| Title: |
Multiple Imputation for Exploratory Factor Analysis |
| Version: |
0.2.1 |
| URL: |
https://github.com/teebusch/mifa |
| BugReports: |
https://github.com/teebusch/mifa/issues |
| Imports: |
stats, mice, dplyr, checkmate |
| Suggests: |
psych, testthat, knitr, rmarkdown, ggplot2, tidyr, covr |
| Description: |
Impute the covariance matrix of incomplete data so that factor
analysis can be performed. Imputations are made using multiple imputation
by Multivariate Imputation with Chained Equations (MICE) and combined with
Rubin's rules. Parametric Fieller confidence intervals and nonparametric
bootstrap confidence intervals can be obtained for the variance explained by
different numbers of principal components. The method is described in
Nassiri et al. (2018) <doi:10.3758/s13428-017-1013-4>. |
| License: |
MIT + file LICENSE |
| Encoding: |
UTF-8 |
| RoxygenNote: |
7.3.2 |
| NeedsCompilation: |
no |
| Packaged: |
2025-05-10 20:04:10 UTC; tobiasbusch |
| Author: |
Vahid Nassiri [aut],
Anikó Lovik [aut],
Geert Molenberghs [aut],
Geert Verbeke [aut],
Tobias Busch 
[aut, cre] |
| Maintainer: |
Tobias Busch <teebusch@gmail.com> |
| Repository: |
CRAN |
| Date/Publication: |
2025-05-10 20:30:02 UTC |
Check and clean n_pc argument
Description
Check and clean n_pc argument
Usage
clean_n_pc(n_pc, n_cov_vars)
Arguments
n_pc |
User-supplied n_pc argument. An integer vector.
|
n_cov_vars |
Number of variables in the covariance matrix
|
Value
Cleaned n_pc. An integer vector. Sorted, if applicable.
Combine results from different imputations using Rubin's rules
Description
Applies Rubin's rules to combine estimates and
variance-covariance matrices from different imputations.
Usage
combine_rubin(param_imps, cov_imps)
Arguments
param_imps |
Matrix containing estimated parameters in each imputation
as its rows.
|
cov_imps |
List of estimated covariance matrices for each imputation.
|
Value
A list:
- param_est
Vector of combined parameter estimates with the same length
as columns in param_imps.
- cov_param
Combined variance-covariance matrix of size n x n, where n
is the number of columns in param_imps.
- between_cov
Between imputations variance-covariance matrix of size
n x n, where n is the number of columns in param_imps.
References
Rubin D. B. Multiple imputation for nonresponse in surveys (2004).
John Wiley & Sons.
Find the Fieller interval for each k
Description
This function is used by mifa_ci_fieller() to compute Fieller's confidence
intervals for each of the components of n_pc.
Usage
get_fieller_ci(eig_imp, n_pc, conf, N, m)
Arguments
eig_imp |
A matrix with each of its columns the eigenvalues of the
estimated covariance matrix for each imputed data.
|
n_pc |
Integer or integer vector indicating number of principal
components (eigenvectors) for which explained variance (eigenvalues) should
be obtained and for which confidence intervals should be computed.
Defaults to all principal components, i.e., the number of variables in the
data.
|
conf |
Confidence level for constructing confidence intervals. The
default is .95 that is, 95% confidence intervals.
|
N |
A scalar specifying sample size.
|
m |
A scalar specifying number of multiple imputations.
|
Value
A vector of length 2, containing the lower and upper bounds of
estimated Fieller's interval.
Sequential Imputation
Description
Sequential imputations in case that some of the columns are
not imputed due to collinearity, etc.
Usage
mice_impute_all_NA(data, ...)
Arguments
data |
A data frame with missing values coded as NA.
|
Details
This function will keep imputing the same data over and over
until there are no NA values left.
Value
A data frame without NAs
Imputes a single dataset using mice
Description
Imputes a single dataset using mice
Usage
mice_impute_once(data, ...)
Arguments
data |
A data frame with missing values coded as NA.
|
Value
A data frame with missing values imputed.
Get covariance matrix of incomplete data using multiple imputation
Description
Compute covariance matrix of incomplete data using multiple imputation.
For multiple imputation, Multivariate Imputation by Chained Equations
(MICE) from the mice package is used. The covariance matrices of
the imputed data sets are combined using Rubin's rules.
