Bootstrap confidence intervals for explained variance

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.

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` `m` Number of multiple imputations. The default is `m=5`. `method` Can 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. `predictorMatrix` A 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. `ignore` A 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. `where` A 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. `blocks` List 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. `visitSequence` A 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). `formulas` A 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. `blots` A 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`. `post` A 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. `defaultMethod` A 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). `maxit` A scalar giving the number of iterations. The default is 5. `printFlag` If `TRUE`, `mice` will print history on console. Use `print=FALSE` for silent computation. `seed` An 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.init` A 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 data frame containing bootstrapped confidence intervals for variance explained by different number of principal components.

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").

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

Examples