imposeMissing: Impose MAR, MCAR, planned missingness, or attrition on a data...
In simsem: SIMulated Structural Equation Modeling
Description
Usage
Arguments
Details
Value
Author(s)
See Also
Examples
View source: R/imposeMissing.R
Description
Function imposes missing values on a data based on the known missing data types,
including MCAR, MAR, planned, and attrition.
Usage
1
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3
4
Arguments
miss
Missing data object (SimMissing) used as the template for impose missing values
data.mat
Data to impose missing upon. Can be either a matrix or a data frame.
cov
Column indices of a covariate to be used to impose MAR missing, or
MAR attrition. Will not be included in any removal procedure. See details.
pmMCAR
Decimal percent of missingness to introduce completely at random on all variables.
pmMAR
Decimal percent of missingness to introduce using the listed
covariate as predictor. See details.
nforms
The number of forms for planned missing data designs, not including
the shared form.
itemGroups
List of lists of item groupings for planned missing data
forms. Unless specified, items will be divided into groups sequentially (e.g. 1-3,4-6,7-9,10-12)
twoMethod
With missing on one variable: vector of (column index, percent missing). Will put a given percent
missing on that column in the matrix to simulate a two method
planned missing data research design. With missing on two or more variables: list of (column indices, percent missing).
prAttr
Probability (or vector of probabilities) of an entire case being removed due to attrition at a
given time point. When a covariate is specified along with this argument, attrition
will be predicted by the covariate (MAR attrition). See details.
timePoints
Number of timepoints items were measured over. For longitudinal
data, planned missing designs will be implemented within each
timepoint. All methods to impose missing values over time assume an equal number of
variables at each time point.
ignoreCols
The columns not imposed any missing values for any missing data patterns.
threshold
The threshold of the covariate used to impose missing values. Values
on the covariate above this threshold are eligible to be
deleted. The default threshold is the mean of the variable.
logit
The script used for imposing missing values by logistic regression. The script is similar to the specification of regression in lavaan such that each line begins with a dependent variable, then '~' is used as regression sign, and the formula of a linear combination of independent variable plus constant, such as y1 ~ 0.5 + 0.2*y2. '#' and '!' can be used as a comment (like lavaan). For the intercept, users may use 'p()' to specify the average proportion of missing, such as y1 ~ p(0.2) + 0.3*y2, which the average missing proportion of y1 is 0.2 and the missing of y1 depends on y2. Users may visualize the missing proportion from the logistic specification by the plotLogitMiss function.
logical
A matrix of logical values (TRUE/FALSE). If a value in the dataset is corresponding to the TRUE in the logical matrix, the value will be missing.
Details
Without specifying any arguments, no missing values will be
introduced.
A single covariate is required to specify MAR missing - this
covariate can be distributed in any way. This covariate can be either continuous or categorical, as long as it is
numerical. If the covariate is categorical, the threshold should be
specified to one of the levels.
MAR missingness is specified using the threshold method - any value on the covariate that is above
the specified threshold indicates a row eligible for deletion. If the
specified total amount of MAR missingness is not possible given the
total rows eligible based on the threshold, the function iteratively
lowers the threshold until the total percent missing is possible.
Planned missingness is parameterized by the number of forms (n). This is used to divide the
cases into n groups. If the column groupings are not specified, a naive
method will be used that divides the columns into n+1 equal forms
sequentially (1-4,5-9,10-13..), where the first group is the shared
form.The first list of column indices given will be used as the shared
group. If this is not desired, this list can be left empty.
For attrition, the probability can be specified as a single value or as
a vector. For a single value, the probability of attrition will be
the same across time points, and affects only
cases not previously lost due to attrition. If this argument is a
vector, this specifies different probabilities of
attrition for each time point. Values will be recycled if this
vector is smaller than the specified number of time points.
An MNAR processes can be generated by specifying MAR missingness and then
dropping the covariate from the subsequent analysis.
Currently, if MAR missing is imposed along with attrition, both processes will use
the same covariate and threshold.
Currently, all types of missingness (MCAR, MAR, planned, and attrition)
are imposed independently. This means that specified global values of
percent missing will not be additive (10 percent MCAR + 10 percent MAR
does not equal 20 percent total missing).
Value
A data matrix with NAs introduced in the way specified by the arguments.