Usage
mifa(
data,
cov_vars = dplyr::everything(),
n_pc,
ci = FALSE,
conf = 0.95,
n_boot = 1000,
...
)
Arguments
data |
A data frame with missing values coded as NA.
|
cov_vars |
Variables in data for which to calculate the covariance
matrix. Supports (tidy selection)dplyr::select(). This allows to
select variables that are used for the imputations of missing values, but not
the calculations of the covariance matrix. This is especially useful when
there are categorical predictors that can improve the imputation of the
response variables, but for which covariance cannot be calculated.
By default, all variables in data are used for both, the imputation and
the covariance matrix. Note: Variables and rows used for the imputation, as
well as the method for imputation can be configured using the ....
See also mice::mice().
|
n_pc |
Integer or integer vector indicating number of principal
components (eigenvectors) for which explained variance (eigenvalues) should
be obtained and for which confidence intervals should be computed.
Defaults to all principal components, i.e., the number of variables in the
data.
|
ci |
A character string indicating which types of confidence intervals
should be constructed for the variance explained by the principal
components. If "boot", "fieller", or "both", the corresponding
intervals are computed. If FALSE (the default) no confidence intervals will
be computed. The components for which confidence intervals should be computed
can be set with n_pc. See mifa_ci_boot() and mifa_ci_fieller() for
details about the two methods.
|
conf |
Confidence level for constructing confidence intervals. The
default is .95 that is, 95% confidence intervals.
|
n_boot |
Number of bootstrap samples to use for bootstrapped confidence
intervals. The default is 1000.
|
... |
Arguments passed on to mice::mice
mNumber of multiple imputations. The default is m=5.
methodCan be either a single string, or a vector of strings with
length length(blocks), specifying the imputation method to be
used for each column in data. If specified as a single string, the same
method will be used for all blocks. The default imputation method (when no
argument is specified) depends on the measurement level of the target column,
as regulated by the defaultMethod argument. Columns that need
not be imputed have the empty method "". See details.
predictorMatrixA numeric matrix of length(blocks) rows
and ncol(data) columns, containing 0/1 data specifying
the set of predictors to be used for each target column.
Each row corresponds to a variable block, i.e., a set of variables
to be imputed. A value of 1 means that the column
variable is used as a predictor for the target block (in the rows).
By default, the predictorMatrix is a square matrix of ncol(data)
rows and columns with all 1's, except for the diagonal.
Note: For two-level imputation models (which have "2l" in their names)
other codes (e.g, 2 or -2) are also allowed.
ignoreA logical vector of nrow(data) elements indicating
which rows are ignored when creating the imputation model. The default
NULL includes all rows that have an observed value of the variable
to imputed. Rows with ignore set to TRUE do not influence the
parameters of the imputation model, but are still imputed. We may use the
ignore argument to split data into a training set (on which the
imputation model is built) and a test set (that does not influence the
imputation model estimates).
Note: Multivariate imputation methods, like mice.impute.jomoImpute()
or mice.impute.panImpute(), do not honour the ignore argument.
whereA data frame or matrix with logicals of the same dimensions
as data indicating where in the data the imputations should be
created. The default, where = is.na(data), specifies that the
missing data should be imputed. The where argument may be used to
overimpute observed data, or to skip imputations for selected missing values.
Note: Imputation methods that generate imptutations outside of
mice, like mice.impute.panImpute() may depend on a complete
predictor space. In that case, a custom where matrix can not be
specified.
blocksList of vectors with variable names per block. List elements
may be named to identify blocks. Variables within a block are
imputed by a multivariate imputation method
(see method argument). By default each variable is placed
into its own block, which is effectively
fully conditional specification (FCS) by univariate models
(variable-by-variable imputation). Only variables whose names appear in
blocks are imputed. The relevant columns in the where
matrix are set to FALSE of variables that are not block members.
A variable may appear in multiple blocks. In that case, it is
effectively re-imputed each time that it is visited.
visitSequenceA vector of block names of arbitrary length, specifying the
sequence of blocks that are imputed during one iteration of the Gibbs
sampler. A block is a collection of variables. All variables that are
members of the same block are imputed
when the block is visited. A variable that is a member of multiple blocks
is re-imputed within the same iteration.
