Add or drop colour classes to RCOX models

Description

Make a test for adding/dropping all colour classes in scope for an RCOX model.

Usage

## S3 method for class 'rcox'
add1(object, scope, details = 0, trace = 0, ...)

## S3 method for class 'rcox'
drop1(object, scope, details = 0, trace = 0, stat = "wald", ...)

Arguments

Value

A list with entries * tab: A dataframe with the test results * cc: A list of colour classes

Note

* Note that the keyword 'stat' is not available for add1 because this function expands the current model and hence the Wald statistic is not available.

* Based on fitting a new model for each new ecc, and may hence be slow.

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

See Also

comparecc, stepadd1, stepdrop1.

Examples

data(math)
gc.sat <- ~me:ve:al:st:an
gc.1   <- ~me+ve+al+st+an

m.sat <- rcox(gm=gc.sat, data=math)
m.1   <- rcox(gm=gc.1,   data=math)

t.sat <- drop1(m.sat)
t.sat$tab
t.sat$cc

t.1   <- add1(m.1)
t.1$tab
t.1$cc

Calculate trace of various matrix products.

Description

Calculate trace of various matrix products.

Usage

trA(A)

trAW(rA, rW)

trAWB(rA, rW, rB)

trAWBW(rA, rW, rB)

trAWBV(rA, rW, rB, rV)

trAWBlist(Alist, W, Blist, mode = 0L)

trAWBWlist(Alist, W, Blist, mode = 0L)

Arguments

Value

A number

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

Examples

## Turn list into "sparse" matrix
to_sp <- function(x){
  ans <- do.call("rbind", x)
  storage.mode(ans)<-"double"
  return(ans)
}

## Turn "sparse" matrix into dense matrix
##
to_de <- function(A,d){
  if (nrow(A) < 1) stop("need non-empty matrix\n")
  ans <- matrix(0,nr=d,nc=d)
  for (i in 1:nrow(A)){
    e <- A[i,]
    if (length(e) == 1){
      ans[e,e] <- 1
    } else { 
      ans[e[1],e[2]] <-   ans[e[2],e[1]] <- 1 
    }
  }  
  return(ans)
}

d <- 5
W <- matrix(rnorm(d * d), nr=d, nc=d);
V <- matrix(rnorm(d * d), nr=d, nc=d); 
W <- W + t(W)
V <- V + t(V)


A1.lst <- list(c(1,2),c(1,3))
A2.lst <- list(1,3,5)

A1.sp <- to_sp(A1.lst)
A2.sp <- to_sp(A2.lst)

A1.de <- to_de(A1.sp, d)
A2.de <- to_de(A2.sp, d)

trAW(A1.sp, W)
sum(diag(A1.de %*% W))

trAW(A2.sp, W)
sum(diag(A2.de %*% W))

trAWB(A1.sp, W, A2.sp)
trAWB(A2.sp, W, A1.sp)
sum(diag(A1.de %*% W %*% A2.de))

trAWBW(A1.sp, W, A2.sp)
trAWBW(A2.sp, W, A1.sp)
sum(diag(A1.de %*% W %*% A2.de %*% W))

trAWBV(A1.sp, W, A2.sp, V)
trAWBV(A2.sp, W, A1.sp, V)
sum(diag(A1.de %*% W %*% A2.de %*% V))

Coerce parameters in RCOX models.

Description

Coerce parameters in RCOX models. These functions should not be called directly by the user.

Usage

theta2K(object, theta, scale = "original")

K2theta(object, K, scale = "original")

## S3 method for class 'rcon'
theta2K(object, theta, scale = "original")

## S3 method for class 'rcor'
theta2K(object, theta, scale = "original")

## S3 method for class 'rcon'
K2theta(object, K, scale = "original")

## S3 method for class 'rcor'
K2theta(object, K, scale = "original")

Arguments

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

Compare colour classes of an RCOX model

Description

A general function for pairwise comparisons of colour classes in an RCOX model, i.e. for testing whether the corresponding parameters are significantly different

Usage

comparecc(
  object,
  cc1 = NULL,
  cc2 = NULL,
  type = "ecc",
  stat = "wald",
  details = 1
)

Arguments

Details

All colour classes specified in cc1 are compared with all those given in cc2 (duplicate entries are not compared). If cc2=NULL (the default) then all colour classes specified in cc1 are compared with all colour classes in the model except those specified in cc1. If cc1=NULL (the default) and cc2=NULL then all pairwise comparisons are made.

