Medflex Manual
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Package ‘medflex’
September 3, 2018
Title Flexible Mediation Analysis Using Natural Effect Models
Version 0.6-6
Date 2018-09-03
Description Run flexible mediation analyses using natural effect models as described in
Lange, Vansteelandt and Bekaert (2012) <DOI:10.1093/aje/kwr525>,
Vansteelandt, Bekaert and Lange (2012) <DOI:10.1515/2161-962X.1014>
and Loeys, Moerkerke, De Smet, Buysse, Steen and Vanstee-
landt (2013) <DOI:10.1080/00273171.2013.832132>.
Depends R (>= 3.1.2),
multcomp (>= 1.3-6)
License GPL-2
URL https://github.com/jmpsteen/medflex
LazyData true
Imports boot (>= 1.3-8),
car (>= 2.0-21),
Matrix (>= 1.1-4),
graphics (>= 3.1.2),
sandwich (>= 2.3-2),
stats (>= 3.1.2),
utils (>= 3.1.2)
Suggests arm (>= 1.7-05),
gam (>= 1.09.1),
glmnet (>= 1.9-8),
mice (>= 2.22),
mitools (>= 2.3),
rpart (>= 4.1-8),
SuperLearner (>= 2.0-15),
VGAM (>= 1.0-0)
RoxygenNote 6.1.0
ByteCompile yes
NeedsCompilation no
Author Johan Steen [aut, cre],
Tom Loeys [aut],
Beatrijs Moerkerke [aut],
Stijn Vansteelandt [aut],
Joris Meys [ctb] (technical support),
1
2expData
Theis Lange [ctb] (valuable suggestions),
Joscha Legewie [ctb],
Paul Fink [ctb]
Maintainer Johan Steen <johan.steen@gmail.com>
Rtopics documented:
expData ........................................... 2
expData-methods ...................................... 3
neImpute .......................................... 4
neImpute.default ...................................... 5
neImpute.formula...................................... 8
neLht ............................................ 10
neLht-methods ....................................... 13
neModel........................................... 15
neModel-methods...................................... 18
neWeight .......................................... 21
neWeight.default ...................................... 22
neWeight.formula...................................... 24
plot.neLht.......................................... 26
plot.neModel ........................................ 27
UPBdata........................................... 28
Index 30
expData Expanded dataset
Description
Expanded dataset including either ratio-of-mediator probability weights or imputed nested counter-
factual outcomes.
Value
A data frame, resulting from applying neWeight or neImpute on an original dataset data. This
data frame has nRep * length(data) rows, containing all original variables (except the original
exposure variable) and two variables reflecting observed and hypothetical values of the exposure
for each observation unit.
These auxiliary variables (xand x*) are named after the exposure variable and carry integers as
suffixes. Suffixes 0and 1are used for variables whose corresponding parameters in the final natural
effect model index natural direct and indirect effects, respectively.
This object also stores some additional attributes, which are used as input for neModel, such as
model the fitted working model object
data original dataset
call the matched call
terms the neTerms (internal class) object used
weights ratio-of-mediator probability weights (only stored if object inherits from class
weightData)
expData-methods 3
Note
If the weighting-based approach (neWeight) is applied, the original outcome values are copied
for the nested counterfactual outcomes and the object stores an additional attribute, "weights",
containing a vector with ratio-of-mediator probability weights.
If the imputation-based approach (neImpute) is applied, the nested counterfactual outcomes are
imputed by predictions from the imputation model.
In the former case, this object inherits from classes c("data.frame", "expData", "impData"),
whereas in the latter case it inherits from classes c("data.frame", "expData", "weightData").
See Also
neImpute,neWeight
expData-methods Methods for expanded datasets
Description
Regression weights, residuals and residual plots for expanded datasets.
Usage
## S3 method for class 'expData'
residuals(object, ...)
## S3 method for class 'expData'
residualPlot(object, ...)
## S3 method for class 'expData'
residualPlots(object, ...)
## S3 method for class 'expData'
weights(object, ...)
Arguments
object an expanded dataset (of class "expData").
... additional arguments.
Details
weights extracts regression weights (to be used in the natural effect model) for each observation of
an expanded dataset.
residuals extracts residuals from the working model which is stored as an attribute of the expanded
dataset. These can be used to assess normality of the residuals of the mediator working model when
using the weighting-based approach (see example).
residualPlot and residualPlots are convenience functions from the car package. These can be
used to assess the adequacy of the working model.
4neImpute
See Also
expData,neWeight,residualPlot,residualPlots,residuals,weights
Examples
data(UPBdata)
weightData <- neWeight(negaff ~ att + gender + educ + age,
data = UPBdata, nRep = 2)
## extract regression weights for natural effect model
head(weights(weightData))
## assess normality
qqnorm(residuals(weightData))
## assess model adequacy
library(car)
residualPlots(weightData)
neImpute Expand the dataset and impute nested counterfactual outcomes
Description
This function both expands the data along hypothetical exposure values and imputes nested coun-
terfactual outcomes.
Usage
neImpute(object, ...)
Arguments
object an object used to select a method.
... additional arguments.
Details
Generic function that both expands the data along hypothetical exposure values (for each observa-
tion unit i) and imputes nested counterfactual outcomes in this expanded dataset in a single run.
Imputed counterfactual outcomes
ˆ
E(Yi|Xi=x, Mi, Ci)
are predictions from the imputation model that can be specified either externally as a fitted model
object (neImpute.default) or internally (neImpute.formula).
Value
A data frame of class c("data.frame", "expData", "impData"). See expData for its structure.
neImpute.default 5
References
Vansteelandt, S., Bekaert, M., & Lange, T. (2012). Imputation Strategies for the Estimation of
Natural Direct and Indirect Effects. Epidemiologic Methods,1(1), Article 7.
Loeys, T., Moerkerke, B., De Smet, O., Buysse, A., Steen, J., & Vansteelandt, S. (2013). Flexi-
ble Mediation Analysis in the Presence of Nonlinear Relations: Beyond the Mediation Formula.
Multivariate Behavioral Research,48(6), 871-894.
See Also
neImpute.default,neImpute.formula,neModel,expData
neImpute.default Expand the dataset and impute nested counterfactual outcomes
Description
This function both expands the data along hypothetical exposure values and imputes nested coun-
terfactual outcomes.
Usage
## Default S3 method:
neImpute(object, formula, data, nMed = 1, nRep = 5,
xSampling = c("quantiles", "random"), xFit, percLim = c(0.05, 0.95),
...)
Arguments
object fitted model object representing the imputation model.
formula aformula object providing a symbolic description of the imputation model.
Redundant if already specified in call for fitted model specified in object (see
details).
data data, as matrix or data frame, containing the exposure (and other relevant) vari-
ables. Redundant if already specified in call for fitted model specified in object
(see details).
nMed number of mediators.
nRep number of replications or hypothetical values of the exposure to sample for each
observation unit.
xSampling character string indicating how to sample from the conditional exposure distri-
bution. Possible values are "quantiles" or "random" (see details).
xFit an optional fitted object (preferably glm) for the conditional exposure distribu-
tion (see details).
percLim a numerical vector of the form c(lower, upper) indicating the extreme per-
centiles to sample when using "quantiles" as sampling method to sample from
the conditional exposure distribution (see details).
... additional arguments.
6neImpute.default
Details
Imputed counterfactual outcomes are predictions from the imputation model that needs to be spec-
ified as a fitted object in the object argument.
