.mp <- mostProbable(score.cache = mycache.mle, verbose = FALSE)
        myfit <- fitAbn(object = mydag.mp, method = "mle", centre = FALSE, verbose = FALSE)
        out.sim <- invisible(
          simulateAbn(object = myfit, n.iter = 10000L, verbose = FALSE)
        )
      },
      file = "/dev/null")
      # with original data
      m1 <- myfit
      m2 <- lm(c ~ a + b, data = mydf)
      expect_equal(unname(m1$coef[[3]]), unname(t(coef(summary(object=m2))[, 1])))

      # with simulated data
      capture.output({
        mycache.mle2 <- buildScoreCache(data.df = out.sim,
                                        data.dists = mydists,
                                        method = "mle",
                                        max.parents = 2)
        mydag.mp2 <- mostProbable(score.cache = mycache.mle2, verbose = FALSE)
        m1 <- fitAbn(object = mydag.mp2, method = "mle", centre=FALSE, verbose = FALSE)
        m2 <- lm(c ~ a + b, data = out.sim)
      },
      file = "/dev/null")
      expect_equal(unname(m1$coef[[3]]), unname(t(coef(summary(object=m2))[, 1])))
      ## new: RF 2022 after big merge: tolerance required.
      expect_equal(unname(m1$Stderror[[3]]), unname(t(coef(summary(object=m2))[, 2])), tolerance=1e-06)
    } else {
      skip("fitAbn.mle() is tested mainly on Unix-like systems")
    }
  })
})

test_that("Test fitAbn.mle() with Binomial nodes", {
  suppressMessages({
    if(.Platform$OS.type == "unix") {
      capture.output({
        # Binomial
        mydists <- list(a="binomial",
                        b="binomial")
        a <- rbinom(1000, size = 1, prob = 0.5)
        z <- 1+2*a
        pr <- 1/(1+exp(-z))
        b <- rbinom(1000, size = 1, prob = pr)
        mydf <- data.frame("a" = as.factor(a),
                           "b" = as.factor(b))
        mycache.mle <- buildScoreCache(data.df = mydf,
                                       data.dists = mydists,
                                       method = "mle",
                                       max.parents = 1)
        mydag.mp <- mostProbable(score.cache = mycache.mle, verbose = FALSE)
        myfit <- fitAbn(object = mydag.mp, method = "mle", centre = TRUE, verbose = FALSE)
        out.sim <- invisible(
          simulateAbn(object = myfit, n.iter = 10000L, verbose = FALSE)
        )
      },
      file = "/dev/null")
      # with original data
      m1 <- myfit
      m2 <- glm(a ~ b, data = mydf, family="binomial")
      expect_equal(unname(m1$coef[[1]]), unname(t(coef(summary.glm(object=m2))[, 1])))

      # with simulated data
      capture.output({
        mycache.mle2 <- buildScoreCache(data.df = out.sim,
                                        data.dists = mydists,
                                        method = "mle",
                                        max.parents = 1)
        mydag.mp2 <- mostProbable(score.cache = mycache.mle2, verbose = FALSE)
        m1 <- fitAbn(object = mydag.mp2, method = "mle", centre=TRUE, verbose = FALSE)
        m2 <- glm(a ~ b, data = out.sim, family="binomial")
      },
      file = "/dev/null")
      expect_equal(unname(m1$coef[[1]]), unname(t(coef(summary.glm(object=m2))[, 1])))
      ## new: RF 2022 after big merge: tolerance required.
      expect_equal(unname(m1$Stderror[[1]]), unname(t(coef(summary.glm(object=m2))[, 2])), tolerance=1e-06)
    } else {
      skip("fitAbn.mle() is tested mainly on Unix-like systems")
    }
  })
})

