Package 'micd'

Bootstrap Resampling for the PC-MI- and the FCI-MI-algorithm

Description

Generate R bootstrap replicates for the PC or FCI algorithm for data with missing values.

Usage

boot.graph(
  data,
  select = NULL,
  method = c("pcMI", "fciMI"),
  method.mice = NULL,
  args,
  R,
  m = 10,
  args.residuals = NULL,
  seed = NA,
  quickpred = FALSE,
  ...
)

Arguments

data	Data.frame with missing values
select	Variable of integers, indicating columns to select from a data frame; only continuous variables can be included in the model selection
method	Character string specifying the algorithm for causal discovery from the package 'pcalg'.
method.mice	Character string specifying imputation method; see mice::mice() for more information.
args	Arguments passed to method. NOTE: argument labels is set internally and should not be used!
R	A positive integer number of bootstrap replications.
m	Number of chains included in mice()'.
args.residuals	(Optional) list containing vertices and confounders. May be specified when residuals for vertices should be calculated in each bootstrap data set. See makeResiduals() for more information
seed	A positive integer that is used as argument for set.seed().
quickpred	If true, mice uses quickpred to select predictors.
...	Further arguments passed to the imputation function mice().

Value

List of objects of class pcalgo (see pcalg::pcAlgo) or of fcmialgo (see pcalg::fciAlgo).

Examples

data(windspeed)
daten <- mice::ampute(windspeed)$amp


bgraph <- boot.graph(data = daten,
                     method = "pcMI",
                     args = "solve.confl = TRUE, alpha = 0.05",
                     R = 5)

---

G square Test for (Conditional) Independence between Discrete Variables with Missings

Description

A wrapper for pcalg::disCItest, to be used within pcalg::skeleton, pcalg::pc or pcalg::fci when the data contain missing values. Observations where at least one of the variables involved in the test is missing are deleted prior to performing the test (test-wise deletion).

Usage

disCItwd(x, y, S = NULL, suffStat)

Arguments

x, y, S	(Integer) position of variable X, Y and set of variables S, respectively, in suffStat. It is tested whether X and Y are conditionally independent given the subset S of the remaining variables.
suffStat	A list with three elements, "dm", "nlev", "adaptDF"; each corresponding to the above arguments. Can be obtained from a data.frame of factor variables using the suffStat function (see example section)

Details

See disCItest for details on the G square test. Test-wise deletion is valid if missingness does not jointly depend on X and Y.

Value

A p-value.

See Also

pcalg::disCItest for complete data, disMItest for multiply imputed data

Examples

## load data (200 observations)
data(gmD)
dat <- gmD$x[1:1000,]

## delete some observations of X2 and X3
set.seed(123)
dat[sample(1:1000, 50), 2] <- NA
dat[sample(1:1000, 50), 3] <- NA

## analyse incomplete data
# test-wise deletion ==========
sufftwd <- getSuff(dat, test = "disCItwd")
disCItwd(1, 3, NULL, suffStat = sufftwd)

# list-wise deletion ==========
dat2 <- dat[complete.cases(dat), ]
suffStat2 <- getSuff(dat2, test = "disCItest", adaptDF = FALSE)
disCItest(1, 3, NULL, suffStat = suffStat2)

## use disCItwd within pcalg::pc ==========
pc.fit <- pc(suffStat = sufftwd, indepTest = disCItwd, alpha = 0.1, p = 5)
pc.fit

if (requireNamespace("Rgraphviz", quietly = TRUE))
plot(pc.fit)

---

G square Test for (Conditional) Independence between Discrete Variables after Multiple Imputation

Description

A modified version of pcalg::disCItest, to be used within pcalg::skeleton, pcalg::pc or pcalg::fci when multiply imputed data sets are available. Note that in contrast to pcalg::disCItest, the variables must here be coded as factors.

Usage

disMItest(x, y, S = NULL, suffStat)

Arguments

x, y, S	(Integer) position of variable X, Y and set of variables S, respectively, in suffStat. It is tested whether X and Y are conditionally independent given the subset S of the remaining variables.
suffStat	A list of data.frames containing the multiply imputed data sets. Usually obtained from a mice::mids object using mice::complete with argument action="all". All variables must be coded as factors. NO warning is issued if the variables are not coded as factors!

Details

See pcalg::disCItest for details on the G square test. disMItest applies this test to each data.frame in suffStat, then combines the results using the rules in Meng & Rubin (1992). Degrees of freedom are never adapted, and there is no minimum required sample size, while pcalg::disCItest requires 10*df observations and otherwise returns a p-value of 1.

Value

A p-value.