Value

A list with entries:

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

See Also

add1.rcox, drop1.rcox, stepadd1, stepdrop1, join1, split1, stepjoin1, stepsplit1

Examples

data (math)

gm  = ~al:an:st
vcc = list(~me+st, ~ve+an, ~al)
ecc = list(~me:ve+me:al, ~ve:al+al:st)

m1 <- rcox(gm=gm, vcc=vcc, ecc=ecc, data=math)
m1

comparecc(m1, type="vcc")
comparecc(m1, type="ecc")

Functions used in connection with fitting of RCOX models

Description

This is an overview over core functions used in connection with fitting of RCOX models. The functions described here will typically not be directly called by the user.

Arguments

Value

A list with fitted values (K, logL etc).

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

See Also

fit, rcox

Examples

gm  = ~al:an:st
vcc = list(~me+st, ~ve+an, ~al)
ecc = list(~me:ve+me:al, ~ve:al+al:st)
data(math)

m1 <- rcox(gm=gm, vcc=vcc, ecc=ecc, data=math, fit=FALSE)
f1 <- matching(m1)

## Use f1$K as starting value
scoring(m1, K0=f1$K)
ipm(m1, K0=f1$K)

Fit rcox model

Description

This is a general function for fitting RCOX models (i.e.\ RCON and RCOR models) using different estimation algorithms.

Usage

## S3 method for class 'rcox'
fit(
  object,
  Kstart = object$Kstart,
  method = object$method,
  control = object$control,
  details = object$details,
  trace = object$trace,
  returnModel = TRUE,
  ...
)

matching(object, control = object$control, trace = object$trace)

ipm(object, K0, control = object$control, trace = object$trace)

scoring(
  object,
  K0,
  control = object$control,
  maxit = control$maxouter,
  trace = object$trace
)

Arguments

Details

The fitted parameters etc. can be extracted using 'fitInfo(m)'. The control argument is a list with named entries. Most important are the entries 'maxouter' and 'maxinner' (which both defaults to 25) for controlling the estimation algorithms. For other components please refer to the code.

Value

An RCOX model object.

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

See Also

rcox, update.rcox

Examples

data(math)
gm  = ~al:an:st
vcc = list(~me + st, ~ve + an, ~al)
ecc = list(~me:ve + me:al, ~ve:al + al:st)

m1 <- rcox(gm=gm, vcc=vcc, ecc=ecc, data=math, fit=FALSE)

fit(m1, method="matching")
fit(m1, method="scoring")
fit(m1, method="ipm")

Generating class for RCON / RCOR models

Description

Implementation of generating classes for RCOX models. These functions are not intended to be called by the user.

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

Get slots from RCOX model object.

Description

Get slots from RCOX model object.

Usage

getSlot(object, slot)

dimension(object)

logL(object)

getSlot(object, slot)

dataRep(object, slot = NULL)

intRep(object, slot = NULL)

fitInfo(object, slot = NULL)

getcc(object, type)

getecc(object)

getvcc(object)

getedges(object, complement = FALSE)

Arguments

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

Examples

data(math)
gm  = ~al:an:st
vcc = list(~me+st, ~ve+an, ~al)
ecc = list(~me:ve+me:al, ~ve:al+al:st)

m1 <- rcox(gm=gm, vcc=vcc, ecc=ecc, data=math)
getecc(m1)

getSlot(m1,"type")
fitInfo(m1)
fitInfo(m1,"K")

The package ‘gRc’: summary information

Description

This package is for statistical inference in RCOX models. That is, graphical Gaussian models where specific entries of the inverse covariance matrix or partial correlation matrix have been restricted to being equal. Entries which are restricted to being identical are displayed with identical colours in the independence graph. Hence the name of the package gRc: The "c" stands for colours.

Details

#' @author Søren Højsgaard, sorenh@math.aau.dk

Details

The function for specifying RCOX models is rcox, and we refer to the help page for that function for examples.

See Also

rcox

Internal functions for the gRc package

Description

These functions should not be called directly by the user.

Author(s)

Søren Højsgaard, sorenh@agrsci.dk

Joining and splitting of colour classes in RCOX models

Description

Test for joining of two colour classes (of a specific type) by testing if their corresponding parameters are not significantly different. Split a colour class and test how much this changes the fit of the model.

Arguments

Value

A list with entries:

Note

Note that the keyword 'stat' is not available for split1 because this function expands the current and hence the Wald statistic is not available. Note also that join1 is simply a wrapper for comparecc applied to edge colour classes.