test_that("Test fitAbn.mle() with Poisson nodes", {
  skip("BuildScoreCache(method=mle) crashes with Poisson nodes")
  suppressMessages({
    # Poisson
    mydists <- list(a="poisson",
                    b="poisson")
    a <- rpois(1000, lambda = 0.5)
    z <- exp(1+2*a)
    b <- rpois(1000, lambda = z)
    mydf <- data.frame("a" = a,
                       "b" = as.integer(b))
    # "c" = as.factor(c(rep(1, 999), 0)))
    # glm(b~a, data = mydf, family = "poisson")
    mycache.mle <- buildScoreCache(data.df = mydf,
                                   data.dists = mydists,
                                   method = "mle",
                                   max.parents = 1,
                                   # group.var = "c",
                                   # control = list(max.mode.error=100),
                                   verbose = FALSE,
                                   dag.retained = matrix(c(0,0,1,0), nrow = 2, byrow = TRUE))
    mydag.mp <- mostProbable(score.cache = mycache.mle, verbose = FALSE)
    myfit <- fitAbn(object = mydag.mp, method = "mle", centre = FALSE)
    out.sim <- invisible(
      simulateAbn(object = myfit, n.iter = 10000L, verbose = TRUE)
    )

    # with original data
    m1 <- myfit
    m2 <- glm(b ~ a, data = mydf, family="poisson")
    expect_equal(unname(m1$coef[[2]]), unname(t(coef(summary.glm(object=m2))[, 1])))

    # with simulated data
    mycache.mle2 <- buildScoreCache(data.df = out.sim,
                                    data.dists = mydists,
                                    method = "mle",
                                    max.parents = 1)
    mydag.mp2 <- mostProbable(score.cache = mycache.mle2, verbose = FALSE)
    m1 <- fitAbn(object = mydag.mp2, method = "mle", centre=TRUE, verbose = FALSE)
    m2 <- glm(a ~ b, data = out.sim, family="binomial")

    expect_equal(unname(m1$coef[[1]]), unname(t(coef(summary.glm(object=m2))[, 1])))
    ## new: RF 2022 after big merge: tolerance required.
    expect_equal(unname(m1$Stderror[[1]]), unname(t(coef(summary.glm(object=m2))[, 2])), tolerance=1e-06)
    # dist <- list(a="poisson", b="poisson")
    #
    # data.param <- matrix(data=c(0, 0.5, 0, 0), nrow=2L, ncol=2L, byrow=TRUE)
    # data.param <- matrix(data=c(0, 1, 0, 0), nrow=2L, ncol=2L, byrow=TRUE)
    #
    # # naming
    # colnames(data.param) <- rownames(data.param) <- names(dist)
    #
    # out.sim <- invisible(simulateAbn(data.dists=dist, n.chains=1, n.adapt=100, n.thin=1, n.iter=100, data.param=data.param,
    #                                  simulate=TRUE, seed=132,verbose=FALSE))

    m1 <- fitAbn(method = "mle", dag=data.param, data.df=out.sim, data.dists=dist, centre=FALSE)
    m2 <- glm(formula=out.sim$a ~ out.sim$b, family="poisson")

    ## pvalues and stderr are computed up to 10e-06 precision!
    expect_equal(unname(m1$coef[[1]]), unname(t(coef(summary.glm(object=m2))[, 1])))
    expect_equal(unname(m1$Stderror[[1]]), unname(t(coef(summary.glm(object=m2))[, 2])), tolerance=1e-06)
  })
})

test_that("Test fitAbn.mle() with Multinomial nodes and Gaussians", {
  suppressMessages({
    if(.Platform$OS.type == "unix") {
      capture.output({
        # make data set
        N <- 200
        prob <- c(1,2,3,4)
        coef <- c(1,2,3,4)
        Y <- rmultinom(N, 1, prob=prob)
        Ya <- c(colSums(Y*coef))
        X <- colSums(Y*coef) + rnorm(N,0,sd=1)
        mydf <- data.frame(a=X, b=as.factor(Ya))
        mydists <- list(a="gaussian", b="multinomial")
        mydag <- matrix(c(0,1,0,0), nrow = 2, byrow = TRUE,
                        dimnames = list(c("a", "b"), c("a", "b"))) # b~a