Author(s)

Janine Witte

References

Meng X.-L., Rubin D.B. (1992): Performing likelihood ratio tests with multiply imputed data sets. Biometrika 79(1):103-111.

See Also

pcalg::disCItest for complete data, disCItwd for test-wise deletion

Examples

## load data (200 observations) and factorise
data(gmD)
dat <- gmD$x[1:1000, ]
dat[] <- lapply(dat, as.factor)

## delete some observations of X2 and X3
set.seed(123)
dat[sample(1:1000, 40), 2] <- NA
dat[sample(1:1000, 40), 3] <- NA

## impute missing values under model with two-way interactions
form <- make.formulas.saturated(dat, d = 2)
imp <- mice::mice(dat, formulas = form, printFlag = FALSE)
imp <- mice::complete(imp, action = "all")

## analyse imputed data
disMItest(1, 3, NULL, suffStat = imp)

## use disMItest within pcalg::pc
pc.fit <- pc(suffStat = imp, indepTest = disMItest, alpha = 0.01, p = 5)
pc.fit

if(require("Rgraphviz", character.only = TRUE, quietly = TRUE)){
plot(pc.fit)
}

---

Estimate a PAG by the FCI-MI Algorithm for Multiple Imputed Data Sets of Continuous Data

Description

This function is a modification of pcalg::fci() to be used for multiple imputation.

Usage

fciMI(
  data,
  alpha,
  labels,
  p,
  skel.method = c("stable", "original"),
  type = c("normal", "anytime", "adaptive"),
  fixedGaps = NULL,
  fixedEdges = NULL,
  NAdelete = TRUE,
  m.max = Inf,
  pdsep.max = Inf,
  rules = rep(TRUE, 10),
  doPdsep = TRUE,
  biCC = FALSE,
  conservative = FALSE,
  maj.rule = FALSE,
  verbose = FALSE
)

Arguments

data	An object of type mids, which stands for 'multiply imputed data set', typically created by a call to function mice()
alpha	Significance level (number in (0,1) for the conditional independence tests
labels	(Optional) character vector of variable (or "node") names. Typically preferred to specifying p.
p	(Optional) number of variables (or nodes). May be specified if labels are not, in which case labels is set to 1:p.
skel.method	Character string specifying method; the default, "stable" provides an order-independent skeleton, see pcalg::skeleton() for details.
type	Character string specifying the version of the FCI algorithm to be used. See pcalg::fci() for details.
fixedGaps	See pcalg::fci() for details.
fixedEdges	See pcalg::fci() for details.
NAdelete	See pcalg::fci() for details.
m.max	Maximum size of the conditioning sets that are considered in the conditional independence tests.
pdsep.max	See pcalg::fci() for details.
rules	Logical vector of length 10 indicating which rules should be used when directing edges. The order of the rules is taken from Zhang (2008).
doPdsep	See pcalg::fci() for details.
biCC	See pcalg::fci() for details.
conservative	See pcalg::fci() for details.
maj.rule	See pcalg::fci() for details.
verbose	If true, more detailed output is provided.

Value

See pcalg::fci() for details.

Author(s)

Original code by Diego Colombo, Markus Kalisch, and Joris Mooij. Modifications by Ronja Foraita.

Examples

daten <- windspeed[,1]
for(i in 2:ncol(windspeed)) daten <- c(daten, windspeed[,i])
daten[sample(1:length(daten), 260)] <- NA
daten <- matrix(daten, ncol = 6)

## Impute missing values
imp <- mice(daten, printFlag = FALSE)
fc.res <- fciMI(data = imp, label = colnames(imp$data), alpha = 0.01)

if (requireNamespace("Rgraphviz", quietly = TRUE))
plot(fc.res)

---

Wrapper for gaussCItest, disCItest and mixCItest

Description

A plug-in conditional independence test for pcalg::skeleton(), pcalg::pc() or pcalg::fci() when multiply imputed data sets are available. flexCItest() detects whether variables are continuous, discrete or mixed, and automatically switches between gaussCItest() (continuous only), disCItest() (discrete only) and mixCItest() (mixed variables).

Usage

flexCItest(x, y, S = NULL, suffStat)

Arguments

x, y, S	(integer) position of variable X, Y and set of variables S, respectively, in the dataset. It is tested whether X and Y are conditionally independent given the subset S of the remaining variables.
suffStat	a list generated using getSuff() with test="flexMItest". See below for details.

Details

suffStat needs to be a list with four elements named datlist, corlist, conpos and dispos. datlist is the list of imputed datasets. corlist is a list with M+1 elements, where M is the number of imputed datasets. For i=1,...,M, the the i-th element of corlist is the correlation matrix of the continuous variables in the i-th imputed dataset; the (M+1)-the element is the number of rows in each imputed dataset. conpos is a vector containing the integer positions of the continuous variables in the original dataset. dispos is a vector containing the integer positions of the discrete variables in the original dataset.

