Create all possible pairs

Description

Create all possible pairs of two character vectors.

Usage

all_pairs(x, y = character(0), sort = FALSE, result = "matrix")

names2pairs(x, y = NULL, sort = TRUE, result = "list")

Arguments

Details

NOTICE: If y is not NULL then x and y must be disjoint (no checks are made); otherwise pairs of identical elements wil also be obtained.

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

Examples

x <- letters[1:4]
y <- letters[5:7]

all_pairs(x)
all_pairs(x, result="matrix")

all_pairs(x, y)
all_pairs(x, y, result="matrix")

Create all subsets

Description

Create all subsets of a vector

Usage

all_subsets(x)

all_subsets0(x)

Arguments

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

Array operations (2007)

Description

Array operations; created to facilitate the gRain package in 2007. Now largely replaceable by other (often faster) functions implemented in Rcpp.

Usage

tablePerm(tab, perm, resize = TRUE, keep.class = FALSE)

tableMult(tab1, tab2)

tableDiv(tab1, tab2)

tableOp(tab1, tab2, op = "*")

tableOp2(tab1, tab2, op = `*`, restore = FALSE)

tableOp0(tab1, tab2, op = `*`)

tableSlice(tab, margin, level, impose)

tableSlicePrim(tab, mar.idx, lev.idx)

tableMargin(tab, margin, keep.class = FALSE)

tableGetSliceIndex(tab, margin, level, complement = FALSE)

tableSetSliceValue(tab, margin, level, complement = FALSE, value = 0)

Arguments

Details

tableOp0 is brute force implementation based on dataframes. It is very slow, but useful for error checking.

Check if object is array

Description

Check if object is array (that it is a vector with a dim attribute) and that the object has dimnames and that dimnames are named.

Usage

is.named.array(obj)

is_named_array_(obj)

is_number_vector_(obj)

is_dimnames_(obj)

dimnames_match(a1, a2)

Arguments

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

Examples

is.named.array( HairEyeColor )
is.named.array( matrix(1:4, nrow=2) )
is_named_array_( HairEyeColor )
is_named_array_( matrix(1:4, nrow=2) )
is_number_vector_(1:4)
is_number_vector_(list(1:4))

ar1 = tabNew(c("a", "b"), levels=c(2, 3))
ar2 = tabNew(c("c", "a"), levels=c(2, 2))
ar1
ar2
## dimension a has levels a1,a2 in both ar1 and ar2.
# Hence we have a match.
dimnames_match(ar1, ar2)

ar1 = tabNew(c("a", "b"), levels=c(2, 3))
ar2 = tabNew(c("c", "a"), levels=c(2, 3))
ar1
ar2
## dimension a has levels a1,a2 in ar1 and levels a1,a2,a3 in ar2.
# Hence we do not have a match.
dimnames_match(ar1, ar2)

ar2 = tabNew(c("c", "a"), levels=list(c=c("c1", "c2"), a=c("a2", "a1")))
ar2
## dimension a has levels a1,a2 in ar1 and levels a2,a1 in ar2.
# Hence we do not have a match.
dimnames_match(ar1, ar2)

Table cell operations.

Description

Low level table cell operations.

Usage

cell2entry(cell, dim)

entry2cell(entry, dim)

next_cell(cell, dim)

next_cell2(cell, dim)

next_cell_slice(cell, dim, slice_marg)

slice2entry(slice_cell, slice_marg, dim)

cell2entry_perm(cell, dim, perm)

perm_cell_entries(perm, dim)

fact_grid(dim, slice_cell = NULL, slice_marg = NULL)

Arguments

Examples

di <- c(2, 2, 3)

cell2entry(c(1, 1, 1), dim=di)
cell2entry(c(2, 2, 3), dim=di)

entry2cell(1, dim=di)
entry2cell(12, dim=di)

next_cell(c(1, 1, 1), dim=di)
next_cell(c(2, 1, 1), dim=di)

## The first two entries are kept fixed
next_cell_slice(c(2, 1, 1), dim=di, slice_marg=c(1, 2))
next_cell_slice(c(2, 1, 2), dim=di, slice_marg=c(1, 2))

## Cell (2, 2, 1) corresponds to entry 4
cell2entry(c(2, 2, 1), dim=di)
## Same as
cell2entry_perm(c(2, 2, 1), dim=di, perm=c(1, 2, 3))
## If the table dimensions are permuted as (3, 1, 2)
## the entry becomes
cell2entry_perm(c(2, 2, 1), dim=di, perm=c(3, 1, 2))

Low level table cell operations implemented in c++

Description

Corresponding R functions without the trailing underscore exist.

Usage

cell2entry_(cell, dim)

make_plevels_(dim)

entry2cell_(entry, dim)

next_cell_(cell, dim)

next_cell2_(cell, dim)

next_cell_slice_(cell, dim, slice_marg)

slice2entry_(slice_cell, slice_marg, dim)

cell2entry_perm_(cell, dim, perm)

perm_cell_entries_(perm, dim)

Arguments

Representation of and operations on multidimensional arrays

Description

General representation of multidimensional arrays (with named dimnames, also called named arrays.)

Usage

parray(varNames, levels, values = 1, normalize = "none", smooth = 0)

as.parray(values, normalize = "none", smooth = 0)

data2parray(data, varNames = NULL, normalize = "none", smooth = 0)

makeDimNames(varNames, levels, sep = "")

Arguments

Details

A named array object represents a table defined by a set of variables and their levels, together with the values of the table. E.g. f(a,b,c) can be a table with a,b,c representing levels of binary variable

If normalize="first" then for each configuration of all other variables than the first, the probabilities are normalized to sum to one. Thus f(a,b,c) becomes a conditional probability table of the form p(a|b,c).

If normalize="all" then the sum over all entries of f(a,b,c) is one.

If smooth is positive then smooth is added to values before normalization takes place.

Value

A a named array.

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

See Also

is.named.array

Examples

 
t1 <- parray(c("gender","answer"), list(c('male','female'),c('yes','no')), values=1:4)
t1 <- parray(~gender:answer, list(c('male','female'),c('yes','no')), values=1:4)
t1 <- parray(~gender:answer, c(2,2), values=1:4)

t2 <- parray(c("answer","category"), list(c('yes','no'),c(1,2)), values=1:4+10)
t3 <- parray(c("category","foo"), c(2,2), values=1:4+100)

varNames(t1)
nLevels(t1)
valueLabels(t1)

## Create 1-dimensional vector with dim and dimnames
x1 <- 1:5
as.parray(x1)
x2 <- parray("x", levels=length(x1), values=x1)
dim(x2)
dimnames(x2)

## Matrix
x1 <- matrix(1:6, nrow=2)
as.parray(x1)
parray(~a:b, levels=dim(x1), values=x1)

## Extract parrays from data
## 1) a dataframe
data(cad1) 
data2parray(cad1, ~Sex:AngPec:AMI)
data2parray(cad1, c("Sex","AngPec","AMI"))
data2parray(cad1, c(1,2,3))
## 2) a table
data2parray(UCBAdmissions,c(1,2), normalize="first")

Array algebra

Description

Addition, subtraction etc. of arrays

Usage

a1 %a+% a2

a1 %a-% a2

a1 %a*% a2

a1 %a/% a2

a1 %a/0% a2

tab1 %a_% marg

tab1 %a==% tab2

tab1 %a^% extra

tab1 %aperm% perm

tab1 %aalign% tab2

tab1 %aslice% slice

tab1 %aslice*% slice

tab1 %amarg% marg

Arguments

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

Examples

hec <- HairEyeColor
a1 <- tabMarg(hec, c("Hair", "Eye"))
a2 <- tabMarg(hec, c("Hair", "Sex"))
a3 <- tabMarg(hec, c("Eye", "Sex"))

## Binary operations
a1 %a+% a2
a1 %a-% a2
a1 %a*% a2
a1 %a/% a2

Marginalize and condition in multidimensional array.

Description

Marginalize and condition in a multidimensional array which is assumed to represent a discrete multivariate distribution.

Usage

tabDist(tab, marg = NULL, cond = NULL, normalize = TRUE)

Arguments

Value

A multidimensional array.

