Computation of CIs for standardized regression coefficients

[wviechtb]

At the moment, CIs for standardized regression coefficients are computed with convert_b_to_beta() which applies b * (sd_pred/sd_crit) to the coefficient and regular CI bounds. However, for the CI, this ignores the sampling variability in ci_crit and sd_pred (if the predictor is random). See:

• Jones, J. A., & Waller, N. G. (2013). Computing confidence intervals for standardized regression coefficients. Psychological Methods, 18(4), 435-453.
• Jones, J. A., & Waller, N. G. (2015). The normal-theory and asymptotic distribution-free (adf) covariance matrix of standardized regression coefficients: Theoretical extensions and finite sample behavior. Psychometrika, 80(2), 365-378.
• Yuan, K.-H., & Chan, W. (2011). Biases and standard errors of standardized regression coefficients. Psychometrika, 76(4), 670-690.

Would be nice to implement maybe the delta method approach, which seems to work well. Also, there is the fungible package, which provides more appropriate SEs (from which the CI can be computed).

[bwiernik]

I have implemented these more accurate normal-theory SE methods in the configural package. Happy to make a pull request to add them here.