Value

A p-value.

See Also

gaussCItest(), disCItest() and mixCItest().

Examples

# load data (numeric and factor variables)
dat <- toenail2[1:400, ]

# obtain correct input 'suffStat' for 'flexCItest'
suff <- getSuff(dat, test="flexCItest")

flexCItest(2,3,NULL, suffStat = suff)

---

Wrapper for gaussCItwd, disCItwd and mixCItwd

Description

A plug-in conditional independence test for pcalg::skeleton, pcalg::pc or pcalg::fci when the data contain missing values. Observations where at least one of the variables involved in the test is missing are deleted prior to performing the test (test-wise deletion). The function flexCItwd detects whether variables are continuous, discrete or mixed, and automatically switches between gaussCItwd (continuous only), link{disCItwd} (discrete only) and mixCItwd (mixed).

Usage

flexCItwd(x, y, S = NULL, data)

Arguments

x, y, S	(Integer) position of variable X, Y and set of variables S, respectively, in each correlation matrix in suffStat. It is tested whether X and Y are conditionally independent given the subset S of the remaining variables.
data	A data frame

Value

A p-value

Examples

## load data (numeric and factor variables)
dat <- toenail2[1:400, ]

## delete some observations
set.seed(123)
dat[sample(400, 20), 2] <- NA
dat[sample(400, 30), 4] <- NA

## obtain correct input 'suffStat' for 'flexMItest'
suff <- getSuff(imp, test="flexCItwd")

## analyse data
# continuous variables only
flexCItwd(4, 5, NULL, dat)

# discrete variables only
flexCItwd(2, 3, NULL, dat)

# mixed variables
flexCItwd(2, 3, 4, dat)

---

Wrapper for gaussMItest, disMItest and mixMItest

Description

A plug-in conditional independence test for pcalg::skeleton, pcalg::pc or pcalg::fci when multiply imputed data sets are available. flexMItest detects whether variables are continuous, discrete or mixed, and automatically switches between gaussMItest (continuous only), link{disMItest} (discrete only) and mixMItest (mixed).

Usage

flexMItest(x, y, S = NULL, suffStat)

Arguments

x, y, S	(integer) position of variable X, Y and set of variables S, respectively, in the dataset. It is tested whether X and Y are conditionally independent given the subset S of the remaining variables.
suffStat	a list generated using getSuff with test="flexMItest". See below for details.

Details

suffStat needs to be a list with four elements named datlist, corlist, conpos and dispos. datlist is the list of imputed datasets. corlist is a list with M+1 elements, where M is the number of imputed datasets. For i=1,...,M, the the i-th element of corlist is the correlation matrix of the continuous variables in the i-th imputed dataset; the (M+1)-the element is the number of rows in each imputed dataset. conpos is a vector containing the integer positions of the continuous variables in the original dataset. dispos is a vector containing the integer positions of the discrete variables in the original dataset.

Value

A p-value.

See Also

gaussMItest, disMItest and mixMItest

Examples

## load data (numeric and factor variables)
library(ranger)
dat <- toenail2[1:400, ]

## delete some observations
set.seed(123)
dat[sample(400, 20), 2] <- NA
dat[sample(400, 30), 4] <- NA

## impute missing values using random forests
imp <- mice::mice(dat, method = "rf", m = 3, printFlag = FALSE)

## obtain correct input 'suffStat' for 'flexMItest'
suff <- getSuff(imp, test="flexMItest")

## analyse data
# continuous variables only
flexMItest(4,5,NULL, suffStat = suff)
implist <- complete(imp, action="all")
gaussSuff <- c(lapply(implist, function(i){cor(i[ ,c(4,5)])}), n = 400)
gaussMItest(1,2,NULL, suffStat = gaussSuff)
flexCItwd(4, 5, NULL, dat)

# discrete variables only
flexMItest(2,3,NULL, suffStat = suff)
disMItest(2,3,NULL, suffStat = complete(imp, action="all"))
flexCItwd(2,3,NULL, dat)

# mixed variables
flexMItest(2,3,4, suffStat = suff)
mixMItest(2,3,4, suffStat = complete(imp, action="all"))
flexCItwd(2,3,4, dat)

---

Fisher's z-Test for (Conditional) Independence between Gaussian Variables with Missings

Description

A wrapper for pcalg::gaussCItest, to be used within pcalg::skeleton, pcalg::pc or pcalg::fci when the data contain missing values. Observations where at least one of the variables involved in the test is missing are deleted prior to performing the test (test-wise deletion).

