Resample data from a data set using common resampling methods. For bootstrap or jackknife resampling, package users usually do not need to call this function but directly use resamplecSEMResults() instead.

resampleData(
.object          = NULL,
.data            = NULL,
.resample_method = c("bootstrap", "jackknife", "permutation",
"cross-validation"),
.cv_folds        = 10,
.id              = NULL,
.R               = 499,
.seed            = NULL
)

Arguments

.object

An R object of class cSEMResults resulting from a call to csem().

.data

A data.frame, a matrix or a list of data of either type. Possible column types or classes of the data provided are: "logical", "numeric" ("double" or "integer"), "factor" (ordered and unordered) or a mix of several types. The data may also include one character column whose column name must be given to .id. This column is assumed to contain group identifiers used to split the data into groups. If .data is provided, .object is ignored. Defaults to NULL.

.resample_method

Character string. The resampling method to use. One of: "bootstrap", "jackknife", "permutation", or "cross-validation". Defaults to "bootstrap".

.cv_folds

Integer. The number of cross-validation folds to use. Setting .cv_folds to N (the number of observations) produces leave-one-out cross-validation samples. Defaults to 10.

.id

Character string or integer. A character string giving the name or an integer of the position of the column of .data whose levels are used to split .data into groups. Defaults to NULL.

.R

Integer. The number of bootstrap runs, permutation runs or cross-validation repetitions to use. Defaults to 499.

.seed

Integer or NULL. The random seed to use. Defaults to NULL in which case an arbitrary seed is chosen. Note that the scope of the seed is limited to the body of the function it is used in. Hence, the global seed will not be altered!

Value

The structure of the output depends on the type of input and the resampling method:

Bootstrap

If a matrix or data.frame without grouping variable is provided (i.e., .id = NULL), the result is a list of length .R (default 499). Each element of that list is a bootstrap (re)sample. If a grouping variable is specified or a list of data is provided (where each list element is assumed to contain data for one group), resampling is done by group. Hence, the result is a list of length equal to the number of groups with each list element containing .R bootstrap samples based on the N_g observations of group g.

Jackknife

If a matrix or data.frame without grouping variable is provided (.id = NULL), the result is a list of length equal to the number of observations/rows (N) of the data set provided. Each element of that list is a jackknife (re)sample. If a grouping variable is specified or a list of data is provided (where each list element is assumed to contain data for one group), resampling is done by group. Hence, the result is a list of length equal to the number of group levels with each list element containing N jackknife samples based on the N_g observations of group g.

Permutation

If a matrix or data.frame without grouping variable is provided an error is returned as permutation will simply reorder the observations. If a grouping variable is specified or a list of data is provided (where each list element is assumed to contain data of one group), group membership is permutated. Hence, the result is a list of length .R where each element of that list is a permutation (re)sample.

Cross-validation

If a matrix or data.frame without grouping variable is provided a list of length .R is returned. Each list element contains a list containing the k splits/folds subsequently used as test and training data sets. If a grouping variable is specified or a list of data is provided (where each list element is assumed to contain data for one group), cross-validation is repeated .R times for each group. Hence, the result is a list of length equal to the number of groups, each containing .R list elements (the repetitions) which in turn contain the k splits/folds.

Details

The function resampleData() is general purpose. It simply resamples data from a data set according to the resampling method provided via the .resample_method argument and returns a list of resamples. Currently, bootstrap, jackknife, permutation, and cross-validation (both leave-one-out (LOOCV) and k-fold cross-validation) are implemented.

The user may provide the data set to resample either explicitly via the .data argument or implicitly by providing a cSEMResults objects to .object in which case the original data used in the call that created the cSEMResults object is used for resampling. If both, a cSEMResults object and a data set via .data are provided the former is ignored.

As csem() accepts a single data set, a list of data sets as well as data sets that contain a column name used to split the data into groups, the cSEMResults object may contain multiple data sets. In this case, resampling is done by data set or group. Note that depending on the number of data sets/groups provided this computation may be slower as resampling will be repeated for each data set/group.

To split data provided via the .data argument into groups, the column name or the column index of the column containing the group levels to split the data must be given to .id. If data that contains grouping is taken from a cSEMResults object, .id is taken from the object information. Hence, providing .id is redundant in this case and therefore ignored.

The number of bootstrap or permutation runs as well as the number of cross-validation repetitions is given by .R. The default is 499 but should be increased in real applications. See e.g., Hesterberg (2015) , p.380 for recommendations concerning the bootstrap. For jackknife .R is ignored as it is based on the N leave-one-out data sets.