If the model-fitting function used to fit the imputation model does not require specification of a
formula or data argument (when using e.g. SuperLearner), these need to be specified explicitly
in order to enable neImpute.default to extract pointers to variable types relevant for mediation
analysis.
Whether a formula is specified externally (in the call for the fitted imputation model object which
is specified in object) or internally (via the formula argument), it always needs to be of the form
Y~X+M1+M2+M3+C1+C2, with the same outcome as in the final natural effect model
and with predictor variables entered in the following prespecified order:
1. exposure X: The first predictor is coded as exposure or treatment.
2. mediator(s) M: The second predictor is coded as mediator. In case of multiple mediators
(nMed > 1), then predictors 2:(nMed + 1) are coded as mediators.
3. baseline covariates C: All remaining predictor variables are automatically coded as baseline
covariates.
It is important to adhere to this prespecified order to enable neImpute to create valid pointers
to these different types of predictor variables. This requirement extends to the use of operators
different than the +operator, such as the :and *operators (when e.g. adding interaction terms).
For instance, the formula specifications Y~X*M+C1+C2,Y~X+M+X:M+C1+C2
and Y ~ X + X:M + M + C1 + C2 will create identical pointers to the different types of variables,
as the order of the unique predictor variables is identical in all three specifications.
Furthermore, categorical exposures that are not coded as factors in the original dataset, should be
specified as factors in the formula, using the factor function, e.g. Y ~ factor(X) + M + C1 + C2.
Quadratic or higher-order polynomial terms can be included as well, by making use of the Ifunc-
tion or by using the poly function. For instance, Y ~ X + I(X^2) + M + C1 + C2 and
Y ~ poly(X, 2, raw = TRUE) + M + C1 + C2 are equivalent and result in identical pointers to
the different types of variables.
The command terms(object, "vartype") (with object replaced by the name of the resulting
expanded dataset) can be used to check whether valid pointers have been created.
If multiple mediators are specified (nMed > 1), the natural indirect effect parameter in the natural
effect model captures the joint mediated effect. That is, the effect of the exposure on the outcome
via these mediators considered jointly. The remaining effect of the exposure on the outcome (not
mediated through the specified mediators) is then captured by the natural indirect effect parameter.
In contrast to imputation models with categorical exposures, additional arguments need to be spec-
ified if the exposure is continuous. All of these additional arguments are related to the sampling
procedure for the exposure.
Whereas the number of replications nRep for categorical variables equals the number of levels for
the exposure coded as a factor (i.e. the number of hypothetical exposure values), the number of
desired replications needs to be specified explicitly for continuous exposures. Its default is 5.
If xFit is left unspecified, the hypothetical exposure levels are automatically sampled from a linear
model for the exposure, conditional on a linear combination of all covariates. If one wishes to use
another model for the exposure, this default model specification can be overruled by referring to a
fitted model object in the xFit argument. Misspecification of this sampling model does not induce
bias in the estimated coefficients and standard errors of the natural effect model.
The xSampling argument allows to specify how the hypothetical exposure levels should be sam-
pled from the conditional exposure distribution (which is either entered explicitly using the xFit
neImpute.default 7
argument or fitted automatically as described in the previous paragraph). The "random" option
randomly samples nRep draws from the exposure distribution, whereas the "quantiles" option
(default) samples nRep quantiles at equal-sized probability intervals. Only the latter hence yields
fixed exposure levels given nRep and xFit.
In order to guarantee that the entire support of the distribution is being sampled (which might be a
concern if nRep is chosen to be small), the default lower and upper sampled quantiles are the 5th
and 95th percentiles. The intermittent quantiles correspond to equal-sized probability intervals. So,
for instance, if nRep = 4, then the sampled quantiles will correspond to probabilities 0.05, 0.35,
0.65 and 0.95. These default ’outer’ quantiles can be changed by specifying the percLim argument
accordingly. By specifying percLim = NULL, the standard quantiles will be sampled (e.g., 0.2, 0.4,
0.6 and 0.8 if nRep = 4).
Value
A data frame of class c("data.frame", "expData", "impData"). See expData for its structure.
See Also
neImpute,neImpute.formula,neModel,expData
Examples
data(UPBdata)
## example using glm imputation model with binary exposure
fit.glm <- glm(UPB ~ factor(attbin) + negaff + gender + educ + age,
family = binomial, data = UPBdata)
impData <- neImpute(fit.glm)
head(impData)
## example using glm imputation model with continuous exposure
fit.glm <- glm(UPB ~ att + negaff + gender + educ + age,
family = binomial, data = UPBdata)
impData <- neImpute(fit.glm, nRep = 2)
head(impData)
## example using vglm (yielding identical results as with glm)
library(VGAM)
fit.vglm <- vglm(UPB ~ att + negaff + gender + educ + age,
family = binomialff, data = UPBdata)
impData2 <- neImpute(fit.vglm, nRep = 2)
head(impData2)
## Not run:
## example using SuperLearner
library(Matrix)
library(SuperLearner)
SL.library <- c("SL.glm", "SL.glm.interaction", "SL.rpart",
"SL.step", "SL.stepAIC", "SL.step.interaction",
"SL.bayesglm", "SL.glmnet")
pred <- c("att", "negaff", "gender", "educ", "age")
fit.SL <- SuperLearner(Y = UPBdata$UPB, X = subset(UPBdata, select = pred),
SL.library = SL.library, family = binomial())
impSL <- neImpute(fit.SL,
formula = UPB ~ att + negaff + gender + educ + age,
8neImpute.formula
data = UPBdata)
head(impSL)
## End(Not run)
neImpute.formula Expand the dataset and impute nested counterfactual outcomes
Description
This function both expands the data along hypothetical exposure values and imputes nested coun-
terfactual outcomes.
Usage
## S3 method for class 'formula'
neImpute(object, family, data, FUN = glm, nMed = 1,
nRep = 5, xSampling = c("quantiles", "random"), xFit,
percLim = c(0.05, 0.95), ...)
Arguments
object aformula object providing a symbolic description of the imputation model (see
details).
family a description of the error distribution and link function to be used in the model.
Consult the help files of the model-fitting function specified in FUN for more
details on appropriate argument specification.
data data, as matrix or data frame, containing the exposure (and other relevant) vari-
ables. Redundant if already specified in call for fitted model specified in object
(see details).
FUN function used to fit model specified in formula.
nMed number of mediators.
nRep number of replications or hypothetical values of the exposure to sample for each
observation unit.
xSampling character string indicating how to sample from the conditional exposure distri-
bution. Possible values are "quantiles" or "random" (see details).
xFit an optional fitted object (preferably glm) for the conditional exposure distribu-
tion (see details).
percLim a numerical vector of the form c(lower, upper) indicating the extreme per-
centiles to sample when using "quantiles" as sampling method to sample from
the conditional exposure distribution (see details).
... additional arguments (passed to FUN).
neImpute.formula 9
Details
Imputed counterfactual outcomes are predictions from the imputation model that is fitted internally
by extracting information from the arguments object,family,data,FUN and ....
For imputation model specification via the object argument, use a formula of the form
Y~X+M1+M2+M3+C1+C2,
with the same outcome as in the final natural effect model and with predictor variables entered in
the following prespecified order:
1. exposure X: The first predictor is coded as exposure or treatment.
2. mediator(s) M: The second predictor is coded as mediator. In case of multiple mediators
(nMed > 1), then predictors 2:(nMed + 1) are coded as mediators.
