Mean, covariance and counts for grouped data (statistics for conditional Gaussian distribution).

Description

CGstats provides what corresponds to calling cow.wt on different strata of data where the strata are defined by the combinations of factors in data.

Usage

CGstats(object, varnames = NULL, homogeneous = TRUE, simplify = TRUE)

Arguments

Value

A list whose form depends on the type of input data and the varnames.

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

See Also

cov.wt

Examples

data(milkcomp)
# milkcomp <- subset(milkcomp, (treat %in% c("a", "b")) & (lactime %in% c("t1", "t2")))
# milkcomp <- milkcomp[,-1]
# milkcomp$treat 	<- factor(milkcomp$treat)
# milkcomp$lactime 	<- factor(milkcomp$lactime)

CGstats(milkcomp)
CGstats(milkcomp, c(1, 2))
CGstats(milkcomp, c("lactime", "treat"))
CGstats(milkcomp, c(3, 4))
CGstats(milkcomp, c("fat", "protein"))

CGstats(milkcomp, c(2, 3, 4), simplify=FALSE)
CGstats(milkcomp, c(2, 3, 4), homogeneous=FALSE)
CGstats(milkcomp, c(2, 3, 4), simplify=FALSE, homogeneous=FALSE)

Test for conditional independence in a contingency table

Description

Test for conditional independence in a contingency table represented as an array.

Usage

ciTest_table(
  x,
  set = NULL,
  statistic = "dev",
  method = "chisq",
  adjust.df = TRUE,
  slice.info = TRUE,
  L = 20,
  B = 200,
  ...
)

Arguments

Details

set can be 1) a vector or 2) a right-hand sided formula in which variables are separated by '+'. In either case, it is tested if the first two variables in the set are conditionally independent given the remaining variables in set. (Notice an abuse of the '+' operator in the right-hand sided formula: The order of the variables does matter.)

If set is NULL then it is tested whether the first two variables are conditionally independent given the remaining variables.

Value

An object of class citest (which is a list).

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

See Also

ciTest, ciTest_df, ciTest_mvn, chisq.test

Examples

data(lizard)

## lizard is has named dimnames
names( dimnames( lizard ))
## checked with
is.named.array( lizard )

## Testing for conditional independence:
# the following are all equivalent:
ciTest(lizard, set=~diam + height + species)
# ciTest(lizard, set=c("diam", "height", "species"))
# ciTest(lizard, set=1:3)
# ciTest(lizard)
# (The latter because the names in lizard are as given above.)

## Testing for marginal independence
ciTest(lizard, set=~diam + height)
ciTest(lizard, set=1:2)

## Getting slice information:
ciTest(lizard, set=c("diam", "height", "species"), slice.info=TRUE)$slice

## Do Monte Carlo test instead of usual likelihood ratio test. Different
# options:

# 1) Do B*10 simulations divided equally over each slice: 
ciTest(lizard, set=c("diam", "height", "species"), method="mc", B=400)
# 2) Do at most B*10 simulations divided equally over each slice, but stop
# when at most L extreme values are found
ciTest(lizard, set=c("diam", "height", "species"), method="smc", B=400)

Test for conditional independence in a dataframe

Description

Test for conditional independence in a dataframe.

Usage

ciTest_df(x, set = NULL, ...)

Arguments

Details

• set can be 1) a vector or 2) a right-hand sided formula in which variables are separated by '+'. In either case, it is tested if the first two variables in the set are conditionally independent given the remaining variables in set. (Notice an abuse of the '+' operator in the right-hand sided formula: The order of the variables does matter.)

• If set is NULL then it is tested whether the first two variables are conditionally independent given the remaining variables.

• If set consists only of factors then x[,set] is converted to a contingency table and the test is made in this table using ciTest_table().

• If set consists only of numeric values and integers then x[,set] is converted to a list with components cov and n.obs by calling cov.wt(x[,set], method='ML'). This list is then passed on to ciTest_mvn() which makes the test.

Value

An object of class citest (which is a list).