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

See Also

rcox, update, comparecc

Examples

data(math)
g1     <- ~me:ve:al+al:st:an
m1     <- rcox(gm=g1, data=math)
join1(m1)

gm  = ~al:an:st
vcc = list(~me+st, ~ve+an)
ecc = list(~me:ve+me:al, ~ve:al+al:st)
m2 <- rcox(gm=gm, vcc=vcc, ecc=ecc, data=math, type="rcon")
split1(m2)

Plot rcox object

Description

Plot rcox object

Usage

## S3 method for class 'rcox'
plot(x, y, ...)

Arguments

Examples

gm  = ~al:an:st
vcc = list(~me+st, ~ve+an, ~al)
ecc = list(~me:ve+me:al, ~ve:al+al:st)
m1 <- rcox(gm=gm, vcc=vcc, ecc=ecc, data=math, method='matching')
plot(m1)

Main function for specifying RCON/RCOR models.

Description

This is the main function for specifying and fitting RCON/RCOR models in the package along with certain utility functions.

Usage

rcox(
  gm = NULL,
  vcc = NULL,
  ecc = NULL,
  type = c("rcon", "rcor"),
  method = "ipm",
  fit = TRUE,
  data = NULL,
  S = NULL,
  n = NULL,
  Kstart = NULL,
  control = list(),
  details = 1,
  trace = 0
)

Arguments

Details

Estimation methods:

* 'ipm' (default) is iterative partial maximization which when finished calculates the information matrix so that approximate variances of the parameters can be obtained using vcov().

* 'ipms' is iterative partial maximization without calculating the information matrix. This is the fastest method.

* 'scoring' is stabilised Fisher scoring.

* 'matching' is score matching followed by one step with Fisher scoring.

* 'hybrid1' is for internal use and should not be called directly

Value

A model object of type 'RCOX'.

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

Examples

data(math)
gm  = ~al:an:st
vcc = list(~me+st, ~ve+an, ~al)
ecc = list(~me:ve+me:al, ~ve:al+al:st)

m1 <- rcox(gm=gm, vcc=vcc, ecc=ecc, data=math, method='matching')
m2 <- rcox(gm=gm, vcc=vcc, ecc=ecc, data=math, method='scoring')
m3 <- rcox(gm=gm, vcc=vcc, ecc=ecc, data=math, method='ipm')

m1
m2
m3

summary(m1)
summary(m2)
summary(m3)

coef(m1)
coef(m2)
coef(m3)

vcov(m1)
vcov(m2)
vcov(m3)

Get score and information for RCOX models.

Description

Get score and information for RCOX models.

Usage

getScore(m, K, scale = "original")

## S3 method for class 'rcon'
getScore(m, K, scale = "original")

## S3 method for class 'rcor'
getScore(m, K, scale = "original")

Arguments

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

Stepwise model selection in RCOX models

Description

These allow for stepwise model selection in RCOX models by. Model expansion (i.e. forward selection) is obtained by adding edge colour classes and by splitting edge/vertex colour classes. Model reduction (i.e. backward selection) is obtained by dropping edge colour classes and by joining edge/vertex colour classes.

Arguments

Value

Either NULL or a new RCOX model.

Note

Note that the keyword 'stat' is not available for stepadd1 and stepsplit1 because these functions expand the current model and hence the Wald statistic is not available.

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

See Also

split1 join1 add1.rcox drop1.rcox comparecc

For printing in lisp style

Description

For printing in lisp style

Usage

toLisp(v)

Arguments

Update an RCOX model

Description

update will update and (by default) re-fit an RCOX model. It does this by extracting the call stored in the object, updating the call and (by default) evaluating that call. Sometimes it is useful to call update with only one argument, for example if the data frame has been corrected

Arguments

Value

A new model object of class 'rcox'.

Warning

Only one of the arguments pertaining to edge colour classes (i.e. ecc, splitecc, joinecc, dropecc, addecc) should be applied at the time. Likewise for the arguments pertaining to the vertex colour classes.

The result will otherwise be highly unpredictable and is likely to cause an error.

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

See Also

rcox

Examples

data(math)
gm  = ~al:an:st
vcc = list(~me+st, ~ve+an, ~al)
ecc = list(~me:ve+me:al, ~ve:al+al:st)

m1 <- rcox(gm=gm, vcc=vcc, ecc=ecc, data=math, method='matching', trace=0)

update(m1, joinvcc=list(~me+st, ~ve+an))
update(m1, joinecc=list(~al:an, ~an:st))

update(m1, splitvcc=~ve+an)
update(m1, splitecc=~me:ve+me:al)


update(m1, dropecc=list(~me:st+st:an,~al:an,~st:al))
update(m1, addecc=list(~an:me+st:ve))

Conversions of the type xxx2yyy

Description

Conversions of the type xxx2yyy.

Author(s)

Søren Højsgaard, sorenh@math.aau.dk