        ###
        # Multinomial parent with one gaussian child
        ###
        mycache.mle <- buildScoreCache(data.df = mydf,data.dists = mydists, method = "mle", max.parents = 1, dag.retained = mydag)
        mydag.mp <- mostProbable(score.cache = mycache.mle, verbose = FALSE)
        myfit <- fitAbn(object = mydag.mp, method = "mle", centre = FALSE)
      },
      file = "/dev/null")
      # with original data
      m1 <- myfit
      m2 <- glm(a ~ -1+ b, data = mydf, family="gaussian")
      expect_equal(unname(m1$coef[[1]]), unname(t(coef(summary.glm(object=m2))[, 1])))
      expect_equal(unname(m1$Stderror[[1]]), unname(t(coef(summary.glm(object=m2))[, 2])), tolerance=1e-02)
      # with simulated data
      capture.output({
        out.sim <- invisible(
          simulateAbn(object = myfit, verbose = FALSE, debug = FALSE)
        )
        mycache.mle2 <- buildScoreCache(data.df = out.sim,
                                        data.dists = mydists,
                                        method = "mle",
                                        max.parents = 1,
                                        dag.retained = mydag)
        mydag.mp2 <- mostProbable(score.cache = mycache.mle2, verbose = FALSE)
        m1 <- fitAbn(object = mydag.mp2, method = "mle", centre=FALSE)
        m2 <- glm(a ~ -1+ b, data = out.sim, family="gaussian")
      },
      file = "/dev/null")
      expect_equal(unname(m1$coef[[1]]), unname(t(coef(summary.glm(object=m2))[, 1])))
      expect_equal(unname(m1$Stderror[[1]]), unname(t(coef(summary.glm(object=m2))[, 2])), tolerance=1e-3)

      ###
      # Multinomial response with two gaussian parents
      ###
      capture.output({
        # make data set
        mydf3 <- cbind(mydf, c=rnorm(N,0,sd=1))
        mydists3 <- list(a="gaussian", b="multinomial", c="gaussian")
        dag3 <- matrix(c(0,0,0,
                         1,0,1,
                         0,0,0), 3, 3, byrow = T, dimnames = list(names(mydists3), names(mydists3)))
        mycache.mle3 <- buildScoreCache(data.df = mydf3,data.dists = mydists3, method = "mle", max.parents = 2, dag.retained = dag3)
        mydag.mp3 <- mostProbable(score.cache = mycache.mle3, verbose = FALSE)
        myfit3 <- fitAbn(object = mydag.mp3, method = "mle", centre = FALSE)
        # with original data
        m1 <- myfit3
        m2 <- summary(nnet::multinom(b~a+c, data =mydf3, trace = FALSE))
      },
      file = "/dev/null")
      expect_equal(unname(as.vector(m1$coef[[2]])), unname(as.vector(coefficients(m2))))
      expect_equal(unname(as.vector(m1$Stderror[[2]])), unname(as.vector(m2$standard.errors)))
      # with simulated data
      capture.output({
        out.sim3 <- invisible(
          simulateAbn(object = myfit3, verbose = FALSE, debug = FALSE)
        )
        mycache.mle4 <- buildScoreCache(data.df = out.sim3,
                                        data.dists = mydists3,
                                        method = "mle",
                                        max.parents = 2,
                                        dag.retained = dag3)
        mydag.mp4 <- mostProbable(score.cache = mycache.mle4, verbose = FALSE)
        m1 <- fitAbn(object = mydag.mp4, method = "mle", centre=FALSE)
        m2 <- summary(nnet::multinom(b~a+c, data =out.sim3, trace = FALSE))
      },
      file = "/dev/null")
      expect_equal(unname(as.vector(m1$coef[[2]])), unname(as.vector(coefficients(m2))))
      expect_equal(unname(as.vector(m1$Stderror[[2]])), unname(as.vector(m2$standard.errors)))
    } else {
      skip("fitAbn.mle() is tested mainly on Unix-like systems")
    }
  })
})

test_that("Test fitAbn.mle() with Multinomial nodes and Binomials", {
  suppressMessages({
    if(.Platform$OS.type == "unix") {
      capture.output({
        # make data set
        N <- 200
        prob <- c(1,2,3)
        coef <- c(1,2,3)
        Y <- rmultinom(N, 1, prob=prob)
        Ya <- c(colSums(Y*coef))
        X <- rbinom(n = N, size = 1, prob = 0.2) # Bernoulli
        mydf <- data.frame(a=as.factor(X), b=as.factor(Ya))
        mydists <- list(a="binomial", b="multinomial")
        mydag <- matrix(c(0,1,0,0), nrow = 2, byrow = TRUE,
                        dimnames = list(c("a", "b"), c("a", "b"))) # b~a