Choosing resample_method = "permutation" for ungrouped data causes an error as permutation will simply reorder the observations which is usually not meaningful. If a list of data is provided each list element is assumed to represent the observations belonging to one group. In this case, data is pooled and group adherence permutated.

For cross-validation the number of folds (k) defaults to 10. It may be changed via the .cv_folds argument. Setting k = 2 (not 1!) splits the data into a single training and test data set. Setting k = N (where N is the number of observations) produces leave-one-out cross-validation samples. Note: 1.) At least 2 folds required (k > 1); 2.) k can not be larger than N; 3.) If N/k is not not an integer the last fold will have less observations.

Random number generation (RNG) uses the L'Ecuyer-CRMR RGN stream as implemented in the future.apply package (Bengtsson 2018) . See ?future_lapply for details. By default a random seed is chosen.

References

Bengtsson H (2018). future.apply: Apply Function to Elements in Parallel using Futures. R package version 1.0.1, https://CRAN.R-project.org/package=future.apply.

Hesterberg TC (2015). “What Teachers Should Know About the Bootstrap: Resampling in the Undergraduate Statistics Curriculum.” The American Statistician, 69(4), 371--386. doi:10.1080/00031305.2015.1089789 .

csem(), cSEMResults, resamplecSEMResults()

Examples

# ===========================================================================
# Using the raw data
# ===========================================================================
### Bootstrap (default) -----------------------------------------------------

res_boot1 <- resampleData(.data = satisfaction)
str(res_boot1, max.level = 3, list.len = 3)
#> List of 499
#>  $:'data.frame': 250 obs. of 27 variables: #> ..$ imag1: int [1:250] 8 5 10 8 7 9 6 10 7 4 ...
#>   ..$imag2: int [1:250] 8 5 10 5 9 9 8 10 7 2 ... #> ..$ imag3: int [1:250] 10 6 10 6 8 9 8 10 7 2 ...
#>   .. [list output truncated]
#>  $:'data.frame': 250 obs. of 27 variables: #> ..$ imag1: int [1:250] 8 9 8 10 8 4 6 9 7 8 ...
#>   ..$imag2: int [1:250] 9 10 8 10 8 2 8 9 9 8 ... #> ..$ imag3: int [1:250] 9 7 7 10 9 2 8 9 9 10 ...
#>   .. [list output truncated]
#>  $:'data.frame': 250 obs. of 27 variables: #> ..$ imag1: int [1:250] 8 8 6 8 9 7 5 9 8 10 ...
#>   ..$imag2: int [1:250] 8 9 6 10 9 9 3 9 5 10 ... #> ..$ imag3: int [1:250] 8 5 4 9 10 8 4 9 6 10 ...
#>   .. [list output truncated]
#>   [list output truncated]

## To replicate a bootstrap draw use .seed:
res_boot1a <- resampleData(.data = satisfaction, .seed = 2364)
res_boot1b <- resampleData(.data = satisfaction, .seed = 2364)

identical(res_boot1, res_boot1a) # TRUE
#> [1] FALSE

### Jackknife ---------------------------------------------------------------

res_jack <- resampleData(.data = satisfaction, .resample_method = "jackknife")
str(res_jack, max.level = 3, list.len = 3)
#> List of 250
#>  $:'data.frame': 249 obs. of 27 variables: #> ..$ imag1: int [1:249] 9 9 8 10 7 5 9 9 10 2 ...
#>   ..$imag2: int [1:249] 9 8 9 10 8 5 9 8 10 2 ... #> ..$ imag3: int [1:249] 10 8 8 8 8 5 9 9 10 8 ...
#>   .. [list output truncated]
#>  $:'data.frame': 249 obs. of 27 variables: #> ..$ imag1: int [1:249] 8 9 8 10 7 5 9 9 10 2 ...
#>   ..$imag2: int [1:249] 8 8 9 10 8 5 9 8 10 2 ... #> ..$ imag3: int [1:249] 9 8 8 8 8 5 9 9 10 8 ...
#>   .. [list output truncated]
#>  $:'data.frame': 249 obs. of 27 variables: #> ..$ imag1: int [1:249] 8 9 8 10 7 5 9 9 10 2 ...
#>   ..$imag2: int [1:249] 8 9 9 10 8 5 9 8 10 2 ... #> ..$ imag3: int [1:249] 9 10 8 8 8 5 9 9 10 8 ...
#>   .. [list output truncated]
#>   [list output truncated]

### Cross-validation --------------------------------------------------------
## Create dataset for illustration:
dat <- data.frame(
"x1" = rnorm(100),
"x2" = rnorm(100),
"group" = sample(c("male", "female"), size = 100, replace = TRUE),
stringsAsFactors = FALSE)

