Shrout-Fleiss reliability coefficients

Computes five reliability coefficients from the Shrout and Fleiss (1979) framework using variance components extracted from a person × item × time mixed model (see extract_components). The coefficients cover between-person and within-person reliability under both fixed and random time designs, and are appropriate for longitudinal or repeated-measures measurement studies.

Usage

compute_shrout(sperson, spersonitem, stime, spersontime, serror, m, k)

Arguments

sperson

Variance component of the person main effect.

spersonitem

Variance component of the person × item interaction.

stime

Variance component of the time main effect.

spersontime

Variance component of the person × time interaction.

serror

Variance component of residual error.

m

Number of items (reports) averaged over.

k

Number of time points averaged over.

Value

A data frame with one row per reliability coefficient containing columns measure, result, and description:

r1f

Between-person reliability of a single measure at fixed time points.

r1r

Between-person reliability of a single measure at random time points (different people, different days).

rkf

Between-person reliability of scores averaged over m items and k fixed time points.

rkr

Between-person reliability of scores averaged over k random time points.

rc

Within-person reliability of change across time points.

References

Shrout, P. E., & Fleiss, J. L. (1979). Intraclass correlations: Uses in assessing rater reliability. Psychological Bulletin, 86(2), 420–428.

Examples

design <- expand.grid(time = 1:3, item = 1:2, person = 1:10)
design <- change_data_type(design, type = "factor")
design$response <- rnorm(30, 0, 0.1)
model <- mixlm::lm(response ~ r(time) * r(person) + r(item) * r(person), data = design)
result <- extract_components(model)
vc <- result$components
compute_shrout(
  sperson = vc[2, 3], spersonitem = vc[5, 3], stime = vc[1, 3],
  spersontime = vc[4, 3], serror = vc[6, 3], 3, 3
)
#>   measure    result                                                                                         description
#> 1     r1f 0.2251901                            Reliability (between persons) of measures taken on the same fixed k time
#> 2     r1r 0.1284004                           Reliability (between persons) of measures taken on the same random k time
#> 3      rc 0.4795683                                                              Reliability (within persons) of change
#> 4     rkf 0.4657885        Reliability (between persons) of average measures taken over fixed m items and fixed k times
#> 5     rkr 0.3064935 Reliability (between persons) of different random time with same number of points k between periods