#devtools::test("asremlPlus") context("model_selection3") asr3.lib <- "D:\\Analyses\\R oldpkg" cat("#### Test for chooseModel.data.frame with asreml3\n") test_that("choose.model.data.frame_asreml3", { skip_if_not_installed("asreml") skip_on_cran() library(dae) library(asreml, lib.loc = asr3.lib) library(asremlPlus) print(packageVersion("asreml")) #'## Load data data("Ladybird.dat") #'## ANOVA of logits Ladybird.aov <- aov(logitP ~ Host*Cadavers*Ladybird + Error(Run/Plant), data=Ladybird.dat) summary(Ladybird.aov) #'## Mixed model analysis of logits m <- asreml(logitP ~ Host*Cadavers*Ladybird, random = ~ Run, rcov = ~ Run:Plant, data = Ladybird.dat) testthat::expect_true(all(summary(m)$varcomp$bound == c("B", "P"))) #shows bound Run component #'### Unconstrain Reps to make the analysis equivalent to ANOVA m <- setvarianceterms(m$call, terms = "Run", bounds = "U") summary(m)$varcomp #shows negative Run component testthat::expect_true(m$gammas["Run!Run.var"] < 0) #'### Use chooseModel.data.frame wald.tab <- wald.asreml(m, denDF = "numeric")$Wald testthat::expect_equal(nrow(wald.tab), 8) #'### Choose marginality-compliant model from wald.tab, obtaining marginality using pstructure Ladybird.pstr <- pstructure(formula = ~ Host*Cadavers*Ladybird, data = Ladybird.dat) HCL.marg <- marginality(Ladybird.pstr) testthat::expect_equal(nrow(HCL.marg), 7) sigmod <- chooseModel(wald.tab, terms.marginality = HCL.marg) testthat::expect_true(all(unlist(lapply(sigmod$sig.terms, function(term) term)) == c("Cadavers:Ladybird", "Host"))) testthat::expect_equal(nrow(sigmod$choose.summary), 5) testthat::expect_true(all(names(sigmod$choose.summary) == c("terms", "DF", "denDF", "p", "action"))) #'### Rechoose marginality-compliant model from wald.tab, but omit DF and denDF sigmod <- chooseModel(wald.tab, omit.DF = TRUE, terms.marginality = HCL.marg) testthat::expect_equal(nrow(sigmod$choose.summary), 5) testthat::expect_true(all(names(sigmod$choose.summary) == c("terms", "p", "action"))) sigmod <- chooseModel(wald.tab, denDF = NA, terms.marginality = HCL.marg) testthat::expect_equal(nrow(sigmod$choose.summary), 5) testthat::expect_true(all(names(sigmod$choose.summary) == c("terms", "DF", "denDF", "p", "action"))) #'### Specify the denDF argument in various ways, all of which result in the overwriting of denDF sigmod <- chooseModel(wald.tab, denDF = wald.tab$denDF, terms.marginality = HCL.marg) testthat::expect_equal(nrow(sigmod$choose.summary), 5) testthat::expect_true(all(names(sigmod$choose.summary) == c("terms", "DF", "denDF", "p", "action"))) den.df <- wald.tab$denDF sigmod <- chooseModel(wald.tab, denDF = den.df, terms.marginality = HCL.marg) testthat::expect_equal(nrow(sigmod$choose.summary), 5) testthat::expect_true(all(names(sigmod$choose.summary) == c("terms", "DF", "denDF", "p", "action"))) sigmod <- chooseModel(wald.tab, denDF = 59, terms.marginality = HCL.marg) testthat::expect_equal(nrow(sigmod$choose.summary), 5) testthat::expect_true(all(names(sigmod$choose.summary) == c("terms", "DF", "denDF", "p", "action"))) new.tab <- wald.tab names(new.tab)[match("denDF", names(new.tab))] <- "den.df" sigmod <- chooseModel(wald.tab, denDF = 59, terms.marginality = HCL.marg) testthat::expect_equal(nrow(sigmod$choose.summary), 5) testthat::expect_true(all(names(sigmod$choose.summary) == c("terms", "DF", "denDF", "p", "action"))) }) cat("#### Test for chooseModel.asrtests with