Package ‘rFSA’ October14,2022 Type Package Title FeasibleSolutionAlgorithmforFindingBestSubsetsand Interactions Version 0.9.6 Date 2020-06-10 Description Assistsinstatisticalmodelbuildingtofindoptimalandsemi-optimalhigherorderinteractions andbestsubsets.Usesthelm(),glm(),andotherRfunctionstofitmodelsgeneratedfromafeasible solutionalgorithm.DiscussedinSubsetSelectioninRegression,AMiller(2002).Ap- pliedandexplained forleastmedianofsquaresinHawkins(1993)<doi:10.1016/0167-9473(93)90246- P>.Thefeasiblesolution algorithmcomesupwithmodelformsofaspecifictypethatcanhavefixedvariables,higherorder interactionsandtheirlowerorderterms. License GPL-2 LazyData TRUE Imports parallel,methods,tibble,rPref,tidyr,hash RoxygenNote 7.1.0 NeedsCompilation no Author JoshuaLambert[aut,cre], LiyuGong[aut], CorrineElliott[aut], SarahJanse[ctb] Maintainer JoshuaLambert<[email protected]> Repository CRAN Date/Publication 2020-06-1020:20:03UTC R topics documented: adj.r.squared . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 apress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1 2 adj.r.squared bdist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 fitmodels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 fitted.FSA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 FSA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 int.p.val . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 list.criterion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 max_abs_resid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 nextswap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 pFSA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 plot.FSA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 predict.FSA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 print.FSA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 QICu.geeglm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 r.squared . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 rmse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 summary.FSA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 swaps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 twFSA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 which.max.na . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 which.min.na . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Index 18 adj.r.squared AnrFSACriterionFunction. Description rFSACriterionFunctiontocomputeAdjustedR-Squared. Usage adj.r.squared(model, name = "Adj R Squared") Arguments model lmorglmfittobepassed. name passedtoprint.FSA apress 3 apress AnrFSACriterionFunction. Description rFSACriterionFunctiontoAllen’sPressStatistic. Usage apress(model, name = "PRESS") Arguments model lmorglmfittobepassed. name passedtoprint.FSA bdist AnrFSACriterionFunction. Description rFSACriterionFunctiontocomputetheBhattacharyyadistance. Usage bdist(model, name = "B Distance") Arguments model lmorglmfittobepassed. name passedtoprint.FSA Examples #To use Bhattacharyya Distance and FSA the response must be binary, and you must #be considering searching for two way continuous interactions. data(mtcars) fit<-FSA(formula = "am~gear*hp",data = mtcars, fitfunc = glm,family="binomial",m = 2,cores=1, interactions = TRUE,criterion = bdist,minmax = "max") 4 fitted.FSA fitmodels ModelfittingfunctionforFSAsolutions Description ModelfittingfunctionforFSAsolutions Usage fitmodels(object, ...) Arguments object FSAobjecttoconstructmodelson. ... otherparameterspassedtolmorglm. Seehelp(lm)orhelp(glm)forotherpo- tentialarguements. Value listofFSAmodelsthathavebeenfitted. Examples #use mtcars package see help(mtcars) data(mtcars) colnames(mtcars) fit<-lmFSA(formula="mpg~hp*wt",data=mtcars,fixvar="hp", quad=FALSE,m=2,numrs=10,save_solutions=FALSE,cores=1) fitmodels(fit) fitted.FSA FittedValuesforFSAsolutions