cSEM (version 0.2.0)

MeanResample: Inference

Description

Calculate common inferential quantities. For users interested in the estimated standard errors and/or confidences intervals summarize() will usually be more helpful as it has a much more user-friendly print method.

Usage

MeanResample(.first_resample)
SdResample(.first_resample, .resample_method, .n)
BiasResample(.first_resample, .resample_method, .n)
StandardCIResample(
  .first_resample,
  .bias_corrected,
  .dist = c("z", "t"),
  .df = c("type1", "type2"),
  .resample_method,
  .n,
  .probs
)
PercentilCIResample(.first_resample, .probs)
BasicCIResample(.first_resample, .bias_corrected, .probs)
TStatCIResample(
  .first_resample,
  .second_resample,
  .bias_corrected,
  .resample_method,
  .resample_method2,
  .n,
  .probs
)
BcCIResample(.first_resample, .probs)
BcaCIResample(.object, .first_resample, .probs)
infer(
 .object            = NULL,
 .alpha             = 0.05,
 .bias_corrected    = TRUE,
 .quantity          = c("all", "mean", "sd", "bias", "CI_standard_z", 
                        "CI_standard_t", "CI_percentile", "CI_basic", 
                        "CI_bc", "CI_bca", "CI_t_interval")
)

Arguments

.first_resample

A list containing the .R resamples based on the original data obtained by resamplecSEMResults().

.resample_method

Character string. The resampling method to use. One of: "none", "bootstrap" or "jackknife". Defaults to "none".

.n

Integer. The number of observations of the original data.

.bias_corrected

Logical. Should the standard and the tStat confidence interval be bias-corrected using the bootstrapped bias estimate? If TRUE the confidence interval for some estimated parameter theta is centered at 2*theta - theta*_hat, where theta*_hat is the average over all .R bootstrap estimates of theta. Defaults to TRUE

.dist

Character string. The distribution to use for the critical value. One of "t" for Student's t-distribution or "z" for the standard normal distribution. Defaults to "z".

.df

Character string. The method for obtaining the degrees of freedom. Choices are "type1" and "type2". Defaults to "type1" .

.probs

A vector of probabilities.

.second_resample

A list containing .R2 resamples for each of the .R resamples of the first run.

.resample_method2

Character string. The resampling method to use when resampling from a resample. One of: "none", "bootstrap" or "jackknife". For "bootstrap" the number of draws is provided via .R2. Currently, resampling from each resample is only required for the studentized confidence intervall ("CI_t_interval") computed by the infer() function. Defaults to "none".

.object

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

.alpha

An integer or a numeric vector of significance levels. Defaults to 0.05.

.quantity

Character string. Which statistic should be returned? One of "all", "mean", "sd", "bias", "CI_standard_z", "CI_standard_t", "CI_percentile", "CI_basic", "CI_bc", "CI_bca", "CI_t_interval" Defaults to "all" in which case all quantities that do not require additional resampling are returned, i.e., all quantities but "CI_bca", "CI_t_interval".

Value

A list of class cSEMInfer.

Functions

• MeanResample: Computes the mean over all resamples for each resampled statistic/parameter.

• SdResample: Computes the standard deviation over all resamples for each resampled statistic/estimator. This is usually taken to be the estimate of the standard error of the statistic/estimator.

• BiasResample: Computes the estimated bias for each resampled statistic/estimator.

• StandardCIResample: Computes the Standard CI with bootstrap SE's. Critical quantiles can be based on both the t- or the standard normal distribution (z). The former may perform better in small samples but there is no clear consenus on what the degrees of freedom should be. We use N - 1 ("type1").

• PercentilCIResample: Computes the Percentile CI. The function takes the distribution F* (the CDF) of the resamples as an estimator for the true distribution F of the statistic/estimator of interest. Quantiles of the estimated distribution are then used as lower and upper bound.

• BasicCIResample: Computes the Basic CI.

• TStatCIResample: Computes the Studentized or t-statistic CI The function computes a boostrap t-statisic (since it is roughly pivotal) and constructs the CI based on bootstraped t-values and bootstraped/jackknife SE's

• BcCIResample: Computes the Basic bias-corrected CI.

• BcaCIResample: Computes the Basic bias-corrected and accelerated CI.

Details

Calculate common inferential quantities (e.g., estimated standard errors, estimated bias, confidence intervals) based on a cSEMResults_resampled object as obtained by calling resamplecSEMResults() or by setting .resample_method = "bootstrap" or "jackknife" when calling csem(). Currently, the following quantities are returned by default (.quantity = "all"):

"mean", "sd" and "bias"

The mean, the standard deviation and the estimated bias (defined as the difference between the resample mean and the original estimate).

"CI_standard_z" and "CI_standard_t"

The standard confidence interval with standard errors estimated by the resample standard deviation. While "CI_standard_z" assumes a standard normally distributed statistic, "CI_standard_t" assumes a t-statistic with N - 1 degrees of freedom.

"CI_percentile"

The percentile confidence interval

"CI_basic"

The basic confidence interval

"CI_bc"

The bias corrected confidence interval

In addition, the bias-corrected and accelerated (.quantity = "CI_bca") and/or the "studentized" confidence interval (".quantity = CI_t_interval") may be computed. The former requires jackknife estimates to compute influence values and the latter requires double bootstrap. Both can potentially be time consuming. Hence, computation is triggerd only if explicitly chosen.

See Also

csem(), resamplecSEMResults(), summarize() cSEMResults

Examples

# NOT RUN {
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
"
  
## Estimate the model with bootstrap resampling 
a <- csem(satisfaction, model, .resample_method = "bootstrap", .R = 20,
          .handle_inadmissibles = "replace")

## Compute inferential quantities
inf <- infer(a)

inf$Path_estimates$CI_basic
inf$Indirect_effect$sd

### Compute the bias-corrected and accelerated and/or the studentized t-inverval.
## For the studentied t-interval confidence interval a double bootstrap is required.
## This is pretty time consuming.
# }
# NOT RUN {
  inf <- infer(a, .quantity = c("all", "CI_bca")) # requires jackknife estimates 
  
## Estimate the model with double bootstrap resampling:
# Notes:
#   1. The .resample_method2 arguments triggers a bootstrap of each bootstrap sample
#   2. The double bootstrap is is very time consuming, consider setting 
#      `.eval_plan = "multiprocess`. 
a1 <- csem(satisfaction, model, .resample_method = "bootstrap", .R = 499,
          .resample_method2 = "bootstrap", .R2 = 199, .handle_inadmissibles = "replace") 
infer(a1, .quantity = "CI_t_interval")
# }
# NOT RUN {
# }