Usage

gaussCItwd(x, y, S = NULL, suffStat)

Arguments

x, y, S	(integer) position of variable X, Y and set of variables S, respectively, in each correlation matrix in suffStat. It is tested whether X and Y are conditionally independent given the subset S of the remaining variables.
suffStat	data.frame containing the raw data.

Value

See pcalg::gaussCItest for details on Fisher's z-test. Test-wise deletion is valid if missingness does not jointly depend on X and Y.

A p-value.

See Also

pcalg::condIndFisherZ() for complete data, gaussCItestMI() for multiply imputed data

Examples

## load data (numeric variables)
dat <- as.matrix(windspeed)

## delete some observations
set.seed(123)
dat[sample(1:length(dat), 260)] <- NA

## analyse data
# complete data:
suffcomplete <- getSuff(windspeed, test="gaussCItest")
gaussCItest(1, 2, c(4,5), suffStat = suffcomplete)

# test-wise deletion: ==========
gaussCItwd(1, 2, c(4,5), suffStat = dat)

# list-wise deletion: ==========
sufflwd <- getSuff(dat[complete.cases(dat), ], test="gaussCItest")
gaussCItest(1, 2, c(4,5), suffStat = sufflwd)

## use gaussCItwd within pcalg::pc
pc.fit <- pc(suffStat = dat, indepTest = gaussCItwd, alpha = 0.01, p = 6)
pc.fit

---

Test Conditional Independence of Gaussians via Fisher's Z Using Multiple Imputations

Description

A modified version of pcalg::gaussCItest, to be used within pcalg::skeleton, pcalg::pc or pcalg::fci when multiply imputated data sets are available.

Usage

gaussMItest(x, y, S, suffStat)

gaussCItestMI(x, y, S = NULL, data)

Arguments

x, y, S	(Integer) position of variable X, Y and set of variables S, respectively, in the adjacency matrix. It is tested, whether X and Y are conditionally independent given the subset S of the remaining nodes.
suffStat	A list of length m+1, where m is the number of imputations; the first m elements are the covariance matrices of the m imputed data sets, the m-th element is the sample size. Can be obtained from a mids object by getSuff(mids, test="gaussMItest")
data	An object of type mids, which stands for 'multiply imputed data set', typically created by a call to function mice()

Details

gaussMItest is faster, as it uses pre-calculated covariance matrices.

Value

A p-value.

Examples

## load data (numeric variables)
dat <- as.matrix(windspeed)

## delete some observations
set.seed(123)
dat[sample(1:length(dat), 260)] <- NA

## Impute missing values under normal model
imp <- mice(dat, method = "norm", printFlag = FALSE)

## analyse data
# complete data:
suffcomplete <- getSuff(windspeed, test = "gaussCItest")
gaussCItest(1, 2, c(4,5), suffStat = suffcomplete)
# multiple imputation:
suffMI <- getSuff(imp, test = "gaussMItest")
gaussMItest(1, 2, c(4,5), suffStat = suffMI)
gaussCItestMI(1, 2, c(4,5), data = imp)
# test-wise deletion:
gaussCItwd(1, 2, c(4,5), suffStat = dat)
# list-wise deletion:
dat2 <- dat[complete.cases(dat), ]
sufflwd <- getSuff(dat2, test = "gaussCItest")
gaussCItest(1, 2, c(4,5), suffStat = sufflwd)

## use gaussMItest or gaussCItestMI within pcalg::pc
(pc.fit <- pc(suffStat = suffMI, indepTest = gaussMItest, alpha = 0.01, p = 6))
(pc.fit <- pc(suffStat = imp, indepTest = gaussCItestMI, alpha = 0.01, p = 6))

---

Obtain 'suffStat' for conditional independence testing

Description

A convenience function for transforming a multiply imputed data set into the 'suffStat' required by pcalg::gaussCItest(), pcalg::disCItest(), mixCItest(), flexCItest(), gaussMItest(), disMItest(), mixMItest() and flexMItest().

Usage

getSuff(
  X,
  test = c("gaussCItest", "gaussMItest", "disCItest", "disMItest", "disCItwd",
    "mixCItest", "mixMItest", "flexMItest", "flexCItest"),
  adaptDF = NULL,
  nlev = NULL
)

Arguments

X	For 'test=xxxCItest': a data.frame or matrix; for 'test=xxxMItest': an object of class mice::mids, or a list of data.frames containing the multiply imputed data sets.
test	one of gaussCItest(), gaussMItest(), disCItest(), disMItest(), mixCItest(), mixMItest(), flexCItest(), flexMItest().
adaptDF	for discrete variables: logical specifying if the degrees of freedom should be lowered by one for each zero count. The value for the degrees of freedom cannot go below 1.
nlev	(Optional) for discrete variables: vector with numbers of levels for each variable in the data.

