ampute: Generate missing data for simulation purposes

In mice: Multivariate Imputation by Chained Equations

Generate missing data for simulation purposes

Description

This function generates multivariate missing data under a MCAR, MAR or MNAR missing data mechanism. Imputation of data sets containing missing values can be performed with mice.

Usage

ampute(
  data,
  prop = 0.5,
  patterns = NULL,
  freq = NULL,
  mech = "MAR",
  weights = NULL,
  std = TRUE,
  cont = TRUE,
  type = NULL,
  odds = NULL,
  bycases = TRUE,
  run = TRUE
)

Arguments

data	A complete data matrix or data frame. Values should be numeric. Categorical variables should have been transformed to dummies.
prop	A scalar specifying the proportion of missingness. Should be a value between 0 and 1. Default is a missingness proportion of 0.5.
patterns	A matrix or data frame of size #patterns by #variables where 0 indicates that a variable should have missing values and 1 indicates that a variable should remain complete. The user may specify as many patterns as desired. One pattern (a vector) is possible as well. Default is a square matrix of size #variables where each pattern has missingness on one variable only (created with ampute.default.patterns). After the amputation procedure, md.pattern can be used to investigate the missing data patterns in the data.
freq	A vector of length #patterns containing the relative frequency with which the patterns should occur. For example, for three missing data patterns, the vector could be c(0.4, 0.4, 0.2), meaning that of all cases with missing values, 40 percent should have pattern 1, 40 percent pattern 2 and 20 percent pattern 3. The vector should sum to 1. Default is an equal probability for each pattern, created with ampute.default.freq.
mech	A string specifying the missingness mechanism, either "MCAR" (Missing Completely At Random), "MAR" (Missing At Random) or "MNAR" (Missing Not At Random). Default is a MAR missingness mechanism.
weights	A matrix or data frame of size #patterns by #variables. The matrix contains the weights that will be used to calculate the weighted sum scores. For a MAR mechanism, the weights of the variables that will be made incomplete should be zero. For a MNAR mechanism, these weights could have any possible value. Furthermore, the weights may differ between patterns and between variables. They may be negative as well. Within each pattern, the relative size of the values are of importance. The default weights matrix is made with ampute.default.weights and returns a matrix with equal weights for all variables. In case of MAR, variables that will be amputed will be weighted with 0. For MNAR, variables that will be observed will be weighted with 0. If the mechanism is MCAR, the weights matrix will not be used.
std	Logical. Whether the weighted sum scores should be calculated with standardized data or with non-standardized data. The latter is especially advised when making use of train and test sets in order to prevent leakage.
cont	Logical. Whether the probabilities should be based on a continuous or a discrete distribution. If TRUE, the probabilities of being missing are based on a continuous logistic distribution function. ampute.continuous will be used to calculate and assign the probabilities. These probabilities will then be based on the argument type. If FALSE, the probabilities of being missing are based on a discrete distribution (ampute.discrete) based on the odds argument. Default is TRUE.
type	A string or vector of strings containing the type of missingness for each pattern. Either "LEFT", "MID", "TAIL" or '"RIGHT". If a single missingness type is given, all patterns will be created with the same type. If the missingness types should differ between patterns, a vector of missingness types should be given. Default is RIGHT for all patterns and is the result of ampute.default.type.
odds	A matrix where #patterns defines the #rows. Each row should contain the odds of being missing for the corresponding pattern. The number of odds values defines in how many quantiles the sum scores will be divided. The odds values are relative probabilities: a quantile with odds value 4 will have a probability of being missing that is four times higher than a quantile with odds 1. The number of quantiles may differ between the patterns, specify NA for cells remaining empty. Default is 4 quantiles with odds values 1, 2, 3 and 4 and is created by ampute.default.odds.
bycases	Logical. If TRUE, the proportion of missingness is defined in terms of cases. If FALSE, the proportion of missingness is defined in terms of cells. Default is TRUE.
run	Logical. If TRUE, the amputations are implemented. If FALSE, the return object will contain everything except for the amputed data set.

Details

This function generates missing values in complete data sets. Amputation of complete data sets is useful for the evaluation of imputation techniques, such as multiple imputation (performed with function mice in this package).

The basic strategy underlying multivariate imputation was suggested by Don Rubin during discussions in the 90's. Brand (1997) created one particular implementation, and his method found its way into the FCS paper (Van Buuren et al, 2006).

Until recently, univariate amputation procedures were used to generate missing data in complete, simulated data sets. With this approach, variables are made incomplete one variable at a time. When more than one variable needs to be amputed, the procedure is repeated multiple times.

With the univariate approach, it is difficult to relate the missingness on one variable to the missingness on another variable. A multivariate amputation procedure solves this issue and moreover, it does justice to the multivariate nature of data sets. Hence, ampute is developed to perform multivariate amputation.

The idea behind the function is the specification of several missingness patterns. Each pattern is a combination of variables with and without missing values (denoted by 0 and 1 respectively). For example, one might want to create two missingness patterns on a data set with four variables. The patterns could be something like: 0,0,1,1 and 1,0,1,0. Each combination of zeros and ones may occur.

