The grbase Package. August 13, Author Søren Højsgaard Claus Dethlefsen

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1 The grbase Package August 13, 2005 Version Date Title grbase - a package for graphical modelling in R Author Søren Højsgaard <sorenh@agrsci.dk>, Claus Dethlefsen <aas.claus.dethlefsen@nja.dk> Maintainer Søren Højsgaard <sorenh@agrsci.dk> Depends R (>= 2.1.0), MASS, dynamicgraph This package defines S3-classes gmdata (graphical meta data), gmodel (graphical model) and illustrates how hierarchical log-linear models (hllm) may be implemented and combined with dynamicgraph. License GPL version 2 or newer URL R topics documented: cadcomplete carcass dietox gmodel grbase-internal grbase grfit gmdata hllm mathmark rats reinis validvartypes Index 11 1

2 2 carcass cadcomplete Coronary artery disease data Coronary artery disease data data(cadcomplete) Format A data frame with 236 observations on the following 14 variables: Sex, AngPec, AMI, QWave, QWavecode, STcode, STchange, SuffHeartF, Hypertrophi, Hyperchol, Smoker, Inherit, Heartfail, CAD data(cadcomplete) carcass lean meat contents of pig carcasses Measurement of lean meat percentage and thickness of meat and fat layers at different locations of 344 pig carcasses. data(carcass) Format A data frame with 7 variables and 344 observations. LMP is the lean meat percentage determined by dissection. F11, F12 and F13 are measurements of fat depth at three different locations on the carcass and M11, M12 and M13 are measurements of meat depth at the same locations. Source Busk, Hans

3 dietox 3 dietox Growth curves of pigs in a 3x3 factorial experiment The dietox data frame has 861 rows and 7 columns. data(dietox) Format This data frame contains the following columns: Weight, Feed, Time, Pig, Evit, Cu, Litter. Source Lauridsen, C., Højsgaard, S.,Sørensen, M.T. C. (1999) Influence of Dietary Rapeseed Oli, Vitamin E, and Copper on Performance and Antioxidant and Oxidative Status of Pigs. J. Anim. Sci.77: data(dietox) gmodel Class "gmodel" - graphical models The general class gmodel contains a formula object and a gmdata object. Implementations of different specific graphical model classes can inherit from this class and provide methods for parsing the formula. This is illustrated in the implementation of a class for hierarchical log linear models, hllm. gmodel(formula, gmdata) addedge(object, name.1, name.2) dropedge(object, name.1, name.2) addvertex(object, name) dropvertex(object, name)

4 4 grbase-internal Arguments formula gmdata object name name.1 name.2 an object of class formula. an object of class gmdata. an object of class gmodel. a string with a name of a variable available in gmdata to be added or removed from the model formula. a string with a name of a variable available in gmdata to mark the first node in the edge to be added or dropped from the model. a string with a name of a variable available in gmdata to mark the second node in the edge to be added or dropped from the model.. Value gmodel creates an object of class gmodel with the two components formula and gmdata. These components can be retrieved or replaced using the accessor functions of the same names. Also, a gmodel object may be manipulated using the dynamicgraph interface. Author(s) Søren Højsgaard, sorenh@agrsci.dk, Claus Dethlefsen, aas.claus.dethlefsen@nja.dk See Also gmdata, grfit, hllm, dynamic.graph. data(rats) rats <- as.gmdata(rats) m1 <- gmodel(~.^., rats) m1.form <- formula(m1) m1.data <- gmdata(m1) observations(gmdata(m1)) <- observations(rats)[1:10,] grbase-internal Internal grbase functions Internal functions called by other functions.

5 grbase 5 grbase The package grbase : summary information This package provides a basis for graphical modelling in R Details grbase provides the general framework for setting up data and model structures and provide examples for fitting hierarchical log linear models for contingency tables and graphical Gaussian models for the multivariate normal distribution. Other graphical model software on CRAN includes: mimr, deal, CoCo, ggm and SIN. The package is intended as a contribution to the gr-project described by Lauritzen (2002). Authors Søren Højsgaard, Biometry Research Unit, Danish Institute of Agricultural Sciences, DK-8830 Tjele, Denmark Claus Dethlefsen, Center for Cardiovascular Research, Aalborg Hospital, Århus University Hospital, DK-9000 Aalborg, Denmark Acknowledgements Thanks to the other members of the gr initiative, in particular to David Edwards for providing functions for formula-manipulation. References Lauritzen, S. L. (2002). graphical Models in R. R News, 3(2)39. grfit Class "grfit" - fitted graphical models Objects of class grfit are created when the function fit is applied to a gmodel object. When adding new types of gmodel objects, one must also supply the appropritate fit function. The grfit object contains the output of the fit which can be accessed by getfit. Separate print and summary methods exist for grfit objects. fit(m, engine) getfit(x)