Value

An R object that can be used as input to the specified conditional independence test:

Examples

# Example 1: continuous variables, no missing values =====================
data(windspeed)
dat1 <- as.matrix(windspeed)

## analyse data
gaussCItest(1, 2, NULL, suffStat = getSuff(windspeed, test = "gaussCItest"))
mixCItest(1, 2, NULL, suffStat = windspeed)

## Example 2: continuous variables, multiple imputation ===================
dat2 <- mice::ampute(windspeed)$amp

## delete some observations
set.seed(123)

## Impute missing values under normal model
imp2 <- mice(dat2, method = "norm", printFlag = FALSE)

## analyse imputed data
gaussMItest(1, 2, c(4,5), suffStat = getSuff(imp2, test="gaussMItest"))
mixMItest(1, 2, c(4,5), suffStat = getSuff(imp2, test="mixMItest"))
mixMItest(1, 2, c(4,5), suffStat = mice::complete(imp2, action="all"))
flexMItest(1, 2, c(4,5), suffStat = getSuff(imp2, test="flexMItest"))

## Example 3: discrete variables, multiple imputation =====================
## simulate factor variables
n <- 200
set.seed(789)
x <- factor(sample(0:2, n, TRUE)) # factor, 3 levels
y <- factor(sample(0:3, n, TRUE)) # factor, 4 levels
z <- factor(sample(0:1, n, TRUE)) # factor, 2 levels
dat3 <- data.frame(x,y,z)

## delete some observations of z
dat3[sample(1:n, 40), 3] <- NA

## impute missing values under saturated model
form <- make.formulas.saturated(dat3)
imp3 <- mice::mice(dat3, method = "logreg", formulas = form, printFlag = FALSE)

## analyse imputed data
disMItest(1, 3, 2, suffStat = getSuff(imp3, test="disMItest"))
disMItest(1, 3, 2, suffStat = mice::complete(imp3, action = "all"))
mixMItest(1, 3, 2, suffStat = getSuff(imp3, test="mixMItest"))
mixMItest(1, 3, 2, suffStat = mice::complete(imp3, action = "all"))
flexMItest(1, 3, 2, suffStat = getSuff(imp3, test="flexMItest"))

# Example 4: mixed variables, multiple imputation =========================
dat4 <- toenail2[1:400, ]
set.seed(123)
dat4[sample(400, 20), 2] <- NA
dat4[sample(400, 30), 4] <- NA

## impute missing values using random forests
imp4 <- mice(dat4, method="rf", m = 3, printFlag = FALSE)
mixMItest(2, 3, 5, suffStat = getSuff(imp4, test="mixMItest"))
mixMItest(2, 3, 5, suffStat = mice::complete(imp4, action="all"))
flexMItest(2, 3, 5, suffStat = getSuff(imp4, test="flexMItest"))

---

Creates a formulas Argument

Description

This helper function creates a valid formulas object. The formulas object is an argument to the mice::mice function. It is a list of formulas that specifies the target variables and the predictors by means of the standard ~ operator. In contrast to mice::make.formulas, which creates main effects formulas, make.formulas.saturated creates formulas including interaction effects.

Usage

make.formulas.saturated(
  data,
  blocks = mice::make.blocks(data),
  predictorMatrix = NULL,
  d = NULL
)

Arguments

data	A data.frame with the source data.
blocks	An optional specification for blocks of variables in the rows. The default assigns each variable in its own block.
predictorMatrix	A predictorMatrix specified by the user.
d	maximum depth of interactions to be considered (1=no interactions, 2=two-way interactions, etc.)

Value

A list of formulas.

Note

A modification of mice::make.formulas by Stef van Buuren et al.

See Also

mice::make.formulas

Examples

## main effects model:
data(nhanes)
f1 <- make.formulas(nhanes)
f1

## saturated model:
f2 <- make.formulas.saturated(nhanes)
f2

---

Generate residuals based on variables in imputed data sets

Description

Generate residuals based on variables in imputed data sets

Usage

makeResiduals(data, v, confounder, method = c("res", "cc", "pd"))

Arguments

data	A data.frame.
v	Vector of integers referring to the location of the variable(s) in the data set
confounder	Vector of integers referring to the location of the variable(s) in the data set (confounders are not included in the network!)
method	Default method 'res' uses residuals, 'cc' uses complete cases and 'pd' uses pairwise deletion

Value

A data matrix of residuals.