Author(s)
Patrick Miller (University of Kansas; patr1ckm@ku.edu),
Alexander M. Schoemann (East Carolina University; schoemanna@ecu.edu)
See Also
-
SimMissing for the alternative way to save missing data feature for using in the sim function.
Examples
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data <- matrix(rep(rnorm(10,1,1),19),ncol=19)
datac <- cbind(data,rnorm(10,0,1),rnorm(10,5,5))
# Imposing Missing with the following arguments produces no missing values
imposeMissing(data)
imposeMissing(data,cov=c(1,2))
imposeMissing(data,pmMCAR=0)
imposeMissing(data,pmMAR=0)
imposeMissing(data,nforms=0)
#Some more usage examples
# No missing at variables 1 and 2
imposeMissing(data,cov=c(1,2),pmMCAR=.1)
# 3-Form design
imposeMissing(data,nforms=3)
# 3-Form design with specified groups of items (XABC)
imposeMissing(data, nforms = 3, itemGroups =
list(c(1,2,3,4,5), c(6,7,8,9,10), c(11,12,13,14,15), c(16,17,18,19)))
# 3-Form design when variables 20 and 21 are not missing
imposeMissing(datac,cov=c(20,21),nforms=3)
# 2 method design where the expensive measure is on Variable 19
imposeMissing(data,twoMethod=c(19,.8))
# Impose missing data with percent attrition of 0.1 in 5 time points
imposeMissing(datac,cov=21,prAttr=.1,timePoints=5)
# Logistic-regression MAR
colnames(data) <- paste("y", 1:ncol(data), sep="")
script <- 'y1 ~ 0.05 + 0.1*y2 + 0.3*y3
y4 ~ -2 + 0.1*y4
y5 ~ -0.5'
imposeMissing(data, logit=script)
Example output
Loading required package: lavaan
This is lavaan 0.5-23.1097
lavaan is BETA software! Please report any bugs.
###############################################################################################
This is simsem 0.5-13
simsem is BETA software! Please report any bugs.
simsem was developed at the University of Kansas Center for Research Methods and Data Analysis.
###############################################################################################
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[2,] 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767
[3,] 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694
[4,] 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704
[5,] 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938
[6,] 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833
[7,] 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003
[8,] 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097
[9,] 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735
[10,] 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317
[,8] [,9] [,10] [,11] [,12] [,13] [,14]
[1,] 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879
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[6,] 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833
[7,] 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003
[8,] 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097
[9,] 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735
[10,] 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317
[,15] [,16] [,17] [,18] [,19]
[1,] 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879
[2,] 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767
[3,] 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694
[4,] 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704
[5,] 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938
[6,] 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833
[7,] 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003
[8,] 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097
[9,] 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735
[10,] 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879
[2,] 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767
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[5,] 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938
[6,] 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833
[7,] 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003
[8,] 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097
[9,] 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735
[10,] 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317
[,8] [,9] [,10] [,11] [,12] [,13] [,14]
[1,] 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879
[2,] 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767
[3,] 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694
[4,] 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704
[5,] 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938
[6,] 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833
[7,] 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003
[8,] 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097
[9,] 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735
[10,] 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317
[,15] [,16] [,17] [,18] [,19]
[1,] 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879
[2,] 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767
[3,] 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694
[4,] 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704
[5,] 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938
[6,] 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833
[7,] 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003
[8,] 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097
[9,] 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735
[10,] 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879
[2,] 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767
[3,] 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694
[4,] 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704
[5,] 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938
[6,] 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833
[7,] 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003
[8,] 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097
[9,] 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735
[10,] 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317
[,8] [,9] [,10] [,11] [,12] [,13] [,14]
[1,] 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879
[2,] 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767
[3,] 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694
[4,] 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704
[5,] 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938
[6,] 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833
[7,] 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003
[8,] 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097
[9,] 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735
[10,] 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317
[,15] [,16] [,17] [,18] [,19]
[1,] 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879
[2,] 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767
[3,] 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694
