Package MMIX. R topics documented: February 15, Type Package. Title Model selection uncertainty and model mixing. Version 1.2.

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1 Package MMIX February 15, 2013 Type Package Title Model selection uncertainty and model mixing Version 1.2 Date Author Marie Morfin and David Makowski Maintainer Description Implement different types of model mixing and model selection methods for linear or logistic models. License GPL (>= 2) LazyLoad yes Repository CRAN Date/Publication :10:51 NeedsCompilation no R topics documented: MMIX-package arms bmabic bootfreq fullmodel pmsecv print.mmixclass stepsel varselec Index 20 1

2 2 MMIX-package MMIX-package Model selection uncertainty and model mixing Description Details Implement different types of model mixing and model selection methods for linear or logistic models. Package: MMIX Type: Package Version: Date: License: GPL (>= 2) LazyLoad: yes This package implements three model mixing methods, two model selection procedures and three functions for model evaluation. Author(s) Marie Morfin and David Makowski Maintainer: Who to complain to References Barbottin A., Makowski D., Le Bail M., Jeuffroy M.-H., Bouchard C., Barrier C. (2008) Comparison of models and indicators for categorizing soft wheat fields according to their grain protein contents, European Journal of Agronomy 29, Buckland, S.T., Burnham, K.P. and Augustin, N.H. (1997) Model selection: an integral part of inference, Biometrics 53, Burnham, K.P. and Anderson, D.R. (2002) Model selection and multimodel inference: a practical information-theoretic approach, Springer-Verlag, New York. Casagrande, M., David, C., Valantin-Morison, M., Makowski, D. and Jeuffroy, M.-H. (2009) Factors limiting protein content of organic winter wheat in south- eastern France: a mixed-model approach, Agronomy for Sustainable Development, In press. Chatfield, C. (1995) Model uncertainty, data mining and statistical inference, Journal of the Royal Statistical Society /A 158, Efron, B. (1979) Bootstrap methods : another look at the jackknife, American Statistician 7, Efron, B. and Tibshirani, R.J. (1993) An introduction to the bootstrap, Chapman & Hall. Hammersley, J.M. and Handscomb, D.C. (1964) Monte Carlo Methods, Chapman & Hall, London & New York.

3 MMIX-package 3 Hoeting, JA., Madigan, D., Raftery, A.E. and Volinsky, C.T. (1999), Bayesian model averaging: a tutorial, Statistical Science, 14, Miller A. (2002) Subset selection in regression, 2nd edition Chapman & Hall/CRC, New York. Mooney, C.Z. and Duval, R.D. (1993) Bootstrapping : a nonparametric approach to statistical inference, Sage Publications, London. Prost, L., Makowski, D. and Jeuffroy, M.-H. (2006) Comparison of stepwise selection and Bayesian model averaging for yield gap analysis, Ecological Modelling 219, Raftery, A.E., Madigan D. and Hoeting J.A. (1997) Bayesian model averaging for linear regression models, Journal of the American Statistical Association 92, Sing, T., Sander, O., Beerenwinkel, N. and Lengauer, T. (2005) ROCR: visualizing classifier performance, Bioinformatics applications note 21, Viallefont, V., Raftery A.E. and Richardson, S. (2001) Variable selection and Bayesian model averaging in case-control studies, Statistics in medicine 20, Yuan, Z. and Ghosh, D. (2008) Combining Multiple Biomarker Models in Logistic Regression, Biometrics 64, Yuan, Z. and Yang, Y. (2005) Combining Linear Regression Models: When and How?, Journal of the American Statistical Association 100, Examples ###Data #Explanatory variables X1<-c(-0.2,-2.4,-0.7,1.2,0.0,-1.1,-2.1,-0.3,2.0,-1.7,1.4,-1.3,-3.4,0.4,-1.3, -4.8) X2<- c(-3, 2, 1, -2, -2, -4, 0, 1, 1, -1, -1, -4, 0, 2, 0, -4) X3<-c(2,1,0,-2,1,-2, 0, -1, -4, 1, -3, -3, -3, -1, 0, 2) ##Linear model Y1<- c(8.7, 6, 9.1, 10.4, 7.6,10.4, 7.9, 11.9, 18, 10.5, 16.5, 8.8, 7.7, 13.5, 8.2, 0.8) data1<-data.frame(y1,x1,x2,x3) ##Logistic model Y2<-c(1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1) data2<-data.frame(y2,x1,x2,x3) ##bootfreq #Stepwise selection method bootstep1<-bootfreq(data=data1,family=gaussian("identity"),nboot=50,method=2, criterion="bic",trace=0) bootstep1 summary(bootstep1) plot(bootstep1) bootstep2<-bootfreq(data=data2,family=binomial("logit"),method=2, criterion="bic",nboot=20,trace=0) bootstep2 summary(bootstep2) plot(bootstep2)