3. baseline covariates C: All remaining predictor variables are automatically coded as baseline
covariates.
It is important to adhere to this prespecified order to enable neImpute to create valid pointers
to these different types of predictor variables. This requirement extends to the use of operators
different than the +operator, such as the :and *operators (when e.g. adding interaction terms).
For instance, the formula specifications Y~X*M+C1+C2,Y~X+M+X:M+C1+C2
and Y ~ X + X:M + M + C1 + C2 will create identical pointers to the different types of variables,
as the order of the unique predictor variables is identical in all three specifications.
Furthermore, categorical exposures that are not coded as factors in the original dataset, should be
specified as factors in the formula, using the factor function, e.g. Y ~ factor(X) + M + C1 + C2.
Quadratic or higher-order polynomial terms can be included as well, by making use of the Ifunc-
tion or by using the poly function. For instance, Y ~ X + I(X^2) + M + C1 + C2 and
Y ~ poly(X, 2, raw = TRUE) + M + C1 + C2 are equivalent and result in identical pointers to
the different types of variables.
The command terms(object, "vartype") (with object replaced by the name of the resulting
expanded dataset) can be used to check whether valid pointers have been created.
If multiple mediators are specified (nMed > 1), the natural indirect effect parameter in the natural
effect model captures the joint mediated effect. That is, the effect of the exposure on the outcome
via these mediators considered jointly. The remaining effect of the exposure on the outcome (not
mediated through the specified mediators) is then captured by the natural indirect effect parameter.
The type of imputation model can be defined by specifying an appropriate model-fitting function
via the FUN argument (its default is glm). This method can only be used with model-fitting functions
that require a formula argument (so not when using e.g. SuperLearner).
In contrast to imputation models with categorical exposures, additional arguments need to be spec-
ified if the exposure is continuous. All of these additional arguments are related to the sampling
procedure for the exposure.
Whereas the number of replications nRep for categorical variables equals the number of levels for
the exposure coded as a factor (i.e. the number of hypothetical exposure values), the number of
desired replications needs to be specified explicitly for continuous exposures. Its default is 5.
If xFit is left unspecified, the hypothetical exposure levels are automatically sampled from a linear
model for the exposure, conditional on a linear combination of all covariates. If one wishes to use
another model for the exposure, this default model specification can be overruled by referring to a
fitted model object in the xFit argument. Misspecification of this sampling model does not induce
bias in the estimated coefficients and standard errors of the natural effect model.
The xSampling argument allows to specify how the hypothetical exposure levels should be sam-
pled from the conditional exposure distribution (which is either entered explicitly using the xFit
argument or fitted automatically as described in the previous paragraph). The "random" option
10 neLht
randomly samples nRep draws from the exposure distribution, whereas the "quantiles" option
(default) samples nRep quantiles at equal-sized probability intervals. Only the latter hence yields
fixed exposure levels given nRep and xFit.
In order to guarantee that the entire support of the distribution is being sampled (which might be a
concern if nRep is chosen to be small), the default lower and upper sampled quantiles are the 5th
and 95th percentiles. The intermittent quantiles correspond to equal-sized probability intervals. So,
for instance, if nRep = 4, then the sampled quantiles will correspond to probabilities 0.05, 0.35,
0.65 and 0.95. These default ’outer’ quantiles can be changed by specifying the percLim argument
accordingly. By specifying percLim = NULL, the standard quantiles will be sampled (e.g., 0.2, 0.4,
0.6 and 0.8 if nRep = 4).
Value
A data frame of class c("data.frame", "expData", "impData"). See expData for its structure.
See Also
neImpute,neImpute.default,neModel,expData
Examples
data(UPBdata)
## example using glm imputation model with binary exposure
impData <- neImpute(UPB ~ factor(attbin) + negaff + gender + educ + age,
family = binomial, data = UPBdata)
head(impData)
## example using glm imputation model with continuous exposure
impData <- neImpute(UPB ~ att + negaff + gender + educ + age,
family = binomial, data = UPBdata, nRep = 2)
head(impData)
## example using vglm (yielding identical results as with glm)
library(VGAM)
impData2 <- neImpute(UPB ~ att + negaff + gender + educ + age,
family = binomialff, data = UPBdata,
nRep = 2, FUN = vglm)
head(impData2)
neLht Linear hypotheses for natural effect models
Description
neLht allows to calculate linear combinations of natural effect model parameter estimates.
neEffdecomp automatically extracts relevant causal parameter estimates from a natural effect model.
neLht 11
Usage
neEffdecomp(model, xRef, covLev, ...)
## S3 method for class 'neModel'
neEffdecomp(model, xRef, covLev, ...)
neLht(model, ...)
## S3 method for class 'neModel'
neLht(model, ...)
Arguments
model a fitted natural effect model object.
xRef a vector including reference levels for the exposure, x* and x, at which natural
effect components need to be evaluated (see details).
covLev a vector including covariate levels at which natural effect components need to
be evaluated (see details).
... additional arguments (passed to glht).
Details
neLht is a wrapper of glht and offers the same functionality (see ‘Details’ section of glht for
details on argument specification). It returns objects that inherit from the class "neLht" in order
to make output of their corresponding methods (see neLht-methods) more compatible for natural
effect models containing bootstrap variance-covariance matrices and standard errors.
neEffdecomp is a convenience function that automatically extracts causal parameter estimates from
a natural effect model and derives natural effect components. That is, natural direct, natural indirect
and total causal effect estimates are returned if no exposure-mediator interaction is modelled (i.e.
two-way decomposition). If mediated interaction is allowed for in the natural effect model, there
are two ways of decomposing the total effect into (natural) direct and indirect effects components:
either as the sum of the pure direct and the total indirect effect or as the sum of the pure indirect
and the total direct effect (i.e. three-way decomposition). In total, five causal effect estimates are
returned in this case.
For continuous exposures, default exposure levels at which natural effect components are evaluated
are x* = 0 and x= 1. For multicategorical exposures, default levels are the reference level of the
factor that encodes the exposure variable and the level corresponding to its first dummy variable
for x* and x, respectively. If one wishes to evaluate natural effect components at different reference
levels (e.g. if the natural effect model includes mediated interaction, quadratic or higher-order
polynomial terms for the exposure; see examples), these can be specified as a vector of the form
c(x*,x) via the xRef argument.
If applicable, covariate levels at which natural effect components are evaluated can also be speci-
fied. This is particularly useful for natural effect models encoding effect modification by baseline
covariates (e.g. moderated mediation). By default, these levels are set to 0 for continuous covariates
and to the reference level for categorical covariates coded as factors. Different covariate levels can
be specified via the covLev argument, which requires a vector including valid levels for covariates
that are specified in the natural effect model (or a subset of covariates that are specified as modifiers
of either the natural direct or indirect effect or both). Levels need to be preceded by the name of
the corresponding covariate, e.g., covLev = c(gender = "M", age = 30). Covariates for which
the levels are left unspecified are set to their default levels (see examples). The print and summary
functions for neEffdecomp objects return the covariate levels at which natural effect components
12 neLht
are evaluated. No specific levels are returned for covariates that are not specified as modifier since
effect decomposition is independent of the level of these covariates (see examples).
Value
An object of class c("neLht", "glht") (see glht). If the bootstrap is used for obtaining stan-
dard errors when fitting the neModel object, the returned object additionally inherits from class
"neLhtBoot".neEffdecomp returns an object that additionally inherits from class "neEffdecomp".
