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.

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. 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(). 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. 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. Confidence level for constructing confidence intervals. The default is .95 that is, 95% confidence intervals. 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. 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). 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. 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.

## 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.

## Details

The function also computes the variance explained by different numbers of principal components and the corresponding Fieller (parametric) or bootstrap (nonparametric) confidence intervals.

## 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

mifa_ci_boot(), mifa_ci_fieller(), mice::mice()

## Examples

# \donttest{
if(requireNamespace("psych")) {
data <- psych::bfi
mifa(data, cov_vars = -c(age, education, gender), ci = "fieller", print = FALSE)
}
#>
#> Variable:   A1 A2 A3 A4 A5 C1 C2 C3 C4 C5 E1 E2 E3 E4 E5 N1 N2 N3 N4 N5 O1 O2 O3 O4 O5
#> N Imputed:  16 27 26 19 16 21 24 20 26 16 23 16 25  9 21 22 21 11 36 29 22  0 28 14 20
#>
#> Number of MICE imputations: 5
#> Additional variables used for imputations:
#> gender education age
#>
#> Cumulative proportion of variance explained by n principal components:
#>
#>  n  prop  Fieller CI
#>  1  0.21  [0.20, 0.22]
#>  2  0.33  [0.32, 0.34]
#>  3  0.41  [0.40, 0.42]
#>  4  0.48  [0.47, 0.49]
#>  5  0.54  [0.53, 0.55]
#>  6  0.58  [0.58, 0.59]
#>  7  0.62  [0.61, 0.63]
#>  8  0.66  [0.65, 0.66]
#>  9  0.69  [0.68, 0.69]
#> 10  0.72  [0.71, 0.72]
#> 11  0.74  [0.74, 0.75]
#> 12  0.77  [0.76, 0.77]
#> 13  0.79  [0.79, 0.79]
#> 14  0.81  [0.81, 0.82]
#> 15  0.83  [0.83, 0.84]
#> 16  0.85  [0.85, 0.86]
#> 17  0.87  [0.87, 0.88]
#> 18  0.89  [0.89, 0.90]
#> 19  0.91  [0.91, 0.91]
#> 20  0.93  [0.93, 0.93]
#> 21  0.94  [0.94, 0.95]
#> 22  0.96  [0.96, 0.96]
#> 23  0.97  [0.97, 0.97]
#> 24  0.99  [0.99, 0.99]
#> 25  1.00  [1.00, 1.00]
#> # }