cohend: Use Cohen's d as the effect size in 'study_parameters'
In powerlmm: Power Analysis for Longitudinal Multilevel Models

Description Usage Arguments Details Value References See Also Examples

This function is used as input to the effect_size argument in study_parameters, if standardized effect sizes should be used. The choice of the denominator differs between fields, and this function supports the common ones: pre- or posttest SD, or the random slope SD.

1	cohend(ES, standardizer = "pretest_SD", treatment = "control")

`ES`	`numeric`; value of the standardized effect size. Can be a vector.
`standardizer`	`character`; the standardizer (denominator) used to calculate Cohen's d. Allows options are: "pretest_SD", "posttest_SD", or "slope_SD". See Details from more information.
`treatment`	`character`; indicates if the `standardizer` should be based on the "treatment" or "control" group—this only matters for 3-level partially nested designs.

Standardizing using the pretest_SD or posttest_SD

For these effect sizes, ES indicates the standardized difference between the treatment groups at posttest (T_end), standardized by using either the implied standard deviation at pretest or posttest. Thus, the actual raw differences in average slopes between the treatments are,

slope_diff = (ES * SD)/T_end.

slope_SD: standardizing using the random slopes

This standardization is quite different from using the pretest or posttest SD. Here the average slope difference is standardized using the total SD of the random slopes. This is done by e.g. Raudenbush and Liu (2001). NB, for this effect size ES indicates the difference in change per unit time, and not at posttest. Thus, the raw difference in average slopes is,

slope_diff = ES * slope_SD.

For a 3-level model, slope_SD = sqrt(sigma_subject_slope^2 + sigma_cluster_slope^2).

A list of the same length as ES. Each element is a named list of class plcp_cohend, with the elements:

set: A helper function that converts the standardized ES to raw values. Accepts a study_parameters objects, and returns a numeric indicating the raw difference between the treatment at posttest.
get: contains a list with the original call: "ES", "standardizer", and "treatment".

Raudenbush, S. W., & Liu, X. F. (2001). Effects of study duration, frequency of observation, and sample size on power in studies of group differences in polynomial change. Psychological methods, 6(4), 387.

study_parameters

# Pretest SD
p <- study_parameters(n1 = 11,
                      n2 = 20,
                      icc_pre_subject = 0.5,
                      cor_subject = -0.4,
                      var_ratio = 0.03,
                      effect_size = cohend(0.4, standardizer = "pretest_SD"))

get_slope_diff(p)

# using posttest SD,
# due to random slope SD will be larger at posttest
# thus ES = 0.4 indicate larger raw slope difference
# using posttest SD
p <- update(p, effect_size = cohend(0.4,
                                    standardizer = "posttest_SD"))
get_slope_diff(p)


# Random slope SD
p <- study_parameters(n1 = 11,
                      n2 = 20,
                      icc_pre_subject = 0.5,
                      cor_subject = -0.4,
                      var_ratio = 0.03,
                      effect_size = cohend(0.4, standardizer = "slope_SD"))

# Partially nested ----------------------------------------------------------
p <- study_parameters(n1 = 11,
                      n2 = 20,
                      n3 = 4,
                      icc_pre_subject = 0.5,
                      icc_pre_cluster = 0.25,
                      cor_subject = -0.4,
                      var_ratio = 0.03,
                      partially_nested = TRUE,
                      effect_size = cohend(0.4, standardizer = "pretest_SD")
                      )
# Default is to use control groups SD
get_slope_diff(p)

# Treatment group's SD also include cluster-level intercept variance.
# Thus, ES of 0.4 will indicate a larger raw difference
# using the treatment group's SD
p <- update(p, effect_size = cohend(0.4,
                                    standardizer = "pretest_SD",
                                    treatment = "treatment"))
get_slope_diff(p)

## Combine multiple values, and raw and standardized effects ----------------
p <- study_parameters(n1 = 11,
                      n2 = 20,
                      icc_pre_subject = 0.5,
                      cor_subject = -0.4,
                      var_ratio = 0.03,
                      effect_size = c(-5, 9,
                                      cohend(c(0.5, 0.8), standardizer = "pretest_SD"),
                                      cohend(c(0.5, 0.8), standardizer = "posttest_SD")))


## Recreate results in Raudenbush & Liu 2001 --------------------------------
rauden_liu <- function(D, f, n = 238) {
    n1 <- f * D + 1
    p <- study_parameters(n1 = n1,
                          n2 = n/2,
                          T_end = D,
                          sigma_subject_intercept = sqrt(0.0333),
                          sigma_subject_slope = sqrt(0.0030),
                          sigma_error = sqrt(0.0262),
                          effect_size = cohend(0.4, standardizer = "slope_SD"))
    x <- get_power(p)
    round(x$power, 2)
}

## Table 1 in Raudenbush & Liu 2001
## NB, it looks like they made an error in column 1.
g <- expand.grid(D = 2:8,
                 f = c(0.5, 1:6))
g$power <- mapply(rauden_liu, D = g$D, f = g$f)
tidyr::spread(g, f, power)


## Table 3 Table 1 in Raudenbush & Liu 2001
g <- expand.grid(n = seq(100, 800, by = 100),
                 D = 4,
                 f = c(0.5, 1:6))
g$power <- mapply(rauden_liu, n = g$n, f = g$f, D = g$D)
tidyr::spread(g, n, power)