4 4 arms ##ARMS method armsresult1<-arms(data=data1,family=gaussian("identity"),nbest=5,nsample=10, criterion="both",weight="aic") armsresult1 summary(armsresult1) plot(armsresult1) armsresult2<-arms(data=data2,family=binomial("logit"),nbest=5,nsample=10, criterion="both",weight="aic") armsresult2 summary(armsresult2) plot(armsresult2) ##Root Mean Square Error by cross-validation #Stepwise selection with BIC pmsestepbic<-pmsecv(data=data1,method=2,np=1,random=false,direction="both", criterion="bic",trace=0) pmsestepbic #BMA pmsebma<-pmsecv(data=data1,method=3,np=1,random=false) pmsebma ##Area Under ROC Curve by cross-validation aucstepbic<-auccv(data=data2,method=2,np=1,random=false,direction="both", criterion="bic",trace=0) aucstepbic aucbma<-auccv(data=data2,method=3,np=1,random=false) aucbma arms Adaptative Regression by Mixing with model Screening Description Apply ARMS for linear and logistic models. Usage arms(data, family, nsample = 20, nbest = 20, criterion= "both", weight = "aic", maxvar=10) Arguments data a data frame including the response variable (first column) and the explanatory variables. All the variables must be numeric and the response variable value must be 0 or 1 for the logistic model.

5 arms 5 family nsample nbest criterion weight maxvar a description of the error distribution (gaussian("identity") or binomial("logit")). number of sample permutations number of models selected at the screening step selection criterion used at the screening step. criterion="aic", "bic" or "both". "both" means that nbest models are selected according to AIC, and nbest according to "bic" (between nbest and 2*nbest models may be selected). model weight type, weight = "likeli" or "aic" (the default). See details. maximum number of explanatory variables to include in the model. See varselec. Details Value A set of models including all possible combinations of at most maxvar variables is defined. The models are weighted as follows: Step 1. The sample is splitted in two parts. The first one is used to fit the models. Step 2. Each model is fitted by least squares or maximum likelihood. Step 3. A set of models is selected according to AIC and BIC. Step 4. Weights are computed for the selected models using the second sample. Two weight types can be used, "likeli" or "aic". At each iteration, the sample is permuted. The final weight of each model is the mean across all the permutations. The coefficients are calculated on the whole sample using the averaged model weights. arms returns an object of class "MMIXclass". A data frame with the main results is printed with the function "print" and a graphic with the weights of the explanatory variables is obtained with the function "plot". An arms object is a list including the following components: coef pne0 fitted.values label modweights allcoef a named vector of coefficients. a vector containing the probability of each explanatory variable to be different from zero. the fitted values, obtained by transforming the linear predictors by the inverse of the link function. a list of the explanatory variables used by each model. the weights of all models. matrix with one row per model and one column per coefficient giving the ML estimate of each coefficient for each model. Warning This function does not accept or treat missing values. Author(s) Marie Morfin and David Makowski