See neLht-methods for methods for neLht objects (and glht-methods for additional methods for
glht objects).
Note
neEffdecomp is internally called by plot.neModel to create confidence interval plots for neModel
objects.
See Also
plot.neLht,neLht-methods,glht,glht-methods,neModel,plot.neModel,summary
Examples
data(UPBdata)
impData <- neImpute(UPB ~ att * negaff + gender + educ + age,
family = binomial, data = UPBdata)
neMod <- neModel(UPB ~ att0 * att1 + gender + educ + age,
family = binomial, expData = impData, se = "robust")
lht <- neLht(neMod, linfct = c("att0 = 0", "att0 + att0:att1 = 0",
"att1 = 0", "att1 + att0:att1 = 0",
"att0 + att1 + att0:att1 = 0"))
summary(lht)
## or obtain directly via neEffdecomp
eff <- neEffdecomp(neMod)
summary(eff)
## changing reference levels for multicategorical exposures
UPBdata$attcat <- factor(cut(UPBdata$att, 3), labels = c("L", "M", "H"))
impData <- neImpute(UPB ~ attcat * negaff + gender + educ + age,
family = binomial, data = UPBdata)
neMod <- neModel(UPB ~ attcat0 * attcat1 + gender + educ + age,
family = binomial, expData = impData, se = "robust")
neEffdecomp(neMod)
neEffdecomp(neMod, xRef = c("L", "H"))
neEffdecomp(neMod, xRef = c("M", "H"))
## changing reference levels for continuous exposures
impData <- neImpute(UPB ~ (att + I(att^2)) * negaff + gender + educ + age,
family = binomial, data = UPBdata)
neMod <- neModel(UPB ~ (att0 + I(att0^2)) * (att1 + I(att1^2)) + gender + educ + age,
family = binomial, expData = impData, se = "robust")
neEffdecomp(neMod)
neLht-methods 13
neEffdecomp(neMod, xRef = c(-1, 0))
## changing covariate levels when allowing for modification
## of the indirect effect by baseline covariates
impData <- neImpute(UPB ~ (att + negaff + gender + educ + age)^2,
family = binomial, data = UPBdata)
neMod <- neModel(UPB ~ att0 * att1 + gender + educ + age + att1:gender + att1:age,
family = binomial, expData = impData, se = "robust")
neEffdecomp(neMod)
neEffdecomp(neMod, covLev = c(gender = "F", age = 0)) # default covariate levels
neEffdecomp(neMod, covLev = c(gender = "M", age = 40))
neEffdecomp(neMod, covLev = c(gender = "M", age = 40, educ = "L"))
neEffdecomp(neMod, covLev = c(gender = "M", age = 40, educ = "M"))
neEffdecomp(neMod, covLev = c(gender = "M", age = 40, educ = "H"))
# effect decomposition is independent of education level
neEffdecomp(neMod, covLev = c(gender = "M"))
# age is set to its default level when left unspecified
neLht-methods Methods for linear hypotheses in natural effect models
Description
Obtain confidence intervals and statistical tests for linear hypotheses in natural effect models.
Usage
## S3 method for class 'neLhtBoot'
confint(object, parm, level = 0.95, type = "norm",
...)
## S3 method for class 'neLht'
confint(object, parm, level = 0.95,
calpha = univariate_calpha(), ...)
## S3 method for class 'neLht'
summary(object, test = univariate(), ...)
Arguments
object an object of class neLht.
parm a specification of which parameters are to be given confidence intervals, either
a vector of numbers or a vector of names. If missing, all parameters are consid-
ered.
level the confidence level required.
type the type of bootstrap intervals required. The default "norm" returns normal ap-
proximation bootstrap confidence intervals. Currently, "norm","basic","perc"
and "bca" are supported (see boot.ci).
... additional arguments.
14 neLht-methods
calpha a function computing the critical value. The default univariate_calpha()
returns unadjusted confidence intervals, whereas adjusted_calpha() returns
adjusted confidence intervals.
test a function for computing p-values. The default univariate() does not apply
a multiple testing correction. The function adjusted() allows to correct for
multiple testing (see summary.glht and adjusted) and Chisquare() allows to
test global linear hypotheses.
Details
confint yields bootstrap confidence intervals or confidence intervals based on the sandwich esti-
mator (depending on the type of standard errors requested when fitting the neModel object). Boot-
strap confidence intervals are internally called via the boot.ci function from the boot package.
Confidence intervals based on the sandwich estimator are internally called via the corresponding
confint.glht function from the multcomp package. The default confidence level specified in
level (which corresponds to the conf argument in boot.ci) is 0.95 and the default type of boot-
strap confidence interval, "norm", is based on the normal approximation. Bias-corrected and ac-
celerated ("bca") bootstrap confidence intervals require a sufficiently large number of bootstrap
replicates (for more details see boot.ci).
A summary table with large sample tests, similar to that for glht, can be obtained using summary.
In contrast to summary.glht, which by default returns p-values that are adjusted for multiple testing,
the summary function returns unadjusted p-values. Adjusted p-values can also be obtained by
specifying the test argument (see adjusted for more details).
Global Wald tests considering all linear hypotheses simultaneously (i.e. testing the global null
hypothesis) can be requested by specifying test = Chisqtest().
See glht-methods for additional methods for glht objects.
Note
For the bootstrap, z-values in the summary table are simply calculated by dividing the parameter
estimate by its corresponding bootstrap standard error. Corresponding p-values in the summary
table are only indicative, since the null distribution for each statistic is assumed to be approximately
standard normal. Therefore, whenever possible, it is recommended to focus mainly on bootstrap
confidence intervals for inference, rather than the provided p-values.
See Also
neLht,plot.neLht,glht,glht-methods
Examples
data(UPBdata)
impData <- neImpute(UPB ~ att * negaff + gender + educ + age,
family = binomial, data = UPBdata)
neMod <- neModel(UPB ~ att0 * att1 + gender + educ + age,
family = binomial, expData = impData, se = "robust")
lht <- neLht(neMod, linfct = c("att0 = 0", "att0 + att0:att1 = 0",
"att1 = 0", "att1 + att0:att1 = 0",
"att0 + att1 + att0:att1 = 0"))
## obtain confidence intervals
neModel 15
confint(lht)
confint(lht, parm = c("att0", "att0 + att0:att1"))
confint(lht, parm = 1:2, level = 0.90)
## summary table
summary(lht)
## summary table with omnibus Chisquare test
summary(lht, test = Chisqtest())
neModel Fit a natural effect model
Description
neModel is used to fit a natural effect model on the expanded dataset.
Usage
neModel(formula, family = gaussian, expData, xFit, se = c("bootstrap",
"robust"), nBoot = 1000, parallel = c("no", "multicore", "snow"),
ncpus = getOption("boot.ncpus", 1L), progress = TRUE, ...)
Arguments
formula aformula object providing a symbolic description of the natural effect model.
family a description of the error distribution and link function to be used in the model.
For glm this can be a character string naming a family function, a family function
or the result of a call to a family function. For glm.fit only the third option is
supported. (See family for details of family functions.)
expData the expanded dataset (of class "expData").
xFit fitted model object representing a model for the exposure (used for inverse treat-
ment (exposure) probability weighting).
se character string indicating the type of standard errors to be calculated. The de-
fault type is based on the bootstrap (see details).
nBoot number of bootstrap replicates (see Rargument of boot).
parallel (only for bootstrap) The type of parallel operation to be used (if any). If missing,
the default is taken from the option "boot.parallel" (and if that is not set,
"no").
ncpus (only for bootstrap) integer: number of processes to be used in parallel oper-
ation: typically one would chose this to the number of available CPUs (see
details).
progress (only for bootstrap) logical value indicating whether or not a progress bar should
be displayed. Progress bars are automatically disabled for multicore processing.