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

See Also

ciTest, ciTest_table, ciTest_mvn, chisq.test

Examples

data(milkcomp1)
ciTest(milkcomp1, set=~tre + fat + pro)
ciTest_df(milkcomp1, set=~tre + fat + pro)

Generic function for conditional independence test

Description

Generic function for conditional independence test. Specializes to specific types of data.

Usage

ciTest(x, set = NULL, ...)

Arguments

Details

x can be

1. a table (an array). In this case ciTest_table is called.

2. a dataframe whose columns are numerics and factors. In this case ciTest_df is called.

3. a list with components cov and n.obs. In this case ciTest_mvn is called.

set can be

1. a vector,

2. a right-hand sided formula in which variables are separated by '+'.

In either case, it is tested if the first two variables in the set are conditionally independent given the remaining variables in set. (Notice an abuse of the '+' operator in the right-hand sided formula: The order of the variables does matter.)

Value

An object of class citest (which is a list).

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

See Also

ciTest_table, ciTest_df, ciTest_mvn, chisq.test

Examples

## contingency table:
data(reinis)
## dataframe with only numeric variables:
data(carcass)
## dataframe with numeric variables and factors:
data(milkcomp1)

ciTest(cov.wt(carcass, method='ML'), set=~Fat11 + Meat11 + Fat12)
ciTest(reinis, set=~smo + phy + sys)
ciTest(milkcomp1, set=~tre + fat + pro)

Test for conditional independence in the multivariate normal distribution

Description

Test for conditional independence in the multivariate normal distribution.

Usage

ciTest_mvn(x, set = NULL, statistic = "DEV", ...)

Arguments

Details

set can be 1) a vector or 2) a right-hand sided formula in which variables are separated by '+'. In either case, it is tested if the first two variables in the set are conditionally independent given the remaining variables in set. (Notice an abuse of the '+' operator in the right-hand sided formula: The order of the variables does matter.)

If set is NULL then it is tested whether the first two variables are conditionally independent given the remaining variables.

x must be a list with components cov and n.obs such as returned by calling cov.wt( , method='ML') on a dataframe.

Value

An object of class citest (which is a list).

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

See Also

ciTest, ciTest_table, ciTest_df, ciTest_mvn, chisq.test

Examples

data(carcass)
ciTest(cov.wt(carcass, method='ML'), set=~Fat11 + Meat11 + Fat12)
ciTest_mvn(cov.wt(carcass, method='ML'), set=~Fat11 + Meat11 + Fat12)

A function to compute Monte Carlo and asymptotic tests of conditional independence for ordinal and/or nominal variables.

Description

The function computes tests of independence of two variables, say u and v, given a set of variables, say S. The deviance, Wilcoxon, Kruskal-Wallis and Jonkheere-Terpstra tests are supported. Asymptotic and Monte Carlo p-values are computed.

Usage

ciTest_ordinal(x, set = NULL, statistic = "dev", N = 0, ...)

Arguments

Details

The deviance test is appropriate when u and v are nominal; Wilcoxon, when u is binary and v is ordinal; Kruskal-Wallis, when u is nominal and v is ordinal; Jonckheere-Terpstra, when both u and v are ordinal.

Value

A list including the test statistic, the asymptotic p-value and, when computed, the Monte Carlo p-value.

Author(s)

Flaminia Musella, David Edwards, Søren Højsgaard, sorenh@math.aau.dk

References

See Edwards D. (2000), "Introduction to Graphical Modelling", 2nd ed., Springer-Verlag, pp. 130-153.