The default visitSequence = "roman" visits the blocks (left to right)
in the order in which they appear in blocks.
One may also use one of the following keywords: "arabic"
(right to left), "monotone" (ordered low to high proportion
of missing data) and "revmonotone" (reverse of monotone).
Special case: If you specify both visitSequence = "monotone" and
maxit = 1, then the procedure will edit the predictorMatrix
to conform to the monotone pattern. Realize that convergence in one
iteration is only guaranteed if the missing data pattern is actually
monotone. The procedure does not check this.
formulasA named list of formula's, or expressions that
can be converted into formula's by as.formula. List elements
correspond to blocks. The block to which the list element applies is
identified by its name, so list names must correspond to block names.
The formulas argument is an alternative to the
predictorMatrix argument that allows for more flexibility in
specifying imputation models, e.g., for specifying interaction terms.
blotsA named list of alist's that can be used
to pass down arguments to lower level imputation function. The entries
of element blots[[blockname]] are passed down to the function
called for block blockname.
postA vector of strings with length ncol(data) specifying
expressions as strings. Each string is parsed and
executed within the sampler() function to post-process
imputed values during the iterations.
The default is a vector of empty strings, indicating no post-processing.
Multivariate (block) imputation methods ignore the post parameter.
defaultMethodA vector of length 4 containing the default
imputation methods for 1) numeric data, 2) factor data with 2 levels, 3)
factor data with > 2 unordered levels, and 4) factor data with > 2
ordered levels. By default, the method uses
pmm, predictive mean matching (numeric data) logreg, logistic
regression imputation (binary data, factor with 2 levels) polyreg,
polytomous regression imputation for unordered categorical data (factor > 2
levels) polr, proportional odds model for (ordered, > 2 levels).
maxitA scalar giving the number of iterations. The default is 5.
printFlagIf TRUE, mice will print history on console.
Use print=FALSE for silent computation.
seedAn integer that is used as argument by the set.seed() for
offsetting the random number generator. Default is to leave the random number
generator alone.
data.initA data frame of the same size and type as data,
without missing data, used to initialize imputations before the start of the
iterative process. The default NULL implies that starting imputation
are created by a simple random draw from the data. Note that specification of
data.init will start all m Gibbs sampling streams from the same
imputation.
|
Details
The function also computes the variance explained by different numbers of
principal components and the corresponding Fieller (parametric) or bootstrap
(nonparametric) confidence intervals.
Value
A list:
- cov_combined
The estimated covariance matrix of the
incomplete data, based on the combined covariance matrices of imputed
data sets.
- cov_imputations
A list containing the estimated covariance matrixes
for all imputed data sets.
- var_explained
A data frame containing the estimated proportions of
explained variance for each of specified n_pc components. Depending o
n ci, it will also contain the estimated Fieller's (parametric) and/or
bootstrap (nonparametric) confidence interval for the proportion of
variance explained by the different numbers of principal components defined
by n_pc.
- mids
Object of type mice::mids. This is the results of
the multiple imputation step for the covariance matrix. Can be useful for
diagnosing the multiple imputations.
References
Nassiri, V., Lovik, A., Molenberghs, G., & Verbeke, G. (2018).
On using multiple imputation for exploratory factor analysis of incomplete
data. Behavioral Research Methods 50, 501–517.
doi:10.3758/s13428-017-1013-4
See Also
mifa_ci_boot(), mifa_ci_fieller(), mice::mice()
Examples
if(requireNamespace("psych")) {
data <- psych::bfi
mifa(data, cov_vars = -c(age, education, gender), ci = "fieller", print = FALSE)
}
Bootstrap confidence intervals for explained variance
Description
Compute bootstrap confidence intervals for the proportion of explained
variance for the covariance of an incomplete data imputed using
multiple imputation.
For multiple imputation, Multivariate Imputation by Chained Equations
(MICE) from the mice package is used.
Usage
mifa_ci_boot(
data,
cov_vars = dplyr::everything(),
n_pc,
conf = 0.95,
n_boot = 1000,
progress = FALSE,
...