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

Examples

hec <- HairEyeColor

is.named.array( hec )
## We need dimnames, and names on the dimnames

## Marginalize:
tabDist(hec, marg= ~Hair + Eye)
tabDist(hec, marg= ~Hair:Eye)
tabDist(hec, marg= c("Hair", "Eye"))
tabDist(hec, marg= 1:2)

tabDist(hec, marg= ~Hair + Eye, normalize=FALSE)

## Condition
tabDist(hec, cond= ~Sex + Hair)
tabDist(hec, cond= ~Sex:Hair)
tabDist(hec, cond= c("Sex", "Hair"))
tabDist(hec, cond= c(3,1))

tabDist(hec, cond= list(Hair="Black"))
tabDist(hec, cond= list(Hair=1))

## Not run: 
## This will fail
tabDist(hec, cond= list(Hair=c("Black", "Brown")))
tabDist(hec, cond= list(Hair=1:2))

## End(Not run)
## But this will do the trick
a <- tabSlice(hec, slice=list(Hair=c("Black", "Brown")))
tabDist(a, cond=~Hair)

## Combined
tabDist(hec, marg=~Hair+Eye, cond=~Sex)
tabDist(hec, marg=~Hair+Eye, cond="Sex")

tabDist(hec, marg=~Hair+Eye, cond=list(Sex="Male"))
tabDist(hec, marg=~Hair+Eye, cond=list(Sex="Male"), normalize=FALSE)

tabDist(hec, cond=list(Sex="Male"))
tabDist(hec, cond=list(Sex="Male"), normalize=FALSE)

Create multidimensional arrays

Description

Alternative ways of creating arrays

Usage

tabNew(names, levels, values, normalize = "none", smooth = 0)

Arguments

Details

1. If normalize="first" then for each configuration of all other variables than the first, the probabilities are normalized to sum to one. Thus f(a, b, c) becomes a conditional probability table of the form p(a | b, c).

2. If normalize="all" then the sum over all entries of f(a,b,c) is one.

3. If smooth is positive then smooth is added to values BEFORE normalization takes place.

Value

An array.

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

Examples

universe <- list(gender=c('male', 'female'),
                 answer=c('yes', 'no'),
                 rain=c('yes', 'no'))
t1 <- tabNew(c("gender", "answer"), levels=universe, values=1:4)
t1
t2 <- tabNew(~gender:answer, levels=universe, values=1:4)
t2
t3 <- tabNew(~gender:answer, c(2, 2), values=1:4)
t3

Interface - operations on multidimensional arrays.

Description

Interface functions and minor extensions to cpp functions.

Usage

tabAdd(tab1, tab2)

tabAlign(tab1, tab2)

tabDiv(tab1, tab2)

tabDiv0(tab1, tab2)

tabOp(tab1, tab2, op = "*")

tabEqual(tab1, tab2, eps = 1e-12)

tabExpand(tab, aux, type = 0L)

tabMult(tab1, tab2)

tabSubt(tab1, tab2)

tabListMult(lst)

tabListAdd(lst)

tabPerm(tab, perm)

tabMarg(tab, marg = NULL)

tabSum(tab, ...)

tabProd(tab, ...)

tabNormalize(tab, type = "none")

Arguments

Table operations implemented in c++

Description

Table operations implemented in c++. Corresponding R functions without the trailing underscore exist.

Usage

tab_perm_(tab, perm)

tab_expand_(tab, aux, type = 0L)

tab_align_(tab1, tab2)

tab_marg_(tab, marg)

tab_op_(tab1, tab2, op = "*")

tab_add_(tab1, tab2)

tab_subt_(tab1, tab2)

tab_mult_(tab1, tab2)

tab_div_(tab1, tab2)

tab_div0_(tab1, tab2)

tab_equal_(tab1, tab2, eps = 1e-12)

tab_list_mult_(lst)

tab_list_add_(lst)

Arguments

Array slices

Description

Functions for extracting slices of arrays

Usage

tabSlice(
  tab,
  slice = NULL,
  margin = names(slice),
  drop = TRUE,
  as.array = FALSE
)

tabSlice2(tab, slice, margin.idx, drop = TRUE, as.array = FALSE)

tabSlicePrim(tab, slice, drop = TRUE)

tabSliceMult(tab, slice, val = 1, comp = 0)

tabSlice2Entries(tab, slice, complement = FALSE)

Arguments

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

Examples

x = HairEyeColor
s = list(Hair=c("Black", "Brown"), Eye=c("Brown", "Blue"))

s1 = tabSlice(x, slice=s); s1

tabSlice2Entries(x, slice=s)
tabSlice2Entries(x, slice=s, complement=TRUE)

## tabSliceMult 
s2 = tabSliceMult(x, slice=s); s2

sp = list(c(1,2), c(1,2), TRUE)
tabSlicePrim(x, slice=sp)
tabSlice(x, slice=s)

Simulate data from array.

Description

Simulate data (slice of) an array: Simulate n observations from the array x conditional on the variables in margin (a vector of indices) takes values given by margin.value

Usage

simulateArray(x, nsim = 1, margin, value.margin, seed = NULL)

## S3 method for class 'table'
simulate(object, nsim = 1, seed = NULL, margin, value.margin, ...)

## S3 method for class 'xtabs'
simulate(object, nsim = 1, seed = NULL, margin, value.margin, ...)

## S3 method for class 'array'
simulate(object, nsim = 1, seed = NULL, margin, value.margin, ...)

Arguments

Value

A matrix.

Note

The current implementation is fragile in the sense that it is not checked that the input argument x is an array.

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

Examples

## 2x2 array
x <- parray(c("a", "b"), levels=c(2, 2), values=1:4)

x <- tabNew(c("a", "b"), levels=c(2, 2), values=1:4)

## Simulate from entire array
s <- simulateArray(x, 1000)
xtabs(~., as.data.frame(s))

## Simulate from slice defined by that dimension 1 is fixed at level 2
s <-simulateArray(x, 1000, margin=1, value.margin=2)
xtabs(~., as.data.frame(s))

## 2 x 2 x 2 array
x <- parray(c("a", "b", "c"), levels=c(2, 2, 2), values=1:8)
## Simulate from entire array
s <-simulateArray(x, 36000)
xtabs(~., as.data.frame(s))

## Simulate from slice defined by that dimension 3 is fixed at level 1
s <-simulateArray(x, 10000, 3, 1)
xtabs(~., as.data.frame(s))

Generic function for model comparison

Description

compareModels is a generic functions which invoke particular methods which depend on the class of the first argument

Usage

compareModels(object, object2, ...)

Arguments

Value

The value returned depends on the class of the first argument.

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

Partial correlation (matrix)

Description

cov2pcor calculates the partial correlation matrix from an (empirical) covariance matrix while conc2pcor calculates the partial correlation matrix from a concentration matrix (inverse covariance matrix).

Usage

cov2pcor(V)

conc2pcor(K)

Arguments

Value

A matrix with the same dimension as V.

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

Examples

data(math)
S <- cov.wt(math)$cov
cov2pcor(S)

Body Fat Data

Description

Estimates of the percentage of body fat determined by underwater weighing and various body circumference measurements for 252 men.

Usage

data(BodyFat)

data(BodyFat)

Format

A data frame with 252 observations on the following 15 variables.

Density

Density determined from underwater weighing, a numeric vector

BodyFat

Percent body fat from Siri's (1956) equation, a numeric vector

Age

in years, a numeric vector

Weight

in lbs, a numeric vector

Height

in inches, a numeric vector

Neck

circumference in cm, a numeric vector

Chest

circumference in cm, a numeric vector

Abdomen

circumference in cm, a numeric vector

Hip

circumference in cm, a numeric vector

Thigh

circumference in cm, a numeric vector

Knee

circumference in cm, a numeric vector

Ankle

circumference in cm, a numeric vector

Biceps

circumference in cm, a numeric vector

Forearm

circumference in cm, a numeric vector

Wrist

circumference in cm, a numeric vector

Source

For more information see https://lib.stat.cmu.edu/datasets/bodyfat

References

Bailey, Covert (1994). Smart Exercise: Burning Fat, Getting Fit, Houghton-Mifflin Co., Boston, pp. 179-186.

Behnke, A.R. and Wilmore, J.H. (1974). Evaluation and Regulation of Body Build and Composition, Prentice-Hall, Englewood Cliffs, N.J.

Siri, W.E. (1956), "Gross composition of the body", in Advances in Biological and Medical Physics, vol. IV, edited by J.H. Lawrence and C.A. Tobias, Academic Press, Inc., New York.

Katch, Frank and McArdle, William (1977). Nutrition, Weight Control, and Exercise, Houghton Mifflin Co., Boston.

Wilmore, Jack (1976). Athletic Training and Physical Fitness: Physiological Principles of the Conditioning Process, Allyn and Bacon, Inc., Boston.

Examples

data(BodyFat)
head(BodyFat)

The Nutrimouse Dataset

Description

The data come from a study of the effects of five dietary regimens with different fatty acid compositions on liver lipids and hepatic gene expression in 40 mice.

Usage

data(Nutrimouse)

Format

A data frame with 40 observations on 143 variables of which two are factors and 141 are numeric.

genotype

a factor with levels wt ppar

diet

a factor with levels coc fish lin ref sun

Details

The data come from a study of the effects of five dietary regimens with different fatty acid compositions on liver lipids and hepatic gene expression in wild-type and PPAR-alpha-deficient mice (Martin et al., 2007).