See Also

ciTest_table, ciTest

Examples

library(gRim)
data(dumping, package="gRbase")

ciTest_ordinal(dumping, c(2,1,3), stat="jt", N=1000)
ciTest_ordinal(dumping, c("Operation", "Symptom", "Centre"), stat="jt", N=1000)
ciTest_ordinal(dumping, ~Operation + Symptom + Centre, stat="jt", N=1000)

data(reinis)
ciTest_ordinal(reinis, c(1,3,4:6), N=1000)

# If data is a dataframe
dd     <- as.data.frame(dumping)
ncells <- prod(dim(dumping))
ff     <- dd$Freq
idx    <- unlist(mapply(function(i,n) rep(i,n),1:ncells,ff))
dumpDF <- dd[idx, 1:3]
rownames(dumpDF) <- 1:NROW(dumpDF)

ciTest_ordinal(dumpDF, c(2,1,3), stat="jt", N=1000)
ciTest_ordinal(dumpDF, c("Operation","Symptom","Centre"), stat="jt", N=1000)
ciTest_ordinal(dumpDF, ~ Operation + Symptom + Centre, stat="jt", N=1000)

Graphical Gaussian model

Description

Specification of graphical Gaussian model. The 'c' in the name cmod refers to that it is a (graphical) model for 'c'ontinuous variables

Usage

cmod(
  formula,
  data,
  marginal = NULL,
  fit = TRUE,
  maximal_only = FALSE,
  details = 0
)

Arguments

Details

The independence model can be specified as ~.^1 and the saturated model as ~.^.. The marginal argument can be used for specifying the independence or saturated models for only a subset of the variables.

Value

An object of class cModel (a list)

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

See Also

dmod, mmod, ggmfit

Examples

## Graphical Gaussian model
data(carcass)
cm1 <- cmod(~ .^., data=carcass)

## Stepwise selection based on BIC
cm2 <- backward(cm1, k=log(nrow(carcass)))

## Stepwise selection with fixed edges
cm3 <- backward(cm1, k=log(nrow(carcass)),
 fixin=matrix(c("LeanMeat", "Meat11", "Meat12", "Meat13",
                "LeanMeat", "Fat11", "Fat12", "Fat13"),
                 ncol=2))

Coerce models to different representations

Description

Coerce models to different representations

Usage

as_emat2cq(emat, nvar = NULL)

as_emat_complement(emat, nvar)

as_emat2amat(emat, d)

as_emat2elist(emat)

as_elist2emat(elist)

as_glist2emat(glist)

as_glist2cq(glist)

as_glist2graph(glist, d)

as_glist2igraph(glist, d)

as_emat2graph(emat, d)

as_emat2igraph(emat, d)

as_amat2emat(amat, eps = 1e-04)

as_emat2glist(emat)

as_glist2out_edges(glist)

as_K2amat(K, eps = 1e-04)

as_K2graph(K)

as_sparse(K)

Arguments

Edge matrix operations

Description

Edge matrix operations needed for ips algorithms

Usage

emat_compare(emat1, emat2)

emat_complement(emat1, emat2)

emat_sort(emat1)

order_rows(emat)

Arguments

Details

An emat with p edges is represented by a 2 x p matrix.

Note

These functions may well be removed from the package in future relases

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

Examples

emat1 <- model_saturated(3:4, type="emat")
emat2 <- model_saturated(1:4, type="emat")
emat_complement(emat1, emat2)
emat3 <- model_saturated(2:4, type="emat")
emat_compare(emat1, emat3)

Fast computation of covariance / correlation matrix

Description

Fast computation of covariance / correlation matrix

Usage

fast_cov(x, center = TRUE, scale = TRUE)

Arguments

Fit Gaussian graphical models

Description

Fit Gaussian graphical models using various algorithms.

Usage

fit_ggm_grips(
  S,
  formula = NULL,
  nobs,
  K = NULL,
  maxit = 10000L,
  eps = 0.01,
  convcrit = 1,
  aux = list(),
  method = "ncd",
  print = 0
)

Arguments

Details

Convergence criterion:

• 1: max absolute difference between S and Sigmahat on edges.

• 2: difference in log likelihood divided by number of parameters in the model (number of edges + number of nodes) between successive iterations.

• 3: computed duality gap may turn negative due to rounding error, so its absolute value is returned. This still provides upper bound on error of likelihood function.

Methods:

• "ncd": Neighbour coordinate descent.

• "covips": IPS based on working with the covariance matrix.

