tcl (version 1.0.1)

cml_power: Power and Power Curve Functions

Description

Functions to compute the power of \(\chi^2\) tests, i.e., Wald (W), likelihood ratio (LR), Rao score (RS) and gradient (GR) test, and to plot power curves as functions of effect size and sample size.

cml_power() computes the power of the tests given a specified effect size, type I error prob. alpha, informative sample size, and degrees of freedom.

p_curve() generates a power curve as a function of effect size.

p_ncurve() generates a power curve as a function of sample size.

Usage

cml_power(obj, effect = 0.03, alpha = 0.05, n = "auto", df = "auto")
p_curve(obj, alpha = 0.05, n = 300, df = "auto", from = 0, to = 0.2, ...)
p_ncurve(
  obj,
  effect = 0.03,
  alpha = 0.05,
  df = "auto",
  from = 0,
  to = 600,
  ...
)

Value

• cml_power(): Numeric vector of power values.

• p_curve(), p_ncurve(): A power curve plotted to the active graphics device.

Arguments

obj

An object of class 'tcl_sa_size', typically containing information such as degrees of freedom (df) and informative sample size (n). If missing, values for df and n need to be set manually.

effect

Numeric value representing the effect size. A real number between 0 and 1, interpreted as a proportion of pseudo-variance between persons with different covariate values (but the same person parameter). Default is 0.03.

alpha

Type I error probability. Default is 0.05.

n

Informative sample size (excluding persons with a score of 0 or highest possible score). Default is "auto", in which case the value is extracted from obj.

df

Degrees of freedom. Default is "auto", in which case the value is extracted from obj.

from

Lower bound of the effect or sample size range (default is 0).

to

Upper bound of the effect or sample size range (default is 0.2 for effect size, and 600 for sample site).

...

Additional graphical arguments passed to plot (e.g., col, lwd, ylim) via p_curve and p_ncurve.

Details

The effect is interpreted as a pseudo \(R^2\)-like measure of explained variance (as in linear models). It is 0 when persons with the same person parameters yield the same response probabilities. If two persons with the same person parameter but different covariate values yield different response probabilities, an additional variance component is introduced and the effect is greater than 0

The power of the tests is computed from the cumulative distribution function of the non-central \(\chi^2\) distribution, where the respective non-centrality parameter is obtained by multiplying the effect with the informative sample size. This is only an approximation based on results of asymptotic theory. The approximation may be poor when the informative sample size is small and/or the effect is large.

References

Draxler, C., & Kurz, A. (2025). Testing measurement invariance in a conditional likelihood framework by considering multiple covariates simultaneously. Behavior Research Methods, 57(1), 50.

See Also

sa_sizeRM, sa_sizePCM, and sa_sizeChange

Examples

if (FALSE) {
##### Sample size of Rasch Model #####

res <-  sa_sizeRM(local_dev = list( c(0, -0.5, 0, 0.5, 1) , c(0, 0.5, 0, -0.5, 1)))

cml_power(obj = res)

p_curve(obj = res)
p_curve(obj = res, col = "red", lwd = 2, ylim = c(0, 1))

p_ncurve(obj = res)
p_ncurve(obj = res, col = "red", lwd = 2, ylim = c(0, 1))

}