There were 5 replicates per genotype and diet combination.

There are two design variables: (i) genotype, a factor with two levels: wild-type (wt) and PPAR-alpha-deficient (ppar), and (ii) diet, a factor with five levels. The oils used for experimental diet preparation were: corn and colza oils (50/50) for a reference diet (ref); hydrogenated coconut oil for a saturated fatty acid diet (coc); sunflower oil for an Omega6 fatty acid-rich diet (sun); linseed oil for an Omega3-rich diet (lin); and corn/colza/enriched (43/43/14) fish oils (fish).

There are 141 response variables: (i) the log-expression levels of 120 genes measured in liver cells, and (ii) the concentrations (in percentages) of 21 hepatic fatty acids measured by gas chromatography.

Source

The data were provided by Pascal Martin from the Toxicology and Pharmacology Laboratory, National Institute for Agronomic Research, France.

References

Martin, P. G. P., Guillou, H., Lasserre, F., D'jean, S., Lan, A., Pascussi, J.-M., San Cristobal, M., Legrand, P., Besse, P. and Pineau, T. (2007). Novel aspects of PPARa-mediated regulation of lipid and xenobiotic metabolism revealed through a multrigenomic study. Hepatology 54, 767-777.

Examples

data(Nutrimouse)

Crown dieback in ash trees

Description

This dataset comes from a study of symptoms of crown dieback, cankers and symptoms caused by other pathogens and pests in ash trees (Fraxinus excelsior). In all 454 trees were observed in two plots. There are 8 categorical variables, 6 of which are binary and two are trichotomous with values representing increasing severity of symptoms, and one continuous variable, tree diameter at breast height (DBH).

Usage

data(ashtrees)

Format

A data frame with 454 observations on the following 9 variables.

plot

a factor with levels 2 6

dieback

a factor with levels 0 1 2

dead50

a factor with levels 0 0.5 1

bushy

a factor with levels 0 1

canker

a factor with levels BRNCH MAIN NONE

wilt

a factor with levels 0 1

roses

a factor with levels 0 1

discolour

a factor with levels 0 1

dbh

a numeric vector

References

Skovgaard JP, Thomsen IM, Skovgaard IM and Martinussen T (2009). Associations among symptoms of dieback in even-aged stands of ash (Fraxinus excelsior L.). Forest Pathology.

Examples

data(ashtrees)
head(ashtrees)

Gene expression signatures for p53 mutation status in 250 breast cancer samples

Description

Perturbations of the p53 pathway are associated with more aggressive and therapeutically refractory tumours. We preprocessed the data using Robust Multichip Analysis (RMA). Dataset has been truncated to the 1000 most informative genes (as selected by Wilcoxon test statistics) to simplify computation. The genes have been standardised to have zero mean and unit variance (i.e. z-scored).

Usage

data(breastcancer)

Format

A data frame with 250 observations on 1001 variables. The first 1000 columns are numerical variables; the last column (named code) is a factor with levels case and control.

Details

The factor code defines whether there was a mutation in the p53 sequence (code=case) or not (code=control).

Source

Dr. Chris Holmes, c.holmes at stats dot. ox . ac .uk

References

Miller et al (2005, PubMed ID:16141321)

Examples

data(breastcancer)
## maybe str(breastcancer) ; plot(breastcancer) ...

Lean meat contents of 344 pig carcasses

Description

Measurement of lean meat percentage of 344 pig carcasses together with auxillary information collected at three Danish slaughter houses

Usage

data(carcass)

Format

carcassall: A data frame with 344 observations on the following 17 variables.

weight

Weight of carcass

lengthc

Length of carcass from back toe to head (when the carcass hangs in the back legs)

lengthf

Length of carcass from back toe to front leg (that is, to the shoulder)

lengthp

Length of carcass from back toe to the pelvic bone

Fat02, Fat03, Fat11, Fat12, Fat13, Fat14, Fat16

Thickness of fat layer at different locations on the back of the carcass (FatXX refers to thickness at (or rather next to) rib no. XX. Notice that 02 is closest to the head

Meat11, Meat12, Meat13

Thickness of meat layer at different locations on the back of the carcass, see description above

LeanMeat

Lean meat percentage determined by dissection

slhouse

Slaughter house; a factor with levels a b c

sex

Sex of the pig; a factor with a b c. Notice that it is no an error to have three levels; the third level refers to castrates

Note

carcass: Contains only the variables Fat11, Fat12, Fat13, Meat11, Meat12, Meat13, LeanMeat

Source

Busk, H., Olsen, E. V., Brøndum, J. (1999) Determination of lean meat in pig carcasses with the Autofom classification system, Meat Science, 52, 307-314

Examples

data(carcass)
head(carcass)

Simulated data from the Chest Clinic example

Description

Simulated data from the Chest Clinic example (also known as the Asia example) from Lauritzen and Spiegelhalter, 1988 (see reference below).

Usage

data(chestSim500)

Format

A data frame with 500 observations on the following 8 variables.

asia

Recent visit to Asia?; a factor with levels yes no

tub

Has tuberculosis?; a factor with levels yes no

smoke

Is a smoker?; a factor with levels yes no

lung

Has lung cancer?; a factor with levels yes no

bronc

Has bronchitis?; a factor with levels yes no

either

Either lung cancer or tuberculosis?; a factor with levels yes no

xray

Positive x-ray? a factor with levels yes no

dysp

Dyspnoea (shortness of breath)?; a factor with levels yes no

Details

Notice that the chest clinic example is a contrieved example; it does not originate from an empirical study.

References

Lauritzen and Spiegelhalter (1988) Local Computations with Probabilities on Graphical Structures and their Application to Expert Systems (with Discussion). J. Roy. Stat. Soc. 50, p. 157-224.

Examples

data(chestSim500)
## maybe str(chestSim500) ; plot(chestSim500) ...

Growth curves of pigs in a 3x3 factorial experiment

Description

The dietox data frame has 861 rows and 7 columns.

Usage

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.77:906-916

Examples

data(dietox)

Gastric Dumping

Description

A contingency table relating surgical operation, centre and severity of gastric dumping, a syndrome associated with gastric surgery.

Usage

data(dumping)

Format

A 3x4x4 table of counts cross-classified by Symptom (none/slight/moderate), Operation (Vd/Va/Vh/Gr) and Centre (1:4).

Details

Gastric dumping syndrome is a condition where ingested foods bypass the stomach too rapidly and enter the small intestine largely undigested. It is an undesirable side-effect of gastric surgery. The table summarizes the results of a study comparing four different surgical operations on patients with duodenal ulcer, carried out in four centres, as described in Grizzle et al (1969). The four operations were: vagotomy and drainage, vagotomy and antrectomy (removal of 25\ (removal of 50\ 75\

Source

Grizzle JE, Starmer CF, Koch GG (1969) Analysis of categorical data by linear models. Biometrics 25(3):489-504.

Examples

data(dumping) 
plot(dumping) 

Lizard behaviour

Description

In a study of lizard behaviour, characteristics of 409 lizards were recorded, namely species (S), perch diameter (D) and perch height (H). Perch means preferred place to settle down (a branch on a tree). The focus of interest is in how the propensities of the lizards to choose perch height and diameter are related, and whether and how these depend on species.

Usage

data(lizard)

Format

A 3–dimensional array with factors diam: "<=4" ">4" height: ">4.75" "<=4.75" species: "anoli" "dist"

References

Schoener TW (1968) The anolis lizards of bimini: Resource partitioning in a complex fauna. Ecology 49:704-726

Examples

data(lizard)

# Datasets lizardRAW and lizardDF are generated with the following code
#lizardAGG <- as.data.frame(lizard)
#f   <- lizardAGG$Freq
#idx <- unlist(mapply(function(i, n) rep(i, n), 1:8, f))
#set.seed(0805)
#idx <- sample(idx)
#lizardRAW <- as.data.frame(lizardAGG[idx, 1:3])
#rownames(lizardRAW) <- 1:NROW(lizardRAW)

Mathematics marks for students

Description

The mathmark data frame has 88 rows and 5 columns.

Usage

data(mathmark)

Format

This data frame contains the following columns: mechanics, vectors, algebra, analysis, statistics.

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

References

David Edwards, An Introduction to Graphical Modelling, Second Edition, Springer Verlag, 2000

Examples

data(mathmark)

Mildew fungus

Description

The data stem from a cross between two isolates of the barley powdery mildew fungus. For each offspring 6 binary characteristics, each corresponding to a single locus, were recorded. The object of the analysis is to determine the order of the loci along the chromosome.

Usage

data(mildew)

Format

A 6 dimensional array where each variable has levels "1" and "2". The variables are: la10, locc, mp58, c365, p53a and a365.

