Description Usage Arguments Details Value References Examples
This function computes \mjeqnd_Modd_Mod effect sizes from userdefined descriptive statistics
and regression coefficients. If one has access to a raw data set, the dMod
function may be used
as a wrapper to this function so that the regression equations and descriptive statistics can
be computed automatically within the program.
1 2 3 4 5 6 7 8 9 10 11 12 13  compute_dmod_par(
referent_int,
referent_slope,
focal_int,
focal_slope,
focal_mean_x,
focal_sd_x,
referent_sd_y,
focal_min_x,
focal_max_x,
focal_names = NULL,
rescale_cdf = TRUE
)

referent_int 
Referent group's intercept. 
referent_slope 
Referent group's slope. 
focal_int 
Focal groups' intercepts. 
focal_slope 
Focal groups' slopes. 
focal_mean_x 
Focal groups' predictorscore means. 
focal_sd_x 
Focal groups' predictorscore standard deviations. 
referent_sd_y 
Referent group's criterion standard deviation. 
focal_min_x 
Focal groups' minimum predictor scores. 
focal_max_x 
Focal groups' maximum predictor scores. 
focal_names 
Focalgroup names. If 
rescale_cdf 
Logical argument that indicates whether parametric \mjeqnd_Modd_Mod results
should be rescaled to account for using a cumulative density < 1 in the computations ( 
The \mjeqnd_Mod_Signedd_Mod_Signed effect size (i.e., the average of differences in prediction over the range of predictor scores) is computed as \mjdeqnd_Mod_Signed=\frac1SD_Y_1\intop f_2(X)\left[X\left(b_1_1b_1_2\right)+b_0_1b_0_2\right] dX,d_Mod_Signed = 1/SD_Y_1 * integrate(f_2(X) * [X * (b_1_1  b_1_2) + b_0_1  b_0_2]), where
SD_Y_1Y_1 is the referent group's criterion standard deviation;
f_2(X)f_2(X) is the normaldensity function for the distribution of focalgroup predictor scores;
b_1_1b_1_1 and \mjeqnb_1_0b_1_0 are the slopes of the regression of \mjseqnY on \mjseqnX for the referent and focal groups, respectively;
b_0_1b_0_1 and \mjeqnb_0_0b_0_0 are the intercepts of the regression of \mjseqnY on \mjseqnX for the referent and focal groups, respectively; and
the integral spans all \mjseqnX scores within the operational range of predictor scores for the focal group.
The \mjeqnd_Mod_Underd_Mod_Under and \mjeqnd_Mod_Overd_Mod_Over effect sizes are computed using the same equation as \mjeqnd_Mod_Signedd_Mod_Signed, but \mjeqnd_Mod_Underd_Mod_Under is the weighted average of all scores in the area of underprediction (i.e., the differences in prediction with negative signs) and \mjeqnd_Mod_Overd_Mod_Over is the weighted average of all scores in the area of overprediction (i.e., the differences in prediction with negative signs).
The \mjeqnd_Mod_Unsignedd_Mod_Unsigned effect size (i.e., the average of absolute differences in prediction over the range of predictor scores) is computed as \mjdeqnd_Mod_Unsigned=\frac1SD_Y_1\intop f_2(X)\leftX\left(b_1_1b_1_2\right)+b_0_1b_0_2\rightdX.d_Mod_Unsigned = 1/SD_Y_1 * integrate(f_2(X) * X * (b_1_1  b_1_2) + b_0_1  b_0_2).
The \mjeqnd_Mind_Min effect size (i.e., the smallest absolute difference in prediction observed over the range of predictor scores) is computed as \mjdeqnd_Min=\frac1SD_Y_1Min\left[\leftX\left(b_1_1b_1_2\right)+b_0_1b_0_2\right\right].d_Min = 1/SD_Y_1 * Min[X * (b_1_1  b_1_2) + b_0_1  b_0_2].
The \mjeqnd_Maxd_Max effect size (i.e., the largest absolute difference in prediction observed over the range of predictor scores)is computed as \mjdeqnd_Max=\frac1SD_Y_1Max\left[\leftX\left(b_1_1b_1_2\right)+b_0_1b_0_2\right\right].d_Max = 1/SD_Y_1 * Max[X * (b_1_1  b_1_2) + b_0_1  b_0_2]. Note: When \mjeqnd_Mind_Min and \mjeqnd_Maxd_Max are computed in this package, the output will display the signs of the differences (rather than the absolute values of the differences) to aid in interpretation.
If \mjeqnd_Modd_Mod effect sizes are to be rescaled to compensate for a cumulative density less than 1 (see the rescale_cdf
argument), the result of each
effect size involving integration will be divided by the ratio of the cumulative density of the observed range of scores (i.e., the range bounded by the focal_min_x
and focal_max_x
arguments) to the cumulative density of scores bounded by Inf
and Inf
.
A matrix of effect sizes (\mjeqnd_Mod_Signedd_Mod_Signed,
\mjeqnd_Mod_Unsignedd_Mod_Unsigned, \mjeqnd_Mod_Underd_Mod_Under,
\mjeqnd_Mod_Overd_Mod_Over), proportions of under and overpredicted criterion scores,
minimum and maximum differences (i.e., \mjeqnd_Mod_Underd_Mod_Under and \mjeqnd_Mod_Overd_Mod_Over),
and the scores associated with minimum and maximum differences.
Note that if the regression lines are parallel and infinite focal_min_x
and focal_max_x
values were
specified, the extrema will be defined using the scores 3 focalgroup SDs above and below the corresponding focalgroup means.
Nye, C. D., & Sackett, P. R. (2017). New effect sizes for tests of categorical moderation and differential prediction. Organizational Research Methods, 20(4), 639–664. doi: 10.1177/1094428116644505
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