        ###
        # Multinomial parent with one Binomial child
        ###
        mycache.mle <- buildScoreCache(data.df = mydf,data.dists = mydists, method = "mle", max.parents = 1, dag.retained = mydag)
        mydag.mp <- mostProbable(score.cache = mycache.mle, verbose = FALSE)
        myfit <- fitAbn(object = mydag.mp, method = "mle", centre = FALSE)
        # with original data
        m1 <- myfit
        m2 <- glm(a ~ -1+ b, data = mydf, family="binomial")
      },
      file = "/dev/null")
      expect_equal(unname(m1$coef[[1]]), unname(t(coef(summary.glm(object=m2))[, 1])))
      expect_equal(unname(m1$Stderror[[1]]), unname(t(coef(summary.glm(object=m2))[, 2])), tolerance=1e-02)
      # with simulated data
      capture.output({
        out.sim <- invisible(
          simulateAbn(object = myfit, verbose = FALSE, debug = FALSE)
        )
        mycache.mle2 <- buildScoreCache(data.df = out.sim,
                                        data.dists = mydists,
                                        method = "mle",
                                        max.parents = 1,
                                        dag.retained = mydag)
        mydag.mp2 <- mostProbable(score.cache = mycache.mle2, verbose = FALSE)
        m1 <- fitAbn(object = mydag.mp2, method = "mle", centre=FALSE)
        m2 <- glm(a ~ -1+ b, data = out.sim, family="binomial")
      },
      file = "/dev/null")
      expect_equal(unname(m1$coef[[1]]), unname(t(coef(summary.glm(object=m2))[, 1])), tolerance=1e-6)
      expect_equal(unname(m1$Stderror[[1]]), unname(t(coef(summary.glm(object=m2))[, 2])), tolerance=1e-3)

      ###
      # Multinomial response with two Binomial parents
      ###
      # make data set
      capture.output({
        mydf3 <- cbind(mydf,
                       c=as.factor(rbinom(n = N, size = 1, prob = 0.8))) # Bernoulli
        mydists3 <- list(a="binomial", b="multinomial", c="binomial")
        dag3 <- matrix(c(0,0,0,
                         1,0,1,
                         0,0,0), 3, 3, byrow = T, dimnames = list(names(mydists3), names(mydists3)))
        mycache.mle3 <- buildScoreCache(data.df = mydf3,data.dists = mydists3, method = "mle", max.parents = 2,
                                        dag.retained = dag3,
                                        dag.banned = matrix(c(1,0,1,
                                                              0,0,0,
                                                              1,0,1), 3, 3, byrow = T, dimnames = list(names(mydists3), names(mydists3))))
        mydag.mp3 <- mostProbable(score.cache = mycache.mle3, verbose = FALSE)
        myfit3 <- fitAbn(object = mydag.mp3, method = "mle", centre = FALSE)
        # with original data
        m1 <- myfit3
        m2 <- summary(nnet::multinom(b~a+c, data =mydf3, trace = FALSE))
      },
      file = "/dev/null")
      expect_equal(unname(as.vector(m1$coef[[2]])), unname(as.vector(coefficients(m2))))
      expect_equal(unname(as.vector(m1$Stderror[[2]])), unname(as.vector(m2$standard.errors)))
      # with simulated data
      capture.output({
        out.sim3 <- invisible(
          simulateAbn(object = myfit3, verbose = FALSE, debug = FALSE)
        )
        mycache.mle4 <- buildScoreCache(data.df = out.sim3,
                                        data.dists = mydists3,
                                        method = "mle",
                                        max.parents = 2,
                                        dag.retained = dag3,
                                        dag.banned = matrix(c(1,0,1,
                                                              0,0,0,
                                                              1,0,1), 3, 3, byrow = T, dimnames = list(names(mydists3), names(mydists3))))
        mydag.mp4 <- mostProbable(score.cache = mycache.mle4, verbose = FALSE)
        m1 <- fitAbn(object = mydag.mp4, method = "mle", centre=FALSE)
        m2 <- summary(nnet::multinom(b~a+c, data =out.sim3, trace = FALSE))
      },
      file = "/dev/null")
      expect_equal(unname(as.vector(m1$coef[[2]])), unname(as.vector(coefficients(m2))))
      expect_equal(unname(as.vector(m1$Stderror[[2]])), unname(as.vector(m2$standard.errors)))
    } else {
      skip("fitAbn.mle() is tested mainly on Unix-like systems")
    }
  })
})