Furthermore, the researcher specifies the proportion of missingness, either the proportion of missing cases or the proportion of missing cells, and the relative frequency each pattern occurs. Consequently, the data is split into multiple subsets, one subset per pattern. Now, each case is candidate for a certain missingness pattern, but whether the case will have missing values eventually depends on other specifications.

The first of these specifications is the missing mechanism. There are three possible mechanisms: the missingness depends completely on chance (MCAR), the missingness depends on the values of the observed variables (i.e. the variables that remain complete) (MAR) or on the values of the variables that will be made incomplete (MNAR). For a discussion on how missingness mechanisms are related to the observed data, we refer to \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1177/0049124118799376")}Schouten and Vink, 2018.

When the user specifies the missingness mechanism to be "MCAR", the candidates have an equal probability of becoming incomplete. For a "MAR" or "MNAR" mechanism, weighted sum scores are calculated. These scores are a linear combination of the variables.

In order to calculate the weighted sum scores, the data is standardized. For this reason, the data has to be numeric. Second, for each case, the values in the data set are multiplied with the weights, specified by argument weights. These weighted scores will be summed, resulting in a weighted sum score for each case.

The weights may differ between patterns and they may be negative or zero as well. Naturally, in case of a MAR mechanism, the weights corresponding to the variables that will be made incomplete, have a 0. Note that this may be different for each pattern. In case of MNAR missingness, especially the weights of the variables that will be made incomplete are of importance. However, the other variables may be weighted as well.

It is the relative difference between the weights that will result in an effect in the sum scores. For example, for the first missing data pattern mentioned above, the weights for the third and fourth variables could be set to 2 and 4. However, weight values of 0.2 and 0.4 will have the exact same effect on the weighted sum score: the fourth variable is weighted twice as much as variable 3.

Based on the weighted sum scores, either a discrete or continuous distribution of probabilities is used to calculate whether a candidate will have missing values.

For a discrete distribution of probabilities, the weighted sum scores are divided into subgroups of equal size (quantiles). Thereafter, the user specifies for each subgroup the odds of being missing. Both the number of subgroups and the odds values are important for the generation of missing data. For example, for a RIGHT-like mechanism, scoring in one of the higher quantiles should have high missingness odds, whereas for a MID-like mechanism, the central groups should have higher odds. Again, not the size of the odds values are of importance, but the relative distance between the values.

The continuous distributions of probabilities are based on the logistic distribution function. The user can specify the type of missingness, which, again, may differ between patterns.

For an example and more explanation about how the arguments interact with each other, we refer to the vignette Generate missing values with ampute The amputation methodology is published in \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/00949655.2018.1491577")}Schouten, Lugtig and Vink, 2018.

Value

Returns an S3 object of class mads-class (multivariate amputed data set)

Author(s)

Rianne Schouten [aut, cre], Gerko Vink [aut], Peter Lugtig [ctb], 2016

References

Brand, J.P.L. (1999) Development, implementation and evaluation of multiple imputation strategies for the statistical analysis of incomplete data sets. pp. 110-113. Dissertation. Rotterdam: Erasmus University.

Schouten, R.M., Lugtig, P and Vink, G. (2018) Generating missing values for simulation purposes: A multivariate amputation procedure.. Journal of Statistical Computation and Simulation, 88(15): 1909-1930. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/00949655.2018.1491577")}

Schouten, R.M. and Vink, G. (2018)The Dance of the Mechanisms: How Observed Information Influences the Validity of Missingness Assumptions. Sociological Methods and Research, 50(3): 1243-1258. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1177/0049124118799376")}

Van Buuren, S., Brand, J.P.L., Groothuis-Oudshoorn, C.G.M., Rubin, D.B. (2006) Fully conditional specification in multivariate imputation. Journal of Statistical Computation and Simulation, 76(12): 1049-1064. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/10629360600810434")}

Van Buuren, S. (2018) Flexible Imputation of Missing Data. Second Edition. Chapman & Hall/CRC. Boca Raton, FL.

Vink, G. (2016) Towards a standardized evaluation of multiple imputation routines.

See Also

mads-class, bwplot, xyplot, mice

Examples

# start with a complete data set
compl_boys <- cc(boys)[1:3]

# Perform amputation with default settings
mads_boys <- ampute(data = compl_boys)
mads_boys$amp

# Change default matrices as desired
my_patterns <- mads_boys$patterns
my_patterns[1:3, 2] <- 0

my_weights <- mads_boys$weights
my_weights[2, 1] <- 2
my_weights[3, 1] <- 0.5

# Rerun amputation
my_mads_boys <- ampute(
  data = compl_boys, patterns = my_patterns, freq =
    c(0.3, 0.3, 0.4), weights = my_weights, type = c("RIGHT", "TAIL", "LEFT")
)
my_mads_boys$amp

mice documentation built on June 7, 2023, 5:38 p.m.