Calculate confidence intervals from bootstrapped model effects.

bootCI(mod, conf = 0.95, type = "bca", digits = 3, bci.arg = NULL, ...)

## Arguments

mod A fitted model object. Alternatively, a boot object (class "boot"), containing bootstrapped model effects. Can also be a list or nested list of such objects. A numeric value specifying the confidence level for the intervals. The type of confidence interval to return (defaults to "bca" – see Details). See boot.ci() for further options. The number of significant digits to return for numeric values. A named list of any additional arguments to boot.ci(), excepting argument index. Arguments to bootEff().

## Value

A summary table of the effects and bootstrapped confidence intervals (data frame), or a list or nested list of same.

## Details

bootCI() uses boot::boot.ci() to calculate confidence intervals of the specified type and level calculated from bootstrapped model effects. If a model or models is supplied, bootstrapping will first be performed via bootEff().

Nonparametric bias-corrected and accelerated confidence intervals (BCa; Efron, 1987) are calculated by default, which should provide the most accurate coverage across a range of bootstrap sampling distributions (Puth et al., 2015). They will, however, be inappropriate for parametric resampling – in which case the default will be set to the bootstrap percentile method instead ("perc").

Effects and confidence intervals are returned in a summary table, along with the bootstrap standard errors (standard deviations of the samples) and the bootstrap biases (sample means minus original estimates). Effects for which the confidence intervals do not contain zero are highlighted with a star (i.e. 'significant' at the conf level).

## Note

All bootstrapped confidence intervals will tend to underestimate the true nominal coverage to some extent when sample size is small (Chernick & Labudde, 2009), so the appropriate caution should be exercised in interpretation in such cases. Comparison of different interval types may be informative. For example, normal-theory based intervals may outperform bootstrap percentile methods when n < 34 (Hesterberg, 2015). Ultimately however, the bootstrap is not a solution to small sample size.

## References

Chernick, M. R., & Labudde, R. A. (2009). Revisiting Qualms about Bootstrap Confidence Intervals. American Journal of Mathematical and Management Sciences, 29(3–4), 437–456. doi: 10/c8zv

Efron, B. (1987). Better Bootstrap Confidence Intervals. Journal of the American Statistical Association, 82(397), 171–185. doi: 10/gfww2z

Hesterberg, T. C. (2015). What Teachers Should Know About the Bootstrap: Resampling in the Undergraduate Statistics Curriculum. The American Statistician, 69(4), 371–386. doi: 10/gd85v5

Puth, M.-T., Neuhäuser, M., & Ruxton, G. D. (2015). On the variety of methods for calculating confidence intervals by bootstrapping. Journal of Animal Ecology, 84(4), 892–897. doi: 10/f8n9rq

## Examples

# CIs calculated from bootstrapped SEM
(shipley.sem.ci <- bootCI(shipley.sem.boot))
#> $DD #> Effect Bias Std. Err. Lower CI Upper CI #> ------ ------ --------- -------- -------- #> (Intercept) | -0.056 | -0.026 | 0.069 | -0.167 0.085 | #> lat | -0.688 | 0.026 | 0.101 | -0.828 -0.459 | * #> #>$Date
#>                Effect     Bias   Std. Err.   Lower CI Upper CI
#>                ------   ------   ---------   -------- --------
#>  (Intercept) | -0.015 | -0.005 |     0.082 |   -0.167    0.179 |
#>  DD          | -0.628 |  0.000 |     0.057 |   -0.741   -0.519 | *
#>
#> $Growth #> Effect Bias Std. Err. Lower CI Upper CI #> ------ ------ --------- -------- -------- #> (Intercept) | -0.292 | -0.006 | 0.090 | -0.497 -0.141 | * #> Date | 0.382 | 0.011 | 0.058 | 0.293 0.515 | * #> #>$Live
#>                Effect    Bias   Std. Err.   Lower CI Upper CI
#>                ------   -----   ---------   -------- --------
#>  (Intercept) |  0.311 | 0.255 |     0.213 |    0.170    0.354 | *
#>  Growth      |  0.368 | 0.151 |     0.130 |    0.246    0.411 | *
#>
# From original SEM (models)
# (not typically recommended – better to use saved boot objects)
# system.time(
#   shipley.sem.ci <- bootCI(shipley.sem, R = 1000, seed = 13,
#                            ran.eff = "site")
# )