References

Christiansen, S.K., Giese, H (1991) Genetic analysis of obligate barley powdery mildew fungus based on RFLP and virulence loci. Theor. Appl. Genet. 79:705-712

Examples

data(mildew)
## maybe str(mildew) ; plot(mildew) ...

Milk composition data

Description

Data from an experiment on composition of sow milk. Milk composition is measured on four occasions during lactation on a number of sows. The treatments are different types of fat added to the sows feed.

Usage

data(milkcomp)

Format

A data frame with 214 observations on the following 7 variables.

sow

a numeric vector

lactime

a numeric vector

treat

a factor with levels a b c d e f g

fat

a numeric vector

protein

a numeric vector

dm

(dry matter) a numeric vector

lactose

a numeric vector

Details

a is the control, i.e. no fat has been added.

fat + protein + lactose almost add up to dm (dry matter)

References

Charlotte Lauridsen and Viggo Danielsen (2004): Lactational dietary fat levels and sources influence milk composition and performance of sows and their progeny Livestock Production Science 91 (2004) 95-105

Examples

data(milkcomp)
## maybe str(milk) ; plot(milk) ...

Personality traits

Description

The peronality dataframe has 240 rows and 32 columns

Usage

data(personality)

Format

This dataframe has recordings on the following 32 variables: distant, talkatv, carelss, hardwrk, anxious, agreebl, tense, kind, opposng, relaxed, disorgn, outgoin, approvn, shy, discipl, harsh, persevr, friendl, worryin, respnsi, contrar, sociabl, lazy, coopera, quiet, organiz, criticl, lax, laidbck, withdrw, givinup, easygon

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

References

Origin unclear

Examples

data(personality)
str(personality)

Weightloss of rats

Description

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.

Usage

data(rats)

Format

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.

Risk factors for coronary heart disease.

Description

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.

Usage

data(reinis)

Format

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.

References

Edwards and Havranek (1985): A fast procedure for model search in multidimensional contingency tables. Biometrika, 72: 339-351.

Reinis et al (1981): Prognostic significance of the risk profile in the prevention of coronary heart disease. Bratis. lek. Listy. 76: 137-150.

Chemical composition of wine

Description

Using chemical analysis determine the origin of wines

Usage

data(wine)

Format

A data frame with 178 observations on the following 14 variables.

Cult

a factor with levels v1 v2 v3: 3 different graph varieties

Alch

Alcohol

Mlca

Malic acid

Ash

Ash

Aloa

Alcalinity of ash

Mgns

Magnesium

Ttlp

Total phenols

Flvn

Flavanoids

Nnfp

Nonflavanoid phenols

Prnt

Proanthocyanins

Clri

Color intensity

Hue

Hue

Oodw

OD280/OD315 of diluted wines

Prln

Proline

Details

Data comes from the UCI Machine Learning Repository. The grape variety Cult is the class identifier.

Source

Frank, A. & Asuncion, A. (2010). UCI Machine Learning Repository https://archive.ics.uci.edu/ml/. Irvine, CA: University of California, School of Information and Computer Science.

References

See references at https://archive.ics.uci.edu/ml/datasets/Wine/

Examples

data(wine)
## maybe str(wine) ; plot(wine) ...

Coronary artery disease data

Description

A cross classified table with observational data from a Danish heart clinic. The response variable is CAD (coronary artery disease, some times called heart attack).

Usage

data(cad1)

Format

A data frame with 236 observations on the following 14 variables.

Sex

Sex; a factor with levels Female Male

AngPec

Angina pectoris (chest pain attacks); a factor with levels Atypical None Typical

AMI

Acute myocardic infarct; a factor with levels Definite NotCertain

QWave

A reading from an electrocardiogram; a factor with levels No Yes; Yes means pathological and is a sign of previous myocardial infarction.

QWavecode

a factor with levels Nonusable Usable. An assesment of whether QWave is reliable.

STcode

a factor with levels Nonusable Usable. An assesment of whether STchange is reliable.

STchange

A reading from an electrocardiogram; a factor with levels No Yes. An STchange indicates a blockage of the coronary artery.

SuffHeartF

Sufficient heart frequency; a factor with levels No, Yes

Hypertrophi

a factor with levels No, Yes. Hypertrophy refers to an increased size of the heart muscle due to exercise.

Hyperchol

a factor with levels No Yes. Hypercholesterolemia, also called high cholesterol, is the presence of high levels of cholesterol in the blood.

Smoker

Is the patient a smoker; a factor with levels No, Yes.

Inherit

Hereditary predispositions for CAD; a factor with levels No, Yes.

Heartfail

Previous heart failures; a factor with levels No Yes

CAD

Coronary Artery Disease; a factor with levels No Yes

. CAD refers to a reduction of blood flow to the heart muscle (commonly known as a heart attack). The diagnosis made from biopsies.

Details

Notice that data are collected at a heart clinic, so data do not represent the population, but are conditional on patients having ended up at the clinic.

• cad1: Complete dataset, 236 cases.

• cad2: Incomplete dataset, 67 cases. Information on (some of) the variables 'Hyperchol', 'Smoker' and 'Inherit' is missing.

References

Hansen, J. F. (1980). The clinical diagnoisis of ichaeme heart disease du to coronary artery disease. Danish Medical Bulletin

Højsgaard, Søren and Thiesson, Bo (1995). BIFROST - Block recursive models Induced From Relevant knowledge, Observations and Statistical Techniques. Computational Statistics and Data Analysis, vol. 19, p. 155-175

Examples

data(cad1)
## maybe str(cad1) ; plot(cad1) ...

Utilities for data handling

Description

Utilities for data handling

Usage

valueLabels(x)

## Default S3 method:
valueLabels(x)

varNames(x)

## Default S3 method:
varNames(x)

nLevels(x)

## Default S3 method:
nLevels(x)

Arguments

Downstream aliases

Description

Downstream aliases for other graphical modelling packages. Will be deprecated in due course.

Coerce dag to edge matrix

Description

A DAG can be represented as a triangular matrix of regression coefficients.

Usage

dag2edge_matrix(object, out = 1)

edge_matrix2dag(edge_matrix)

Arguments

Examples

g <- dag(~x2|x1 + x3|x1:x2 + x4|x3)
dag2edge_matrix(g, out=1)
dag2edge_matrix(g, out=2)
dag2edge_matrix(g, out=3)
dag2edge_matrix(g, out=4)
d2 <- dag(~c|a:b+d:c)
dag2edge_matrix(d2)

Generate All Combinations of n Elements Taken m at a Time

Description

Generate all combinations of the elements of x taken m at a time. If x is a positive integer, returns all combinations of the elements of seq(x) taken m at a time.

Usage

fastcombn(x, m, FUN = NULL, simplify = TRUE, ...)

combn_prim(x, m, simplify = TRUE)

Arguments

Details

• Factors x are accepted.

• combn_prim is a simplified (but faster) version of the combn function. Does nok take the FUN argument.

• fastcombn is intended to be a faster version of the combn function.

Value

A matrix or a list.

Author(s)

Søren Højsgaard

See Also

combn

Examples

x <- letters[1:5]; m <- 3

fastcombn(x, m)
combn(x, m)
combn_prim(x, m)

x <- letters[1:4]; m <- 3
fastcombn(x, m, simplify=FALSE)
combn(x, m, simplify=FALSE)
combn_prim(x, m, simplify=FALSE)

x <- 1:10; m <- 3
fastcombn(x, m, min)
combn(x, m, min)

x <- factor(letters[1:8]); m <- 5

if (require(microbenchmark)){
  microbenchmark(
    combn(x, m, simplify=FALSE),
    combn_prim(x, m, simplify=FALSE),
    fastcombn(x, m, simplify=FALSE),
    times=50
  )
}

The package ‘gRbase’: summary information

Description

This package provides a basis for graphical modelling in R and in particular for other graphical modelling packages, most notably gRim, gRain and gRc.

Details

gRbase provides the following:

• Implementation of various graph algorithms, including maximum cardinality search, maximal prime subgraph decomposition, triangulation. See the vignette graphs.

• Implementation of various "high level" array operations, including multiplication/division, marginalization, slicing, permutation. See the vignette ArrayOps.

• Implementation of various "low level" array operations. See the vignette ArrayOpsPrim.

• A collection of datasets

• A 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. (Notice: This last part is not maintained / developed further.)

Authors

Soren Hojsgaard, Department of Mathematical Sciences, Aalborg University, Denmark

Contributions from Claus Dethlefsen, Clive Bowsher, David Edwards.

Acknowledgements

Thanks to the other members of the gR initiative, in particular to David Edwards for providing functions for formula-manipulation.