6 6 bmabic References Yuan, Zheng and Ghosh, Debashis (2008) Combining Multiple Biomarkers Models in Logistic Regression, Biometrics 64, Yuan, Zheng and Yang, Yuhong (2005) Combining Linear Regression Models : When and How?, Journal of the American Statistical Association 100, See Also fullmodel, bmabic, mixaic, stepsel, bootfreq Examples ##Data #Explanatory variables X1<-c(-0.2,-2.4,-0.7,1.2,0.0,-1.1,-2.1,-0.3,2.0,-1.7,1.4,-1.3,-3.4,0.4,-1.3, -4.8) X2<- c(-3, 2, 1, -2, -2, -4, 0, 1, 1, -1, -1, -4, 0, 2, 0, -4) X3<-c(2,1,0,-2,1,-2, 0, -1, -4, 1, -3, -3, -3, -1, 0, 2) #Linear model Y1<- c(8.7, 6, 9.1, 10.4, 7.6,10.4, 7.9, 11.9, 18, 10.5, 16.5, 8.8, 7.7, 13.5, 8.2, 0.8) data1<-data.frame(y1,x1,x2,x3) #Logistic model Y2<-c(1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1) data2<-data.frame(y2,x1,x2,x3) #arms method armsresult1<-arms(data=data1,family=gaussian( identity ),nbest=5,nsample=10, criterion="both",weight="aic") armsresult1 summary(armsresult1) plot(armsresult1) armsresult2<-arms(data=data2,family=binomial("logit"),nbest=5,nsample=10, criterion="both",weight="aic") armsresult2 summary(armsresult2) plot(armsresult2) bmabic Model mixing methods for linear or logistic regression Description bmabic is a Bayesian Model Averaging method based on the bic criterion, and mixaic is a model mixing method based on the aic criterion.

7 bmabic 7 Usage bmabic(data, family, maxvar=10) mixaic(data, family, maxvar=10) Arguments data family maxvar a data frame including the response variable (first column) and the explanatory variables. All the variables must be numeric and the response variable value must be 0 or 1 for the logistic model. a description of the error distribution (gaussian("identity") or binomial("logit")). maximum number of explanatory variables to include in the model. See varselec. Details Value A set of models including all possible combinations of at most maxvar variables is defined. The models are weighted using aic (mixaic) or bic (bmabic). Computation time may be very long if maxvar is set to a high value. When the number of explanatory variables in data is higher than maxvar, this number is reduced to at most maxvar variables by stepwise selection ("forward", "aic"). bmabic and mixaic return an object of class "MMIXclass". A data frame with the main results is printed when calling the function "print", the detailed results are obtained with the function "summary" and a graphic of the weights of the explanatory variables is plotted with the function "plot". A bmabic or mixaic object is a list including the following components : coef pne0 fitted.values BestModels sd label modweights allcoef a named vector of coefficients. a vector containing the probability of each explanatory variable to be different from zero. the fitted values, obtained by transforming the linear predictors by the inverse of the link function. the best three models selected by AIC (mixaic) or BIC (bmabic). standard deviation of the estimated parameter values. a list of the explanatory variables used by each model. the weights of all models. matrix with one row per model and one column per coefficient giving the ML estimate of each coefficient for each model. Warning These functions do not accept or treat missing values. Author(s) Marie Morfin and David Makowski