[4,] 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704
[5,] 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938
[6,] 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833
[7,] 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003
[8,] 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097
[9,] 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735
[10,] 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879
[2,] 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767
[3,] 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694
[4,] 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704
[5,] 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938
[6,] 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833
[7,] 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003
[8,] 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097
[9,] 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735
[10,] 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317
[,8] [,9] [,10] [,11] [,12] [,13] [,14]
[1,] 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879
[2,] 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767
[3,] 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694
[4,] 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704
[5,] 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938
[6,] 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833
[7,] 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003
[8,] 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097
[9,] 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735
[10,] 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317
[,15] [,16] [,17] [,18] [,19]
[1,] 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879
[2,] 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767
[3,] 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694
[4,] 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704
[5,] 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938
[6,] 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833
[7,] 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003
[8,] 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097
[9,] 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735
[10,] 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879
[2,] 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767
[3,] 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694
[4,] 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704
[5,] 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938
[6,] 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833
[7,] 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003
[8,] 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097
[9,] 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735
[10,] 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317
[,8] [,9] [,10] [,11] [,12] [,13] [,14]
[1,] 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879
[2,] 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767
[3,] 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694
[4,] 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704
[5,] 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938
[6,] 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833
[7,] 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003
[8,] 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097
[9,] 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735
[10,] 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317
[,15] [,16] [,17] [,18] [,19]
[1,] 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879
[2,] 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767
[3,] 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694
[4,] 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704
[5,] 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938
[6,] 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833
[7,] 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003
[8,] 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097
[9,] 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735
[10,] 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] 0.3873879 0.3873879 0.3873879 NA 0.3873879 0.3873879 0.3873879
[2,] 1.9786767 1.9786767 NA 1.9786767 NA 1.9786767 NA
[3,] 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 NA
[4,] 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704
[5,] 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 NA
[6,] 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 NA
[7,] 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 NA 0.6039003
[8,] 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097
[9,] 1.3587735 1.3587735 1.3587735 NA 1.3587735 1.3587735 1.3587735
[10,] 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317
[,8] [,9] [,10] [,11] [,12] [,13] [,14]
[1,] NA 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879
[2,] 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 NA
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[4,] 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704
[5,] NA 1.6159938 1.6159938 NA NA 1.6159938 1.6159938
[6,] 1.1433833 1.1433833 NA 1.1433833 1.1433833 1.1433833 1.1433833
[7,] 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 NA 0.6039003
[8,] 1.7694097 1.7694097 1.7694097 NA 1.7694097 1.7694097 1.7694097
[9,] 1.3587735 1.3587735 NA 1.3587735 1.3587735 1.3587735 1.3587735
[10,] 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 NA
[,15] [,16] [,17] [,18] [,19]
[1,] 0.3873879 0.3873879 NA 0.3873879 0.3873879
[2,] 1.9786767 NA 1.9786767 1.9786767 1.9786767
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[4,] 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704
[5,] 1.6159938 1.6159938 1.6159938 NA 1.6159938
[6,] 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833
[7,] 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003
[8,] 1.7694097 1.7694097 NA 1.7694097 1.7694097
[9,] 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735
[10,] 0.4619317 0.4619317 0.4619317 0.4619317 NA
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] 0.3873879 0.3873879 0.3873879 0.3873879 NA NA NA
[2,] 1.9786767 1.9786767 1.9786767 1.9786767 NA NA NA
[3,] 0.7243694 0.7243694 0.7243694 0.7243694 NA NA NA
[4,] 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704
[5,] 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938
[6,] 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833
[7,] 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003
[8,] 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097
[9,] 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735
[10,] 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317
[,8] [,9] [,10] [,11] [,12] [,13] [,14]
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[2,] NA NA 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767