References

Hojsgaard, S., Edwards, D., Lauritzen, S. (2012) Graphical models with R. Springer. ISBN: 978-1-4614-2298-3

Lauritzen, S. L. (2002). gRaphical Models in R. R News, 3(2)39.

Functions from Graphical Modelling with R book

Description

Functions that must be retained to make code from gmwr-book work

Usage

as.adjMAT(object)

Arguments

Get cliques of an undirected graph

Description

Return a list of (maximal) cliques of an undirected graph.

Usage

get_cliques(object)

max_cliqueMAT(amat)

getCliques(object)

maxCliqueMAT(amat)

maxClique(object)

Arguments

Details

In graph theory, a clique is often a complete subset of a graph. A maximal clique is a clique which can not be enlarged. In statistics (and that is the convention we follow here) a clique is usually understood to be a maximal clique.

Finding the cliques of a general graph is an NP complete problem. Finding the cliques of triangualted graph is linear in the number of cliques.

The workhorse is the max_cliqueMAT function which calls the maxClique function in the RBGL package.

Value

A list.

Synonymous functions

For backward compatibility with downstream packages we have the following synonymous functions:

• getCliques = get_cliques

• maxCliqueMAT = max_cliqueMAT

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

See Also

ug, dag, mcs, mcsMAT, rip, ripMAT, moralize, moralizeMAT

Examples

uG0 <- ug(~a:b + b:c + c:d + d:e + e:f + f:a)
get_cliques(uG0)

uG1 <- as(uG0, "igraph")
get_cliques(uG1)

uG2 <- as(uG0, "matrix") 
get_cliques(uG2)

uG3 <- as(uG1, "dgCMatrix") 
get_cliques(uG3)

Graph coercion

Description

Methods for changing graph representations

Usage

coerceGraph(object, class)

graph_as(object, outtype, intype = NULL)

Arguments

Details

coerceGraph is used in the book "Graphical models with R". A more generic approach is as().

Examples

g1 <- ug(~a:b+b:c)
as(g1, "igraph")
as(g1, "matrix")
as(g1, "Matrix")
as(g1, "dgCMatrix")

## graph_as(g1, "ugList") ## Fails
## getCliques(g1)         ## Works

l1 <- list(c("a" ,"b"), c("b", "c"))

API for coercing graph representations

Description

API for coercing graph representations.

Usage

g_dm2sm_(object)

g_dm2ig_(object)

g_sm2dm_(object)

g_sm2ig_(object)

g_ig2dm_(object)

g_ig2sm_(object)

g_xm2ig_(object)

g_xm2dm_(object)

g_xm2sm_(object)

g_xm2xm_(object, result = "matrix")

Arguments

Details

No checking is made. In the function the following names are used:

• "ig": "igraph";

• "sm": "dgCMatrix" (sparse matrix);

• "dm": "matrix" (dense matrix)

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

See Also

ug, dag

Create undirected and directed graphs

Description

These functions are wrappers for creation of graphs as primarily igraph objects but also as adjacency matrices

Usage

ug(..., result = "igraph")

ugi(...)

ugList(x, result = "igraph")

dag(..., result = "igraph", forceCheck = FALSE)

dagi(..., forceCheck = FALSE)

dagList(x, result = "igraph", forceCheck = FALSE)

Arguments

Value

Functions ug(), and dag() can return a an igraph object, a sparse or a dense adjacency matrix.

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

Examples

## The following specifications of undirected graphs are equivalent:
uG1 <- ug(~ a:b:c + c:d)
uG2 <- ug(c("a", "b", "c"), c("c", "d"))
uG3 <- ug(c("a", "b"), c("a", "c"), c("b", "c"), c("c", "d"))

## The following specifications of directed acyclig graphs are equivalent:
daG1 <- dag(~ a:b:c + b:c + c:d)
daG2 <- dag(c("a", "b", "c"), c("b", "c"), c("c", "d"))

## dag() allows to specify directed graphs with cycles:
daG4 <- dag(~ a:b + b:c + c:a) # A directed graph but with cycles

## A check for acyclicity can be done with
## daG5 <- dag(~ a:b + b:c + c:a, forceCheck=TRUE) 

## A check for acyclicity is provided by topoSort
topo_sort( daG2 )
topo_sort( daG4 )

## Different representations
uG7 <- ug(~a:b:c + c:d, result="igraph")    # igraph
uG8 <- ug(~a:b:c + c:d, result="matrix")    # dense matrix
uG9 <- ug(~a:b:c + c:d, result="dgCMatrix") # sparse matrix

Find edges in a graph and edges not in a graph.

Description

Returns the edges of a graph (or edges not in a graph) where the graph can be either an igraph object or an adjacency matrix.

Usage

edgeList(object, matrix = FALSE)

edgeListMAT(adjmat, matrix = FALSE)

nonEdgeList(object, matrix = FALSE)

nonEdgeListMAT(adjmat, matrix = FALSE)

Arguments

Examples

## A graph with edges
g  <- ug(~a:b + b:c + c:d)
gm <- as(g, "matrix")
edgeList(g)
edgeList(gm)
edgeListMAT(gm)
edgeList(g, matrix=TRUE)
edgeList(gm, matrix=TRUE)
edgeListMAT(gm, matrix=TRUE)
nonEdgeList(g)
nonEdgeList(gm)
nonEdgeListMAT(gm)
## A graph without edges
g  <- ug(~a + b + c)
gm <- as(g, "matrix")
edgeList(g)
edgeList(gm)
edgeListMAT(gm)
edgeList(g, matrix=TRUE)
edgeList(gm, matrix=TRUE)
edgeListMAT(gm, matrix=TRUE)
nonEdgeList(g)
nonEdgeList(gm)
nonEdgeListMAT(gm)

Properties of a generating class (for defining a graph).

Description

A set of generators define an undirected graph, here called a dependence graph. Given a set of generators it is checked 1) if the dependence dependence graph is in 1-1-correspondance with the genrators (such that the corresponding model is graphical) and 2) if the dependence graph is chordal (triangulated) (such that the corresponding model is decomposable).

Usage

isGraphical(x)

isDecomposable(x)

Arguments

Details

A set of sets of variables, say A_1, A_2, ... A_K is called a generating class for a graph with vertices V and edges E. If two variables a,b are in the same generator, say A_j, then a and b are vertices in the graph and there is an undirected edge between a and b.

The graph induced by \code{g1 = ~a:b + a:c + b:c + c:d} has
edges \code{ab, ac, bc, cd}. The
cliques of this graph are \code{abc, cd}. Hence there is not a
1-1-correspondance between the graph and the generators.

On the other hand, \code{g2 <- ~a:b:c + c:d} induces the same
graph in this case there is a 1-1-correspondance.

The graph induced by \code{g3 <- ~a:b + b:c + c:d + d:a} is in
1-1-correspondance with its dependence graph, but the graph is
not chordal.

Value

TRUE or FALSE

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

See Also

mcs, rip

Examples

g1 <- ~a:b + a:c + b:c + c:d
g2 <- ~a:b:c + c:d
g3 <- ~a:b + b:c + c:d + d:a

isGraphical( g1 ) # FALSE
isGraphical( g2 ) # TRUE
isGraphical( g3 ) # TRUE

isDecomposable( g1 ) # FALSE
isDecomposable( g2 ) # TRUE
isDecomposable( g3 ) # TRUE

## A generating class can be given as a list:
f <- list(c("a","b"), c("b","c"), c("a","c"))
isGraphical( f )
isDecomposable( f )

Maximum cardinality search on undirected graph.

Description

Returns (if it exists) a perfect ordering of the vertices in an undirected graph.

Usage

mcs(object, root = NULL, index = FALSE)

## Default S3 method:
mcs(object, root = NULL, index = FALSE)

mcsMAT(amat, vn = colnames(amat), root = NULL, index = FALSE)

mcs_marked(object, discrete = NULL, index = FALSE)

## Default S3 method:
mcs_marked(object, discrete = NULL, index = FALSE)

mcs_markedMAT(amat, vn = colnames(amat), discrete = NULL, index = FALSE)

Arguments

Details

An undirected graph is decomposable iff there exists a perfect ordering of the vertices. The maximum cardinality search algorithm returns a perfect ordering of the vertices if it exists and hence this algorithm provides a check for decomposability. The mcs() functions finds such an ordering if it exists.

The notion of strong decomposability is used in connection with
e.g. mixed interaction models where some vertices represent
discrete variables and some represent continuous
variables. Such graphs are said to be marked. The
\code{mcsmarked()} function will return a perfect ordering iff
the graph is strongly decomposable. As graphs do not know about
whether vertices represent discrete or continuous variables,
this information is supplied in the \code{discrete} argument.

Value

A vector with a linear ordering (obtained by maximum cardinality search) of the variables or character(0) if such an ordering can not be created.