Description FittedValuesforFSAsolutions Usage ## S3 method for class 'FSA' fitted(object, ...) Arguments object FSAobjecttogetfittedvaluesfrom. ... other parameters passed to fitmodels or fitted function. See help(fitmodels) or help(fitted)forassistance. FSA 5 Value listoffittedvaluesfromeachFSAmodel. Examples #use mtcars package see help(mtcars) data(mtcars) colnames(mtcars) fit<-lmFSA(formula="mpg~hp*wt",data=mtcars,fixvar="hp", quad=FALSE,m=2,numrs=10,save_solutions=FALSE,cores=1) fitted(fit) FSA FSA:FeasibleSolutionAlgorithm Description A function using a Feasible Solution Algorithm to find a set of feasible solutions for a statistical model of a specific form that could include mth-order interactions (Note that these solutions are optimalinthesensethatnooneswaptoanyofthevariableswillincreasethecriterionfunction.) Usage FSA( formula, data, fitfunc = lm, fixvar = NULL, quad = FALSE, m = 2, numrs = 1, cores = 1, interactions = T, criterion = AIC, minmax = "min", checkfeas = NULL, var4int = NULL, min.nonmissing = 1, return.models = FALSE, fix.formula = NULL, ... ) lmFSA(...) glmFSA(...) 6 FSA Arguments formula anobjectofclass"formula"(oronethatcanbecoercedtothatclass):asymbolic descriptionofthemodeltobefitted. data adataframe,listorenvironment(orobjectcoerciblebyas.data.frametoadata frame)containingthevariablesinthemodel. fitfunc themethodthatshouldbeusedtofitthemodel. ForExample: lm,glm,orother methodsthatrelyonformula,data,andotherinputs. fixvar variable(s) to fix in the model. Usually a covariate that should always be in- cluded(Example: Age,Sex). Willstillconsideritwithinteractions. Defaultis NULL. quad Includequadratictermsornot. Logical. m orderoftermstoinclude. IfinteractionsissettoTRUEthenmistheorderof interactionstobeconsidered. ForSubsetselection(interaction=F),misthesize ofthesubsettoexamine. Defaultsto2. numrs numberofrandomstartstoperform. cores numberofcorestousewhilerunning. Note: Windowscanonlyuse1core. See mclapplyfordetails.IffunctiondetectsaWindowsuseritwillautomaticallyset cores=1. interactions whethertoincludeinteractionsinmodel. DefaultstoTRUE. criterion whichcriterionfunctiontoeithermaximizeorminimize. Forlinearmodelsone can use: r.squared, adj.r.squared, cv5.lmFSA (5 Fold Cross Validation error), cv10.lmFSA (10 Fold Cross Validation error), apress (Allen’s Press Statistic), int.p.val(InteractionP-value),AIC,BIC. minmax whethertominimizeormaximizethecriterionfunction checkfeas vectorofvariablesthatcouldbeafeasiblesolution.Thesevariableswillbeused asthelastrandomstart. var4int specification of which variables to check for marginal feasiblilty. Default is NULL min.nonmissing thecombinationofpredictorswillbeignoredunlessthismanyofobservations arenotmissing return.models bool value to specify whether return all the fitted models which have been checked fix.formula ... ... otherargumentspassedtofitfunc. Value matrixofresults Functions • FSA:findbestsetofvariablesforstatisticalmodels • lmFSA:aliasforFSA(fitfunc=lm,...) • glmFSA:aliasforFSA(fitfunc=glm,...) int.p.val 7 Examples N <- 10 #number of obs P <- 100 #number of variables data <- data.frame(matrix(rnorm(N*(P+1)), nrow = N, ncol = P+1)) sln <- FSA(formula = "X101~1", data = data, cores = 1, m = 2, interactions = FALSE, criterion = AIC, minmax = "min", numrs = 10) sln int.p.val AnrFSACriterionFunction. Description rFSA Criterion Function to compute Liklihood Ratio Test Statistics p-value for the largest order interationterm. Usage int.p.val(model, name = "Interaction P-Value") Arguments model lmorglmfittobepassed. name passedtoprint.FSA list.criterion ListallincludedCriteriafunctionforlmFSAandglmFSA. Description ListallincludedCriteriafunctionforlmFSAandglmFSA. Usage list.criterion() Value listoffunctionsandwhetherlmFSAorglmFSAworkwiththosefunctions. Examples list.criterion() 8 nextswap