## 10-fold cross-validation (repeated 100 times)
cv_10a <- resampleData(.data = dat, .resample_method = "cross-validation",
.R = 100)
str(cv_10a, max.level = 3, list.len = 3)
#> List of 100
#>  $:List of 10 #> ..$ 1 :'data.frame':	10 obs. of  3 variables:
#>   .. ..$x1 : num [1:10] -1.093 -0.084 -0.901 -0.977 1.234 ... #> .. ..$ x2   : num [1:10] 0.892 -0.708 -0.755 0.693 -0.564 ...
#>   .. ..$group: chr [1:10] "female" "female" "female" "male" ... #> ..$ 2 :'data.frame':	10 obs. of  3 variables:
#>   .. ..$x1 : num [1:10] 0.903 -1.428 -1.568 -1.277 -0.242 ... #> .. ..$ x2   : num [1:10] 2.454 -0.284 2.708 -1.472 0.667 ...
#>   .. ..$group: chr [1:10] "female" "male" "male" "male" ... #> ..$ 3 :'data.frame':	10 obs. of  3 variables:
#>   .. ..$x1 : num [1:10] 0.596 -1.595 -0.773 0.193 -0.464 ... #> .. ..$ x2   : num [1:10] 0.549 -0.265 0.536 -0.61 -0.535 ...
#>   .. ..$group: chr [1:10] "male" "female" "female" "male" ... #> .. [list output truncated] #>$ :List of 10
#>   ..$1 :'data.frame': 10 obs. of 3 variables: #> .. ..$ x1   : num [1:10] 0.837 -0.779 -0.628 -0.62 -0.768 ...
#>   .. ..$x2 : num [1:10] 0.796 0.975 0.736 -1.57 -2.102 ... #> .. ..$ group: chr [1:10] "female" "male" "male" "male" ...
#>   ..$2 :'data.frame': 10 obs. of 3 variables: #> .. ..$ x1   : num [1:10] -0.665 0.41 -0.977 1.397 -0.279 ...
#>   .. ..$x2 : num [1:10] 0.96 -1.276 0.693 -1.911 2.196 ... #> .. ..$ group: chr [1:10] "female" "female" "male" "male" ...
#>   ..$3 :'data.frame': 10 obs. of 3 variables: #> .. ..$ x1   : num [1:10] -0.0479 -2.3483 -0.0062 -1.3344 -0.6259 ...
#>   .. ..$x2 : num [1:10] -0.923 -0.3413 1.8448 -1.8135 -0.0422 ... #> .. ..$ group: chr [1:10] "female" "male" "female" "female" ...
#>   .. [list output truncated]
#>  $:List of 10 #> ..$ 1 :'data.frame':	10 obs. of  3 variables:
#>   .. ..$x1 : num [1:10] 0.6193 -0.6203 -1.2613 -0.0887 -0.7685 ... #> .. ..$ x2   : num [1:10] 0.314 -1.57 -1.649 -1.388 -2.102 ...
#>   .. ..$group: chr [1:10] "male" "male" "male" "female" ... #> ..$ 2 :'data.frame':	10 obs. of  3 variables:
#>   .. ..$x1 : num [1:10] 1.764 0.837 -0.686 0.527 0.854 ... #> .. ..$ x2   : num [1:10] 0.37 0.796 -0.982 -0.87 -0.99 ...
#>   .. ..$group: chr [1:10] "female" "female" "female" "female" ... #> ..$ 3 :'data.frame':	10 obs. of  3 variables:
#>   .. ..$x1 : num [1:10] 1.1175 0.4959 -0.264 -0.0062 0.4407 ... #> .. ..$ x2   : num [1:10] -1.152 1.373 -1.196 1.845 0.972 ...
#>   .. ..$group: chr [1:10] "male" "male" "female" "female" ... #> .. [list output truncated] #> [list output truncated] # Cross-validation can be done by group if a group identifyer is provided: cv_10 <- resampleData(.data = dat, .resample_method = "cross-validation", .id = "group", .R = 100) #> Warning: data length is not a multiple of split variable #> Warning: data length is not a multiple of split variable #> Warning: data length is not a multiple of split variable #> Warning: data length is not a multiple of split variable #> Warning: data length is not a multiple of split variable #> Warning: data length is not a multiple of split variable #> Warning: data length is not a multiple of split variable #> Warning: data length is not a multiple of split variable #> Warning: data length is not a multiple of split variable #> Warning: data length is not a multiple of split variable #> Warning: data length is not a multiple of split variable #> Warning: data length is not a multiple of split variable #> Warning: data length is not a multiple of split 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data length is not a multiple of split variable #> Warning: data length is not a multiple of split variable #> Warning: data length is not a multiple of split variable #> Warning: data length is not a multiple of split variable #> Warning: UNRELIABLE VALUE: One of the ‘future.apply’ iterations (‘future_lapply-1’) unexpectedly generated random numbers without declaring so. There is a risk that those random numbers are not statistically sound and the overall results might be invalid. To fix this, specify 'future.seed=TRUE'. This ensures that proper, parallel-safe random numbers are produced via the L'Ecuyer-CMRG method. To disable this check, use 'future.seed = NULL', or set option 'future.rng.onMisuse' to "ignore". ## Leave-one-out-cross-validation (repeated 50 times) cv_loocv <- resampleData(.data = dat[, -3], .resample_method = "cross-validation", .cv_folds = nrow(dat), .R = 50) str(cv_loocv, max.level = 2, list.len = 3) #> List of 50 #>$ :List of 100
#>   ..$1 :'data.frame': 1 obs. of 2 variables: #> ..$ 2  :'data.frame':	1 obs. of  2 variables:
#>   ..$3 :'data.frame': 1 obs. of 2 variables: #> .. [list output truncated] #>$ :List of 100
#>   ..$1 :'data.frame': 1 obs. of 2 variables: #> ..$ 2  :'data.frame':	1 obs. of  2 variables:
#>   ..$3 :'data.frame': 1 obs. of 2 variables: #> .. [list output truncated] #>$ :List of 100
#>   ..$1 :'data.frame': 1 obs. of 2 variables: #> ..$ 2  :'data.frame':	1 obs. of  2 variables:
#>   ..$3 :'data.frame': 1 obs. of 2 variables: #> .. [list output truncated] #> [list output truncated] ### Permuation --------------------------------------------------------------- res_perm <- resampleData(.data = dat, .resample_method = "permutation", .id = "group") str(res_perm, max.level = 2, list.len = 3) #> List of 499 #>$ :'data.frame':	100 obs. of  3 variables:
#>   ..$x1: num [1:100] -0.242 -0.468 -0.773 2.15 -1.334 ... #> ..$ x2: num [1:100] 1.066 -0.536 0.536 -1.829 -1.814 ...
#>   ..$id: chr [1:100] "male" "female" "female" "male" ... #>$ :'data.frame':	100 obs. of  3 variables:
#>   ..$x1: num [1:100] -0.242 -0.468 -0.773 2.15 -1.334 ... #> ..$ x2: num [1:100] 1.066 -0.536 0.536 -1.829 -1.814 ...
#>   ..$id: chr [1:100] "female" "male" "female" "female" ... #>$ :'data.frame':	100 obs. of  3 variables:
#>   ..$x1: num [1:100] -0.242 -0.468 -0.773 2.15 -1.334 ... #> ..$ x2: num [1:100] 1.066 -0.536 0.536 -1.829 -1.814 ...
#>   ..\$ id: chr [1:100] "female" "female" "female" "male" ...
#>   [list output truncated]