8 8 bmabic References Barbottin A., Makowski D., Le Bail M., Jeuffroy M.-H., Bouchard C., Barrier C. (2008) Comparison of models and indicators for categorizing soft wheat fields according to their grain protein contents, European Journal of Agronomy 29, Burnham, K.P. and Anderson, D.R. (2002) Model selection and multimodel inference: a practical information-theoretic approach, Springer-Verlag, New York. Casagrande, M., David, C., Valantin-Morison, M., Makowski, D. and Jeuffroy, M.-H. (2009) Factors limiting protein content of organic winter wheat in south- eastern France: a mixed-model approach, Agronomy for Sustainable Development, In press. Hoeting, J.A., Madigan, D., Raftery, A.E. and Volinsky, C.T. (1999) Bayesian model averaging: a tutorial, Statistical Science 14, Prost, L., Makowski, D. and Jeuffroy, M.-H. (2006) Comparison of stepwise selection and Bayesian model averaging for yield gap analysis, Ecological Modelling 219, Raftery, A.E., Madigan D. and Hoeting, J.A. (1997) Bayesian model averaging for linear regression models, Journal of the American Statistical Association 92, Raftery, A.E., Painter, I.S. and Volinsky, C.T. (2005) BMA : An R package for Bayesian Model Averaging, R News 5, 2-8. Viallefont, V., Raftery, A.E. and Richardson, S. (2001) Variable selection and Bayesian model averaging in case-control studies, Statistics in medicine 20, See Also family, varselec Examples ##Data #Explanatory variables X1<-c(-0.2,-2.4,-0.7,1.2,0.0,-1.1,-2.1,-0.3,2.0,-1.7,1.4,-1.3,-3.4,0.4,-1.3, -4.8) X2<- c(-3, 2, 1, -2, -2, -4, 0, 1, 1, -1, -1, -4, 0, 2, 0, -4) X3<-c(2,1,0,-2,1,-2, 0, -1, -4, 1, -3, -3, -3, -1, 0, 2) #Linear model Y1<- c(8.7, 6, 9.1, 10.4, 7.6,10.4, 7.9, 11.9, 18, 10.5, 16.5, 8.8, 7.7, 13.5, 8.2, 0.8) data1<-data.frame(y1,x1,x2,x3) #Logistic model Y2<-c(1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1) data2<-data.frame(y2,x1,x2,x3) ##bmabic method bmaresult1<-bmabic(data=data1,family=gaussian("identity")) bmaresult1 summary(bmaresult1) plot(bmaresult1)

9 bootfreq 9 bmaresult2<-bmabic(data=data2,family=binomial("logit")) bmaresult2 summary(bmaresult2) plot(bmaresult2) ##mixaic method mixresult1<-mixaic(data=data1,family=gaussian("identity")) mixresult1 summary(mixresult1) plot(mixresult1) mixresult2<-mixaic(data=data2,family=binomial("logit")) mixresult2 summary(mixresult2) plot(mixresult2) bootfreq Stability of selection and mixing methods Description This function analyses the stability of the stepwise selection and mixing methods using a bootstrap procedure. Usage bootfreq(data, family, nboot = 100, method = 1, file = NULL,...) Arguments data family nboot method file a data frame including the response variable (first column) and the explanatory variables. All the variables must be numeric and the response variable value must be 0 or 1 for the logistic model. a description of the error distribution (gaussian("identity") or binomial("logit")). number of bootstrap samples drawn. the statistical method used to estimate the model parameters. method = 1 for fullmodel, method = 2 for stepsel, method = 3 for bmabic, method = 4 for mixaic, method = 5 for arms. the path of the file where the results are stored during the run. If file = NULL no file is created.... the specific arguments of the called method.

10 10 bootfreq Details nboot samples are generated with replacement from the original dataset. For each sample, the parameters are estimated using the chosen method. The frequency of selection of a variable is the part of the samples for which the estimated value of its coefficient is different from zero. Selection frequency is an indicator of the stability of the method. Frequencies close to 0 or 1 indicates that the corresponding variables was almost never or always selected in the bootstrap samples. Value bootfreq returns an object of class "classmmix". A data frame with the main results is printed with the function "print", and a graphic with the weights of the explanatory variables is plotted with the function "plot". A bootfreq object is a list including the following components: frequency coef mean sd pne0 frequency of selection of each variable across the bootstrap samples estimated parameter values across the bootstrap samples; a matrix with nsample rows mean of the estimated parameter values across the bootstrap samples standard deviation of the estimated parameter values across the bootstrap samples mean values of the variable weights computed using a model mixing method. Pne0 = frequency if method = 1 or 2. Warning This function does not accept or treat missing values. Author(s) Marie Morfin and David Makowski <makowski@grignon.inra.fr> References Buckland, S.T., Burnham, K.P. and Augustin, N.H. (1997) Model selection: an integral part of inference, Biometrics 53, Chatfield, C. (1995) Model uncertainty, data mining and statistical inference, Journal of the Royal Statistical Society /A 158, Efron, B. (1979) Bootstrap methods : another look at the jackknife, American Statistician 7, Efron, B. and Tibshirani, R.J. (1993) An introduction to the bootstrap, Chapman & Hall. Hammersley, J.M. and Handscomb, D.C. (1964) Monte Carlo Methods, Chapman & Hall. Miller A. (2002) Subset selection in regression, 2nd edition Chapman & Hall/CRC, New York. Mooney, C.Z. and Duval, R.D. (1993) Bootstrapping: a nonparametric approach to statistical inference, Sage Publications, London. Prost, L., Makowski, D. and Jeuffroy, M.-H. (2006) Comparison of stepwise selection and Bayesian model averaging for yield gap analysis, Ecological Modelling 219,

