VCA-package {VCA}

(V)ariance (C)omponent (A)nalysis.

Description

This package implements ANOVA-type estimation of variance components (VC) for linear mixed models (LMM), and provides Restricted Maximum Likelihood (REML) estimation incorporating functionality of the lme4 package. For models fitted by REML the typical VCA-table is derived, also containing the variances of VC, which are approximated by the method outlined in Giesbrecht & Burns (1985). REML-estimation is available via functions remlVCA for variance component analysis (VCA) and remlMM for fitting general LMM.

ANOVA-methodology is a special method of moments approach for estimating (predicting) variance components implemented in functions anovaMM and anovaVCA. The former represents a general, unrestricted approach to fitting linear mixed models, whereas the latter is tailored for performing a VCA on random models. Experiments of this type frequently occur in performance evaluation analyses of diagnostic tests or analyzers (devices) quantifying various types of precision (see e.g. guideline EP05-A2/A3 of the Clinical and Laboratory Standards Institute - CLSI).

The general Satterthwaite approximation of denominator degrees of freedom for tests of fixed effects (test.fixef) and LS Means (test.lsmeans) is implemented as used in SAS PROC MIXED. Results differ for unbalanced designs because of the different approaches to estimating the covariance matrix of variance components. Here, two algorithms are implemented for models fitted via ANOVA, 1^{st} the "exact" method described in Searle et. al (1992), 2^{nd} an approximation described in Giesbrecht & Burns (1985). The latter is also used for models fitted by REML. See test.fixef and getGB for details on this topic.

Furthermore, the Satterthwaite approximation of degrees of freedom for individual VCs and total variance is implemented. These are employed in Chi-Squared tests of estimated variances against a claimed value (total, error), as well as in Chi-Squared based confidence intervals (CI) (see VCAinference). Whenever ANOVA-type estimated VCs become negative, the default is to set them equal to 0. ANOVA mean squares used within the Satterthwaite approximation will be adapted to this situation by re-computing ANOVA mean squares (s_{MS}) as s_{MS} = C * \sigma^{2 }, where C is a coefficient matrix and a function of the design matrix and \sigma^{2} is the column-vector of adapted variance components. Total variance corresponds to a conservative estimate of the total variability in these cases, i.e. it will be larger than e.g. the total variance of the same model fitted by REML, because the negative VC will not contribute to total variance. See the documentation anovaVCA and anovaMM for details, specifically argument NegVC.

Additionally to fitting linear mixed models and performing VCA-analyses, various plotting methods are implemented, e.g. a variability chart visualizing the variability in sub-classes emerging from an experimental design (varPlot). Random effects and residuals can be transformed and plotted using function plotRandVar. Standardization and studentization are generally available, Pearson-type transformation is only available for residuals. Plotting (studentized) random variates of a LMM should always be done to reveal potential problems of the fitted model, e.g. violation of model assumptions and/or whether there are outlying observations.

There are not any more two approaches to estimating ANOVA sums (SSQ) of squares as in previous package-versions. Now, only a fast FORTRAN-routine is used generating the column vector of SSQ, coefficient matrix C (previously computed using the Abbreviated Doolittle and Square Root Method), and the covariance matrix of VC. Overall, this leads to a dramatic reduction of computation time for models fitted using ANOVA.

Further reduction of the computation time can be achieved using Intel's Math Kernel Library (MKL). When the package is loaded it will be automatically checked whether this is the case or not.

In LS Means computation of fitted LMM it is possible to compute LS Means using specific values of covariables, which is equivalent to using option 'AT' in the 'lsmeans'-statement of SAS PROC MIXED. It is also possible to apply other than the default weighting scheme for (fixed) factor-variables. See the details section in lsmeans and the description of argument at.

Note: The 'UnitTests' directory within the package-directory contains a pre-defined test-suite which can be run by sourcing 'RunAllTests.R' for user side testing (installation verification). It requires the 'RUnit' package and checks the numerical equivalence to reference results (SAS PROC MIXED method=type1/reml, SAS PROC VARCOMP) for balanced and unbalanced data and different experimental designs.

Details

Package:	VCA
Type:	Package
Version:	1.5.1
Date:	2024-02-07
License:	GPL (>=3)
LazyLoad:	yes

Author(s)

Andre Schuetzenmeister [e-mail], Florian Dufey [e-mail]

References

Searle, S.R, Casella, G., McCulloch, C.E. (1992), Variance Components, Wiley New York

Goodnight, J.H. (1979), A Tutorial on the SWEEP Operator, The American Statistician, 33:3, 149-158

Giesbrecht, F.G. and Burns, J.C. (1985), Two-Stage Analysis Based on a Mixed Model: Large-Sample Asymptotic Theory and Small-Sample Simulation Results, Biometrics 41, p. 477-486

Satterthwaite, F.E. (1946), An Approximate Distribution of Estimates of Variance Components., Biometrics Bulletin 2, 110-114

Gaylor,D.W., Lucas,H.L., Anderson,R.L. (1970), Calculation of Expected Mean Squares by the Abbreviated Doolittle and Square Root Methods., Biometrics 26 (4): 641-655

SAS Help and Documentation PROC MIXED, SAS Institute Inc., Cary, NC, USA