[3,] NA NA 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694
[4,] 0.8386704 0.8386704 NA NA NA NA NA
[5,] 1.6159938 1.6159938 NA NA NA NA NA
[6,] 1.1433833 1.1433833 NA NA NA NA NA
[7,] 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003
[8,] 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097
[9,] 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735
[10,] 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317
[,15] [,16] [,17] [,18] [,19]
[1,] 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879
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[5,] 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938
[6,] 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833
[7,] NA NA NA NA NA
[8,] NA NA NA NA NA
[9,] NA NA NA NA NA
[10,] NA NA NA NA NA
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 NA NA
[2,] 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 NA NA
[3,] 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 NA NA
[4,] 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704
[5,] 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938
[6,] 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833
[7,] 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003
[8,] 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097
[9,] 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735
[10,] 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317
[,8] [,9] [,10] [,11] [,12] [,13] [,14]
[1,] NA NA NA 0.3873879 0.3873879 0.3873879 0.3873879
[2,] NA NA NA 1.9786767 1.9786767 1.9786767 1.9786767
[3,] NA NA NA 0.7243694 0.7243694 0.7243694 0.7243694
[4,] 0.8386704 0.8386704 0.8386704 NA NA NA NA
[5,] 1.6159938 1.6159938 1.6159938 NA NA NA NA
[6,] 1.1433833 1.1433833 1.1433833 NA NA NA NA
[7,] 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003
[8,] 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097
[9,] 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735
[10,] 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317
[,15] [,16] [,17] [,18] [,19]
[1,] 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879
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[3,] 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694
[4,] NA 0.8386704 0.8386704 0.8386704 0.8386704
[5,] NA 1.6159938 1.6159938 1.6159938 1.6159938
[6,] NA 1.1433833 1.1433833 1.1433833 1.1433833
[7,] 0.6039003 NA NA NA NA
[8,] 1.7694097 NA NA NA NA
[9,] 1.3587735 NA NA NA NA
[10,] 0.4619317 NA NA NA NA
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] 0.3873879 0.3873879 0.3873879 0.3873879 NA NA NA
[2,] 1.9786767 1.9786767 1.9786767 1.9786767 NA NA NA
[3,] 0.7243694 0.7243694 0.7243694 0.7243694 NA NA NA
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[5,] 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938
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[7,] 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003
[8,] 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097
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[10,] 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317
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[1,] NA NA 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879
[2,] NA NA 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767
[3,] NA NA 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694
[4,] 0.8386704 0.8386704 NA NA NA NA NA
[5,] 1.6159938 1.6159938 NA NA NA NA NA
[6,] 1.1433833 1.1433833 NA NA NA NA NA
[7,] 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003
[8,] 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097
[9,] 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735
[10,] 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317
[,15] [,16] [,17] [,18] [,19] [,20] [,21]
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[2,] 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 0.2786190 7.3342355
[3,] 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 -0.7782005 3.1844103
[4,] 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 1.6678996 8.5823825
[5,] 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 0.2427529 -1.1325097
[6,] 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.3309634 5.5199217
[7,] NA NA NA NA NA -0.5735181 4.3123289
[8,] NA NA NA NA NA -0.7118208 1.2823821
[9,] NA NA NA NA NA 0.1152620 2.4573361
[10,] NA NA NA NA NA 0.2980464 10.0431525
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879
[2,] 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767
[3,] 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694
[4,] 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704
[5,] 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938
[6,] 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833
[7,] 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003
[8,] 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097
[9,] 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735
[10,] 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317
[,8] [,9] [,10] [,11] [,12] [,13] [,14]
[1,] 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879
[2,] 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767
[3,] 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694
[4,] 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704
[5,] 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938
[6,] 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833
[7,] 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003
[8,] 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097
[9,] 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735
[10,] 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317
[,15] [,16] [,17] [,18] [,19]
[1,] 0.3873879 0.3873879 0.3873879 0.3873879 NA
[2,] 1.9786767 1.9786767 1.9786767 1.9786767 NA
[3,] 0.7243694 0.7243694 0.7243694 0.7243694 NA
[4,] 0.8386704 0.8386704 0.8386704 0.8386704 NA
[5,] 1.6159938 1.6159938 1.6159938 1.6159938 NA
[6,] 1.1433833 1.1433833 1.1433833 1.1433833 NA
[7,] 0.6039003 0.6039003 0.6039003 0.6039003 NA
[8,] 1.7694097 1.7694097 1.7694097 1.7694097 NA
[9,] 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735
[10,] 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879
[2,] 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767
[3,] 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694
[4,] 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704
[5,] 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938
[6,] 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833
[7,] NA NA NA NA NA NA NA
[8,] 1.7694097 1.7694097 1.7694097 1.7694097 NA NA NA
[9,] 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735
[10,] 0.4619317 0.4619317 0.4619317 0.4619317 NA NA NA
[,8] [,9] [,10] [,11] [,12] [,13] [,14]
[1,] 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879
[2,] 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767
[3,] 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 NA NA
