measurement.error: Evaluation of measurement error for two or more multivariate...

In RRPP: Linear Model Evaluation with Randomized Residuals in a Permutation Procedure

Evaluation of measurement error for two or more multivariate measurements, for common research subjects

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

measurement.error(
  Y,
  subj,
  reps,
  groups = NULL,
  iter = 999,
  seed = NULL,
  multivariate = FALSE,
  use.PCs = TRUE,
  tol = 0.001,
  Parallel = TRUE,
  print.progress = FALSE,
  verbose = FALSE
)

Arguments

Y	A matrix (n x p) of data for n observations and p variables.
subj	A vector or factor of research subjects (each subject should occur twice or more). The length of the vector must equal the number of observations and will be coerced into a factor.
reps	A vector or factor for replicate measurements for research subjects. The length of the vector must equal the number of observations and will be coerced into a factor.
groups	An optional vector, coercible to factor, to be included in the linear model (as an interaction with replicates).. This would be of interest if one were concerned with systematic ME occurring perhaps differently among certain strata within the data. For example, systematic ME because of an observer bias might only be observed with females or males.
iter	Number of iterations for significance testing
seed	An optional argument for setting the seed for random permutations of the resampling procedure. If left NULL (the default), the exact same P-values will be found for repeated runs of the analysis (with the same number of iterations). If seed = "random", a random seed will be used, and P-values will vary. One can also specify an integer for specific seed values, which might be of interest for advanced users.
multivariate	Logical value for whether to include multivariate analyses. Intraclass correlation matrices and relative eigenanalysis are based on products of sums of squares and cross-products (SSCP) matrices, some of which must be inverted and potentially require significant computation time. If FALSE, only statistics based on dispersion of values are calculated.
use.PCs	A logical argument for whether to use the principal components of the data. This might be helpful for relative eigenanalysis, and if p > n, in which case inverting singular covariance matrices would not be possible.
tol	A value indicating the magnitude below which components should be omitted., if use.PCs is TRUE. (Components are omitted if their standard deviations are less than or equal to tol times the standard deviation of the first component.) See ordinate for more details.
Parallel	The same argument as in lm.rrpp to govern parallel processing ( either a logical vale – TRUE or FALSE – or the number of threaded cores to use). See lm.rrpp for additional details.
print.progress	A logical value to indicate whether a progress bar should be printed to the screen.
verbose	A logical value to indicate if all the output from an lm.rrpp analysis should be retained. If FALSE, only the needed output for summaries and plotting is retained.

Details

This function performs analyses as described in Collyer and Adams (in review) to assess systematic and random components of measurement error (ME). It basically performs ANOVA with RRPP, but with different restricted randomization strategies. The reliability of research subject variation can be considered by restricting randomization within replicates; the consistency of replicate measures can be considered by restricting randomization within subjects. Inter-subject variation remains constant across all random permutations within subjects and inter-replicate variation remains constant across all random permutations within replicates. Type II sums of squares and cross-products (SSCP) are calculated to assure conditional estimation.

The results include univariate-like statistics based on dispersion of values and eigenanalysis performed on a signal to noise matrix product of SSCP matrices (sensu Bookstein and Mitteroecker, 2014) including the inverse of the random component of ME and the systematic component of ME. The multivariate test is a form of multivariate ANOVA (MANOVA), using RRPP to generate sampling distributions of the major eigenvalue (Roy's maximum root). Intraclass correlation coefficients (ICC) are also calculated, both based on dispersion of values and covariance matrices, as descriptive statistics. Multivariate generalizations of the statistics described by Liljequist et al. (2019) are also used, along with eigenanalysis. 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.

More details will be made and examples provided after publication of articles introducing the novel RRPP approach for measurement error analysis.

Value

Objects of class "measurement.error" return a list of the following:

AOV	Analysis of variance to test for systematic error, based on dispersion of values.
mAOV	Multivariate AOV based on product of the inverse of the random component (SSCP) of ME times the systematic component of ME.
icc	The intraclass correlation coefficient (ICC) based on the dispersion of values.
mult.icc.eigs	The eigenvalues of ICC matrices, culled to principal dimensions with positive eigenvalues.
SSCP	The sums of squares and cross-products matrices for model effects.
SSCP.ME.product	The products of the inverse of the random ME SSCP and the SSCP matrices for systematic ME,. These are the same matrix products used for eigenanalysis. This is the observed matrix.
SSCP.ME.product.std	A list of the symmetric forms of standardized SSCP.ME.products that yield orthogonal eigenvectors.
all.stats	All SS, MS, eigen values, etc., from the RRPP analyses performed. This is the same as the output found in an lm.rrpp object, updated with manova.update. This object only contains the many RRPP ANOVA and MANOVA statistics if verbose = TRUE.

Author(s)

Michael Collyer

References

Collyer, M. L., & Adams, D.C. (In review). Interrogating random and systematic measurement error in morphometric sata. Evolutionary Biology.

Bookstein, F. L., & Mitteroecker, P. (2014). Comparing covariance matrices by relative eigenanalysis, with applications to organismal biology. Evolutionary biology, 41(2), 336-350.

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

See Also

lm.rrpp, manova.update

Examples

# TBD

RRPP documentation built on Aug. 16, 2023, 1:06 a.m.