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.