• "conips": IPS based on working with the concentration matrix.

ncd is very fast but may fail to converge in rare cases. Both covips and conips are guaranteed to converge provided the maximum likelihood estimate exists, and covips are considerably faster than conips.

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

Examples

options("digits"=3)
data(math, package="gRbase")

S <- cov(math)
nobs <- nrow(math)
gl <- list(1:3, 3:5)
em <- matrix(c(1,2, 2,3, 1,3, 3,4, 3,5, 4,5), nrow=2)

EPS = 1e-2

fit_cov = fit_ggm_grips(S, gl, nobs=nobs, eps=EPS, method="cov")
fit_con = fit_ggm_grips(S, gl, nobs=nobs, eps=EPS, method="con")
fit_ncd = fit_ggm_grips(S, gl, nobs=nobs, eps=EPS, method="ncd")

K <- solve(S)
(fit_con$K - K)  |> abs() |> max()
(fit_cov$K - K)  |> abs() |> max()
(fit_ncd$K - K)  |> abs() |> max()

Generate various grapical models

Description

Models are represented in various forms

Usage

emat_saturated_model(index)

model_saturated(index, type = "emat", nms = NULL)

model_random_tree(index, prob = 0, type = "emat", nms = NULL)

model_rectangular_grid(dim, type = "emat", nms = NULL)

model_line(index, type = "emat", nms = NULL)

model_star(index, type = "emat", nms = NULL)

model_loop(index, prob = 0, type = "emat", nms = NULL)

model_random(index, prob = 0.1, type = "emat", nms = NULL)

Arguments

Genrate matrix of N(0, 1) variables

Description

Genrate matrix of N(0, 1) variables

Usage

generate_n01(n.obs, nvar, seed = 2022)

Arguments

Find edges in a graph or edges not in an undirected graph.

Description

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

Usage

getEdges(object, type = "unrestricted", ingraph = TRUE, discrete = NULL, ...)

Arguments

Details

When ingraph=TRUE: If type="decomposable" then getEdges() returns those edges e for which the graph with e removed is decomposable.

When ingraph=FALSE: Likewise, if type="decomposable" then getEdges() returns those edges e for which the graph with e added is decomposable.

The functions getInEdges() and getInEdges() are just wrappers for calls to getEdges().

The workhorses are getInEdgesMAT() and getOutEdgesMAT() and these work on adjacency matrices.

Regarding the argument discrete, please see the documentation of mcs_marked.

Value

A p * 2 matrix with edges.

Note

These functions work on undirected graphs. The behaviour is undocumented for directed graphs.

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

See Also

edgeList, nonEdgeList.

Examples

gg     <- ug(~a:b:d + a:c:d + c:e, result="igraph")
glist  <- getCliques(gg)
adjmat <- as(gg, "matrix")

#### On a glist
getEdges(glist)
getEdges(glist, type="decomposable")
# Deleting (a,d) would create a 4-cycle

getEdges(glist, ingraph=FALSE)
getEdges(glist, type="decomposable", ingraph=FALSE)
# Adding (e,b) would create a 4-cycle

#### On a graphNEL
getEdges(gg)
getEdges(gg, type="decomposable")
# Deleting (a,d) would create a 4-cycle

getEdges(gg, ingraph=FALSE)
getEdges(gg, type="decomposable", ingraph=FALSE)
# Adding (e,b) would create a 4-cycle

#### On an adjacency matrix
getEdges(adjmat)
getEdges(adjmat, type="decomposable")
# Deleting (a,d) would create a 4-cycle

getEdges(adjmat, ingraph=FALSE)
getEdges(adjmat, type="decomposable", ingraph=FALSE)
# Adding (e,b) would create a 4-cycle


## Marked graphs; vertices a,b are discrete; c,d are continuous
UG <- ug(~a:b:c + b:c:d, result="igraph")
disc <- c("a", "b")
getEdges(UG)
getEdges(UG, discrete=disc)
## Above: same results; there are 5 edges in the graph

getEdges(UG, type="decomposable")
## Above: 4 edges can be removed and will give a decomposable graph
##(only removing the edge (b,c) would give a non-decomposable model)

getEdges(UG, type="decomposable", discrete=c("a","b"))
## Above: 3 edges can be removed and will give a strongly decomposable
## graph. Removing (b,c) would create a 4--cycle and removing (a,b)
## would create a forbidden path; a path with only continuous vertices
## between two discrete vertices.