... additional arguments (passed to glm).
16 neModel
Details
This function is a wrapper for glm, providing unbiased bootstrap (se = "bootstrap", the default)
or robust (se = "robust") standard errors for the parameter estimates (see below for more details).
The formula argument requires to be specified in function of the variables from the expanded
dataset (specified in expData) whose corresponding parameters index the direct and indirect effect.
Stratum-specific natural effects can be estimated by additionally modeling the relation between
the outcome and baseline covariates. If the set of baseline covariates adjusted for in the formula
argument is not sufficient to control for confounding (e.g. when fitting a population-average natural
effect model), an adequate model for the exposure (conditioning on a sufficient set of baseline
covariates) should be specified in the xFit argument. In this case, such a model for the exposure
distribution is needed to weight by the reciprocal of the probability (density) of the exposure (i.e.
inverse probability weighting) in order to adjust for confounding. Just as for ratio-of-mediator
probability weighting (see paragraph below), this kind of weighting is done internally.
Quadratic or higher-order polynomial terms can be included in the formula by making use of the
Ifunction or by using the poly function. However, we do not recommend the use of orthogonal
polynomials (i.e. using the default argument specification raw = FALSE in poly), as these are not
compatible with the neEffdecomp function.
In contrast to glm, the expData argument (rather than data argument) requires specification of a
data frame that inherits from class "expData", which contains additional information about e.g.
the fitted working model, the variable types or terms of this working model and possibly ratio-of-
mediator probability weights. The latter are automatically extracted from the expData object and
weighting is done internally.
As the default glm standard errors fail to reflect the uncertainty inherent to the working model(s)
(i.e. either a model for the mediator or an imputation model for the outcome and possibly a model
for the exposure), bootstrap standard errors (using the boot function from the boot package) or
robust standard errors are calculated. The default type of standard errors is bootstrap standard
errors. Robust standard errors (based on the sandwich estimator) can be requested (to be calculated)
instead by specifying se = "robust".
Value
An object of class "neModel"(which additionally inherits from class "neModelBoot" if the boot-
strap is used) consisting of a list of 3 objects:
neModelFit the fitted natural model object (of class "glm") with downwardly biased standard
errors
bootRes, vcov the bootstrap results (of class "boot"; if se = "bootstrap") or the robust
variance-covariance matrix (if se = "robust")
terms the neTerms (internal class) object used. This object is equivalent to the terms
object returned by the glm function, but has an additional "vartype" attribute,
a list including pointers to the names of the outcome variable (Y), exposure (X),
mediator (M), covariates (C) and auxiliary hypothetical variables xand x* (Xexp).
See neModel-methods for methods for neModel objects.
Bootstrap standard errors
The bootstrap procedure entails refitting all working models on each bootstrap sample, reconstruct-
ing the expanded dataset and subsequently refitting the specified natural effect model on this dataset.
In order to obtain stable standard errors, the number of bootstrap samples (specified via the nBoot
argument) should be chosen relatively high (default is 1000).
neModel 17
To speed up the bootstrap procedure, parallel processing can be used by specifying the desired type
of parallel operation via the parallel argument (for more details, see boot). The number of parallel
processes (ncpus) is suggested to be specified explicitly (its default is 1, unless the global option
options("boot.cpus") is specified). The function detectCores from the parallel package can
be helpful at determining the number of available cores (although this may not always correspond
to the number of allowed cores).
Robust standard errors
Robust variance-covariance matrices for the model parameters, based on the sandwich estimator,
are calculated using core functions from the sandwich package. Additional details and derivations
for the sandwich estimator for natural effect models can be found in the corresponding vignette that
can be obtained by the command vignette("sandwich", package = "medflex").
Note
It is important to note that the original mediator(s) should not be specified in the formula argument,
as the natural indirect effect in natural effect models should be captured solely by parameter(s)
corresponding to the auxiliary hypothetical variable x* in the expanded dataset (see expData).
References
Lange, T., Vansteelandt, S., & Bekaert, M. (2012). A Simple Unified Approach for Estimating
Natural Direct and Indirect Effects. American Journal of Epidemiology,176(3), 190-195.
Vansteelandt, S., Bekaert, M., & Lange, T. (2012). Imputation Strategies for the Estimation of
Natural Direct and Indirect Effects. Epidemiologic Methods,1(1), Article 7.
Loeys, T., Moerkerke, B., De Smet, O., Buysse, A., Steen, J., & Vansteelandt, S. (2013). Flexi-
ble Mediation Analysis in the Presence of Nonlinear Relations: Beyond the Mediation Formula.
Multivariate Behavioral Research,48(6), 871-894.
See Also
neModel-methods,plot.neModel,neImpute,neWeight,neLht,neEffdecomp
Examples
data(UPBdata)
##############################
## weighting-based approach ##
##############################
weightData <- neWeight(negaff ~ att + gender + educ + age,
data = UPBdata)
## stratum-specific natural effects
# bootstrap SE
## Not run:
weightFit1b <- neModel(UPB ~ att0 * att1 + gender + educ + age,
family = binomial, expData = weightData)
summary(weightFit1b)
## End(Not run)
# robust SE
weightFit1r <- neModel(UPB ~ att0 * att1 + gender + educ + age,
18 neModel-methods
family = binomial, expData = weightData, se = "robust")
summary(weightFit1r)
## population-average natural effects
expFit <- glm(att ~ gender + educ + age, data = UPBdata)
# bootstrap SE
## Not run:
weightFit2b <- neModel(UPB ~ att0 * att1, family = binomial,
expData = weightData, xFit = expFit)
summary(weightFit2b)
## End(Not run)
# robust SE
weightFit2r <- neModel(UPB ~ att0 * att1, family = binomial,
expData = weightData, xFit = expFit, se = "robust")
summary(weightFit2r)
###############################
## imputation-based approach ##
###############################
impData <- neImpute(UPB ~ att * negaff + gender + educ + age,
family = binomial, data = UPBdata)
## stratum-specific natural effects
# bootstrap SE
## Not run:
impFit1b <- neModel(UPB ~ att0 * att1 + gender + educ + age,
family = binomial, expData = impData)
summary(impFit1b)
## End(Not run)
# robust SE
impFit1r <- neModel(UPB ~ att0 * att1 + gender + educ + age,
family = binomial, expData = impData, se = "robust")
summary(impFit1r)
## population-average natural effects
# bootstrap SE
## Not run:
impFit2b <- neModel(UPB ~ att0 * att1, family = binomial,
expData = impData, xFit = expFit)
summary(impFit2b)
## End(Not run)
# robust SE
impFit2r <- neModel(UPB ~ att0 * att1, family = binomial,
expData = impData, xFit = expFit, se = "robust")
summary(impFit2r)
neModel-methods Methods for natural effect models
neModel-methods 19
Description
Extractor functions, confidence intervals, residual plots and statistical tests for natural effect models.
Usage
## S3 method for class 'neModel'
coef(object, ...)
## S3 method for class 'neModelBoot'
confint(object, parm, level = 0.95,
type = "norm", ...)
## S3 method for class 'neModel'
confint(object, parm, level = 0.95, ...)
