Summarize per-person SSM parameters at the group level

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 class 'circumplex_ssm_id'
summary(object, ...)

Arguments

object

Required. An object of class "circumplex_ssm_id" created by ssm_parameters_id().

...

Ignored (S3 consistency).

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).

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.

See also

Other ssm functions: plot.circumplex_ci_accuracy(), ssm_analyze(), ssm_analyze_long(), ssm_ci_accuracy(), ssm_draws(), ssm_parameters(), ssm_parameters_id(), ssm_score(), ssm_sem(), ssm_sem_parameters(), ssm_table()

Other analysis functions: cpm_fit(), cpm_simulate(), ssm_analyze(), ssm_analyze_long(), ssm_ci_accuracy(), ssm_draws(), ssm_parameters(), ssm_parameters_id(), ssm_score(), ssm_sem(), ssm_sem_parameters()

Examples

data("aw2009")
res <- ssm_parameters_id(
  aw2009,
  scales = c("PA", "BC", "DE", "FG", "HI", "JK", "LM", "NO")
)
summary(res)
#>   n n_na_d e_mean    x_mean     y_mean   a_mean   d_mean     d_res
#> 1 5      0  0.423 0.9445214 -0.2644691 1.164276 344.4394 0.8429474