asreml3\n") test_that("choose.model.asrtests_asreml3", { skip_if_not_installed("asreml") skip_on_cran() library(dae) library(asreml, lib.loc = asr3.lib) library(asremlPlus) print(packageVersion("asreml")) data(WaterRunoff.dat) current.asr <- asreml(log.Turbidity ~ Benches + (Sources * (Type + Species)) * Date, random = ~Benches:MainPlots:SubPlots:spl(xDay), data = WaterRunoff.dat, keep.order = TRUE) current.asrt <- as.asrtests(current.asr, NULL, NULL) #some tests for validWaldTab testthat::expect_error(test.wald <- as.asrtests(current.asr, wald.tab = WaterRunoff.dat)) asrt.wald <- testranfix(current.asrt, term = "Sources:Species", ssType = "conditional") testthat::expect_equal(ncol(asrt.wald$wald.tab), 6) testthat::expect_true("F.con" %in% colnames(asrt.wald$wald.tab)) terms.treat <- c("Sources", "Type", "Species", "Sources:Type", "Sources:Species") terms <- sapply(terms.treat, FUN=function(term){paste("Date:",term,sep="")}, simplify=TRUE) terms <- c("Date", terms) terms <- unname(terms) marginality <- matrix(c(1,0,0,0,0,0, 1,1,0,0,0,0, 1,0,1,0,0,0, 1,0,1,1,0,0, 1,1,1,0,1,0, 1,1,1,1,1,1), nrow=6) rownames(marginality) <- terms colnames(marginality) <- terms choose <- chooseModel(current.asrt, marginality, denDF="algebraic") current.asrt <- choose$asrtests.obj sig.terms <- choose$sig.terms testthat::expect_equal(length(sig.terms), 2) testthat::expect_equal(sig.terms[[1]], "Date:Species") testthat::expect_equal(sig.terms[[2]], "Date:Sources") }) cat("#### Test for testing at terms with asreml3\n") test_that("at_testing_asreml3", { skip_if_not_installed("asreml") skip_on_cran() library(dae) library(asreml, lib.loc = asr3.lib) library(asremlPlus) print(packageVersion("asreml")) #'## Load data data("Exp355.Control.dat") dat <- with(dat, dat[order(Genotype, Salt, NP_AMF, InTreat), ]) #Fit model with quotes around AMF_plus # NB must have quotes for character levels, # but cannot have in testranfix term because not in wald.tab rownames current.asr <- asreml(fixed = TSP ~ Lane + xPosn + AMF*Genotype*NP + at(AMF, "AMF_plus"):per.col + (Genotype*NP):at(AMF, "AMF_plus"):per.col, random = ~ spl(xPosn) + Position , rcov = ~ Genotype:idh(NP_AMF):InTreat, keep.order=TRUE, data = dat, maxit=50, na.method.X = "include") current.asrt <- asrtests(current.asr, NULL, NULL) current.asrt <- rmboundary(current.asrt) testthat::expect_equal(nrow(current.asrt$wald.tab),14) testthat::expect_equal(nrow(summary(current.asrt$asreml.obj)$varcomp),7) t.asrt <- testranfix(current.asrt, term = "Genotype:NP:at(AMF, AMF_plus):per.col", drop.fix.ns = TRUE) t.asrt$wald.tab testthat::expect_equal(nrow(t.asrt$wald.tab), 13) #Change position of at term in testranfix t.asrt <- testranfix(current.asrt, term = "at(AMF, AMF_plus):per.col:Genotype:NP", drop.fix.ns = TRUE) t.asrt$wald.tab testthat::expect_equal(nrow(t.asrt$wald.tab), 13) #Fit model with level index of 2 current.asr <- asreml(fixed = TSP ~ Lane + xPosn + AMF*Genotype*NP + at(AMF, "AMF_plus"):per.col + (Genotype*NP):at(AMF, 2):per.col, random = ~ spl(xPosn) + Position , rcov = ~ Genotype:idh(NP_AMF):InTreat, keep.order=TRUE, data = dat, maxit=50, na.method.X = "include") current.asrt <- asrtests(current.asr, NULL, NULL) current.asrt <- rmboundary(current.asrt) testthat::expect_equal(nrow(current.asrt$wald.tab),14) testthat::expect_equal(nrow(summary(current.asrt$asreml.obj)$varcomp),7) t.asrt <- testranfix(current.asrt, term = "at(AMF, AMF_plus):per.col:Genotype:NP", drop.fix.ns = TRUE) t.asrt$wald.tab testthat::expect_equal(nrow(t.asrt$wald.tab), 