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Confidence Interval for a Standardized Regression Coefficient

Source: R/ci_src.R
ci_src.Rd

Computes a confidence interval for a population standardized regression coefficient, by the standard t-based approach or the noncentral t approach. A thin convenience wrapper around ci_reg_coef, which is the general engine; for the coefficient in its raw metric use ci_rc.

Usage

ci_src(
  beta_j = NULL,
  SE_beta_j = NULL,
  N = NULL,
  p = NULL,
  R2_Y_X = NULL,
  R2_j_X_without_j = NULL,
  conf_level = 0.95,
  R2_Y_X_without_j = NULL,
  t_value = NULL,
  b_j = NULL,
  SE_b_j = NULL,
  s_Y = NULL,
  s_X = NULL,
  alpha_lower = NULL,
  alpha_upper = NULL,
  ...
)

Arguments

beta_j

The standardized regression coefficient

SE_beta_j

The standard error of the standardized regression coefficient

N

Sample size

p

The number of predictors

R2_Y_X

The squared multiple correlation coefficient predicting Y from the p predictor variables

R2_j_X_without_j

The squared multiple correlation coefficient predicting the jth predictor variable (i.e., the predictor of interest) from the remaining p-1 predictor variables

conf_level

Desired level of confidence for the computed interval (i.e., 1 - the Type I error rate)

R2_Y_X_without_j

The squared multiple correlation coefficient predicting Y from the p-1 predictor variable with the jth predictor of interest excluded

t_value

The t-value evaluating the null hypothesis that the population regression coefficient for the jth predictor equals zero

b_j

The unstandardized regression coefficient

SE_b_j

The standard error of the unstandardized regression coefficient

s_Y

Standard deviation of Y, the dependent variable

s_X

Standard deviation of X, the predictor variable of interest

alpha_lower

The Type I error rate for the lower confidence interval limit

alpha_upper

The Type I error rate for the upper confidence interval limit

...

Optional additional specifications for nested functions

Value

A 3-row data.frame with columns term, value, prob_less, and prob_greater. The term values are "lower_limit", "src" (the standardized regression coefficient point estimate), and "upper_limit", so the estimate sits between its confidence limits. The prob_less and prob_greater columns report the achieved tail probabilities at each limit when the noncentral t method is used (NA for the estimate row).

Details

For standardized variables, do not specify the standard deviation of the variables and input the standardized regression coefficient for b_j.

Note

This function calls upon ci_reg_coef in DMAR, but has a different naming scheme. See ci_reg_coef for more details.

To form a confidence interval for the unstandardized regression coefficient, use ci_rc. This function is used to form a confidence interval for the standardized regression coefficient.

Not all of the values need to be specified, only those that contain all of the necessary information in order to compute the confidence interval (options are thus given for the values that need to be specified).

References

Kelley, K. (2007). Confidence intervals for standardized effect sizes: Theory, application, and implementation. Journal of Statistical Software, 20(8), 1–24. doi:10.18637/jss.v020.i08

Kelley, K., & Maxwell, S. E. (2003). Sample size for multiple regression: Obtaining regression coefficients that are accurate, not simply significant. Psychological Methods, 8(3), 305–321. doi:10.1037/1082-989X.8.3.305

Kelley, K., & Maxwell, S. E. (2008). Sample size planning with applications to multiple regression: Power and accuracy for omnibus and targeted effects. In P. Alasuutari, L. Bickman, & J. Brannen (Eds.), The Sage handbook of social research methods (pp. 166–192). Sage.

Maxwell, S. E., Delaney, H. D., & Kelley, K. (2027). Designing experiments and analyzing data: A model comparison perspective (4th ed.). Routledge. (See Chapter 4 on individual comparisons of means and Chapter 6 on trend analysis.)

Smithson, M. (2003). Confidence intervals. Thousand Oaks, CA: Sage Publications.

Steiger, J. H. (2004). Beyond the F Test: Effect size confidence intervals and tests of close fit in the Analysis of Variance and Contrast Analysis. Psychological Methods, 9(2), 164–182. doi:10.1037/1082-989X.9.2.164

See also

ss_aipe_reg_coef, conf_limits_nct, ci_reg_coef, ci_rc

Other confidence intervals for effect sizes: ci_R2(), ci_c(), ci_c_ancova(), ci_c_ancova_bp(), ci_correlation, ci_cv(), ci_eta_squared(), ci_eta_squared_generalized(), ci_eta_squared_partial(), ci_mahalanobis(), ci_omega_squared(), ci_pvaf(), ci_rc(), ci_reg_coef(), ci_rmsea(), ci_sc(), ci_sc_ancova(), ci_sm(), ci_smd(), ci_smd_c(), ci_snr(), ci_srsnr(), contrast_adjusted(), plot_smd()

Author

Ken Kelley kkelley@nd.edu

Examples

ci_src(beta_j = .6707, .1761, N = 30, p = 6, conf_level = .95)
#>  term        value prob_less prob_greater
#>  lower_limit 0.27  0.025     0.975       
#>  src         0.671 <NA>      <NA>        
#>  upper_limit 1.06  0.975     0.025       
#> 
#> Confidence level: 95%