)
Arguments
data |
A data frame with missing values coded as NA.
|
cov_vars |
Variables in data for which to calculate the covariance
matrix. Supports (tidy selection)dplyr::select(). This allows to
select variables that are used for the imputations of missing values, but not
the calculations of the covariance matrix. This is especially useful when
there are categorical predictors that can improve the imputation of the
response variables, but for which covariance cannot be calculated.
By default, all variables in data are used for both, the imputation and
the covariance matrix. Note: Variables and rows used for the imputation, as
well as the method for imputation can be configured using the ....
See also mice::mice().
|
n_pc |
Integer or integer vector indicating number of principal
components (eigenvectors) for which explained variance (eigenvalues) should
be obtained and for which confidence intervals should be computed.
Defaults to all principal components, i.e., the number of variables in the
data.
|
conf |
Confidence level for constructing confidence intervals. The
default is .95 that is, 95% confidence intervals.
|
n_boot |
Number of bootstrap samples to use for bootstrapped confidence
intervals. The default is 1000.
|
progress |
Logical. Whether to show progress bars for computation of
bootstrap confidence intervals. Default is FALSE.
|
... |
Arguments passed on to mice::mice
mNumber of multiple imputations. The default is m=5.
methodCan be either a single string, or a vector of strings with
length length(blocks), specifying the imputation method to be
used for each column in data. If specified as a single string, the same
method will be used for all blocks. The default imputation method (when no
argument is specified) depends on the measurement level of the target column,
as regulated by the defaultMethod argument. Columns that need
not be imputed have the empty method "". See details.
predictorMatrixA numeric matrix of length(blocks) rows
and ncol(data) columns, containing 0/1 data specifying
the set of predictors to be used for each target column.
Each row corresponds to a variable block, i.e., a set of variables
to be imputed. A value of 1 means that the column
variable is used as a predictor for the target block (in the rows).
By default, the predictorMatrix is a square matrix of ncol(data)
rows and columns with all 1's, except for the diagonal.
Note: For two-level imputation models (which have "2l" in their names)
other codes (e.g, 2 or -2) are also allowed.
ignoreA logical vector of nrow(data) elements indicating
which rows are ignored when creating the imputation model. The default
NULL includes all rows that have an observed value of the variable
to imputed. Rows with ignore set to TRUE do not influence the
parameters of the imputation model, but are still imputed. We may use the
ignore argument to split data into a training set (on which the
imputation model is built) and a test set (that does not influence the
imputation model estimates).
Note: Multivariate imputation methods, like mice.impute.jomoImpute()
or mice.impute.panImpute(), do not honour the ignore argument.
whereA data frame or matrix with logicals of the same dimensions
as data indicating where in the data the imputations should be
created. The default, where = is.na(data), specifies that the
missing data should be imputed. The where argument may be used to
overimpute observed data, or to skip imputations for selected missing values.
Note: Imputation methods that generate imptutations outside of
mice, like mice.impute.panImpute() may depend on a complete
predictor space. In that case, a custom where matrix can not be
specified.
blocksList of vectors with variable names per block. List elements
may be named to identify blocks. Variables within a block are
imputed by a multivariate imputation method
(see method argument). By default each variable is placed
into its own block, which is effectively
fully conditional specification (FCS) by univariate models
(variable-by-variable imputation). Only variables whose names appear in
blocks are imputed. The relevant columns in the where
matrix are set to FALSE of variables that are not block members.
A variable may appear in multiple blocks. In that case, it is
effectively re-imputed each time that it is visited.
visitSequenceA vector of block names of arbitrary length, specifying the
sequence of blocks that are imputed during one iteration of the Gibbs
sampler. A block is a collection of variables. All variables that are
members of the same block are imputed
when the block is visited. A variable that is a member of multiple blocks
is re-imputed within the same iteration.
The default visitSequence = "roman" visits the blocks (left to right)
in the order in which they appear in blocks.
One may also use one of the following keywords: "arabic"
(right to left), "monotone" (ordered low to high proportion
of missing data) and "revmonotone" (reverse of monotone).
Special case: If you specify both visitSequence = "monotone" and
maxit = 1, then the procedure will edit the predictorMatrix
to conform to the monotone pattern. Realize that convergence in one
iteration is only guaranteed if the missing data pattern is actually
monotone. The procedure does not check this.
formulasA named list of formula's, or expressions that
can be converted into formula's by as.formula. List elements
correspond to blocks. The block to which the list element applies is
identified by its name, so list names must correspond to block names.