test_that("Test fitAbn.mle() with Multinomial nodes and Poissons", {
  suppressMessages({
    if(.Platform$OS.type == "unix") {
      capture.output({
        # make data set
        N <- 200
        prob <- c(1,2,3)
        coef <- c(1,2,3)
        Y <- rmultinom(N, 1, prob=prob)
        Ya <- c(colSums(Y*coef))
        X <- rpois(n = N, lambda = 0.2) # Poisson
        mydf <- data.frame(a=X, b=as.factor(Ya))
        mydists <- list(a="poisson", b="multinomial")
        mydag <- matrix(c(0,1,0,0), nrow = 2, byrow = TRUE,
                        dimnames = list(c("a", "b"), c("a", "b"))) # b~a

        ###
        # Multinomial parent with one Poisson child
        ###
        mycache.mle <- buildScoreCache(data.df = mydf,data.dists = mydists, method = "mle", max.parents = 1, dag.retained = mydag)
        mydag.mp <- mostProbable(score.cache = mycache.mle, verbose = FALSE)
        myfit <- fitAbn(object = mydag.mp, method = "mle", centre = FALSE)
        # with original data
        m1 <- myfit
        m2 <- glm(a ~ -1+ b, data = mydf, family="poisson")
      },
      file = "/dev/null")
      expect_equal(unname(m1$coef[[1]]), unname(t(coef(summary.glm(object=m2))[, 1])))
      expect_equal(unname(m1$Stderror[[1]]), unname(t(coef(summary.glm(object=m2))[, 2])), tolerance=1e-02)
      # with simulated data
      capture.output({
        out.sim <- invisible(
          simulateAbn(object = myfit, verbose = FALSE, debug = FALSE)
        )
        mycache.mle2 <- buildScoreCache(data.df = out.sim,
                                        data.dists = mydists,
                                        method = "mle",
                                        max.parents = 1,
                                        dag.retained = mydag)
        mydag.mp2 <- mostProbable(score.cache = mycache.mle2, verbose = FALSE)
        m1 <- fitAbn(object = mydag.mp2, method = "mle", centre=FALSE)
        m2 <- glm(a ~ -1+ b, data = out.sim, family="poisson")
      },
      file = "/dev/null")
      expect_equal(unname(m1$coef[[1]]), unname(t(coef(summary.glm(object=m2))[, 1])), tolerance=1e-6)
      expect_equal(unname(m1$Stderror[[1]]), unname(t(coef(summary.glm(object=m2))[, 2])), tolerance=1e-3)

