RRPP (version 2.0.3)

ICCstats: Intraclass correlation statistics from an lm.rrpp model fits

Description

Function performs analyses concerned with the repeatability (reliability) of multivariate data (measurements) collected from the same research subjects. Although there is no requirement for repeated measurements on all research subjects, the analysis assumes that multiple observations are made.

Usage

ICCstats(
  fit,
  subjects = NULL,
  with_in = NULL,
  groups = NULL,
  multivariate = FALSE,
  print.AOV = TRUE
)

Value

Objects of class "ICCstats" return the following:

ICC_disp

The intraclass correlation coefficient (ICC) based on the dispersion of values.

ICC_mult

The eigenvalues of ICC matrices

Arguments

fit

The lm.rrpp, previously evaluated.

subjects

A single character value indicating which term in an ANOVA table corresponds to research subjects.

with_in

One or more character values indicating which terms in an ANOVA table are measured within subjects (replications, plus maybe interactions). If NULL, the only replication within-subject will be considered as residuals.

groups

An optional character value to indicate if a factor in the model frame of the lm.rrpp fit that could account for subject variation. Using this argument might minimize the importance of subject variation, if subjects have disparate values that could inflate ICC. Note that this name could be different than what is shown in the ANOVA table, if measurement.error was used. Use names(fit$LM$data), substituting fit with the name assigned to the measurement.error object, to know the groups factor, if used.

multivariate

Logical value for whether to include to calculate ICC matrix generalizations and perform eigenanalysis.

print.AOV

Logical value for whether to include ANOVA table as screen output, when calculating ISS statistics.

Note that this function can return ICC statistics, even if they do not make sense. It is possible to generate ICC stats with any ANOVA table, with at least one term.

Author

Michael Collyer

Details

Function uses ANOVA statistics or SSCP matrices to find the ratio of among-subject to within-subject variance. The former is a dispersion-based approach and the latter is a multivariate generalization of the ICC statistic (as a matrix product). The multivariate generalizations of the statistics described by Liljequist et al. (2019) are used to find matrix products, from which eigenanalysis is performed, providing ICC statistics by eigenvectors.

Three statistics describe the ICC for the population, agreement of measurements among subjects, and consistency between measurements. The last statistic does not necessarily measure the sameness between measurements but the consistency of change between measurements, which might be indicative of a systematic measurement error. If groups are used, these three statistics are repeated, using the SSCP for groups-adjusted data. This approach accounts for group differences, which would avoid large subject variation compared to measurement error inflating ICC values. If there are inherently disparate groups from which subjects are sampled, this approach can elucidate better agreement and consistency in light of group differences.

This function is most useful for analyses performed with measurement.error, but any lm.rrpp fit can be used, so long as research subjects can be defined.

It is essential that all arguments are terms that can be found in the model frame of the model fit, as provoke by ANOVA. Using anova(fit) will elucidate the row names of the ANOVA that could be used.

References

Liljequist, D., Elfving, B., & Skavberg Roaldsen, K. (2019). Intraclass correlation–A discussion and demonstration of basic features. PloS one, 14(7), e0219854.

Examples

if (FALSE) {
# Measurement error analysis on simulated data of fish shapes

data(fishy)

# Analysis unconcerned with groups 

ME1 <- measurement.error(
  Y = "coords",
  subjects = "subj",
  replicates = "reps",
  data = fishy)

anova(ME1)
ICCstats(ME1, subjects = "Subjects", with_in = "Systematic ME")

# Analysis concerned with groups 

ME2 <- measurement.error(
  Y = "coords",
  subjects = "subj",
  replicates = "reps",
  groups = "groups",
  data = fishy)

anova(ME2)
ICCstats(ME2, subjects = "Subjects", 
  with_in = "Systematic ME", groups = "groups")
ICCstats(ME2, subjects = "Subjects", 
  with_in = c("Systematic ME", "Systematic ME:Groups"), 
  groups = "groups")
  }