## S3 method for class 'neModel'
residualPlot(object, ...)
## S3 method for class 'neModel'
residualPlots(object, ...)
## S3 method for class 'neModel'
summary(object, ...)
## S3 method for class 'neModel'
vcov(object, ...)
## S3 method for class 'neModel'
weights(object, ...)
Arguments
object a fitted natural effect model object.
... additional arguments.
parm a specification of which parameters are to be given confidence intervals, either
a vector of numbers or a vector of names. If missing, all parameters are consid-
ered.
level the confidence level required.
type the type of bootstrap intervals required. The default "norm" returns normal ap-
proximation bootstrap confidence intervals. Currently, "norm","basic","perc"
and "bca" are supported (see boot.ci).
Details
confint yields bootstrap confidence intervals or confidence intervals based on the sandwich estima-
tor (depending on the type of standard errors requested when fitting the neModel object). Bootstrap
confidence intervals are internally called via the boot.ci function from the boot package. Confi-
dence intervals based on the sandwich estimator are internally called via confint.default. The
default confidence level specified in level (which corresponds to the conf argument in boot.ci) is
0.95 and the default type of bootstrap confidence interval, "norm", is based on the normal approxi-
mation. Bias-corrected and accelerated ("bca") bootstrap confidence intervals require a sufficiently
large number of bootstrap replicates (for more details see boot.ci).
20 neModel-methods
A summary table with large sample tests, similar to that for glm output, can be obtained using
summary.
vcov returns either the bootstrap variance-covariance matrix (calculated from the bootstrap samples
stored in
object$bootRes; see neModel) or the robust variance-covariance matrix (which is a diagonal block
matrix of the original sandwich covariance matrix).
weights returns a vector containing the regression weights used to fit the natural effect model.
These weights can be based on
1. ratio-of-mediator probability (density) weights (only if the weighting-based approach is used)
2. inverse probability of treatment (exposure) weights (only if xFit was specified in neModel)
residualPlot and residualPlots are convenience functions from the car package. These can be
used to assess model adequacy.
Note
For the bootstrap, z-values in the summary table are calculated by dividing the parameter estimate
by its corresponding bootstrap standard error. Corresponding p-values in the summary table are
indicative, since the null distribution for each statistic is assumed to be approximately standard
normal. Therefore, whenever possible, it is recommended to focus mainly on bootstrap confidence
intervals for inference, rather than the provided p-values.
See Also
neModel,plot.neModel,residualPlot,residualPlots,weights
Examples
data(UPBdata)
weightData <- neWeight(negaff ~ att + educ + gender + age,
data = UPBdata)
neMod <- neModel(UPB ~ att0 * att1 + educ + gender + age,
family = binomial, expData = weightData, se = "robust")
## extract coefficients
coef(neMod)
## extract variance-covariance matrix
vcov(neMod)
## extract regression weights
w <- weights(neMod)
head(w)
## obtain bootstrap confidence intervals
confint(neMod)
confint(neMod, parm = c("att0"))
confint(neMod, type = "perc", level = 0.90)
## summary table
summary(neMod)
## residual plots
neWeight 21
library(car)
residualPlots(neMod)
neWeight Expand the dataset and calculate ratio-of-mediator probability
weights
Description
This function both expands the data along hypothetical exposure values and calculates ratio-of-
mediator probability weights.
Usage
neWeight(object, ...)
Arguments
object an object used to select a method.
... additional arguments.
Details
Generic function that both expands the data along hypothetical exposure values and calculates ratio-
of-mediator probability weights
ˆ
P(Mi|Xi=x∗, Ci)
ˆ
P(Mi|Xi=x, Ci)
for each observation unit iin this expanded dataset in a single run. These weights are ratios of
probabilities or probability densities from the mediator model distribution, which can be specified
either externally as a fitted model object (neWeight.default) or internally (neWeight.formula).
Value
A data frame of class c("data.frame", "expData", "weightData"). See expData for its struc-
ture.
References
Hong, G. (2010). Ratio of mediator probability weighting for estimating natural direct and indirect
effects. In Proceedings of the American Statistical Association, Biometrics Section, pp. 2401-2415.
American Statistical Association, Alexandria, VA.
Lange, T., Vansteelandt, S., & Bekaert, M. (2012). A Simple Unified Approach for Estimating
Natural Direct and Indirect Effects. American Journal of Epidemiology,176(3), 190-195.
See Also
neWeight.default,neWeight.formula,expData
22 neWeight.default
neWeight.default Expand the dataset and calculate ratio-of-mediator probability
weights
Description
This function both expands the data along hypothetical exposure values and calculates ratio-of-
mediator probability weights.
Usage
## Default S3 method:
neWeight(object, formula, data, nRep = 5,
xSampling = c("quantiles", "random"), xFit, percLim = c(0.05, 0.95),
...)
Arguments
object fitted model object representing the mediator model.
formula aformula object providing a symbolic description of the mediator model. Re-
dundant if already specified in call for fitted model specified in object (see
details).
data data, as matrix or data frame, containing the exposure (and other relevant) vari-
ables. Redundant if already specified in call for fitted model specified in object
(see details).
nRep number of replications or hypothetical values of the exposure to sample for each
observation unit.
xSampling character string indicating how to sample from the conditional exposure distri-
bution. Possible values are "quantiles" or "random" (see details).
xFit an optional fitted object (preferably glm) for the conditional exposure distribu-
tion (see details).
percLim a numerical vector of the form c(lower, upper) indicating the extreme per-
centiles to sample when using "quantiles" as sampling method to sample from
the conditional exposure distribution (see details).
... additional arguments.
Details
The calculated weights are ratios of fitted probabilities or probability densities from the distribution
of the mediator model. This model needs to be specified as a fitted object in the object argument.
If the model-fitting function used to fit the mediator model does not require specification of a
formula or data argument, these need to be specified explicitly in order to enable neWeight.default
to extract pointers to variable types relevant for mediation analysis.
Whether a formula is specified externally (in the call for the fitted mediator model object which
is specified in object) or internally (via the formula argument), it always needs to be of the form
M~X+C1+C2, with predictor variables entered in the following prespecified order:
1. exposure X: The first predictor is coded as exposure or treatment.
neWeight.default 23
2. baseline covariates C: All remaining predictor variables are automatically coded as baseline
covariates.
It is important to adhere to this prespecified order to enable neWeight to create valid pointers
to these different types of predictor variables. This requirement extends to the use of operators
different than the +operator, such as the :and *operators (when e.g. adding interaction terms).
For instance, the formula specifications M ~ X * C1 + C2,M ~ X + C1 + X:C1 + C2 and
Y ~ X + X:C1 + C1 + C2 will create identical pointers to the different types of variables, as the
order of the unique predictor variables is identical in all three specifications.
Furthermore, categorical exposures that are not coded as factors in the original dataset, should be
specified as factors in the formula, using the factor function, e.g. M ~ factor(X) + C1 + C2.
Quadratic or higher-order polynomial terms can be included as well, by making use of the I
function or by using the poly function. For instance, M ~ X + I(X^2) + C1 + C2 and
M ~ poly(X, 2, raw = TRUE) + C1 + C2 are equivalent and result in identical pointers to
the different types of variables.
The command terms(object, "vartype") (with object replaced by the name of the resulting
expanded dataset) can be used to check whether valid pointers have been created.