11 fullmodel 11 See Also fullmodel, stepsel, bmabic, mixaic, arms Examples ##Data #Explanatory variables X1<-c(-0.2,-2.4,-0.7,1.2,0.0,-1.1,-2.1,-0.3,2.0,-1.7,1.4,-1.3,-3.4,0.4,-1.3, -4.8) X2<- c(-3, 2, 1, -2, -2, -4, 0, 1, 1, -1, -1, -4, 0, 2, 0, -4) X3<-c(2,1,0,-2,1,-2, 0, -1, -4, 1, -3, -3, -3, -1, 0, 2) #Linear model Y1<- c(8.7, 6, 9.1, 10.4, 7.6,10.4, 7.9, 11.9, 18, 10.5, 16.5, 8.8, 7.7, 13.5, 8.2, 0.8) data1<-data.frame(y1,x1,x2,x3) #Logistic model Y2<-c(1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1) data2<-data.frame(y2,x1,x2,x3) ##Analysis of a stepwise selection bootstep1<-bootfreq(data=data1,family=gaussian("identity"),nboot=50,method=2, criterion="bic",trace=0) bootstep1 summary(bootstep1) plot(bootstep1) bootstep2<-bootfreq(data=data2,family=binomial("logit"),method=2, criterion="bic",nboot=20,trace=0) bootstep2 summary(bootstep2) plot(bootstep2) fullmodel Linear and logistic regressions Description Linear or logistic model without any variable selection. Usage fullmodel(data, family)

12 12 fullmodel Arguments data family a data frame including the response variable (first column) and the explanatory variables. All the variables must be numeric and the response variable value must be 0 or 1 for the logistic model. a description of the error distribution (gaussian("identity") or binomial("logit")). Value fullmodel returns an object of class "MMIXclass". A data frame with the main results is printed when calling the function "print", and the detailed results are obtained with the function "summary". A fullmodel object is a list including the following components: cv coef aic bic fitted.values logical. Was the IWLS algorithm judged to have converged? a named vector of coefficients estimated by least squares or maximum likelihood. Akaike Information Criterion, minus twice the maximized log-likelihood plus twice the number of coefficients. Bayesian information criterion, minus twice the maximized log-likelihood plus the logarithm of the number of observation multiplied by the number of coefficients the fitted values, obtained by transforming the linear predictors by the inverse of the link function. Author(s) Marie Morfin and David Makowski References Venables, W.N. and Ripley, B.D. (2002) Modern Applied Statistics with S., Springer, New York. See Also family, arms, bmabic, mixaic, stepsel, bootfreq Examples ###Data #Explanatory variables X1<-c(-0.2,-2.4,-0.7,1.2,0.0,-1.1,-2.1,-0.3,2.0,-1.7,1.4,-1.3,-3.4,0.4,-1.3, -4.8) X2<- c(-3, 2, 1, -2, -2, -4, 0, 1, 1, -1, -1, -4, 0, 2, 0, -4) X3<-c(2,1,0,-2,1,-2, 0, -1, -4, 1, -3, -3, -3, -1, 0, 2) ##Linear model Y1<- c(8.7, 6, 9.1, 10.4, 7.6,10.4, 7.9, 11.9, 18, 10.5, 16.5, 8.8, 7.7, 13.5, 8.2, 0.8) data1<-data.frame(y1,x1,x2,x3)