Examples

data(windspeed)
daten <- mice::ampute(windspeed)$amp

# Impute missing values
imp <- mice(daten, m = 5)

# Build residuals
knoten <- 1:4
confounder <- 5:6

# Residuals based on dataset with missing values
res.pd <- makeResiduals(daten, v = knoten, confounder = confounder, method = "pd")

# Residuals based in multiple imputed data
residuals <- list(data = list(), m = 5)
imp_c <- mice::complete(imp, "all")
for (i in 1:imp$m){
   residuals$data[[i]] <- makeResiduals(imp_c[[i]],
                          v = knoten, confounder = confounder)
 }

pc.res <- pcMI(data = residuals, p = length(knoten), alpha = 0.05)
fci.res <- fciMI(data = imp, p = length(knoten), alpha = 0.05)

if (requireNamespace("Rgraphviz", quietly = TRUE)){
oldpar <- par(mfrow = c(1,2)) 
  plot(pc.res)
  plot(fci.res)
par(oldpar)
}

---

Likelihood Ratio Test for (Conditional) Independence between Mixed Variables

Description

A likelihood ratio test for (conditional) independence between mixed (continuous and unordered categorical) variables, to be used within pcalg::skeleton, pcalg::pc or pcalg::fci. It assumes that the variables in the test follow a Conditional Gaussian distribution, i.e. conditional on each combination of values of the discrete variables, the continuous variables are multivariate Gaussian. Each multivariate Gaussian distribution is allowed to have its own mean vector and covariance matrix.

Usage

mixCItest(x, y, S = NULL, suffStat, moreOutput = FALSE)

Arguments

x, y, S	(Integer) position of variable X, Y and set of variables S, respectively, in suffStat. It is tested whether X and Y are conditionally independent given the subset S of the remaining variables.
suffStat	A data.frame. Discrete variables must be coded as factors.
moreOutput	If TRUE, the test statistic and the degrees of freedom are returned in addition to the p-value (only for mixed variables). Defaults to FALSE.

Details

The implementation follows Andrews et al. (2018). The same test is also implemented in TETRAD and in the R-package rcausal, a wrapper for the TETRAD Java library. Small differences in the p-values returned by CGtest and the TETRAD/rcausal equivalent are due to differences in handling sparse or empty cells.

Value

A p-value. If moreOutput=TRUE, the test statistic and the degrees of freedom are returned as well.

Author(s)

Janine Witte

References

Andrews B., Ramsey J., Cooper G.F. (2018): Scoring Bayesian networks of mixed variables. International Journal of Data Science and Analytics 6:3-18.

Lauritzen S.L., Wermuth N. (1989): Graphical models for associations between variables, some of which are qualitative and some quantitative. The Annals of Statistics 17(1):31-57.

Scheines R., Spirtes P., Glymour C., Meek C., Richardson T. (1998): The TETRAD project: Constraint based aids to causal model specification. Multivariate Behavioral Research 33(1):65-117. http://www.phil.cmu.edu/tetrad/index.html

Examples

# load data (numeric and factor variables)
dat <- toenail2[,-1]

# analyse data
mixCItest(4, 1, NULL, suffStat = dat)
mixCItest(1, 2, 3, suffStat = dat)

## use mixCItest within pcalg::fci
fci.fit <- fci(suffStat = dat, indepTest = mixCItest, alpha = 0.01, p = 4)
if (requireNamespace("Rgraphviz", quietly = TRUE))
 plot(fci.fit)

---

Likelihood Ratio Test for (Conditional) Independence between Mixed Variables with Missings

Description

A version of mixCItest, to be used within pcalg::skeleton, pcalg::pc or pcalg::fci when the data contain missing values. Observations where at least one of the variables involved in the test is missing are deleted prior to performing the test (test-wise deletion).

Usage

mixCItwd(x, y, S = NULL, suffStat)

Arguments

x, y, S	(Integer) position of variable X, Y and set of variables S, respectively, in suffStat. It is tested whether X and Y are conditionally independent given the subset S of the remaining variables.
suffStat	data.frame. Discrete variables must be coded as factors.

Details

See mixCItest for details on the assumptions of the Conditional Gaussian likelihood ratio test. Test-wise deletion is valid if missingness does not jointly depend on X and Y.

Value

A p-value.