In contrast to imputation models with categorical exposures, additional arguments need to be spec-
ified if the exposure is continuous. All of these additional arguments are related to the sampling
procedure for the exposure.
Whereas the number of replications nRep for categorical variables equals the number of levels for
the exposure coded as a factor (i.e. the number of hypothetical exposure values), the number of
desired replications needs to be specified explicitly for continuous exposures. Its default is 5.
If xFit is left unspecified, the hypothetical exposure levels are automatically sampled from a linear
model for the exposure, conditional on a linear combination of all covariates. If one wishes to use
another model for the exposure, this default model specification can be overruled by referring to a
fitted model object in the xFit argument. Misspecification of this sampling model does not induce
bias in the estimated coefficients and standard errors of the natural effect model.
The xSampling argument allows to specify how the hypothetical exposure levels should be sam-
pled from the conditional exposure distribution (which is either entered explicitly using the xFit
argument or fitted automatically as described in the previous paragraph). The "random" option
randomly samples nRep draws from the exposure distribution, whereas the "quantiles" option
(default) samples nRep quantiles at equal-sized probability intervals. Only the latter hence yields
fixed exposure levels given nRep and xFit.
In order to guarantee that the entire support of the distribution is being sampled (which might be a
concern if nRep is chosen to be small), the default lower and upper sampled quantiles are the 5th
and 95th percentiles. The intermittent quantiles correspond to equal-sized probability intervals. So,
for instance, if nRep = 4, then the sampled quantiles will correspond to probabilities 0.05, 0.35,
0.65 and 0.95. These default ’outer’ quantiles can be changed by specifying the percLim argument
accordingly. By specifying percLim = NULL, the standard quantiles will be sampled (e.g., 0.2, 0.4,
0.6 and 0.8 if nRep = 4).
Value
A data frame of class c("data.frame", "expData", "weightData"). See expData for its struc-
ture.
See Also
neWeight,neWeight.formula,expData
24 neWeight.formula
Examples
data(UPBdata)
## example using glm
fit.glm <- glm(negaff ~ att + gender + educ + age, data = UPBdata)
weightData <- neWeight(fit.glm, nRep = 2)
neWeight.formula Expand the dataset and calculate ratio-of-mediator probability
weights
Description
This function both expands the data along hypothetical exposure values and calculates ratio-of-
mediator probability weights.
Usage
## S3 method for class 'formula'
neWeight(object, family, data, FUN = glm, nRep = 5,
xSampling = c("quantiles", "random"), xFit, percLim = c(0.05, 0.95),
...)
Arguments
object aformula object providing a symbolic description of the mediator model (see
details).
family a description of the error distribution and link function to be used in the model.
Consult the help files of the model-fitting function specified in FUN for more
details on appropriate argument specification.
data data, as matrix or data frame, containing the exposure (and other relevant) vari-
ables. Redundant if already specified in call for fitted model specified in object
(see details).
FUN function used to fit model specified in formula.
nRep number of replications or hypothetical values of the exposure to sample for each
observation unit.
xSampling character string indicating how to sample from the conditional exposure distri-
bution. Possible values are "quantiles" or "random" (see details).
xFit an optional fitted object (preferably glm) for the conditional exposure distribu-
tion (see details).
percLim a numerical vector of the form c(lower, upper) indicating the extreme per-
centiles to sample when using "quantiles" as sampling method to sample from
the conditional exposure distribution (see details).
... additional arguments (passed to FUN).
neWeight.formula 25
Details
The calculated weights are ratios of fitted probabilities or probability densities from the distribution
of the mediator model. This model is fitted internally by extracting information from the arguments
object,family,data,FUN and ....
For mediation model specification via the object argument, use a formula of the form
M~X+C1+C2, with predictor variables entered in the following prespecified order:
1. exposure X: The first predictor is coded as exposure or treatment.
2. baseline covariates C: All remaining predictor variables are automatically coded as baseline
covariates.
It is important to adhere to this prespecified order to enable neWeight to create valid pointers
to these different types of predictor variables. This requirement extends to the use of operators
different than the +operator, such as the :and *operators (when e.g. adding interaction terms).
For instance, the formula specifications M ~ X * C1 + C2,M ~ X + C1 + X:C1 + C2 and
Y ~ X + X:C1 + C1 + C2 will create identical pointers to the different types of variables, as the
order of the unique predictor variables is identical in all three specifications.
Furthermore, categorical exposures that are not coded as factors in the original dataset, should be
specified as factors in the formula, using the factor function, e.g. M ~ factor(X) + C1 + C2.
Quadratic or higher-order polynomial terms can be included as well, by making use of the I
function or by using the poly function. For instance, M ~ X + I(X^2) + C1 + C2 and
M ~ poly(X, 2, raw = TRUE) + C1 + C2 are equivalent and result in identical pointers to
the different types of variables.
The command terms(object, "vartype") (with object replaced by the name of the resulting
expanded dataset) can be used to check whether valid pointers have been created.
The type of mediator model can be defined by specifying an appropriate model-fitting function via
the FUN argument (its default is glm). This method can only be used with model-fitting functions
that require a formula argument.
In contrast to imputation models with categorical exposures, additional arguments need to be spec-
ified if the exposure is continuous. All of these additional arguments are related to the sampling
procedure for the exposure.
Whereas the number of replications nRep for categorical variables equals the number of levels for
the exposure coded as a factor (i.e. the number of hypothetical exposure values), the number of
desired replications needs to be specified explicitly for continuous exposures. Its default is 5.
If xFit is left unspecified, the hypothetical exposure levels are automatically sampled from a linear
model for the exposure, conditional on a linear combination of all covariates. If one wishes to use
another model for the exposure, this default model specification can be overruled by referring to a
fitted model object in the xFit argument. Misspecification of this sampling model does not induce
bias in the estimated coefficients and standard errors of the natural effect model.
The xSampling argument allows to specify how the hypothetical exposure levels should be sam-
pled from the conditional exposure distribution (which is either entered explicitly using the xFit
argument or fitted automatically as described in the previous paragraph). The "random" option
randomly samples nRep draws from the exposure distribution, whereas the "quantiles" option
(default) samples nRep quantiles at equal-sized probability intervals. Only the latter hence yields
fixed exposure levels given nRep and xFit.
In order to guarantee that the entire support of the distribution is being sampled (which might be a
concern if nRep is chosen to be small), the default lower and upper sampled quantiles are the 5th
and 95th percentiles. The intermittent quantiles correspond to equal-sized probability intervals. So,
for instance, if nRep = 4, then the sampled quantiles will correspond to probabilities 0.05, 0.35,
26 plot.neLht
0.65 and 0.95. These default ’outer’ quantiles can be changed by specifying the percLim argument
accordingly. By specifying percLim = NULL, the standard quantiles will be sampled (e.g., 0.2, 0.4,
0.6 and 0.8 if nRep = 4).
Value
A data frame of class c("data.frame", "expData", "weightData")). See expData for its
structure.
See Also
neWeight.default,expData
Examples
data(UPBdata)
## example using glm
weightData <- neWeight(negaff ~ att + gender + educ + age,
data = UPBdata, nRep = 2)
plot.neLht Confidence interval plots for linear hypotheses in natural effect models
Description
Confidence interval plots for linear hypotheses in natural effect models.
Usage
## S3 method for class 'neEffdecomp'
plot(x, level = 0.95, transf = identity, ylabels,
yticks.at, ...)
## S3 method for class 'neLht'
plot(x, level = 0.95, transf = identity, ylabels,
yticks.at, ...)