# Forgetting to set .id causes an error
if (FALSE) {
res_perm <- resampleData(.data = dat, .resample_method = "permutation")
}

# ===========================================================================
# Using a cSEMResults object
# ===========================================================================

model <- "
# Structural model
QUAL ~ EXPE
EXPE ~ IMAG
SAT  ~ IMAG + EXPE + QUAL + VAL
LOY  ~ IMAG + SAT
VAL  ~ EXPE + QUAL

# Measurement model
EXPE =~ expe1 + expe2 + expe3 + expe4 + expe5
IMAG =~ imag1 + imag2 + imag3 + imag4 + imag5
LOY  =~ loy1  + loy2  + loy3  + loy4
QUAL =~ qual1 + qual2 + qual3 + qual4 + qual5
SAT  =~ sat1  + sat2  + sat3  + sat4
VAL  =~ val1  + val2  + val3  + val4
"
a <- csem(satisfaction, model)

# Create bootstrap and jackknife samples
res_boot <- resampleData(a, .resample_method = "bootstrap", .R = 499)
res_jack <- resampleData(a, .resample_method = "jackknife")

# Since satisfaction is the dataset used the following approaches yield
# identical results.
res_boot_data   <- resampleData(.data = satisfaction, .seed = 2364)
res_boot_object <- resampleData(a, .seed = 2364)

identical(res_boot_data, res_boot_object) # TRUE
#> [1] TRUE