See Also

mixCItest() for complete data, mixMItest() for multiply imputed data

Examples

## load data (numeric and factor variables)
data(toenail2)
dat <- toenail2[, -1]

## delete some observations
set.seed(123)
dat[sample(2000, 20), 1] <- NA
dat[sample(2000, 30), 3] <- NA

## analyse data 
# complete data: ==========
mixCItest(1, 2, 4, suffStat=toenail2)

# test-wise deletion: ==========
mixCItwd(1, 2, 4, suffStat = dat)

# list-wise deletion: ==========
dat2 <- dat[complete.cases(dat), ]
mixCItest(1, 2, 4, suffStat = dat2)

## use mixCItwd within pcalg::pc
pc.fit <- pc(suffStat = dat, indepTest = mixCItwd, alpha = 0.01, p = 4)

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Likelihood Ratio Test for (Conditional) Independence between Mixed Variables after Multiple Imputation

Description

A modified version of mixCItest, to be used within pcalg::skeleton, pcalg::pc or pcalg::fci when multiply imputed data sets are available.

Usage

mixMItest(x, y, S = NULL, suffStat, moreOutput = FALSE)

Arguments

x, y, S	(integer) position of variable X, Y and set of variables S, respectively, in suffStat. It is tested whether X and Y are conditionally independent given the subset S of the remaining variables.
suffStat	A list of data.frames containing the multiply imputed data sets. Usually obtained from a mice::mids object using mice::complete with argument action="all". Discrete variables must be coded as factors.
moreOutput	(only for mixed of discrete variables) If TRUE, the test statistic, its main components and the degrees of freedom are returned in addition to the p-value. Defaults to FALSE.

Details

See mixCItest for details on the assumptions of the Conditional Gaussian likelihood ratio test. CGtestMI applies this test to each data.frame in suffStat, then combines the results using the rules in Meng & Rubin (1992).

Value

A p-value. If moreOutput=TRUE, the test statistic, its main components and the degrees of freedom are returned as well.

Author(s)

Janine Witte

References

Meng X.-L., Rubin D.B. (1992): Performing likelihood ratio tests with multiply imputed data sets. Biometrika 79(1):103-111.

Examples

## load data (numeric and factor variables)
data(toenail2)
dat <- toenail2[1:1000, ]

## delete some observations
set.seed(123)
dat[sample(1000, 20), 2] <- NA
dat[sample(1000, 30), 4] <- NA

## impute missing values using random forests (because of run time we just impute 2 chains)
imp <- mice(dat, method = "rf", m = 2, printFlag = FALSE)

## analyse data
# complete data:
mixCItest(2, 3, 5, suffStat = toenail2[1:1000, ])
# multiple imputation:
suffMI <- complete(imp, action = "all")
mixMItest(2, 3, 5, suffStat =  suffMI)
# test-wise deletion:
mixCItwd(2, 3, 5, suffStat = dat)
# list-wise deletion:
sufflwd <- dat[complete.cases(dat), ]
mixCItest(2, 3, 5, suffStat = sufflwd)

## use mixMItest within pcalg::pc

pc.fit <- pc(suffStat =  suffMI, indepTest = mixMItest, alpha = 0.01, p = 5)
pc.fit

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Estimate the Equivalence Class of a DAG Using the PC-MI Algorithm for Multiple Imputed Data Sets

Description

This function is a modification of pcalg::pc() to be used for multiple imputation.

Usage

pcMI(
  data,
  alpha,
  labels,
  p,
  fixedGaps = NULL,
  fixedEdges = NULL,
  NAdelete = TRUE,
  m.max = Inf,
  u2pd = c("relaxed", "rand", "retry"),
  skel.method = c("stable", "original"),
  conservative = FALSE,
  maj.rule = FALSE,
  solve.confl = FALSE,
  verbose = FALSE
)

Arguments

data	An object of type mids, which stands for 'multiply imputed data set', typically created by a call to function mice()
alpha	Significance level (number in (0,1) for the conditional independence tests
labels	(Optional) character vector of variable (or "node") names. Typically preferred to specifying p.
p	(Optional) number of variables (or nodes). May be specified if labels are not, in which case labels is set to 1:p.
fixedGaps	A logical matrix of dimension p*p. If entry [i,j] or [j,i] (or both) are TRUE, the edge i-j is removed before starting the algorithm. Therefore, this edge is guaranteed to be absent in the resulting graph.
fixedEdges	A logical matrix of dimension p*p. If entry [i,j] or [j,i] (or both) are TRUE, the edge i-j is never considered for removal. Therefore, this edge is guaranteed to be present in the resulting graph
NAdelete	If indepTest returns NA and this option is TRUE, the corresponding edge is deleted. If this option is FALSE, the edge is not deleted.
m.max	Maximal size of the conditioning sets that are considered in the conditional independence tests.
u2pd	String specifying the method for dealing with conflicting information when trying to orient edges (see details below).
skel.method	Character string specifying method; the default, "stable" provides an order-independent skeleton, see pcalg::skeleton() for details.
conservative	Logical indicating if the conservative PC is used. See pcalg::pc() for details.
maj.rule	Logical indicating that the triples shall be checked for ambiguity using a majority rule idea, which is less strict than the conservative PC algorithm. For more information, see pcalg::pc().
solve.confl	See pcalg::pc() for more details.
verbose	If TRUE, detailed output is provided.