## S3 method for class 'neLhtBoot'
plot(x, level = 0.95, ci.type = "norm",
transf = identity, ylabels, yticks.at, ...)
Arguments
xan object of class neLht.
level the confidence level required.
transf transformation function to be applied internally on the (linear hypothesis) esti-
mates and their confidence intervals (e.g. exp for logit or Poisson regression).
The default is identity (i.e. no transformation).
ylabels character vector containing the labels for the (linear hypothesis) estimates to be
plotted on the y-axis.
plot.neModel 27
yticks.at numeric vector containing the y-coordinates (from 0 to 1) to draw the tick marks
for the different estimates and their corresponding confidence intervals.
... additional arguments.
ci.type the type of bootstrap intervals required (see type argument in neModel-methods).
Details
This function is an adapted version of plot.glht from the multcomp package and yields confi-
dence interval plots for each of the linear hypothesis parameters.
See Also
neModel,neLht,neEffdecomp
Examples
data(UPBdata)
impData <- neImpute(UPB ~ att * negaff + gender + educ + age,
family = binomial, data = UPBdata)
neMod <- neModel(UPB ~ att0 * att1 + gender + educ + age,
family = binomial, expData = impData, se = "robust")
lht <- neLht(neMod, linfct = c("att0 = 0", "att0 + att0:att1 = 0",
"att1 = 0", "att1 + att0:att1 = 0",
"att0 + att1 + att0:att1 = 0"))
## all pairs return identical output
plot(confint(lht), transf = exp)
plot(lht, transf = exp)
plot(neEffdecomp(neMod), transf = exp)
plot(neMod, transf = exp)
plot.neModel Confidence interval plots for natural effect components
Description
Obtain effect decomposition confidence interval plots for natural effect models.
Usage
## S3 method for class 'neModel'
plot(x, xRef, covLev, level = 0.95,
transf = identity, ylabels, yticks.at, ...)
## S3 method for class 'neModelBoot'
plot(x, xRef, covLev, level = 0.95,
ci.type = "norm", transf = identity, ylabels, yticks.at, ...)
28 UPBdata
Arguments
xa fitted natural effect model object.
xRef a vector including reference levels for the exposure, x* and x, at which natural
effect components need to be evaluated (see details).
covLev a vector including covariate levels at which natural effect components need to
be evaluated (see details).
level the confidence level required.
transf transformation function to be applied internally on the (linear hypothesis) esti-
mates and their confidence intervals (e.g. exp for logit or Poisson regression).
The default is identity (i.e. no transformation).
ylabels character vector containing the labels for the (linear hypothesis) estimates to be
plotted on the y-axis.
yticks.at numeric vector containing the y-coordinates (from 0 to 1) to draw the tick marks
for the different estimates and their corresponding confidence intervals.
... additional arguments.
ci.type the type of bootstrap intervals required (see type argument in neModel-methods).
Details
This function yields confidence interval plots for the natural effect components. These causal pa-
rameter estimates are first internally extracted from the neModel object by applying the effect de-
composition function neEffdecomp(x, xRef, covLev).
Examples
data(UPBdata)
impData <- neImpute(UPB ~ att * negaff + educ + gender + age,
family = binomial, data = UPBdata)
neMod <- neModel(UPB ~ att0 * att1 + educ + gender + age,
family = binomial, expData = impData, se = "robust")
plot(neMod)
plot(neMod, transf = exp,
ylabels = c("PDE", "TDE", "PIE", "TIE", "TE"))
plot(neMod, level = 0.9, xRef = c(-1, 0))
UPBdata UPB data
Description
Data from a survey study that was part of the Interdisciplinary Project for the Optimization of
Separation trajectories (IPOS). This large-scale project involved the recruitment of individuals who
divorced between March 2008 and March 2009 in four major courts in Flanders. It aimed to improve
the quality of life in families during and after the divorce by translating research findings into
practical guidelines for separation specialists and by promoting evidence-based policy. This dataset
involves a subsample of 385 individuals, namely those who responded to a battery of questionnaires
related to romantic relationship and breakup characteristics (De Smet, 2012).
UPBdata 29
Format
A data frame with 385 rows and 9 variables:
att self-reported anxious attachment level (standardized)
attbin binary version of self-reported anxious attachment level: 1 = higher than sample mean, 0 =
lower than sample mean
attcat multicategorical version of self-reported anxious attachment level: L= low, M= intermediate,
H= high
negaff level of self-reported experienced negative affectivity (standardized)
initiator initiator of the divorce
gender gender: F= female, M= male
educ education level: either H= high (at least a bachelor’s degree), M= intermediate (having fin-
ished secondary school) or L= low (otherwise)
age age (in years)
UPB binary variable indicating whether the individual reported having displayed unwanted pursuit
behavior(s) towards the ex-partner
Source
Ghent University and Catholic University of Louvain (2010). Interdisciplinary Project for the Op-
timisation of Separation trajectories - divorce and separation in Flanders.
http://www.scheidingsonderzoek.ugent.be/index-eng.html
References
De Smet, O., Loeys, T., & Buysse, A. (2012). Post-Breakup Unwanted Pursuit: A Refined Analysis
of the Role of Romantic Relationship Characteristics. Journal of Family Violence,27(5), 437-452.
Loeys, T., Moerkerke, B., De Smet, O., Buysse, A., Steen, J., & Vansteelandt, S. (2013). Flexi-
ble Mediation Analysis in the Presence of Nonlinear Relations: Beyond the Mediation Formula.
Multivariate Behavioral Research,48(6), 871-894.
Index
adjusted,14
boot,15–17
boot.ci,13,14,19
coef.neModel (neModel-methods),18
confint.default,19
confint.glht,14
confint.neLht (neLht-methods),13
confint.neLhtBoot (neLht-methods),13
confint.neModel (neModel-methods),18
confint.neModelBoot (neModel-methods),
18
detectCores,17
expData,2,3–5,7,10,15–17,21,23,26
expData-methods,3
factor,6,9,23,25
family,15
formula,5,6,8,9,15,22,24,25
glht,11,12,14
glm,9,15,16,20,25
I,6,9,16,23,25
neEffdecomp,16,17,27,28
neEffdecomp (neLht),10
neImpute,2,3,4,7,10,17
neImpute.default,4,5,5,10
neImpute.formula,4,5,7,8
neLht,10,14,17,27
neLht-methods,13
neModel,2,5,7,10,12,14,15,16,19,20,27
neModel-methods,18
neWeight,2–4,17,21,23
neWeight.default,21,22,26
neWeight.formula,21,23,24
plot.glht,27
plot.neEffdecomp (plot.neLht),26
plot.neLht,12,14,26
plot.neLhtBoot (plot.neLht),26
plot.neModel,12,17,20,27
plot.neModelBoot (plot.neModel),27
poly,6,9,16,23,25
print,11
residualPlot,4,20
residualPlot.expData (expData-methods),
3
residualPlot.neModel (neModel-methods),
18
residualPlots,4,20
residualPlots.expData
(expData-methods),3
residualPlots.neModel
(neModel-methods),18
residuals,4
residuals.expData (expData-methods),3
summary,11,12
summary.glht,14
summary.neLht (neLht-methods),13
summary.neModel (neModel-methods),18
SuperLearner,6,9
terms,16
UPBdata,28
vcov.neModel (neModel-methods),18
weights,4,20
weights.expData (expData-methods),3
weights.neModel (neModel-methods),18
30