13 pmsecv 13 ##Logistic model Y2<-c(1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1) data2<-data.frame(y2,x1,x2,x3) ##fullmodel method fullresult1<-fullmodel(data=data1,family=gaussian("identity")) fullresult1 summary(fullresult1) fullresult2<-fullmodel(data=data2,family=binomial("logit")) fullresult2 summary(fullresult2) pmsecv Model performance indicators PMSE and AUC Description pmsecv and auccv calculate the Predictive Mean Square Error (PMSE) by "leave-np-out" crossvalidation and Area Under Roc Curve (AUC) by "leave-np-pair-out" cross-validation. They can be applied to models created using fullmodel, stepsel, bmabic, mixaic and arms. Usage pmsecv(data, method = 1, np, random = TRUE, npermu = 100, file = NULL,...) auccv(data, method = 1, np, random = TRUE, npermu = 100, file = NULL,...) Arguments data method np random npermu file a data frame including the response variable (first column) and the explanatory variables. All the variables must be numeric and the response variable value must be 0 or 1 for the logistic model. the statistical method used to estimate the model parameters. method = 1 for fullmodel, method = 2 for stepsel, method = 3 for bmabic, method = 4 for mixaic, method = 5 for arms. number of observations (pmsecv) or pairs of observations (auccv) left out for computing the PMSE or AUC. observations are selected at random if TRUE. random can be FALSE only if np = 1. In this case all the possible sets are selected. number of random samples of np observations if random = TRUE. the path of the file where the results are stored during the run. If file = NULL no file is created.... the specific arguments of the called method

14 14 pmsecv Details Value These two cross validation procedures are implemented to assess the accuracy of model predictions. Linear models should be evaluated using pmsecv and logistic models should be evaluated using auccv. In the auccv procedure, data are held out by pair (one data from each class, 0 and 1) at each iteration in order to calculate the corresponding AUC. The PMSE (AUC) estimated by cross validation is the mean of the PMSE (AUC) calculated for possible sets of np observations (pairs). If file is not NULL, the np predictions (first column) and the np corresponding observations (second column) are saved at each iteration. pmsecv (auccv) returns a one-row data frame including the PMSE (AUC) calculated from the whole sample in the first column and by cross validation in the other one. Warning These functions do not accept or treat the missing values. Author(s) Marie Morfin and David Makowski References Sing, T., Sander, O., Beerenwinkel, N. and Lengauer, T. (2005) ROCR: visualizing classifier performance, Bioinformatics applications note 21, Yuan, Z. and Ghosh, D. (2008) Combining Multiple Biomarker Models in Logistic Regression, Biometrics 64, Yuan, Z. and Yang, Y. (2005) Combining Linear Regression Models: When and How?, Journal of the American Statistical Association 100, See Also fullmodel, stepsel, bmabic, mixaic, arms Examples ##Data #Explanatory variables X1<-c(-0.2,-2.4,-0.7,1.2,0.0,-1.1,-2.1,-0.3,2.0,-1.7,1.4,-1.3,-3.4,0.4,-1.3, -4.8) X2<- c(-3, 2, 1, -2, -2, -4, 0, 1, 1, -1, -1, -4, 0, 2, 0, -4) X3<-c(2,1,0,-2,1,-2, 0, -1, -4, 1, -3, -3, -3, -1, 0, 2) #Linear model Y1<- c(8.7, 6, 9.1, 10.4, 7.6,10.4, 7.9, 11.9, 18, 10.5, 16.5, 8.8, 7.7, 13.5, 8.2, 0.8) data1<-data.frame(y1,x1,x2,x3) #Logistic model Y2<-c(1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1)

