summary.circumplex_ssm_id: Summarize per-person SSM parameters at the group level

Description

Aggregate a per-person SSM parameter table (from ssm_parameters_id()) into group-level summaries, using circular statistics for displacement: arithmetic means are meaningless for angles, so displacement is summarized by its circular mean (the direction of the summed unit vectors) and the mean resultant length (a 0 to 1 measure of directional concentration).

Usage

# S3 method for circumplex_ssm_id
summary(object, ...)

Value

A one-row data frame with columns n (persons), n_na_d

(persons with undefined displacement, excluded from the circular summaries), e_mean, x_mean, y_mean, a_mean (arithmetic means), d_mean (circular mean of displacement, degrees in [0, 360], the 0/360 pole reported as 360), and d_res (mean resultant length in [0, 1]; NA when no displacement is defined, and undefined direction at zero resultant reports d_mean = NA).

Arguments

object: Required. An object of class "circumplex_ssm_id" created by ssm_parameters_id().
...: Ignored (S3 consistency).

Details

Persons with undefined (NA) displacement are stripped before the circular aggregation -- n_na_d reports how many -- while the arithmetic means of the other parameters use all persons with defined values. Two aggregation caveats apply. (1) The circular mean of per-person displacements weights every person's direction equally; it is a different quantity from the displacement of the group mean profile (e.g., from ssm_analyze()), which weights persons by amplitude -- on heterogeneous samples the two can differ substantially. (2) By the triangle inequality, the amplitude of the group mean profile is at most the mean per-person amplitude (a_mean), strictly smaller when directions disperse; relatedly, the mean resultant length d_res falls below 1 as directions disperse.

Examples

Run this code

data("aw2009")
res <- ssm_parameters_id(
  aw2009,
  scales = c("PA", "BC", "DE", "FG", "HI", "JK", "LM", "NO")
)
summary(res)