The formulas argument is an alternative to the
predictorMatrix argument that allows for more flexibility in
specifying imputation models, e.g., for specifying interaction terms.
blotsA named list of alist's that can be used
to pass down arguments to lower level imputation function. The entries
of element blots[[blockname]] are passed down to the function
called for block blockname.
postA vector of strings with length ncol(data) specifying
expressions as strings. Each string is parsed and
executed within the sampler() function to post-process
imputed values during the iterations.
The default is a vector of empty strings, indicating no post-processing.
Multivariate (block) imputation methods ignore the post parameter.
defaultMethodA vector of length 4 containing the default
imputation methods for 1) numeric data, 2) factor data with 2 levels, 3)
factor data with > 2 unordered levels, and 4) factor data with > 2
ordered levels. By default, the method uses
pmm, predictive mean matching (numeric data) logreg, logistic
regression imputation (binary data, factor with 2 levels) polyreg,
polytomous regression imputation for unordered categorical data (factor > 2
levels) polr, proportional odds model for (ordered, > 2 levels).
maxitA scalar giving the number of iterations. The default is 5.
printFlagIf TRUE, mice will print history on console.
Use print=FALSE for silent computation.
seedAn integer that is used as argument by the set.seed() for
offsetting the random number generator. Default is to leave the random number
generator alone.
data.initA data frame of the same size and type as data,
without missing data, used to initialize imputations before the start of the
iterative process. The default NULL implies that starting imputation
are created by a simple random draw from the data. Note that specification of
data.init will start all m Gibbs sampling streams from the same
imputation.
|
Details
This function uses the Shao and Sitter (1996) method to combine multiple
imputation and bootstrapping. The imputations are done using mice::mice().
Normally, this function does not need to be called directly. Instead,
use mifa(..., ci = "boot").
Value
A data frame containing bootstrapped confidence intervals for
variance explained by different number of principal components.
References
Shao, J. & Sitter, R. R. (1996). Bootstrap for imputed survey data.
Journal of the American Statistical Association 91.435 (1996): 1278-1288.
doi:10.1080/01621459.1996.10476997
See Also
mifa(), mice::mice()
Other mifa confidence intervals:
mifa_ci_fieller()
Examples
if(requireNamespace("psych")) {
data <- psych::bfi[, 1:25]
mifa_ci_boot(data, n_pc = 3:8, n_boot = 10, print = FALSE)
}
Fieller confidence intervals for explained variance
Description
Computes parametric confidence intervals for proportion of explained
variance for given numbers of principal components using Fieller's method.
Note that by setting ci = TRUE in mifa(), this confidence
interval can be computed as well.
Usage
mifa_ci_fieller(cov_imps, n_pc, conf = 0.95, N)
Arguments
cov_imps |
List containing the estimated covariance matrix within
each imputed data. One can use cov_imputations returned by mifa().
|
n_pc |
Integer or integer vector indicating number of principal
components (eigenvectors) for which explained variance (eigenvalues) should
be obtained and for which confidence intervals should be computed.
Defaults to all principal components, i.e., the number of variables in the
data.
|
conf |
Confidence level for constructing confidence intervals. The
default is .95 that is, 95% confidence intervals.
|
N |
A scalar specifying sample size.
|
Details
Normally, this function does not need to be called directly. Instead,
use mifa(..., ci = "fieller").
Value
A data frame containing confidence intervals for n_pc principal
components.
References
Fieller, E. C. (1954). Some problems in interval estimation.
Journal of the Royal Statistical Society. Series B (Methodological): 175-185.
See Also
mifa()
Other mifa confidence intervals:
mifa_ci_boot()
Examples
if(requireNamespace("psych")) {
data <- psych::bfi[, 1:25]
mi <- mifa(data, print = FALSE)
mifa_ci_fieller(mi$cov_imputations, n_pc = 3:8, N = nrow(data))
}
A wrapper for a call to mice that throws an error if there are
constants in the data
Description
A wrapper for a call to mice that throws an error if there are
constants in the data
Usage
stop_constants(f)
Arguments
Value
The result of calling the provided function or an Error if there is
a constant in one of the columns.