      ###
      # Multinomial response with two Poisson parents
      ###
      # make data set
      capture.output({
        mydf3 <- cbind(mydf,
                       c=rpois(n = N, lambda = 0.8)) # Poisson
        mydists3 <- list(a="poisson", b="multinomial", c="poisson")
        dag3 <- matrix(c(0,0,0,
                         1,0,1,
                         0,0,0), 3, 3, byrow = T, dimnames = list(names(mydists3), names(mydists3)))
        mycache.mle3 <- buildScoreCache(data.df = mydf3,data.dists = mydists3, method = "mle", max.parents = 2,
                                        dag.retained = dag3,
                                        dag.banned = matrix(c(1,0,1,
                                                              0,0,0,
                                                              1,0,1), 3, 3, byrow = T, dimnames = list(names(mydists3), names(mydists3))))
        mydag.mp3 <- mostProbable(score.cache = mycache.mle3, verbose = FALSE)
        myfit3 <- fitAbn(object = mydag.mp3, method = "mle", centre = FALSE)
        # with original data
        m1 <- myfit3
        m2 <- summary(nnet::multinom(b~a+c, data =mydf3, trace = FALSE))
      },
      file = "/dev/null")
      expect_equal(unname(as.vector(m1$coef[[2]])), unname(as.vector(coefficients(m2))))
      expect_equal(unname(as.vector(m1$Stderror[[2]])), unname(as.vector(m2$standard.errors)))
      # with simulated data
      capture.output({
        out.sim3 <- invisible(
          simulateAbn(object = myfit3, verbose = FALSE, debug = FALSE)
        )
        mycache.mle4 <- buildScoreCache(data.df = out.sim3,
                                        data.dists = mydists3,
                                        method = "mle",
                                        max.parents = 2,
                                        dag.retained = dag3,
                                        dag.banned = matrix(c(1,0,1,
                                                              0,0,0,
                                                              1,0,1), 3, 3, byrow = T, dimnames = list(names(mydists3), names(mydists3))))
        mydag.mp4 <- mostProbable(score.cache = mycache.mle4, verbose = FALSE)
        m1 <- fitAbn(object = mydag.mp4, method = "mle", centre=FALSE)
        m2 <- summary(nnet::multinom(b~a+c, data =out.sim3, trace = FALSE))
      },
      file = "/dev/null")
      expect_equal(unname(as.vector(m1$coef[[2]])), unname(as.vector(coefficients(m2))))
      expect_equal(unname(as.vector(m1$Stderror[[2]])), unname(as.vector(m2$standard.errors)))
    } else {
      skip("fitAbn.mle() is tested mainly on Unix-like systems")
    }
  })
})

test_that("fitAbn's regressionLoop() works w/o group.var.", {
  # load("tests/testthat/testdata/fitAbn_regressionLoop_data.Rdata")
  load("testdata/fitAbn_regressionLoop_data.Rdata")
  verbose <- FALSE

  # Running on one child node (predictor)
  suppressWarnings({
    suppressMessages({
      if(.Platform$OS.type == "unix") {
        capture.output({
          expect_no_error({
            res <- regressionLoop(
              i = 1,
              dag = dag,
              data.df = data.df,
              data.df.multi = data.df.multi,
              data.dists = data.dists,
              group.var = group.var,
              grouped.vars = grouped.vars,
              group.ids = group.ids,
              control = control,
              nvars = nvars,
              nobs = nobs,
              dag.multi = dag.multi,
              verbose = verbose
            )
          })
          expect_equal(names(res), c("mliknode", "mlik", "aicnode", "aic", "bicnode", "bic", "mdlnode", "mdl", "sse", "mse", "df", "mu", "betas", "sigma", "sigma_alpha"))

          # Running on all child nodes (predictor)
          expect_no_error({
            res <- list()
            for (childno in 1:nrow(dag)){
              res[[childno]] <- regressionLoop(
                i = childno,
                dag = dag,
                data.df = data.df,
                data.df.multi = data.df.multi,
                data.dists = data.dists,
                group.var = group.var,
                grouped.vars = grouped.vars,
                group.ids = group.ids,
                control = control,
                nvars = nvars,
                nobs = nobs,
                dag.multi = dag.multi,
                verbose = verbose
              )
            }
          })
          expect_equal(length(res), nrow(dag))

          # Running on all child nodes (predictor) with foreach on single core
          expect_no_error({
            res2 <- foreach(childno = 1:nrow(dag)) %do% {
              regressionLoop(
                i = childno,
                dag = dag,
                data.df = data.df,
                data.df.multi = data.df.multi,
                data.dists = data.dists,
                group.var = group.var,
                grouped.vars = grouped.vars,
                group.ids = group.ids,
                control = control,
                nvars = nvars,
                nobs = nobs,
                dag.multi = dag.multi,
                verbose = verbose
              )
            }
          })
          expect_equal(res, res2)