6 6 gmdata Arguments m engine x an object of class gmodel a string with the possibility of implementing different fitting engines for the same gmodels. an object of class grfit as created from fit applied to a gmodel object. Value fit creates an object of class grfit. getfit returns the fit information created by the fitting algorithm. Author(s) Søren Højsgaard, sorenh@agrsci.dk, Claus Dethlefsen, aas.claus.dethlefsen@nja.dk See Also gmodel. data(reinis) reinis <- as.gmdata(reinis) m1 <- hllm(~.^., reinis) m1 <- fit(m1,engine="loglm") gmdata Class "gmdata" graphical meta data A common class for representing data. No matter the actual representation of data, the important characteristics are contained in a graphical metadata object. newgmdata(varnames, vartypes=rep(validvartypes()[1],length(varnames)), nlevels=na, latent=na, valuelabels=null, observations=null, description=na, shortnames=c(letters,letters) )

7 hllm 7 Arguments Value varnames vartypes nlevels latent valuelabels a vector of strings with names of variables. a vector of strings with values from validvartypes giving the types of the variables. a numeric vector with integer values for discrete or ordinal variables giving the number of levels. a vector of strings with names of the latent variables. a list of vectors of strings with names of the levels for each discrete or ordinal variable. observations an object containing the observations, eg. a dataframe or a table. description shortnames a string describing the origin of the data. a vector of strings giving a short name of each variable. An object of class gmdata holds information about the data and can be retrieved and changed by accessor functions. Objects from the Class Objects can be created by calls of the form newgmdata( varnames, vartypes, nlevels, latent, valuelabels, observations, description). More often, gmdata objects will be created from a data.frame or table. A gmdata object contains the abstraction of data into a meta data object including variable names and types etc. However, the actual data might not be present or may be represented by a reference to data, such as a database file. Also, it may be possible to work without data, which may be valuable if the point of interest is in the model alone. Separating the specification of the variables from data has the benefit, that some properties of a model can be investigated without any reference to data, for example decomposability and collapsibility. Author(s) Søren Højsgaard, sorenh@agrsci.dk, Claus Dethlefsen, dethlef@math.aau.dk See Also demo(gmdata) hllm Hierarchical log-linear models An implementation of hierarchical log-linear models using the framework of grbase. A model object is defined using hllm, fitted using fit (which calls loglm) and a model search performed using stepwise. The models may be displayed and manipulated using the grbase functions, eg. dynamic.graph.

8 8 mathmark hllm(formula = ~.^1, gmdata, marginal) Arguments formula gmdata marginal an object of class formula. The right hand side of the formula is a list of the generators separated by +. A generator is specified by variable names with separated by *. Commonly used models have short hand notations: saturated model (~.^.), main effects (~.^1), all k th order interactions (~.^k). an object of class gmdata. an optional argument specifying a subset of the variables from the gmdata object. Value hllm returns an object of class hllm, inheriting from the superclass gmodel. Author(s) Søren Højsgaard, sorenh@agrsci.dk, Claus Dethlefsen, aas.claus.dethlefsen@nja.dk See Also gmdata, grfit, ggm, dynamic.graph data(reinis) reinis <- as.gmdata(reinis) m2 <- hllm(~smoke*phys*protein+mental*phys+mental*family+smoke*systol*protein, reinis) m2 <- fit(m2,engine="loglm") ## Not run: dynamic.graph(m2) mathmark Mathematics marks for students The mathmark data frame has 88 rows and 5 columns. data(mathmark) Format This data frame contains the following columns: mechanics, vectors, algebra, analysis, statistics.