13) #Test for a numeric level that is not the same as the levels index (1:no.levels) current.asr <- asreml(fixed = TSP ~ at(Lane, 4) + xPosn + AMF*Genotype*NP + at(AMF, "AMF_plus"):per.col + (Genotype*NP):at(AMF, c(2)):per.col, random = ~ spl(xPosn) + Position , rcov = ~ Genotype:idh(NP_AMF):InTreat, keep.order=TRUE, data = dat, maxit=50, na.method.X = "include") current.asrt <- asrtests(current.asr, NULL, NULL) current.asrt <- rmboundary(current.asrt) current.asrt$wald.tab t.asrt <- testranfix(current.asrt, term = "at(Lane, 8)", drop.fix.ns = TRUE) t.asrt$wald.tab testthat::expect_equal(nrow(t.asrt$wald.tab), 14) }) cat("#### Test for testing MET at terms with asreml3\n") test_that("at_multilevel_asreml3", { skip_if_not_installed("asreml") skip_on_cran() library(dae) library(asreml, lib.loc = asr3.lib) library(asremlPlus) print(packageVersion("asreml")) #'## Load data data(MET) #Test at asreml.obj <-asreml(fixed = GY.tha ~ + at(expt, c(1:5)):rep + at(expt, c(1)):vrow + at(expt, c(2,3,6,7)):colblocks + at(expt, c(1:5,7)):vcol + Genotype*Condition*expt, random = ~ at(expt, c(1)):dev(vrow) + at(expt, c(2)):spl(vcol) + at(expt, c(3,5,7)):dev(vcol) + at(expt, c(7)):units, data=comb.dat, maxit = 100, workspace = 1e08) summary(asreml.obj)$varcomp current.asrt <- asrtests(asreml.obj, NULL, NULL) testthat::expect_equal(nrow(current.asrt$wald.tab), 24) #Single term in at expresion with the level and drop.fix.ns = TRUE -- works t.asrt <- testranfix(current.asrt, term = "at(expt, mtnue10):vrow", drop.fix.ns = TRUE, dDF.na = "residual", update = FALSE) testthat::expect_equal(nrow(t.asrt$wald.tab), 23) #Multiple fixed terms in an at expresion generates an error testthat::expect_error(t.asrt <- testranfix(current.asrt, term = "at(expt, c(1:5)):rep", drop.fix.ns = TRUE, dDF.na = "residual", update = FALSE)) #Multiple random terms in an at expression generates an error testthat::expect_error(t.asrt <- testranfix(current.asrt, term = "at(expt, c(3,5,7)):dev(vcol)", drop.ran.ns = TRUE, dDF.na = "residual", update = FALSE)) #Single random term in an at expression - thinks absent t.asrt <- testranfix(current.asrt, term = "at(expt, tarlee13):dev(vcol)", drop.ran.ns = TRUE, dDF.na = "residual", update = FALSE) testthat::expect_equal(t.asrt$test.summary$action[1], "Absent") #Test multiple at term with changeTerms t.asrt <- changeTerms(current.asrt, dropFixed = "at(expt, c(1:5)):rep", update = FALSE) testthat::expect_equal(nrow(t.asrt$wald.tab), 19) }) cat("#### Test for at terms in testswapran with asreml3\n") test_that("at_testswapran_asreml3", { skip_if_not_installed("asreml") skip_on_cran() library(dae) library(asreml, lib.loc = asr3.lib) library(asremlPlus) print(packageVersion("asreml")) #'## Load data data(longit.dat) current.asr <- do.call(asreml, args=list(fixed = Area ~ Block + Treatments + Treatments:xDAP, random = ~ Block:Cart + at(Treatments):spl(xDAP, k = 10) + Treatments:DAP + Block:Cart:spl(xDAP) + Block:Cart:xDAP, rcov = ~ Block:Cart:ar1h(DAP), keep.order=TRUE, data = longit.dat, maxit=100)) #'## Function to deal with bound variances - set to 1e-04 fixBoundResidualVariances <-function(current.asr) { repeat { current.call <- current.asr$call vpR <- grepl("R!DAP", names(current.asr$gammas), fixed = TRUE) vpR <- vpR & names(current.asr$gammas.con) == "Boundary" vpR <- current.asr$gammas[vpR] (terms <- names(vpR)) if (length(terms) == 0 || length(sum(vpR == 4)) > 5) break current.asr <- setvarianceterms(current.call, terms = terms, bounds = "F", initial.values = 0.0001, ignore.suffices = FALSE, stepsize = 0.001) } invisible(current.asr) } current.asr <- fixBoundResidualVariances(current.asr) testthat::expect_true(all(table(summary(current.asr)$varcomp$bound) == c(2,46,1))) #'## Load starting model into an asrtests object current.asrt <- as.asrtests(current.asr, NULL, NULL, label = "Selected variance model") testthat::expect_false(current.asrt$asreml.obj$converge) #'### Test for Treatments:DAP deviations terms current.asrt <- testranfix(current.asrt, term = "Treatments:DAP", positive.zero = TRUE) testthat::expect_equal(current.asrt$test.summary$action[2], "Dropped") testthat::expect_true(all(table(summary(current.asrt$asreml.obj)$varcomp$bound) == c(2,45,1))) #'### Test for different curvatures in splines current.asrt <- testswapran(current.asrt, oldterms = "at(Treatments):spl(xDAP, k = 10)", newterms = "at(AMF):Zn:spl(xDAP, k = 10)", simpler = TRUE, label = "Heterogeneous Treatment splines") testthat::expect_true(getTestPvalue(current.asrt, label = "Heterogeneous Treatment splines") < 0.05) testthat::expect_true(names(current.asrt$asreml.obj$gammas[1]) == "at(Treatments, -,0):spl(xDAP, k = 10)") testthat::expect_true(names(current.asrt$asreml.obj$gammas[5]) == "at(Treatments, +,0):spl(xDAP, k = 10)") testthat::expect_true(all(abs(current.asrt$asreml.obj$vparameters[1:8] - c(233.152932, 502.667930, 74.955973, 2.540186, 42.003197, 61.206138, 32.367734, 36.902978)) < 1e-02)) }) cat("#### Test for spline testing with asreml3\n") test_that("spl.asrtests_asreml3", { skip_if_not_installed("asreml") skip_on_cran() library(dae) library(asreml, lib.loc = asr3.lib) library(asremlPlus) print(packageVersion("asreml")) data(WaterRunoff.dat) current.asr <- do.call("asreml", args = list(fixed = log.Turbidity ~ Benches + (Sources * (Type + Species)) * Date, random = ~Benches:MainPlots:SubPlots:spl(xDay, k = 6), keep.order = TRUE, data = WaterRunoff.dat)) current.asrt <- as.asrtests(current.asr, NULL, NULL) #Test random splines current.asrt <- testranfix(current.asrt, term = "Benches:MainPlots:SubPlots:spl(xDay, k = 6)") current.asrt$test.summary testthat::expect_equal(nrow(current.asrt$test.summary), 1) testthat::expect_true(abs(current.asrt$test.summary$p - 0.08013755) < 1e-08) data(Wheat.dat) #'## Add cubic trend to Row so that spline is not bound Wheat.dat <- within(Wheat.dat, { vRow <- as.numeric(Row) vRow <- vRow - mean(unique(vRow)) yield <- yield + 10*vRow + 5 * (vRow^2) + 5 * (vRow^3) }) #'## Fit model using asreml asreml.obj <- asreml(fixed = yield ~ Rep + vRow + Variety, random = ~spl(vRow, k=6) + units, rcov = ~ar1(Row):ar1(Column), data = Wheat.dat, trace = FALSE) testthat::expect_true(summary(asreml.obj)$varcomp$constraint[1] == "Boundary") asreml.obj <- asreml(fixed = yield ~ Rep + vRow + Variety, random = ~spl(vRow) + units, rcov = ~ar1(Row):ar1(Column), data = Wheat.dat, trace = FALSE) testthat::expect_true(summary(asreml.obj)$varcomp$constraint[1] == "Boundary") }) cat("#### Test for reparamSigDevn.asrtests with asreml3\n") test_that("reparamSigDevn.asrtests_asreml3", { skip_if_not_installed("asreml") skip_on_cran() library(dae) library(asreml, lib.loc = asr3.lib) library(asremlPlus) data(WaterRunoff.dat) current.asr <- asreml(fixed = log.Turbidity ~ Benches + Sources + Type + Species + Sources:Type + Sources:Species + Sources:Species:xDay + Sources:Species:Date, data = WaterRunoff.dat, keep.order = TRUE) current.asrt <- as.asrtests(current.asr, NULL, NULL) #Examine terms that describe just the interactions of Date and the treatment factors terms.treat <- c("Sources", "Type", "Species", "Sources:Type", "Sources:Species") date.terms <- sapply(terms.treat, FUN=function(term){paste("Date:",term,sep="")}, simplify=TRUE) date.terms <- c("Date", date.terms) date.terms <- unname(date.terms) treat.marginality <- matrix(c(1,0,0,0,0,0, 1,1,0,0,0,0, 1,0,1,0,0,0, 1,0,1,1,0,0, 1,1,1,0,1,0, 1,1,1,1,1,1), nrow=6) rownames(treat.marginality) <- date.terms colnames(treat.marginality) <- date.terms choose <- chooseModel(current.asrt, treat.marginality, denDF="algebraic") current.asrt <- choose$asrtests.obj current.asr <- current.asrt$asreml.obj sig.date.terms <- choose$sig.terms #Remove all Date terms left in the fixed model terms <- "(Date/(Sources * (Type + Species)))" current.asrt <- changeTerms(current.asrt, dropFixed = terms) #if there are significant date terms, reparameterize to xDays + spl(xDays) + Date if (length(sig.date.terms) != 0) { #add lin + spl + devn for each to fixed and random models trend.date.terms <- sapply(sig.date.terms, FUN=function(term){sub("Date","xDay",term)}, simplify=TRUE) trend.date.terms <- paste(trend.date.terms, collapse=" + ") current.asrt <- changeTerms(current.asrt, addFixed=trend.date.terms) trend.date.terms <- sapply(sig.date.terms, FUN=function(term){sub("Date","spl(xDay)",term)}, simplify=TRUE) trend.date.terms <- c(trend.date.terms, sig.date.terms) trend.date.terms <- paste(trend.date.terms, collapse=" + ") current.asrt <- changeTerms(current.asrt, addRandom = trend.date.terms) current.asrt <- rmboundary.asrtests(current.asrt) } #Now test terms for sig date terms spl.terms <- sapply(terms.treat, FUN=function(term){paste("spl(xDay):",term,sep="")}, simplify=TRUE) spl.terms <- c("spl(xDay)",spl.terms) lin.terms <- sapply(terms.treat, FUN=function(term){paste(term,":xDay",sep="")}, simplify=TRUE) lin.terms <- c("xDay",lin.terms) systematic.terms <- c(terms.treat, lin.terms, spl.terms, date.terms) systematic.terms <- unname(systematic.terms) treat.marginality <- matrix(c(1,0,0,0,0,0, 1,1,0,0,0,0, 1,0,1,0,0,0, 1,0,1,1,0,0, 1,1,1,1,1,0, 1,1,1,1,1,1), nrow=6) systematic.marginality <- kronecker(matrix(c(1,0,0,0, 1,1,0,0, 1,1,1,0, 1,1,1,1), nrow=4), treat.marginality) systematic.marginality <- systematic.marginality[-1, -1] rownames(systematic.marginality) <- systematic.terms colnames(systematic.marginality) <- systematic.terms choose <- chooseModel(current.asrt, systematic.marginality, denDF="algebraic", pos=TRUE) current.asrt <- choose$asrtests.obj #Check if any deviations are significant and, for those that are, go back to #fixed dates current.asrt <- reparamSigDevn(current.asrt, choose$sig.terms, trend.num = "xDay", devn.fac = "Date", denDF = "algebraic") k <- match("Sources:Species:Date",rownames(current.asrt$wald.tab)) testthat::expect_equal(nrow(current.asrt$wald.tab), 9) testthat::expect_equal(nrow(current.asrt$test.summary), 6) testthat::expect_true(!is.na(k)) }) cat("#### Test for changeModelOnIC with wheat94 using asreml3\n") test_that("changeModelOnIC_wheat94_asreml3", { skip_if_not_installed("asreml") skip_on_cran() library(dae) library(asreml) library(asremlPlus) ## use asremlPlus to analyse the 1994 wheat example from Gilmour et al. (1995) data(wheat94.dat) #Start with Maximal model fm.max <- asreml(yield ~ lin(Row) + lin(Col) + Rowcode + Colcode, random = ~ Variety + Block + Row + spl(Col) + Col + units, rcov = ~ ar1(Col):ar1(Row), data = wheat94.dat) #Use REML likelihood and BIC current.asrt <- as.asrtests(fm.max, NULL, label = "Maximal model", IClikelihood = "REML") current.asrt <- iterate(current.asrt) current.asrt <- rmboundary(current.asrt) testthat::expect_equal(nrow(current.asrt$test.summary), 2) #Drop random Row and Col terms current.asrt <- changeModelOnIC(current.asrt, dropRandom = "Row + Col", label = "Drop Row + Col", which.IC = "BIC", IClikelihood = "REML") testthat::expect_equal(current.asrt$test.summary$denDF[3], -2) testthat::expect_equal(current.asrt$test.summary$action[current.asrt$test.summary$terms == "Drop Row + Col"], "Swapped") #Drop random spl(Col) term current.asrt <- changeModelOnIC(current.asrt, dropRandom = "spl(Col)", label = "Drop spl(Col)", which.IC = "BIC", IClikelihood = "REML") testthat::expect_equal(current.asrt$test.summary$denDF[4], -1) testthat::expect_equal(current.asrt$test.summary$action[current.asrt$test.summary$terms == "Drop spl(Col)"], "Swapped") testthat::expect_true((abs(current.asrt$test.summary$BIC[4]) - 1.764507) < 1e-02) #Drop random units term current.asrt <- changeModelOnIC(current.asrt, dropRandom = "units", label = "Drop units", which.IC = "BIC", IClikelihood = "REML") testthat::expect_equal(current.asrt$test.summary$denDF[5], -1) testthat::expect_equal(current.asrt$test.summary$action[current.asrt$test.summary$terms == "Drop units"], "Unswapped") testthat::expect_true((abs(current.asrt$test.summary$AIC[5]) -60.520592) < 1e-02) mod <- printFormulae(current.asrt$asreml.obj) testthat::expect_equal(length(mod), 3) }) cat("#### Test for changeModelOnIC example using asreml3\n") test_that("changeModelOnIC_Example_asreml3", { skip_if_not_installed("asreml") skip_on_cran() library(dae) library(asreml) library(asremlPlus) ## use asremlPlus to analyse the wheat (barley) example from section 8.6 of the asreml manual (Butler et al. 2010) data(Wheat.dat) #'## Fit maximal model current.asr <- asreml(yield ~ Rep + WithinColPairs + Variety, random = ~ Row + Column + units, rcov = ~ ar1(Row):ar1(Column), data=Wheat.dat) current.asr <- update(current.asr) current.asrt <- as.asrtests(current.asr, NULL, NULL, label = "Maximal model", IClikelihood = "REML") current.asrt <- rmboundary(current.asrt) testthat::expect_true(current.asrt$asreml.obj$converge) testthat::expect_true(current.asrt$test.summary$action[1] == "Starting model") testthat::expect_equal(current.asrt$test.summary$DF[1], 0) testthat::expect_equal(current.asrt$test.summary$denDF[1], 5) testthat::expect_equal(nrow(summary(current.asrt$asreml.obj)$varcomp), 5) # Drop both Row and Column terms current.asrt <- changeModelOnIC(current.asrt, dropRandom = "Row + Column", label = "Drop Row + Column", checkboundaryonly = TRUE, which.IC = "AIC", IClikelihood = "REML") testthat::expect_true(current.asrt$asreml.obj$converge) testthat::expect_equal(current.asrt$test.summary$denDF[3], -1) # Replace residual with model without Row autocorrelation current.asrt <- changeModelOnIC(current.asrt, newResidual = "Row:ar1(Column)", label="Row autocorrelation", IClikelihood = "REML") testthat::expect_true(current.asrt$asreml.obj$converge) testthat::expect_equal(current.asrt$test.summary$denDF[4], -2) testthat::expect_true((abs(current.asrt$test.summary$AIC[4]) - 24.158777) < 1e-03) mod <- printFormulae(current.asrt$asreml.obj) testthat::expect_equal(length(mod), 3) testthat::expect_true(grepl("units", mod[2], fixed = TRUE)) })