Iterative proportional fitting of graphical Gaussian model

Description

Fit graphical Gaussian model by iterative proportional fitting.

Usage

ggmfit(
  S,
  n.obs,
  glist,
  start = NULL,
  eps = 1e-12,
  iter = 1000,
  details = 0,
  ...
)

Arguments

Details

ggmfit is based on a C implementation. ggmfitr is implemented purely in R (and is provided mainly as a benchmark for the C-version).

Value

A list with

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

See Also

cmod, loglin

Examples

## Fitting "butterfly model" to mathmark data
## Notice that the output from the two fitting functions is not
## entirely identical.
data(math)
glist <- list(c("al", "st", "an"), c("me", "ve", "al"))
d <- cov.wt(math, method="ML")
ggmfit (d$cov, d$n.obs, glist)

Discrete interaction model (log-linear model)

Description

Specification of log–linear (graphical) model. The 'd' in the name dmod refers to that it is a (graphical) model for 'd'iscrete variables

Usage

dmod(
  formula,
  data,
  marginal = NULL,
  interactions = NULL,
  fit = TRUE,
  details = 0,
  ...
)

Arguments

Details

The independence model can be specified as ~.^1 and ~.^. specifies the saturated model. Setting e.g. interactions=3 implies that there will be at most three factor interactions in the model.

Data can be specified as a table of counts or as a dataframe. If data is a dataframe then it will be converted to a table (using xtabs()). This means that if the dataframe contains numeric values then the you can get a very sparse and high dimensional table. When a dataframe contains numeric values it may be worthwhile to discretize data using the cut() function.

The marginal argument can be used for specifying the independence or saturated models for only a subset of the variables. When marginal is given the corresponding marginal table of data is formed and used in the analysis (notice that this is different from the behaviour of loglin() which uses the full table.

The triangulate() method for discrete models (dModel objects) will for a model look at the dependence graph for the model.

Value

An object of class dModel.

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

See Also

cmod, mmod

Examples

 
## Graphical log-linear model
data(reinis)
dm1 <- dmod(~ .^., reinis)
dm2 <- backward(dm1, k=2)
dm3 <- backward(dm1, k=2, fixin=list(c("family", "phys", "systol")))
## At most 3-factor interactions
dm1<-dmod(~ .^., data=reinis, interactions=3)

General functions related to iModels

Description

General functions related to iModels

Usage

## S3 method for class 'iModel'
logLik(object, ...)

## S3 method for class 'iModel'
extractAIC(fit, scale, k = 2, ...)

## S3 method for class 'iModel'
summary(object, ...)

## S3 method for class 'iModelsummary'
print(x, ...)

## S3 method for class 'iModel'
formula(x, ...)

## S3 method for class 'iModel'
terms(x, ...)

## S3 method for class 'dModel'
isGraphical(x)

## S3 method for class 'dModel'
isDecomposable(x)

modelProperties(object)

## S3 method for class 'dModel'
modelProperties(object)

Arguments

Get information about mixed interaction model objects

Description

General functions related to iModels

Usage

getmi(object, name)

Arguments

Mixed interaction model.

Description

A mixed interaction model is a model (often with conditional independence restrictions) for a combination of discrete and continuous variables.

Usage

mmod(formula, data, marginal = NULL, fit = TRUE, details = 0)

Arguments

Value

An object of class mModel and the more general class iModel.

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

See Also

dmod, cmod.

Examples

### FIXME: To be written

Impose zeros in matrix entries which do not correspond to an edge.

Description

Impose zeros in matrix entries which do not correspond to an edge.