[4,] 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704
[5,] 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938
[6,] 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833
[7,] NA NA NA NA NA NA NA
[8,] NA NA NA NA NA NA NA
[9,] 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735
[10,] NA NA NA NA NA NA NA
[,15] [,16] [,17] [,18] [,19] [,20] [,21]
[1,] 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 -0.4516057 0.3690535
[2,] 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 0.2786190 7.3342355
[3,] NA NA NA NA NA NA 3.1844103
[4,] 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 1.6678996 8.5823825
[5,] 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 0.2427529 -1.1325097
[6,] 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.3309634 5.5199217
[7,] NA NA NA NA NA NA 4.3123289
[8,] NA NA NA NA NA NA 1.2823821
[9,] 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 0.1152620 2.4573361
[10,] NA NA NA NA NA NA 10.0431525
y1 y2 y3 y4 y5 y6 y7
[1,] NA 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879
[2,] NA 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767
[3,] 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694
[4,] NA 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704
[5,] NA 1.6159938 1.6159938 1.6159938 NA 1.6159938 1.6159938
[6,] NA 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833
[7,] NA 0.6039003 0.6039003 0.6039003 NA 0.6039003 0.6039003
[8,] NA 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097
[9,] NA 1.3587735 1.3587735 NA NA 1.3587735 1.3587735
[10,] NA 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317
y8 y9 y10 y11 y12 y13 y14
[1,] 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879
[2,] 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767
[3,] 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694
[4,] 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704
[5,] 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938
[6,] 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833
[7,] 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003
[8,] 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097
[9,] 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735
[10,] 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317
y15 y16 y17 y18 y19
[1,] 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879
[2,] 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767
[3,] 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694
[4,] 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704
[5,] 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938
[6,] 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833
[7,] 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003
[8,] 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097
[9,] 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735
[10,] 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317
simsem documentation built on March 29, 2021, 1:07 a.m.
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Description Usage Arguments Details Value Author(s) See Also Examples
View source: R/imposeMissing.R
Description
Function imposes missing values on a data based on the known missing data types, including MCAR, MAR, planned, and attrition.
Usage
1 2 3 4 |
Arguments
miss |
Missing data object ( |
data.mat |
Data to impose missing upon. Can be either a matrix or a data frame. |
cov |
Column indices of a covariate to be used to impose MAR missing, or MAR attrition. Will not be included in any removal procedure. See details. |
pmMCAR |
Decimal percent of missingness to introduce completely at random on all variables. |
pmMAR |
Decimal percent of missingness to introduce using the listed covariate as predictor. See details. |
nforms |
The number of forms for planned missing data designs, not including the shared form. |
itemGroups |
List of lists of item groupings for planned missing data forms. Unless specified, items will be divided into groups sequentially (e.g. 1-3,4-6,7-9,10-12) |
twoMethod |
With missing on one variable: vector of (column index, percent missing). Will put a given percent missing on that column in the matrix to simulate a two method planned missing data research design. With missing on two or more variables: list of (column indices, percent missing). |
prAttr |
Probability (or vector of probabilities) of an entire case being removed due to attrition at a given time point. When a covariate is specified along with this argument, attrition will be predicted by the covariate (MAR attrition). See details. |
timePoints |
Number of timepoints items were measured over. For longitudinal data, planned missing designs will be implemented within each timepoint. All methods to impose missing values over time assume an equal number of variables at each time point. |
ignoreCols |
The columns not imposed any missing values for any missing data patterns. |
threshold |
The threshold of the covariate used to impose missing values. Values on the covariate above this threshold are eligible to be deleted. The default threshold is the mean of the variable. |
logit |
The script used for imposing missing values by logistic regression. The script is similar to the specification of regression in |
logical |
A matrix of logical values ( |
Details
Without specifying any arguments, no missing values will be introduced.
A single covariate is required to specify MAR missing - this covariate can be distributed in any way. This covariate can be either continuous or categorical, as long as it is numerical. If the covariate is categorical, the threshold should be specified to one of the levels.
MAR missingness is specified using the threshold method - any value on the covariate that is above the specified threshold indicates a row eligible for deletion. If the specified total amount of MAR missingness is not possible given the total rows eligible based on the threshold, the function iteratively lowers the threshold until the total percent missing is possible.
Planned missingness is parameterized by the number of forms (n). This is used to divide the cases into n groups. If the column groupings are not specified, a naive method will be used that divides the columns into n+1 equal forms sequentially (1-4,5-9,10-13..), where the first group is the shared form.The first list of column indices given will be used as the shared group. If this is not desired, this list can be left empty.
For attrition, the probability can be specified as a single value or as a vector. For a single value, the probability of attrition will be the same across time points, and affects only cases not previously lost due to attrition. If this argument is a vector, this specifies different probabilities of attrition for each time point. Values will be recycled if this vector is smaller than the specified number of time points.