Details

An object of class "pcAlgo" (see pcAlgo) containing an estimate of the equivalence class of the underlying DAG.

Value

See pcalg::pc() for more details.

Note

This is a modified function of pcalg::pc() from the package 'pcalg' (Kalisch et al., 2012; http://www.jstatsoft.org/v47/i11/).

Author(s)

Original code by Markus Kalisch, Martin Maechler, and Diego Colombo. Modifications by Ronja Foraita.

Examples

daten <- mice::ampute(windspeed)$amp

## Impute missing values
imp <- mice(daten)
pcMI(data = imp, label = colnames(imp$data), alpha = 0.01)

---

Estimate (Initial) Skeleton of a DAG using the PC Algorithm for Multiple Imputed Data Sets of Continuous Data

Description

This function is a modification of pcalg::skeleton() to be used for multiple imputation.

Usage

skeletonMI(
  data,
  alpha,
  labels,
  p,
  method = c("stable", "original"),
  m.max = Inf,
  fixedGaps = NULL,
  fixedEdges = NULL,
  NAdelete = TRUE,
  verbose = FALSE
)

Arguments

data	An object of type mids, which stands for 'multiply imputed data set', typically created by a call to function mice()
alpha	Significance level
labels	(Optional) character vector of variable (or "node") names. Typically preferred to specifying p
p	(Optional) number of variables (or nodes). May be specified if labels are not, in which case labels is set to 1:p.
method	Character string specifying method; the default, "stable" provides an order-independent skeleton, see pcalg::pc() for details.
m.max	Maximal size of the conditioning sets that are considered in the conditional independence tests.
fixedGaps	Logical symmetric matrix of dimension p*p. If entry [i,j] is true, the edge i-j is removed before starting the algorithm. Therefore, this edge is guaranteed to be absent in the resulting graph.
fixedEdges	A logical symmetric matrix of dimension p*p. If entry [i,j] is true, the edge i-j is never considered for removal. Therefore, this edge is guaranteed to be present in the resulting graph.
NAdelete	Logical needed for the case indepTest(*) returns NA. If it is true, the corresponding edge is deleted, otherwise not.
verbose	If TRUE, detailed output is provided.

Value

See pcalg::skeleton() for more details.

Note

This is a modified function of pcalg::skeleton() from the package 'pcalg' (Kalisch et al., 2012; http://www.jstatsoft.org/v47/i11/).

Author(s)

Original code by Markus Kalisch, Martin Maechler, Alain Hauser, and Diego Colombo. Modifications by Ronja Foraita.

Examples

data(gmG)
n <- nrow(gmG8$x)
V <- colnames(gmG8$x) # labels aka node names
## estimate Skeleton
data_mids <- mice(gmG8$x, printFlag = FALSE)
(skel.fit <- skeletonMI(data = data_mids, alpha = 0.01, labels = V, verbose = FALSE))

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Evaluate Causal Graph Discovery Algorithm in Multiple Imputed Data sets

Description

Evaluate Causal Graph Discovery Algorithm in Multiple Imputed Data sets

Usage

with_graph(data, algo = c("pc", "fci", "fciPlus", "ges"), args, score = FALSE)

Arguments

data	An object of type mids, which stands for 'multiply imputed data set', typically created by a call to function mice()
algo	An algorithm for causal discovery from the package 'pcalg' (see details).
args	Additional arguments passed to the algo. Must be a string vector starting with comma, i.e. ", ..."
score	Logical indicating whether a score-based or a constrained-based algorithm is applied.

Value

A list object of S3 class mice::mira-class.

Examples

data(windspeed)
dat <- as.matrix(windspeed)

## delete some observations
set.seed(123)
dat[sample(1:length(dat), 260)] <- NA

## Impute missing values under normal model
imp <- mice(dat, method = "norm", printFlag = FALSE)
mylabels <- names(imp$imp)
out.fci <- with_graph(data = imp, 
                      algo = "fciPlus", 
                      args = ", indepTest = gaussCItest, verbose = FALSE,
                      labels = mylabels, alpha = 0.01")
                          
 out.ges <- with_graph(data = imp, algo = "ges", arg = NULL, score = TRUE)
 
if (requireNamespace("Rgraphviz", quietly = TRUE)){
 oldpar <- par(mfrow = c(1,2)) 
   plot(out.fci$res[[1]])
   plot(out.ges$res[[1]]$essgraph)
 par(oldpar)
 }

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