Note

The workhorse is the mcsMAT function.

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

See Also

moralize, junction_tree, rip, ug, dag

Examples

uG <- ug(~ me:ve + me:al + ve:al + al:an + al:st + an:st)
mcs(uG)
mcsMAT(as(uG, "matrix"))
## Same as
uG <- ug(~ me:ve + me:al + ve:al + al:an + al:st + an:st, result="matrix")
mcsMAT(uG)

## Marked graphs
uG1 <- ug(~ a:b + b:c + c:d)
uG2 <- ug(~ a:b + a:d + c:d)
## Not strongly decomposable:
mcs_marked(uG1, discrete=c("a","d"))
## Strongly decomposable:
mcs_marked(uG2, discrete=c("a","d"))

Minimal triangulation of an undirected graph

Description

An undirected graph uG is triangulated (or chordal) if it has no cycles of length >= 4 without a chord which is equivalent to that the vertices can be given a perfect ordering. Any undirected graph can be triangulated by adding edges to the graph, so called fill-ins which gives the graph TuG. A triangulation TuG is minimal if no fill-ins can be removed without breaking the property that TuG is triangulated.

Usage

minimal_triang(
  object,
  tobject = triangulate(object),
  result = NULL,
  details = 0
)

minimal_triangMAT(amat, tamat = triangulateMAT(amat), details = 0)

Arguments

Details

For a given triangulation tobject it may be so that some of the fill-ins are superflous in the sense that they can be removed from tobject without breaking the property that tobject is triangulated. The graph obtained by doing so is a minimal triangulation.

Notice: A related concept is the minimum
triangulation, which is the the graph with the smallest number
of fill-ins. The minimum triangulation is unique. Finding the
minimum triangulation is NP-hard.

Value

minimal_triang() returns an igraph object while minimal_triangMAT() returns an adjacency matrix.

Author(s)

Clive Bowsher C.Bowsher@statslab.cam.ac.uk with modifications by Søren Højsgaard, sorenh@math.aau.dk

References

Kristian G. Olesen and Anders L. Madsen (2002): Maximal Prime Subgraph Decomposition of Bayesian Networks. IEEE TRANSACTIONS ON SYSTEMS, MAN AND CYBERNETICS, PART B: CYBERNETICS, VOL. 32, NO. 1, FEBRUARY 2002

See Also

mpd, rip, triangulate

Examples

## An igraph object
g1 <- ug(~a:b + b:c + c:d + d:e + e:f + a:f + b:e, result="igraph")
x <- minimal_triang(g1)

tt <- ug(~a:b:e:f + b:e:c:d, result="igraph")
x <- minimal_triang(g1, tobject=tt)

## g2 is a triangulation of g1 but it is not minimal
g2 <- ug(~a:b:e:f + b:c:d:e, result="igraph")
x <- minimal_triang(g1, tobject=g2)

## An adjacency matrix
g1m <- ug(~a:b + b:c + c:d + d:e + e:f + a:f + b:e, result="matrix")
x <- minimal_triangMAT(g1m)

Moralize a directed acyclic graph

Description

Moralize a directed acyclic graph which means marrying parents and dropping directions.

Usage

moralize(object, ...)

## Default S3 method:
moralize(object, result = NULL, ...)

Arguments

Value

A moralized graph represented either as an igraph, a dense matrix or a sparse dgCMatrix.

Note

The workhorse is the moralizeMAT function.

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

See Also

mcs, junction_tree, rip, ug, dag

Examples

daG <- dag(~me+ve,~me+al,~ve+al,~al+an,~al+st,~an+st)
moralize(daG)

daG <- dag(~me+ve,~me+al,~ve+al,~al+an,~al+st,~an+st, result="matrix")
moralizeMAT(daG)

if (require(igraph)){
M <- matrix(c(1,2,3,3), nrow=2)
G <- graph.edgelist(M)
G
V(G)$name
moralize(G)
}

Maximal prime subgraph decomposition

Description

Finding a junction tree representation of the MPD (maximal prime subgraph decomposition) of an undirected graph The maximal prime subgraph decomposition of a graph is the smallest subgraphs into which the graph can be decomposed.

Usage

mpd(object, tobject = minimal_triang(object), details = 0)

## Default S3 method:
mpd(object, tobject = triangulate(object), details = 0)

mpdMAT(amat, tamat = minimal_triangMAT(amat), details = 0)

Arguments

Value

A list with components "nodes", "cliques", "separators", "parents", "children", "nLevels". The component "cliques" defines the subgraphs.

Author(s)

Clive Bowsher C.Bowsher@statslab.cam.ac.uk with modifications by Søren Højsgaard, sorenh@math.aau.dk

References

Kristian G. Olesen and Anders L. Madsen (2002): Maximal Prime Subgraph Decomposition of Bayesian Networks. IEEE TRANSACTIONS ON SYSTEMS, MAN AND CYBERNETICS, PART B: CYBERNETICS, VOL. 32, NO. 1, FEBRUARY 2002

See Also

mcs, mcsMAT, minimal_triang, minimal_triangMAT, rip, ripMAT, triangulate, triangulateMAT

Examples

## Maximal prime subgraph decomposition 
g1 <- ug(~ a:b + b:c + c:d + d:e + e:f + a:f + b:e)
if (interactive()) plot(g1)
x <- mpd(g1)

## Maximal prime subgraph decomposition - an adjacency matrix
g1m <- ug(~ a:b + b:c + c:d + d:e + e:f + a:f + b:e, result="matrix")
x <- mpdMAT(g1m)

Random directed acyclic graph

Description

Generate a random directed acyclic graph (DAG)

Usage

random_dag(V, maxpar = 3, wgt = 0.1)

Arguments

Details

If the maximum number of parents for a node is, say 3 and wgt=0.1, then the probability of the node ending up with 0,1,2,3 parents is proportional to 0.1^0, 0.1^1, 0.1^2, 0.1^3.

Value

An igraph object.

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

Examples

dg   <- random_dag(1:1000, maxpar=5, wgt=.9)
table(sapply(vpar(dg),length))

dg   <- random_dag(1:1000, maxpar=5, wgt=.5)
table(sapply(vpar(dg),length))

dg   <- random_dag(1:1000, maxpar=5, wgt=.1)
table(sapply(vpar(dg),length))

Create RIP ordering of the cliques of an undirected graph; create junction tree.

Description

A RIP (running intersection property) ordering of the cliques is also called a perfect ordering. If the graph is not chordal, then no such ordering exists.

Usage

rip(object, ...)

## Default S3 method:
rip(object, root = NULL, nLevels = NULL, ...)

ripMAT(amat, root = NULL, nLevels = rep(2, ncol(amat)))

junction_tree(object, ...)

## Default S3 method:
junction_tree(object, nLevels = NULL, ...)

junction_treeMAT(amat, nLevels = rep(2, ncol(amat)), ...)

jTree(object, ...)

Arguments

Details

The RIP ordering of the cliques of a decomposable (i.e. chordal) graph is obtained by first ordering the variables linearly with maximum cardinality search (by mcs). The root argument is transfered to mcs as a way of controlling which clique will be the first in the RIP ordering. The junction_tree() (and junction_tree()) (for "junction tree") is just a wrapper for a call of triangulate() followed by a call of rip().

Value

rip returns a list (an object of class ripOrder. A print method exists for such objects.)

Synonymous functions

For backward compatibility with downstream packages we have the following synonymous functions:

• jTree = junction_tree (Used in rags2ridges)

• junctionTree = junction_tree

Note

The workhorse is the ripMAT() function. The nLevels argument to the rip functions has no meaning.

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

See Also

mcs, triangulate, moralize, ug, dag

Examples

uG <- ug(~me:ve + me:al + ve:al + al:an + al:st + an:st)
mcs(uG)
rip(uG)
junction_tree(uG)

## Adjacency matrix
uG <- ug(~me:ve:al + al:an:st, result="matrix")
mcs(uG)
rip(uG)
junction_tree(uG)

## Sparse adjacency matrix
uG <- ug(c("me", "ve", "al"), c("al", "an", "st"), result="dgCMatrix")
mcs(uG)
rip(uG)
junction_tree(uG)

## Non--decomposable graph
uG <- ug(~1:2 + 2:3 + 3:4 + 4:5 + 5:1)
mcs(uG)
rip(uG)
junction_tree(uG)

Triangulation of an undirected graph

Description

This function will triangulate an undirected graph by adding fill-ins.

Usage

triangulate(object, ...)

## Default S3 method:
triangulate(object, nLevels = NULL, result = NULL, check = TRUE, ...)

triang_mcwh(object, ...)

triang_elo(object, ...)

triang(object, ...)