An MNAR processes can be generated by specifying MAR missingness and then dropping the covariate from the subsequent analysis.
Currently, if MAR missing is imposed along with attrition, both processes will use the same covariate and threshold.
Currently, all types of missingness (MCAR, MAR, planned, and attrition) are imposed independently. This means that specified global values of percent missing will not be additive (10 percent MCAR + 10 percent MAR does not equal 20 percent total missing).
Value
A data matrix with NAs introduced in the way specified by the arguments.
Author(s)
Patrick Miller (University of Kansas; patr1ckm@ku.edu), Alexander M. Schoemann (East Carolina University; schoemanna@ecu.edu)
See Also
-
SimMissingfor the alternative way to save missing data feature for using in thesimfunction.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 | data <- matrix(rep(rnorm(10,1,1),19),ncol=19)
datac <- cbind(data,rnorm(10,0,1),rnorm(10,5,5))
# Imposing Missing with the following arguments produces no missing values
imposeMissing(data)
imposeMissing(data,cov=c(1,2))
imposeMissing(data,pmMCAR=0)
imposeMissing(data,pmMAR=0)
imposeMissing(data,nforms=0)
#Some more usage examples
# No missing at variables 1 and 2
imposeMissing(data,cov=c(1,2),pmMCAR=.1)
# 3-Form design
imposeMissing(data,nforms=3)
# 3-Form design with specified groups of items (XABC)
imposeMissing(data, nforms = 3, itemGroups =
list(c(1,2,3,4,5), c(6,7,8,9,10), c(11,12,13,14,15), c(16,17,18,19)))
# 3-Form design when variables 20 and 21 are not missing
imposeMissing(datac,cov=c(20,21),nforms=3)
# 2 method design where the expensive measure is on Variable 19
imposeMissing(data,twoMethod=c(19,.8))
# Impose missing data with percent attrition of 0.1 in 5 time points
imposeMissing(datac,cov=21,prAttr=.1,timePoints=5)
# Logistic-regression MAR
colnames(data) <- paste("y", 1:ncol(data), sep="")
script <- 'y1 ~ 0.05 + 0.1*y2 + 0.3*y3
y4 ~ -2 + 0.1*y4
y5 ~ -0.5'
imposeMissing(data, logit=script)
|
Example output
Loading required package: lavaan
This is lavaan 0.5-23.1097
lavaan is BETA software! Please report any bugs.
###############################################################################################
This is simsem 0.5-13
simsem is BETA software! Please report any bugs.
simsem was developed at the University of Kansas Center for Research Methods and Data Analysis.
###############################################################################################
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879
[2,] 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767
[3,] 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694
[4,] 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704
[5,] 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938
[6,] 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833
[7,] 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003
[8,] 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097
[9,] 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735
[10,] 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317
[,8] [,9] [,10] [,11] [,12] [,13] [,14]
[1,] 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879
[2,] 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767
[3,] 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694
[4,] 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704
[5,] 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938
[6,] 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833
[7,] 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003
[8,] 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097
[9,] 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735
[10,] 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317
[,15] [,16] [,17] [,18] [,19]
[1,] 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879
[2,] 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767
[3,] 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694
[4,] 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704
[5,] 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938
[6,] 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833
[7,] 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003
[8,] 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097
[9,] 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735
[10,] 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879
[2,] 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767
[3,] 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694
[4,] 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704
[5,] 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938
[6,] 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833
[7,] 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003
[8,] 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097
[9,] 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735
[10,] 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317
[,8] [,9] [,10] [,11] [,12] [,13] [,14]
[1,] 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879
[2,] 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767
[3,] 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694
[4,] 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704
[5,] 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938
[6,] 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833
[7,] 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003
[8,] 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097
[9,] 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735
[10,] 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317
[,15] [,16] [,17] [,18] [,19]
[1,] 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879
[2,] 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767
[3,] 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694
[4,] 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704
[5,] 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938
[6,] 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833
[7,] 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003
[8,] 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097
[9,] 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735
[10,] 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879
[2,] 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767
[3,] 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694
[4,] 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704
[5,] 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938
[6,] 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833
[7,] 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003
[8,] 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097
[9,] 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735
[10,] 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317
[,8] [,9] [,10] [,11] [,12] [,13] [,14]
[1,] 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879
[2,] 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767
[3,] 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694
[4,] 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704
[5,] 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938
[6,] 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833
[7,] 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003
[8,] 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097
[9,] 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735
[10,] 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317
[,15] [,16] [,17] [,18] [,19]
[1,] 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879
[2,] 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767
[3,] 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694