9 rats 9 Author(s) Søren Højsgaard, sorenh@agrsci.dk References David Edwards, An Introduction to Graphical Modelling, Second Edition, Springer Verlag, 2000 data(mathmark) rats Weightloss of rats Format An artificial dataset. 24 rats (12 female, 12 male) have been randomized to use one of three drugs (products for loosing weight). The weightloss for each rat is noted after one and two weeks. data(rats) A dataframe with 4 variables. Sex: "M" (male), "F" (female). Drug: "D1", "D2", "D3" (three types). W1 weightloss, week one. W2 weightloss, week 2. References Morrison, D.F. (1976). Multivariate Statistical Methods. McGraw-Hill, USA. Edwards, D. (1995). Introduction to Graphical Modelling, Springer-Verlag. New York. reinis Risk factors for coronary heart disease. Format Data collected at the beginning of a 15 year follow-up study of probable risk factors for coronary thrombosis. Data are from all men employed in a car factory. data(reinis) A table with 6 discrete variables. A: smoking, B: strenous mental work, D: strenuous physical work, E: systolic blood pressure, F: ratio of lipoproteins, G: Family anamnesis of coronary heart disease.

10 10 validvartypes References Edwards and Havranek (1985): A fast procedure for model search in multidimensional contingency tables. Biometrika, 72: Reinis et al (1981): Prognostic significance of the risk profile in the prevention of coronary heart disease. Bratis. lek. Listy. 76: validvartypes Admissible variable types in gmdata objects Value The variable types in a gmdata object must be from a vector predefined types which may be inspected by the command validvartypes(). The available types may be extended by the package developers as demonstrated in the example. The types of the variables are important for the way they are displayed using the package dynamicgraph. The type is also important when the models are fitted to data. validvartypes() A character vector with the names of the admissible variable types. Author(s) Søren Højsgaard, sorenh@agrsci.dk, Claus Dethlefsen, aas.claus.dethlefsen@nja.dk See Also gmdata, dynamic.graph oldtypes <- validvartypes() validvartypes <- function() c(oldtypes, "MyVarType") validvartypes()

11 Index Topic datasets cadcomplete, 1 carcass, 2 dietox, 2 mathmark, 8 rats, 8 reinis, 9 Topic graphs grbase, 4 Topic internal grbase-internal, 4 Topic models gmdata, 6 gmodel, 3 grbase, 4 grfit, 5 hllm, 7 validvartypes, 9 Topic multivariate grbase, 4 add.edge addedge (gmodel), 3 addvertex (gmodel), 3 all.subsets as.gmdata (gmdata), 6 cadcomplete, 1 cadincomplete (cadcomplete), 1 carcass, 2 contains corr.matrix delete.edge description (gmdata), 6 description<- (gmdata), 6 dietox, 2 dropedge (gmodel), 3 dropvertex (gmodel), 3 dual.rep dynamic.gr.graph dynamic.graph, 3, 7, 10 dynamic.graph dynamic.graph,gmodel-method dynamic.graph,grfit-method ell extract.power fit (grfit), 5 fit.ggm fit.hllm (hllm), 7 formula, 3, 7 formula (gmodel), 3 formula<- (gmodel), 3 fun getfit (grfit), 5 getfit<- (grfit), 5 ggm, 7 ggm gmdata, 3, 6, 7, 9, 10 gmdata (gmodel), 3 gmdata<- (gmodel), 3 gmodel, 3, 5 gmodel-class (gmodel), 3 gmodeltestclass-class grbase, 4, 7 grbase-internal, 4 gredges grfit, 3, 5, 7 grfit-class grvariable hllm, 3, 7 hllm-class (hllm), 7 in.list ips is.cont is.graphical label 11

12 12 INDEX label,gmodeltestclass-method label-methods LabelAllEdges latent (gmdata), 6 latent<- (gmdata), 6 loglm, 7 mathmark, 8 modifymodel modifymodel,gmodel-method valuelabels (gmdata), 6 valuelabels<- (gmdata), 6 varnames (gmdata), 6 varnames<- (gmdata), 6 varset vartypes (gmdata), 6 vartypes<- (gmdata), 6 width width,gmodeltestclass-method width-methods newgmdata (gmdata), 6 nlevels (gmdata), 6 nlevels<- (gmdata), 6 obs (gmdata), 6 observations (gmdata), 6 observations<- (gmdata), 6 out partial.corr.matrix print.gmdata (gmdata), 6 print.gmodel (gmodel), 3 print.grfit (grfit), 5 processformula (grbase-internal), 4 rats, 8 readf readg reinis, 9 remove.redundant selectorder shortnames (gmdata), 6 shortnames<- (gmdata), 6 showf showg stepwise stepwise.hllm (hllm), 7 subsetof summary.gmdata (gmdata), 6 summary.grfit (grfit), 5 testedge testedge,gmodel-method UserMenus validvartypes, 6, 9