## Default S3 method:
triang(object, control = list(), ...)

## Default S3 method:
triang_mcwh(object, nLevels = NULL, result = NULL, check = TRUE, ...)

## Default S3 method:
triang_elo(object, order = NULL, result = NULL, check = TRUE, ...)

triangulateMAT(amat, nLevels = rep(2, ncol(amat)), ...)

triang_mcwhMAT_(amat, nLevels = rep(2, ncol(amat)), ...)

triang_eloMAT_(amat, order)

triang_eloMAT(amat, order = NULL)

Arguments

Details

There are two type of functions: triang and triangulate

The workhorse is the triangulateMAT function.

The triangulation is made so as the total state space is kept low by applying a minimum clique weight heuristic: When a fill-in is necessary, the algorithm will search for an edge to add such that the complete set to be formed will have as small a state-space as possible. It is in this connection that the nLevels values are used.

Default (when nLevels=NULL) is to take nLevels=2 for all nodes. If nLevels is the same for all nodes then the heuristic aims at keeping the clique sizes small.

Value

A triangulated graph represented either as a (dense) matrix or a (sparse) dgCMatrix.

Note

Care should be taken when specifying nLevels for other representations than adjacency matrices: Since the triangulateMAT function is the workhorse, any other representation is transformed to an adjacency matrix and the order of values in nLevels most come in the order of the nodes in the adjacency matrix representation.

Currently there is no check for that the graph is undirected.

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

See Also

ug, dag, mcs, mcsMAT, rip, ripMAT, moralize, moralizeMAT

Examples

uG1 <- ug(~a:b + b:c + c:d + d:e + e:f + f:a)
uG2 <- ug(~a:b + b:c + c:d + d:e + e:f + f:a, result="matrix")
uG3 <- ug(~a:b + b:c + c:d + d:e + e:f + f:a, result="dgCMatrix")

## Default triangulation: minimum clique weight heuristic
# (default is that each node is given the same weight):

tuG1 <- triang(uG1)
## Same as
triang_mcwh(uG1)

## Alternative: Triangulation from a desired elimination order
# (default is that the order is order of the nodes in the graph):

triang(uG1, control=list(method="elo"))
## Same as:
triang_elo(uG1)

## More control: Define the number of levels for each node:
tuG1 <- triang(uG1, control=list(method="mcwh", nLevels=c(2, 3, 2, 6, 4, 9))) 
tuG1 <- triang_mcwh(uG1, nLevels=c(2, 3, 2, 6, 4, 9))

tuG1 <- triang(uG1, control=list(method="elo", order=c("a", "e", "f")))
tuG1 <- triang_elo(uG1, order=c("a", "e", "f"))

uG1 <- ug(~a:b + b:c + c:d + d:e + e:f + f:a)
tuG1 <- triangulate(uG1)

## adjacency matrix
uG2 <- ug(~a:b + b:c + c:d + d:e + e:f + f:a, result="matrix")
tuG2 <- triangulate(uG2)

## adjacency matrix (sparse)
uG2 <- ug(~a:b + b:c + c:d + d:e + e:f + f:a, result="dgCMatrix")
tuG2 <- triangulate(uG2)

Coercion of graphs represented as lists

Description

Coercion of graphs represented as lists to various graph formats.

Usage

g_ugl2ig_(zz, vn = NULL)

g_ugl2dm_(zz, vn = NULL)

g_ugl2sm_(zz, vn = NULL)

g_ugl2XX_(zz, outtype, vn = NULL)

g_dagl2ig_(zz, vn = NULL)

g_dagl2dm_(zz, vn = NULL)

g_dagl2sm_(zz, vn = NULL)

g_dagl2XX_(zz, outtype, vn = NULL)

g_adl2ig_(zz)

g_adl2dm_(zz)

g_adl2sm_(zz)

g_adl2XX_(zz, outtype)

g_M2adl_(amat)

g_M2ugl_(amat)

g_M2dagl_(amat)

g_ugl2M_(glist, vn = NULL, result = "matrix")

g_dagl2M_(glist, vn = NULL, result = "matrix")

g_adl2M_(alist, result = "matrix")

Arguments

Examples

## Sparse and dense adjacency matrices converted to adjacency list 
g1 <- ug(~a:b + b:c + c:d, result="matrix")
g2 <- ug(~a:b + b:c + c:d, result="dgCMatrix")
g_M2adl_( g1 )

## Sparse and dense adjacency matrices converted to cliques
g_M2ugl_( g1 )

## Sparse and dense adjacency matrices converted to cliques
g_M2dagl_( g1 )

## g_M2adl_( g2 ) ## FIXME FAILS for sparse matrix
## g_M2ugl_( g2 ) ## FIXME Is there an issue here??
## g_M2dagList( g2 ) ## Fails for sparse matrix

Function for plotting graphs using the 'igraph' package.

Description

Generic function for plotting graphs using the 'igraph' package.

Usage

iplot(x, ...)

## S3 method for class 'igraph'
iplot(x, ...)

Arguments

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

Examples

UG <- ug(~a:b+b:c:d)
iplot(UG)

Check properties of graphs.

Description

Check if a graph is 1) a directed acyclic graph (DAG), 2) a directed graph (DG), 3) an undirected graph (UG), 4) a triangulated (chordal) undirected graph (TUG).

Usage

is_dag(object)

is_dagMAT(object)

is_ug(object)

is_ugMAT(object)

is_tug(object)

is_tugMAT(object)

is_dg(object)

is_dgMAT(object)

is_adjMAT(object)

is.adjMAT(object)

Arguments

Details

• A non-zero value at entry (i,j) in an adjacency matrix A for a graph means that there is an edge from i to j. If also (j,i) is non-zero there is also an edge from j to i. In this case we may think of a bidirected edge between i and j or we may think of the edge as being undirected. We do not distinguish between undirected and bidirected edges in the gRbase package.

• The function is_ug() checks if the adjacency matrix is symmetric.

• The function is_tug() checks if the graph is undirected and triangulated (also called chordal) by checking if the adjacency matrix is symmetric and the vertices can be given a perfect ordering using maximum cardinality seach.

• The function is_dg() checks if a graph is directed, i.e., that there are no undirected edges. This is done by computing the elementwise product of A and the transpose of A; if there are no non–zero entries in this product then the graph is directed.

• The function is_dag() will return TRUE if all edges are directed and if there are no cycles in the graph. (This is checked by checking if the vertices in the graph can be given a topological ordering which is based on identifying an undirected edge with a bidrected edge).

• There is a special case, namely if the graph has no edges at all (such that the adjacency matrix consists only of zeros). Such a graph is both undirected, triangulated, directed and directed acyclic.

Synonymous functions

The functions

• is.TUG/is.DAG/is.DG/is.UG/is.adjMAT

are synonymous with

• is_tug/is_dag/is_dg/is_ug/is_adjMAT.

The is.X group of functions will be deprecated.

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

See Also

dag, ug

Examples

## DAGs
dag_  <- dag(~ a:b:c + c:d:e)

## Undirected graphs
ug_  <- ug(~a:b:c + c:d:e)

## Is graph a DAG?
is_dag(dag_)
is_dag(ug_)

## Is graph an undirected graph
is_ug(dag_)
is_ug(ug_)
 
## Is graph a triangulated (i.e. chordal) undirected graph
is_tug(dag_)
is_tug(ug_)

## Example where the graph is not triangulated
ug2_  <- ug(~ a:b + b:c + c:d + d:a)
is_tug(ug2_)

Query a graph

Description

Unified approach to query a graph about its properties (based partly on functionality from gRbase and functionality imported from RBGL).

Usage

querygraph(object, op, set = NULL, set2 = NULL, set3 = NULL)

qgraph(object, op, set = NULL, set2 = NULL, set3 = NULL)

ancestors(set, object)

subGraph(set, object)

is.triangulated(object)

connComp(object)

ancestralSet(set, object)

ancestralGraph(set, object)

parents(set, object)

children(set, object)

separates(set, set2, set3, object)

closure(set, object)

adj(object, set)

is.simplicial(set, object)

simplicialNodes(object)

is.complete(object, set = NULL)

is.decomposition(set, set2, set3, object)

nodes_(object)

nodes(object, ...)

## S4 method for signature 'igraph'
nodes(object, ...)

edges(object)

edges_(object)

addEdge(v1, v2, object)

removeEdge(v1, v2, object)

Arguments

Examples

ug0 <- ug(~a:b + b:c:d + e)

separates("a", "d", c("b", "c"), ug0)
separates("a", "d", "c", ug0) 
is.simplicial("b", ug0)
simplicialNodes(ug0)

simplicialNodes(ug0)

Topological sort of vertices in directed acyclic graph

Description

A topological ordering of a directed graph is a linear ordering of its vertices such that, for every edge (u->v), u comes before v in the ordering. A topological ordering is possible if and only if the graph has no directed cycles, that is, if it is a directed acyclic graph (DAG). Any DAG has at least one topological ordering. Can hence be used for checking if a graph is a DAG.