[4,] 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704
[5,] 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938
[6,] 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833
[7,] 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003
[8,] 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097
[9,] 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735
[10,] 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879
[2,] 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767
[3,] 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694
[4,] 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704
[5,] 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938
[6,] 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833
[7,] 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003
[8,] 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097
[9,] 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735
[10,] 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317
[,8] [,9] [,10] [,11] [,12] [,13] [,14]
[1,] 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879
[2,] 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767
[3,] 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694
[4,] 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704
[5,] 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938
[6,] 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833
[7,] 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003
[8,] 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097
[9,] 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735
[10,] 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317
[,15] [,16] [,17] [,18] [,19]
[1,] 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879
[2,] 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767
[3,] 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694
[4,] 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704
[5,] 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938
[6,] 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833
[7,] 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003
[8,] 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097
[9,] 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735
[10,] 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879
[2,] 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767
[3,] 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694
[4,] 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704
[5,] 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938
[6,] 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833
[7,] 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003
[8,] 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097
[9,] 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735
[10,] 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317
[,8] [,9] [,10] [,11] [,12] [,13] [,14]
[1,] 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879
[2,] 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767
[3,] 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694
[4,] 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704
[5,] 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938
[6,] 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833
[7,] 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003
[8,] 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097
[9,] 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735
[10,] 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317
[,15] [,16] [,17] [,18] [,19]
[1,] 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879
[2,] 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767
[3,] 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694
[4,] 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704
[5,] 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938
[6,] 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833
[7,] 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003
[8,] 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097
[9,] 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735
[10,] 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] 0.3873879 0.3873879 0.3873879 NA 0.3873879 0.3873879 0.3873879
[2,] 1.9786767 1.9786767 NA 1.9786767 NA 1.9786767 NA
[3,] 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 NA
[4,] 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704
[5,] 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 NA
[6,] 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 NA
[7,] 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 NA 0.6039003
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[10,] NA NA NA NA NA 0.2980464 10.0431525
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[2,] 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767
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[7,] 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003
[8,] 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097
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[1,] 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879
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[,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879
[2,] 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767
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[10,] 0.4619317 0.4619317 0.4619317 0.4619317 NA NA NA
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[1,] 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879
[2,] 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767
[3,] 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 NA NA
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[10,] NA NA NA NA NA NA NA
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[10,] NA NA NA NA NA NA 10.0431525
y1 y2 y3 y4 y5 y6 y7
[1,] NA 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879
[2,] NA 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767
[3,] 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694
[4,] NA 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704
[5,] NA 1.6159938 1.6159938 1.6159938 NA 1.6159938 1.6159938
[6,] NA 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833
[7,] NA 0.6039003 0.6039003 0.6039003 NA 0.6039003 0.6039003
[8,] NA 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097
[9,] NA 1.3587735 1.3587735 NA NA 1.3587735 1.3587735
[10,] NA 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317
y8 y9 y10 y11 y12 y13 y14
[1,] 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879
[2,] 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767
[3,] 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694
[4,] 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704
[5,] 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938
[6,] 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833
[7,] 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003
[8,] 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097
[9,] 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735
[10,] 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317
y15 y16 y17 y18 y19
[1,] 0.3873879 0.3873879 0.3873879 0.3873879 0.3873879
[2,] 1.9786767 1.9786767 1.9786767 1.9786767 1.9786767
[3,] 0.7243694 0.7243694 0.7243694 0.7243694 0.7243694
[4,] 0.8386704 0.8386704 0.8386704 0.8386704 0.8386704
[5,] 1.6159938 1.6159938 1.6159938 1.6159938 1.6159938
[6,] 1.1433833 1.1433833 1.1433833 1.1433833 1.1433833
[7,] 0.6039003 0.6039003 0.6039003 0.6039003 0.6039003
[8,] 1.7694097 1.7694097 1.7694097 1.7694097 1.7694097
[9,] 1.3587735 1.3587735 1.3587735 1.3587735 1.3587735
[10,] 0.4619317 0.4619317 0.4619317 0.4619317 0.4619317
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