Usage

impose_zero(emat, K)

Arguments

Internal functions for the gRim package

Description

Internal functions for the gRim package

Return the dimension of a log-linear model

Description

Return the dimension of a log-linear model given by the generating class 'glist'. If the model is decomposable and adjusted dimension can be found.

Usage

dim_loglin(glist, tableinfo)

dim_loglin_decomp(glist, tableinfo, adjust = TRUE)

Arguments

Details

glist can be either a list of vectors with variable names or a list of vectors of variable indices.

tableinfo can be one of three different things.

1. A contingency table (a table).

2. A list with the names of the variables and their levels (such as one would get if calling dimnames on a table).

3. A vector with the levels. If glist is a list of vectors with variable names, then the entries of the vector tableinfo must be named.

If the model is decomposable it dim_loglin_decomp is to be preferred over dim_loglin as the former is much faster.

Setting adjust=TRUE will force dim_loglin_decomp to calculated a dimension which is adjusted for sparsity of data. For this to work, tableinfo MUST be a table.

Value

A numeric.

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

See Also

dmod, glm, loglm

Examples

## glist contains variable names and tableinfo is a named vector:
dim_loglin(list(c("a", "b"), c("b", "c")), c(a=4, b=7, c=6))

## glist contains variable names and tableinfo is not named:
dim_loglin(list(c(1, 2), c(2, 3)), c(4, 7, 6))

## For decomposable models:
dim_loglin_decomp(list(c("a", "b"), c("b", "c")), c(a=4, b=7, c=6),adjust=FALSE)

Fitting Log-Linear Models by Message Passing

Description

Fit log-linear models to multidimensional contingency tables by Iterative Proportional Fitting.

Usage

effloglin(table, margin, fit = FALSE, eps = 0.01, iter = 20, print = TRUE)

Arguments

Details

The function differs from loglin in that 1) data can be given in the form of a list of sufficient marginals and 2) the model is fitted only on the cliques of the triangulated interaction graph of the model. This means that the full table is not fitted, which means that effloglin is efficient (in terms of storage requirements). However effloglin is implemented entirely in R and is therefore slower than loglin. Argument names are chosen so as to match those of loglin()

Value

A list.

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

References

Radim Jirousek and Stanislav Preucil (1995). On the effective implementation of the iterative proportional fitting procedure. Computational Statistics & Data Analysis Volume 19, Issue 2, February 1995, Pages 177-189

See Also

loglin

Examples

data(reinis)
glist <-list(c("smoke", "mental"), c("mental", "phys"),
             c("phys", "systol"), c("systol", "smoke"))

stab <- lapply(glist, function(gg) tabMarg(reinis, gg))
fv3 <- effloglin(stab, glist, print=FALSE)

Modify generating class for a graphical/hierarchical model

Description

Modify generating class for a graphical/hierarchical model by 1) adding edges, 2) deleting edges, 3) adding terms and 4) deleting terms.

Usage

modify_glist(glist, items, details = 0)

Arguments

Details

The items is a list with named entries as list(add.edge=, drop.edge=, add.term=, drop.term=)

Not all entries need to be in the list. The corresponding actions are carried out in the order in which they appear in the list.

See section 'examples' below for examples.

Notice that the operations do not in general commute: Adding an edge which is already in a generating class and then removing the edge again does not give the original generating class.

Value

A generating class for the modified model. The elements of the list are character vectors.

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

See Also

cmod, dmod, mmod

Examples

glist <- list(c(1, 2, 3), c(2, 3, 4))

## Add edges
modify_glist(glist, items=list(add.edge=c(1, 4)))
modify_glist(glist, items=list(add.edge=~1:4))

## Add terms
modify_glist(glist, items=list(add.term=c(1, 4)))
modify_glist(glist, items=list(add.term=~1:4))

## Notice: Only the first term is added as the second is already 
## in the model.
modify_glist(glist, items=list(add.term=list(c(1, 4), c(1, 3))))
modify_glist(glist, items=list(add.term=~1:4 + 1:3))

## Notice: Operations are carried out in the order given in the
## items list and hence we get different results: 
modify_glist(glist, items=list(drop.edge=c(1, 4), add.edge=c(1, 4)))
modify_glist(glist, items=list(add.edge=c(1, 4), drop.edge=c(1, 4)))

Conversion between different parametrizations of mixed models

Description

Functions to convert between canonical parametrization (g,h,K), moment parametrization (p,m,S) and mixed parametrization (p,h,K).