Usage

topo_sort(object, index = FALSE)

topo_sortMAT(amat, index = FALSE)

topoSort(object, index = FALSE)

topoSortMAT(amat, index = FALSE)

Arguments

Value

If FALSE, an ordering is returned if it exists and character(0) otherwise. If TRUE, the index of the variables in an adjacency matrix is returned and -1 otherwise.

Synonymous functions

The functions topo_sort / topoSort are synonymous with topo_sortMAT / topoSortMAT. One of the groups may be deprecated in the future.

Note

The workhorse is the topo_sortMAT function which takes an adjacency matrix as input.

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

See Also

dag, ug

Examples

dagMAT  <- dag(~a:b:c + c:d:e, result="matrix")
dagMATS <- as(dagMAT, "dgCMatrix")

topo_sort(dagMAT)
topo_sort(dagMATS)

List of vertices and their parents for graph.

Description

Get list of vertices and their parents for graph.

Usage

vchi(object, getv = TRUE, forceCheck = TRUE)

vchiMAT(object, getv = TRUE, forceCheck = TRUE)

vpar(object, getv = TRUE, forceCheck = TRUE)

vparMAT(object, getv = TRUE, forceCheck = TRUE)

Arguments

Value

A list of vectors where each vector will have the form (v, pa1, pa2, ... paN) where pa1, pa2, ... paN are the parents of v.

See Also

dag, ug

Examples

## DAGs
dag_mat <- dag(~a:b:c + c:d:e, result="matrix")
dag_ig <- dag(~a:b:c + c:d:e)
vpar(dag_mat)
vpar(dag_ig)
vpar(dag_mat, getv=FALSE)
vpar(dag_ig, getv=FALSE)
## Undirected graphs
ug_mat <- ug(~a:b:c + c:d:e, result="matrix")
ug_ig <- ug(~a:b:c + c:d:e)
## Not run: 
## This will fail because the adjacency matrix is symmetric and the
## graph has undirected edges
vpar(ug_mat)
vpar(ug_ig)

## End(Not run)
## When forceCheck is FALSE, it will not be detected that the
#g raphs are undirected.
vpar(ug_mat, forceCheck=FALSE)
vpar(ug_ig, forceCheck=FALSE)

gRbase utilities

Description

Various utility functions for gRbase. Includes 'faster versions' of certain standard R functions.

Usage

rhsFormula2list(form)

rhsf2list(form)

rhsf2vec(form)

listify_dots(dots)

list2rhsFormula(form)

list2rhsf(form)

rowmat2list(X)

colmat2list(X)

matrix2list(X, byrow = TRUE)

which.arr.index(X)

which_matrix_index(X)

rowSumsPrim(X)

colSumsPrim(X)

colwiseProd(v, X)

lapplyV2I(setlist, item)

lapplyI2V(setlist, item)

Arguments

Details

which.arr.ind: Returns matrix n x 2 matrix with indices of non-zero entries in matrix X. Notice which_matrix_index__ is cpp implementation.

colwiseProd: multiplies a vector v and a matrix X columnwise (as opposed to rowwise which is achieved by v * X). Hence colwiseProd does the same as t(v * t(X)) - but it does so faster for numeric values.

• lapplyV2I: same as but much faster than lapply(setlist, function(elt) match(elt, item))

• lapplyI2V: same as but faster than lapply(setlist, function(elt) item[elt])

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

Examples

## colwiseProd
X <- matrix(1:16, nrow=4)
v <- 1:4
t(v * t(X))
colwiseProd(v, X)
## Not run: 
system.time(for (ii in 1:100000)  t(v * t(X)))
system.time(for (ii in 1:100000)  colwiseProd(v, X))

## End(Not run)


setlist <- list(c(1,2,3), c(2,3,4), c(2,4,5))
item <- c(2,3)

lapplyV2I(setlist, item)
lapply(setlist, function(gg) match(gg, item))

lapplyI2V(setlist, item)
lapply(setlist, function(x) item[x])

if (require(microbenchmark)){
microbenchmark(
  lapplyV2I(setlist, item),
  lapply(setlist, function(elt) match(elt, item)))

microbenchmark::microbenchmark(
  lapplyI2V(setlist, item),
  lapply(setlist, function(elt) item[elt]))
}

Compile and propagate functions

Description

compile and propagate are generic functions which invoke particular methods which depend on the class of the first argument

Usage

fit(object, ...)

compile(object, ...)

propagate(object, ...)

stepwise(object, ...)

Arguments

Value

The value returned depends on the class of the first argument.

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

References

Højsgaard, Søren; Edwards, David; Lauritzen, Steffen (2012): Graphical Models with R, Springer

Internal functions for the gRbase package

Description

These functions are not intended to be called directly.

Prostate Tumor Gene Expression Dataset

Description

This is the Prostate Tumor Gene Expression dataset used in Chung and Keles (2010).

Usage

 data(prostate) 

Format

A list with two components:

x

Gene expression data. A matrix with 102 rows and 6033 columns.

y

Class index. A vector with 102 elements.

Details

The prostate dataset consists of 52 prostate tumor and 50 normal samples. Normal and tumor classes are coded in 0 and 1, respectively, in y vector. Matrix x is gene expression data and arrays were normalized, log transformed, and standardized to zero mean and unit variance across genes as described in Dettling (2004) and Dettling and Beuhlmann (2002). See Chung and Keles (2010) for more details.

Source

Singh D, Febbo P, Ross K, Jackson D, Manola J, Ladd C, Tamayo P, Renshaw A, DAmico A, Richie J, Lander E, Loda M, Kantoff P, Golub T, and Sellers W (2002), "Gene expression correlates of clinical prostate cancer behavior", Cancer Cell, Vol. 1, pp. 203–209.

References

Chung D and Keles S (2010), "Sparse partial least squares classification for high dimensional data", Statistical Applications in Genetics and Molecular Biology, Vol. 9, Article 17.

Dettling M (2004), "BagBoosting for tumor classification with gene expression data", Bioinformatics, Vol. 20, pp. 3583–3593.

Dettling M and Beuhlmann P (2002), "Supervised clustering of genes", Genome Biology, Vol. 3, pp. research0069.1–0069.15.

Examples

data(prostate)
prostate$x[1:5,1:5]
prostate$y

Suite of set operations

Description

Set operations for gRbase and related packages.

Usage

maximal_sets(setlist, index = FALSE)

minimal_sets(setlist, index = FALSE)

remove_redundant(setlist, maximal = TRUE, index = FALSE)

is_inset(x, setlist, index = FALSE)

filter_maximal_vectors(setlist, index = FALSE)

get_subset(x, setlist, all = FALSE)

get_superset(x, setlist, all = FALSE)

is_subsetof(set, set2)

is.subsetof(x, set)

subsetof(x, set)

Arguments

Details

'setlist' is a list of vectors representing a set of subsets; i.e. V1,...VQ where Vk is a subset of some base set V.

'all' If true, get_superset will return index of all vectors containing the element; otherwise only the first index is returned.

is_inset: Checks if the set x is in one of the Vk's.

remove_redundant: Returns those Vk which are not contained in other subsets; i.e. gives the maximal sets. If maximal is FALSE then returns the minimal sets; i.e. Vk is returned if Vk is contained in one of the other sets Vl and there are no set Vn contained in Vk.

Notice that the comparisons are made by turning the elements into characters and then comparing these. Hence 1 is identical to "1".

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

Examples

set <- list(c(1, 2), c(1, 2, 3), c(2, 3, 6), c(2, 4), c(5, 6), 5)            
                                                            
el1 <- c(2, 1)                                               
el2 <- c(2, 3)                                               
el3 <- c(4, 3)                                               
el4 <- c(2, 1, 3)                                             
                                                            
maximal_sets(set)                                           
minimal_sets(set)                                           
                                                            
remove_redundant(set)                                       
remove_redundant(set, maximal=FALSE)                        
                                                            
is_inset(el1, set)                                          
is_inset(el2, set)                                          
is_inset(el3, set)                                          
                                                            
get_subset(el1, set)
get_subset(el1, set)                                        
get_subset(el2, set)                                        
get_subset(el3, set)                                        

get_superset(el1, set)                                      
get_superset(el1, set, all=TRUE)                                      
get_superset(el2, set)                                      
get_superset(el3, set)

is_subsetof(el1, el1)                                       
is_subsetof(el1, el2)                                       
is_subsetof(el1, el4)

Coerce between undirected and directed graphs when possible

Description

An undirected graph G can be converted to a dag if G is chordal.

Usage

ug2dag(object)

Arguments