stable
infer(
.object = NULL,
.quantity = c("all", "mean", "sd", "bias", "CI_standard_z",
"CI_standard_t", "CI_percentile", "CI_basic",
"CI_bc", "CI_bca", "CI_t_interval"),
.alpha = 0.05,
.bias_corrected = TRUE
)An R object of class cSEMResults resulting from a call to csem().
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".
An integer or a numeric vector of significance levels.
Defaults to 0.05.
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
A list of class cSEMInfer.
Calculate common inferential quantities. For users interested in the
estimated standard errors, t-values, p-values and/or confidences
intervals of the path, weight or loading estimates, calling summarize()
directly will usually be more convenient as it has a much more
user-friendly print method. infer() is useful for comparing
different confidence interval estimates.
infer() is a convenience wrapper around a
number of internal functions that compute a particular inferential
quantity, i.e., a value or set of values to be used in statistical inference.
cSEM relies on resampling (bootstrap and jackknife) as the basis for
the computation of e.g., standard errors or confidence intervals.
Consequently, infer() requires resamples to work. Technically,
the cSEMResults object used in the call to infer() must
therefore also have class attribute cSEMResults_resampled. If
the object provided by the user does not contain resamples yet,
infer() will obtain bootstrap resamples first.
Naturally, computation will take longer in this case.
infer() does as much as possible in the background. Hence, every time
infer() is called on a cSEMResults object the quantities chosen by
the user are automatically computed for every estimated parameter
contained in the object. By default all possible quantities are
computed (.quantity = all). The following table list the available
inferential quantities alongside a brief description. Implementation and
terminology of the confidence intervals is based on
Hesterberg2015;textualcSEM and
Davison1997;textualcSEM.
"mean", "sd"The mean or the standard deviation
over all M resample estimates of a generic statistic or parameter.
"bias"The difference between the resample mean and the original estimate of a generic statistic or parameter.
"CI_standard_z" and "CI_standard_t"The standard confidence interval
for a generic statistic or parameter 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. The lower and upper bounds of the confidence interval are estimated as the alpha and 1-alpha quantiles of the distribution of the resample estimates.
"CI_basic"The basic confidence interval also called the reverse bootstrap percentile confidence interval. See Hesterberg2015;textualcSEM for details.
"CI_bc"The bias corrected (Bc) confidence interval. See Davison1997;textualcSEM for details.
"CI_bca"The bias-corrected and accelerated (Bca) confidence interval. Requires additional jackknife resampling to compute the influence values. See Davison1997;textualcSEM for details.
"CI_t_interval"The "studentized" t-confidence interval. If based on bootstrap
resamples the interval is also called the bootstrap t-interval
confidence interval. See Hesterberg2015;textualcSEM on page 381.
Requires resamples of resamples. See resamplecSEMResults().
By default, all but the studendized t-interval confidence interval and the bias-corrected and accelerated confidence interval are calculated. The reason for excluding these quantities by default are that both require an additional resampling step. The former requires jackknife estimates to compute influence values and the latter requires double bootstrap. Both can potentially be time consuming. Hence, computation is triggered only if explicitly chosen.
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
#> EXPE ~ IMAG QUAL ~ EXPE VAL ~ EXPE VAL ~ QUAL SAT ~ IMAG SAT ~ EXPE
#> 95%L 0.5721502 1.003766 -5.370667 4.643271 -0.2221538 0.9203283
#> 95%U 0.7068799 1.050534 -3.734023 6.252897 0.2055998 2.5685039
#> SAT ~ QUAL SAT ~ VAL LOY ~ IMAG LOY ~ SAT
#> 95%L -3.565415 1.182486 0.2688096 0.1970682
#> 95%U -1.308261 2.160784 0.6651351 0.5838536
inf$Indirect_effect$sd
#> QUAL ~ IMAG VAL ~ IMAG VAL ~ EXPE SAT ~ IMAG SAT ~ EXPE SAT ~ QUAL
#> 0.03933870 0.04684645 0.53453094 0.07561649 0.50778359 0.92817751
#> LOY ~ IMAG LOY ~ EXPE LOY ~ QUAL LOY ~ VAL
#> 0.08182073 0.09214110 0.28588461 0.20125755
### 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.
if (FALSE) { # \dontrun{
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 = "multisession`.
a1 <- csem(satisfaction, model, .resample_method = "bootstrap", .R = 499,
.resample_method2 = "bootstrap", .R2 = 199, .handle_inadmissibles = "replace")
infer(a1, .quantity = "CI_t_interval")} # }