Usage

parm_pms2ghk(parms)

parm_ghk2pms(parms)

parm_pms2phk(parms)

parm_phk2ghk(parms)

parm_phk2pms(parms)

parm_ghk2phk(parms)

parm_CGstats2mmod(parms, type = "ghk")

parm_moment2pms(SS)

Arguments

Value

Parameters of a mixed interaction model.

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

Parse graphical model formula

Description

Parse graphical model formula to internal representation

Usage

parse_gm_formula(
  formula,
  varnames = NULL,
  marginal = NULL,
  interactions = NULL,
  maximal_only = FALSE
)

Arguments

Examples

vn <- c("me", "ve", "al", "an", "st")

form1 <- ~me:ve:al + ve:al + an
form2 <- ~me:ve:al + ve:al + s
form3 <- ~me:ve:al + ve:al + anaba
parse_gm_formula(form1, varnames=vn)
parse_gm_formula(form2, varnames=vn)
## parse_gm_formula(form3, varnames=vn)
parse_gm_formula(form1)
parse_gm_formula(form2)
parse_gm_formula(form3)

## parse_gm_formula(~.^1)
## parse_gm_formula(~.^.)

parse_gm_formula(~.^1, varnames=vn)
parse_gm_formula(~.^., varnames=vn)
parse_gm_formula(~.^., varnames=vn, interactions=3)

vn2 <- vn[1:3]
## parse_gm_formula(form1, varnames=vn, marginal=vn2)
## parse_gm_formula(form2, varnames=vn, marginal=vn2)
## parse_gm_formula(form3, varnames=vn, marginal=vn2)
parse_gm_formula(~.^1, varnames=vn, marginal=vn2)
parse_gm_formula(~.^., varnames=vn, marginal=vn2)

Stepwise model selection in (graphical) interaction models

Description

Stepwise model selection in (graphical) interaction models

Usage

drop_func(criterion)

## S3 method for class 'iModel'
stepwise(
  object,
  criterion = "aic",
  alpha = NULL,
  type = "decomposable",
  search = "all",
  steps = 1000,
  k = 2,
  direction = "backward",
  fixin = NULL,
  fixout = NULL,
  details = 0,
  trace = 2,
  ...
)

backward(
  object,
  criterion = "aic",
  alpha = NULL,
  type = "decomposable",
  search = "all",
  steps = 1000,
  k = 2,
  fixin = NULL,
  details = 1,
  trace = 2,
  ...
)

forward(
  object,
  criterion = "aic",
  alpha = NULL,
  type = "decomposable",
  search = "all",
  steps = 1000,
  k = 2,
  fixout = NULL,
  details = 1,
  trace = 2,
  ...
)

Arguments

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

See Also

cmod, dmod, mmod, testInEdges, testOutEdges

Examples

data(reinis)
## The saturated model
m1 <- dmod(~.^., data=reinis)
m2 <- stepwise(m1)
m2

Test edges in graphical models with p-value/AIC value

Description

Test edges in graphical models with p-value/AIC value. The models must be iModels.

Usage

testEdges(
  object,
  edgeMAT = NULL,
  ingraph = TRUE,
  criterion = "aic",
  k = 2,
  alpha = NULL,
  headlong = FALSE,
  details = 1,
  ...
)

testInEdges(
  object,
  edgeMAT = NULL,
  criterion = "aic",
  k = 2,
  alpha = NULL,
  headlong = FALSE,
  details = 1,
  ...
)

testOutEdges(
  object,
  edgeMAT = NULL,
  criterion = "aic",
  k = 2,
  alpha = NULL,
  headlong = FALSE,
  details = 1,
  ...
)

Arguments

Details

• testIn: Function which tests whether each edge in "edgeList" can be delete from model "object"

• testOut: Is similar but in the other direction.

