Create missing at random (MAR) values using MAR1:x in a data frame or a matrix
delete_MAR_1_to_x(
ds,
p,
cols_mis,
cols_ctrl,
x,
cutoff_fun = median,
prop = 0.5,
use_lpSolve = TRUE,
ordered_as_unordered = FALSE,
stochastic = FALSE,
add_realized_x = FALSE,
...,
miss_cols,
ctrl_cols
)A data frame or matrix in which missing values will be created.
A numeric vector with length one or equal to length cols_mis;
the probability that a value is missing.
A vector of column names or indices of columns in which missing values will be created.
A vector of column names or indices of columns, which
controls the creation of missing values in cols_mis. Must be of the
same length as cols_mis.
Numeric with length one (0 < x < Inf); odds are 1 to x for
the probability of a value to be missing in group 1 against the probability
of a value to be missing in group 2 (see details).
Function that calculates the cutoff values in the
cols_ctrl.
Numeric of length one; (minimum) proportion of rows in group 1 (only used for unordered factors).
Logical; should lpSolve be used for the determination of
groups, if cols_ctrl[i] is an unordered factor.
Logical; should ordered factors be treated as unordered factors.
Logical; see details.
Logical; if TRUE the realized odds for cols_mis will be returned (as attribute).
Further arguments passed to cutoff_fun.
Deprecated, use cols_mis instead.
Deprecated, use cols_ctrl instead.
An object of the same class as ds with missing values.
If ds[, cols_ctrl[i]] is an unordered factor, then the concept of a
cutoff value is not meaningful and cannot be applied.
Instead, a combinations of the levels of the unordered factor is searched that
guarantees at least a proportion of prop rows are in group 1
minimize the difference between prop and the proportion of
rows in group 1.
This can be seen as a binary search problem, which is solved by the solver
from the package lpSolve, if use_lpSolve = TRUE.
If use_lpSolve = FALSE, a very simple heuristic is applied.
The heuristic only guarantees that at least a proportion of prop rows
are in group 1.
The choice use_lpSolve = FALSE is not recommend and should only be
considered, if the solver of lpSolve fails.
If ordered_as_unordered = TRUE, then ordered factors will be treated
like unordered factors and the same binary search problem will be solved for
both types of factors.
If ordered_as_unordered = FALSE (the default), then ordered factors
will be grouped via cutoff_fun as described in Details.
This function creates missing at random (MAR) values in the columns
specified by the argument cols_mis.
The probability for missing values is controlled by p.
If p is a single number, then the overall probability for a value to
be missing will be p in all columns of cols_mis.
(Internally p will be replicated to a vector of the same length as
cols_mis.
So, all p[i] in the following sections will be equal to the given
single number p.)
Otherwise, p must be of the same length as cols_mis.
In this case, the overall probability for a value to be missing will be
p[i] in the column cols_mis[i].
The position of the missing values in cols_mis[i] is controlled by
cols_ctrl[i].
The following procedure is applied for each pair of cols_ctrl[i] and
cols_mis[i] to determine the positions of missing values:
At first, the rows of ds are divided into two groups.
Therefore, the cutoff_fun calculates a cutoff value for
cols_ctrl[i] (via cutoff_fun(ds[, cols_ctrl[i]], ...)).
The group 1 consists of the rows, whose values in
cols_ctrl[i] are below the calculated cutoff value.
If the so defined group 1 is empty, the rows that have a value equal to the
cutoff value will be added to this group (otherwise, these rows will
belong to group 2).
The group 2 consists of the remaining rows, which are not part of group 1.
Now the probabilities for the rows in the two groups are set in the way
that the odds are 1:x against a missing value in cols_mis[i] for the
rows in group 1 compared to the rows in group 2.
That means, the probability for a value to be missing in group 1 divided by
the probability for a value to be missing in group 2 equals 1 divided
by x.
For example, for two equal sized groups 1 and 2, ideally the number of NAs in
group 1 divided by the number of NAs in group 2 should equal 1 divided by x.
But there are some restrictions, which can lead to some deviations from the
odds 1:x (see below).
If stochastic = FALSE (the default),
then exactly round(nrow(ds) * p[i]) values will be set NA in
column cols_mis[i].
To achieve this, it is possible that the true odds differ from 1:x.
The number of observations that are deleted in group 1 and group 2 are
chosen to minimize the absolute difference between the realized odds and 1:x.
Furthermore, if round(nrow(ds) * p[i]) == 0, then no missing value
will be created in cols_mis[i].
If stochastic = TRUE, the number of missing values in
cols_mis[i] is a random variable.
This random variable is a sum of two binomial distributed variables (one for
group 1 and one for group 2).
If p is not too high and x is not too high or to low (see
below), then the odds 1:x will be met in expectation.
But in a single dataset the odds will be unequal to 1:x most of the time.
If p is high and x is too high or too low, it is possible that
the odds 1:x and the proportion of missing values p cannot be
realized together.
For example, if p[i] = 0.9, then a maximum of x = 1.25 is
possible (assuming that exactly 50 % of the values are below and 50 % of
the values are above the cutoff value in cols_ctrl[i]).
If a combination of p and x that cannot be realized together
is given to delete_MAR_1_to_x, then a warning will be generated and
x will be adjusted in such a way that p can be realized as
given to the function.
The argument add_realized_x controls whether the x of the realized
odds are added to the return value or not.
If add_realized_x = TRUE, then the realized x values for all
cols_mis will be added as an attribute to the returned object.
For stochastic = TRUE these realized x will differ from the given
x most of the time and will change if the function is rerun without
setting a seed.
For stochastic = FALSE, it is also possible that the realized odds
differ (see above). However, the realized odds will be constant over multiple
runs.
Santos, M. S., Pereira, R. C., Costa, A. F., Soares, J. P., Santos, J., & Abreu, P. H. (2019). Generating Synthetic Missing Data: A Review by Missing Mechanism. IEEE Access, 7, 11651-11667
Other functions to create MAR:
delete_MAR_censoring(),
delete_MAR_one_group(),
delete_MAR_rank()
# NOT RUN {
ds <- data.frame(X = 1:20, Y = 101:120)
delete_MAR_1_to_x(ds, 0.2, "X", "Y", 3)
# beware of small datasets and stochastic = FALSE
attr(delete_MAR_1_to_x(ds, 0.4, "X", "Y", 3, add_realized_x = TRUE), "realized_x")
attr(delete_MAR_1_to_x(ds, 0.4, "X", "Y", 4, add_realized_x = TRUE), "realized_x")
attr(delete_MAR_1_to_x(ds, 0.4, "X", "Y", 5, add_realized_x = TRUE), "realized_x")
attr(delete_MAR_1_to_x(ds, 0.4, "X", "Y", 7, add_realized_x = TRUE), "realized_x")
# p = 0.4 and 20 values -> 8 missing values, possible combinations:
# either 6 above 2 below (x = 3) or
# 7 above and 1 below (x = 7)
# Too high combination of p and x:
delete_MAR_1_to_x(ds, 0.9, "X", "Y", 3)
delete_MAR_1_to_x(ds, 0.9, "X", "Y", 3, stochastic = TRUE)
# }
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