          # Running on all child nodes (predictor) with foreach in multiple cores
          skip_on_cran() # workaround to not overconsume threads on CRAN. This is related to an issue reported for lme4 (https://github.com/lme4/lme4/issues/627)
          expect_no_error({
            ncores <- 2
            cl <- makeCluster(ncores)
            registerDoParallel(cl)

            res3 <- foreach(childno = 1:nrow(dag),
                            .export = 'regressionLoop') %dopar% {
                              regressionLoop(
                                i = childno,
                                dag = dag,
                                data.df = data.df,
                                data.df.multi = data.df.multi,
                                data.dists = data.dists,
                                group.var = group.var,
                                grouped.vars = grouped.vars,
                                group.ids = group.ids,
                                control = control,
                                nvars = nvars,
                                nobs = nobs,
                                dag.multi = dag.multi,
                                verbose = verbose
                              )
                            }
          })
          expect_equal(res, res3, tolerance = 10e-8)
          expect_equal(res2, res3, tolerance = 10e-8)
        },
        file = "/dev/null")
      } else {
        skip("fitAbn.mle() is tested mainly on Unix-like systems")
      }
    })
  })
})


test_that("fitAbn's regressionLoop() works w/ group.var.", {
  # load("tests/testthat/testdata/fitAbn_regressionLoop_group_data.Rdata")
  load("testdata/fitAbn_regressionLoop_group_data.Rdata")
  verbose <- FALSE

  # Running on one child node (predictor)
  suppressWarnings({
    suppressMessages({
      if(.Platform$OS.type == "unix") {
        capture.output({
          expect_no_error({
            res <- regressionLoop(
              i = 1,
              dag = dag,
              data.df = data.df,
              data.df.multi = data.df.multi,
              data.dists = data.dists,
              group.var = group.var,
              grouped.vars = grouped.vars,
              group.ids = group.ids,
              control = control,
              nvars = nvars,
              nobs = nobs,
              dag.multi = dag.multi,
              verbose = verbose
            )
          })
          expect_equal(names(res), c("mliknode", "mlik", "aicnode", "aic", "bicnode", "bic", "mdlnode", "mdl", "sse", "mse", "df", "mu", "betas", "sigma", "sigma_alpha"))

          # Running on all child nodes (predictor)
          expect_no_error({
            res <- list()
            for (childno in 1:nrow(dag)){
              res[[childno]] <- regressionLoop(
                i = childno,
                dag = dag,
                data.df = data.df,
                data.df.multi = data.df.multi,
                data.dists = data.dists,
                group.var = group.var,
                grouped.vars = grouped.vars,
                group.ids = group.ids,
                control = control,
                nvars = nvars,
                nobs = nobs,
                dag.multi = dag.multi,
                verbose = verbose
              )
            }
          })
          expect_equal(length(res), nrow(dag))

          # Running on all child nodes (predictor) with foreach on single core
          expect_no_error({
            res2 <- foreach(childno = 1:nrow(dag)) %do% {
              regressionLoop(
                i = childno,
                dag = dag,
                data.df = data.df,
                data.df.multi = data.df.multi,
                data.dists = data.dists,
                group.var = group.var,
                grouped.vars = grouped.vars,
                group.ids = group.ids,
                control = control,
                nvars = nvars,
                nobs = nobs,
                dag.multi = dag.multi,
                verbose = verbose
              )
            }
          })
          expect_equal(res, res2)

          # Running on all child nodes (predictor) with foreach in multiple cores
          skip_on_cran() # workaround to not overconsume threads on CRAN. This is related to an issue reported for lme4 (https://github.com/lme4/lme4/issues/627)
          expect_no_error({
            ncores <- 2
            cl <- makeCluster(ncores)
            registerDoParallel(cl)

            res3 <- foreach(childno = 1:nrow(dag),
                            .export = 'regressionLoop') %dopar% {
                              regressionLoop(
                                i = childno,
                                dag = dag,
                                data.df = data.df,
                                data.df.multi = data.df.multi,
                                data.dists = data.dists,
                                group.var = group.var,
                                grouped.vars = grouped.vars,
                                group.ids = group.ids,
                                control = control,
                                nvars = nvars,
                                nobs = nobs,
                                dag.multi = dag.multi,
                                verbose = verbose
                              )
                            }
          })
          expect_equal(res, res3, tolerance = 10e-8)
          expect_equal(res2, res3, tolerance = 10e-8)
        },
        file = "/dev/null")
      } else {
        skip("fitAbn.mle() is tested mainly on Unix-like systems")
      }
    })
  })
})