max_abs_resid Returnmaximumabsoluteresidualfromamodel Description Returnmaximumabsoluteresidualfromamodel Usage max_abs_resid(model) Arguments model modelobj nextswap Variablestoincludeinthe>1ststepofanmthorderinteractionmodel determinedfromtheFeasibleSoutionAlorithm. Description Findstheswapsavailablegivenacurrentpositiongivenpreviouspicks. Usage nextswap(curpos, n, prevpos, quad) Arguments curpos Avectoroflengthgreaterthan2ofwhatcurrentexplantoryvarialbesarebeing usedinthemodel. n Thenumberofexplanatoryvariablesinavailabletoswap. prevpos Avectorofpreviousbestspots quad Whethertoincludequadraticterms. ie(x1*x1)aspotentialswaps. Value amatrixwiththepossibleformsbycolumn. pFSA 9 pFSA pFSA:ParetoFeasibleSolutionAlgorithm Description AfunctionusingaFeasibleSolutionAlgorithmtoestimateasetofmodelswhichareonthePareto frontiersforchosencriteria Usage pFSA( numFronts = 2, pselExpr = NULL, plot.it = TRUE, formula, data, fitfunc = lm, fixvar = NULL, quad = FALSE, m = 2, numrs = 1, cores = 1, interactions = T, criterion = AIC, minmax = "min", checkfeas = NULL, var4int = NULL, min.nonmissing = 1, return.models = FALSE, fix.formula = NULL, ... ) Arguments numFronts integernumberofestimatedfrontierstoreturn pselExpr expressionusedbyfunctionpseltoestimateparetofrontiers. help(psel). plot.it TRUE/FALSEforwhethertoplottheparetofrontiers formula anobjectofclass"formula"(oronethatcanbecoercedtothatclass):asymbolic descriptionofthemodeltobefitted. data adataframe,listorenvironment(orobjectcoerciblebyas.data.frametoadata frame)containingthevariablesinthemodel. fitfunc themethodthatshouldbeusedtofitthemodel. ForExample: lm,glm,orother methodsthatrelyonformula,data,andotherinputs. 10 pFSA fixvar variable(s) to fix in the model. Usually a covariate that should always be in- cluded(Example: Age,Sex). Willstillconsideritwithinteractions. Defaultis NULL. quad Includequadratictermsornot. Logical. m orderoftermstoinclude. IfinteractionsissettoTRUEthenmistheorderof interactionstobeconsidered. ForSubsetselection(interaction=F),misthesize ofthesubsettoexamine. Defaultsto2. numrs numberofrandomstartstoperform. cores numberofcorestousewhilerunning. Note: Windowscanonlyuse1core. See mclapplyfordetails.IffunctiondetectsaWindowsuseritwillautomaticallyset cores=1. interactions whethertoincludeinteractionsinmodel. DefaultstoTRUE. criterion whichcriterionfunctiontoeithermaximizeorminimize. Forlinearmodelsone can use: r.squared, adj.r.squared, cv5.lmFSA (5 Fold Cross Validation error), cv10.lmFSA (10 Fold Cross Validation error), apress (Allen’s Press Statistic), int.p.val(InteractionP-value),AIC,BIC. minmax whethertominimizeormaximizethecriterionfunction checkfeas vectorofvariablesthatcouldbeafeasiblesolution.Thesevariableswillbeused asthelastrandomstart. var4int specification of which variables to check for marginal feasiblilty. Default is NULL min.nonmissing thecombinationofpredictorswillbeignoredunlessthismanyofobservations arenotmissing return.models bool value to specify whether return all the fitted models which have been checked fix.formula ... ... seeargumentstakenbyfunctionFSAorotherfunctions. help(FSA). Value list of a matrix of all models obtained from FSA (fits) and their criteria. Also a matrix of the estimatedfrontiersthatwererequested. TheKeycolumninfits, andpboundreferstothecolumn number of the variables contined in the model fit. For instance, Key="42,96" would refer to the modelwhichcontainsthevariableinthe42ndcolumnand96thcolumnofthedesignateddataset. Examples N <- 1000 #number of obs P <- 100 #number of variables data <- data.frame(matrix(rnorm(N*(P+1)), nrow = N, ncol = P+1)) sln <- pFSA(formula = "X101~1", data = data, m = 2, criterion = c(max_abs_resid,r.squared), minmax = c("min","max"),numrs = 10,numFronts = 2, pselExpr =rPref::low(max_abs_resid)*rPref::high(r.squared),plot.it = TRUE)