15 print.mmixclass 15 data2<-data.frame(y2,x1,x2,x3) ##Linear models evaluated by pmsecv #for a stepwise selection pmsestepbic<-pmsecv(data=data1,method=2,np=1,random=false,direction="both", criterion="bic",trace=0) pmsestepbic #for the BMA method pmsebma<-pmsecv(data=data1,method=3,np=1,random=false) pmsebma ##Logistic models evaluated by auccv #for a stepwise selection aucstepbic<-auccv(data=data2,method=2,np=1,random=false,direction="both", criterion="bic",trace=0) aucstepbic #for the BMA method aucbma<-auccv(data=data2,method=3,np=1,random=false) aucbma print.mmixclass Summary, print and plot of MMIXclass objects Description summary, print and plot methods for MMIXclass objects. Usage ## S3 method for class MMIXclass print(x,...) ## S3 method for class MMIXclass summary(object,...) ## S3 method for class MMIXclass plot(x,...) Arguments x object of type MMIXclass. object object of type MMIXclass.... other parameters to be passed to plot.mmixclass, print.mmixclass or summary.mmixclass

16 16 stepsel Details print displays a data.frame with the main results of the function. summary displays a detailed list of the results. plot displays explanatory variable weights, i.e. the probability of each variable to be different from zero. Author(s) Marie Morfin and David Makowski <makowski@grignon.inra.fr> Examples ##Data #Explanatory variables X1<-c(-0.2,-2.4,-0.7,1.2,0.0,-1.1,-2.1,-0.3,2.0,-1.7,1.4,-1.3,-3.4,0.4,-1.3, -4.8) X2<- c(-3, 2, 1, -2, -2, -4, 0, 1, 1, -1, -1, -4, 0, 2, 0, -4) X3<-c(2,1,0,-2,1,-2, 0, -1, -4, 1, -3, -3, -3, -1, 0, 2) #Linear model Y1<- c(8.7, 6, 9.1, 10.4, 7.6,10.4, 7.9, 11.9, 18, 10.5, 16.5, 8.8, 7.7, 13.5, 8.2, 0.8) data1<-data.frame(y1,x1,x2,x3) ##bmabic method bmaresult1<-bmabic(data=data1,family=gaussian("identity")) bmaresult1 summary(bmaresult1) plot(bmaresult1) stepsel Stepwise selection Description Select and fit a model by stepwise regression, for linear and logistic models. Usage stepsel(data, family, direction = "both", criterion, trace = 0) Arguments data family direction a data frame including the response variable (first column) and the explanatory variables. All the variables must be numeric and the response variable value must be 0 or 1 for the logistic model. a description of the error distribution (gaussian( identity ) or binomial( logit )). the type of stepwise search, can be one of both (the default), backward or forward

17 stepsel 17 criterion trace selection criterion at each step of the procedure. criterion = aic for the Akaike Information Criterion, and criterion = bic for the Bayesian Information Criterion. print information during the run if trace = 1. Larger values may give more information. If trace = 0 no information is printed. Details This function uses the function step. Value stepsel returns an object of class "MMIXclass". A data frame with the main results is printed whith the function "print", and the detailed results are obtained with the function "summary". A stepsel object is a list including the following components: coef aic bic fitted.values a named vector of coefficients estimated by least squares or maximum likelihood. Akaike Information Criterion, minus twice the maximized log-likelihood plus twice the number of coefficients. Bayesian information criterion, minus twice the maximized log-likelihood plus the logartithm of the number of observation multiplied by the number of coefficients the fitted values, obtained by transforming the linear predictors by the inverse of the link function. Author(s) Marie Morfin and David Makowski References Akaike H. (1974) A new look at the statistical model identification, IEEE Transactions on Automatic Control 19, Miller A. (2002) Subset selection in regression, 2nd edition Chapman & Hall/CRC, New York. Schwarz, G. (1978) Estimating the dimension of a model, Annals of Statistics 6, Whittingham M.J., Stephens P., Bradbury R.B.. Freckleton R.P. (2006) Why do we still use stepwise modelling in ecology and behaviour?, J. Anim. Ecol. 75, See Also family, step