Value

A dataframe with test statistics (p-value or change in AIC), edges and logical telling if the edge can be deleted.

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

See Also

getEdges, testadd, testdelete

Examples

data(math)
cm1 <- cmod(~me:ve + ve:al + al:an, data=math)
testEdges(cm1, ingraph=TRUE)
testEdges(cm1, ingraph=FALSE)
## Same as
# testInEdges(cm1)
# testOutEdges(cm) 

Test addition of edge to graphical model

Description

Performs a test of addition of an edge to a graphical model (an iModel object).

Usage

testadd(object, edge, k = 2, details = 1, ...)

Arguments

Details

Let M0 be the model and e=(u,v) be an edge and let M1 be the model obtained by adding e to M0. If M1 is decomposable AND e is contained in one clique C only of M1 then the test is carried out in the C-marginal model. In this case, and if the model is a log-linear model then the degrees of freedom is adjusted for sparsity.

Value

A list

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

See Also

testdelete

Examples

## Discrete models
data(reinis)

## A decomposable model
mf <- ~smoke:phys:mental + smoke:systol:mental
object <- dmod(mf, data=reinis)
testadd(object, c("systol", "phys"))

## A non-decomposable model
mf <- ~smoke:phys + phys:mental + smoke:systol + systol:mental
object <- dmod(mf, data=reinis)
testadd(object, c("phys", "systol"))

## Continuous models
data(math)

## A decomposable model
mf <- ~me:ve:al + al:an
object <- cmod(mf, data=math)
testadd(object, c("me", "an"))

## A non-decomposable model
mf <- ~me:ve + ve:al + al:an + an:me
object <- cmod(mf, data=math)
testadd(object, c("me", "al"))

Test deletion of edge from an interaction model

Description

Tests if an edge can be deleted from an interaction model.

Usage

testdelete(object, edge, k = 2, details = 1, ...)

Arguments

Details

If the model is decomposable and the edge is contained in one clique only then the test is made in the marginal model given by that clique. In that case, if the model is a log-linear model then degrees of freedom are adjusted for sparsity

If model is decomposable and edge is in one clique only, then degrees of freedom are adjusted for sparsity

Value

A list.

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

See Also

testadd

Examples

## Discrete models
data(reinis)

## A decomposable model
mf <- ~smoke:phys:mental + smoke:systol:mental
object <- dmod(mf, data=reinis)
testdelete(object, c("phys", "mental"))
testdelete(object, c("smoke", "mental"))

## A non-decomposable model
mf <- ~smoke:phys + phys:mental + smoke:systol + systol:mental
object <- dmod(mf, data=reinis)

testdelete(object, c("phys", "mental"))

## Continuous models
data(math)

## A decomposable model
mf <- ~me:ve:al + me:al:an
object <- cmod(mf, data=math)
testdelete(object, c("ve", "al"))
testdelete(object, c("me", "al"))

## A non-decomposable model
mf <- ~me:ve + ve:al + al:an + an:me
object <- cmod(mf, data=math)
testdelete(object, c("me", "ve"))

Utilities for gRips

Description

Utilities for gRips

Usage

## S3 method for class 'gips_fit_class'
logLik(object, ...)

## S3 method for class 'gips_fit_class'
AIC(object, ..., k = 2)

## S3 method for class 'gips_fit_class'
BIC(object, ...)

## S3 method for class 'gips_fit_class'
sigma(object, ...)

concentration(object, ...)

## S3 method for class 'gips_fit_class'
concentration(object, ...)

## S3 method for class 'gips_fit_class'
print(x, ...)

## S3 method for class 'gips_fit_class'
summary(object, ...)

glance.gips_fit_class(x, ...)

Arguments