18 18 varselec Examples ##Data #Explanatory variables X1<-c(-0.2,-2.4,-0.7,1.2,0.0,-1.1,-2.1,-0.3,2.0,-1.7,1.4,-1.3,-3.4,0.4,-1.3, -4.8) X2<- c(-3, 2, 1, -2, -2, -4, 0, 1, 1, -1, -1, -4, 0, 2, 0, -4) X3<-c(2,1,0,-2,1,-2, 0, -1, -4, 1, -3, -3, -3, -1, 0, 2) #Linear model Y1<- c(8.7, 6, 9.1, 10.4, 7.6,10.4, 7.9, 11.9, 18, 10.5, 16.5, 8.8, 7.7, 13.5, 8.2, 0.8) data1<-data.frame(y1,x1,x2,x3) #Logistic model Y2<-c(1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1) data2<-data.frame(y2,x1,x2,x3) ##stepsel method stepresult1<-stepsel(data=data1,family=gaussian("identity"),criterion="bic", direction="both") stepresult1 summary(stepresult1) stepresult2<-stepsel(data=data2,family=binomial("logit"),criterion="bic", direction="both") stepresult2 summary(stepresult2) varselec Variable selection Description Create a data frame from the original data set including a subset of variables. Usage varselec(data,family,maxvar=10,trace=0) Arguments data family maxvar trace a data frame including the response variable (first column) and the explanatory variables. All the variables must be numeric and the response variable value must be 0 or 1 for the logistic model. a description of the error distribution (gaussian("identity") or binomial("logit")). maximum number of explanatory variables to include. print information during the run if trace = 1. Larger values may give more information. If trace = 0 no information is printed.

19 varselec 19 Details Value This function implements a stepwise regression for linear and logistic models, in the direction "forward" and with the criterion "aic". The procedure stops if the model includes more than maxvar factors. The returned data frame includes no more than maxvar explanatory variables. varselec returns a data frame including the response variable and the selected explanatory variables. Author(s) See Also Marie Morfin and David Makowski bmabic, mixaic, arms Examples ##Data #Explanatory variables X1<-c(-0.2,-2.4,-0.7,1.2,0.0,-1.1,-2.1,-0.3,2.0,-1.7,1.4,-1.3,-3.4,0.4,-1.3, -4.8) X2<- c(-3, 2, 1, -2, -2, -4, 0, 1, 1, -1, -1, -4, 0, 2, 0, -4) X3<-c(2,1,0,-2,1,-2, 0, -1, -4, 1, -3, -3, -3, -1, 0, 2) #Linear model Y1<- c(8.7, 6, 9.1, 10.4, 7.6,10.4, 7.9, 11.9, 18, 10.5, 16.5, 8.8, 7.7, 13.5, 8.2, 0.8) data1<-data.frame(y1,x1,x2,x3) #Logistic model Y2<-c(1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1) data2<-data.frame(y2,x1,x2,x3) ##varselec data1bis<-varselec(data=data1,family=gaussian("identity"),maxvar=2) data2bis<-varselec(data=data2,family=binomial("logit"),maxvar=2)

20 Index Topic iteration arms, 4 bootfreq, 9 pmsecv, 13 Topic models fullmodel, 11 Topic package MMIX-package, 2 Topic print print.mmixclass, 15 Topic regression arms, 4 bmabic, 6 bootfreq, 9 fullmodel, 11 pmsecv, 13 stepsel, 16 varselec, 18 Topic robust arms, 4 bmabic, 6 pmsecv, 13 step, 17 stepsel, 6, 9, 11 14, 16 summary.mmixclass (print.mmixclass), 15 varselec, 5, 7, 8, 18 arms, 4, 9, 11 14, 19 auccv (pmsecv), 13 bmabic, 6, 6, 9, 11 14, 19 bootfreq, 6, 9, 12 family, 8, 12, 17 fullmodel, 6, 9, 11, 11, 13, 14 mixaic, 6, 9, 11 14, 19 mixaic (bmabic), 6 MMIX (MMIX-package), 2 MMIX-package, 2 MMIXclass (print.mmixclass), 15 plot.mmixclass (print.mmixclass), 15 pmsecv, 13 print.mmixclass, 15 20