The question is too vague. We need a sample dataset for an adequate answer. In particular, the term "variance component" usually refers to random-effect models which are different from regular anova models. If you're actually talking about variance-component (random-effect) models, you have many possibilities in R. You might want to try the (recommanded) nlme package, function lme and its numerous utility functions. You will find many examples in the companion book

Pinheiro, J. C. & Bates, D. M. Mixed-effect models in S and S-Plus. Springer, 2000, 528 p.

Hi Kisito,

You have to perform an analysis of variance (ANOVA). The method employed would differ depending on the experimental design and the variables (factors) included. I attach you some information regarding this. You will find there some interesting explanations and code in R.

Best,

http://www.personality-project.org/r/r.anova.html

http://www.statmethods.net/stats/anova.html

Thank you dear Martin

The question is too vague. We need a sample dataset for an adequate answer. In particular, the term "variance component" usually refers to random-effect models which are different from regular anova models. If you're actually talking about variance-component (random-effect) models, you have many possibilities in R. You might want to try the (recommanded) nlme package, function lme and its numerous utility functions. You will find many examples in the companion book

Pinheiro, J. C. & Bates, D. M. Mixed-effect models in S and S-Plus. Springer, 2000, 528 p.

If you are interested in getting the variance components (VC values), you could estimate an ANOVA table in VCA package (function anovaVCA). This function will create an pbject with an ANOVA table, with the variance actual values, but withou t performig an analysis of variance to evaluate group means, etc. In order to test the latter, you should use other functios, such as anova (lm()) of the base R-

I hope it is useful.

As Renaud says, the question is too vague, it depends whether you are referring to a random effects models or not, and whether your factors are crossed or nested. In package lmer you can you use the function lmer (with the simplest case) as follows:

model

You may want to try the VCA package, which is available via CRAN. However, I have had difficulties running VCA with this package when the dataset is large, and I have 16 GB on my machine!

Since package-version 1.4.0 (R-package VCA) we implemented ANOVA estimation in FORTRAN. Since the sweep-operator is implemented the variance-covariance variance of variance components is readily available after each model fit.

Large data set can be fitted more efficiently with this implementation. See below an example with N=500,000 observations once fitted with ANOVA, once fitted using R-package lme4 for REML estimation and then extracting the ANOVA table. Both fitted on a laptop with a Intel Core i7-8650U with 16 GB RAM.

> library(VCA)

# simulate some data with N=500,000 observations

> set.seed(23)

> dat dat$fac1 dat$fac2 dat$fac3 dim(dat)

[1] 500000 4

# use ANOVA-estimation, which is now done using a FORTRAN-implementation of # the SWEEP-operator

> system.time(fit1 fit1

Result Variance Component Analysis:

-----------------------------------

Name DF SS MS VC %Total SD CV[%]

1 total 29.754649 15.740646 100 3.967448 32.658888

2 fac1 4 2288723.003035 572180.750759 5.6111 35.647205 2.368776 19.49908

3 fac1:fac2 245 2712327.007202 11070.722478 3.182573 20.218821 1.783977 14.685181

4 fac1:fac2:fac3 250 1176394.113069 4705.576452 4.703333 29.880177 2.168717 17.852251

5 error 499500 1120697.976915 2.24364 2.24364 14.253796 1.497878 12.330102

Mean: 12.14814 (N = 500000)

Experimental Design: balanced | Method: ANOVA

# extract the covariance matrix of variance components

> vcovVC(fit1)

fac1 fac1:fac2 fac1:fac2:fac3 error

fac1 1.636964e+01 -5.002486e-03 -3.129716e-19 8.194873e-28

fac1:fac2 -5.002486e-03 2.944092e-01 -8.856980e-02 -2.185300e-24

fac1:fac2:fac3 -3.129716e-19 -8.856980e-02 1.771396e-01 -2.015583e-08

error 8.194873e-28 -2.185300e-24 -2.015583e-08 2.015583e-05

attr(,"method")

[1] "scm"

# now use REML-estimation with R-package "lme4". For large data sets REML- estimation

# implemented in the VCA-package does not work, the problem size is too large. There

# might be an option in the future to just fit models via REML and extract the VCA-table

# as shown below without getting the covariance-matrix of the variance components.

> system.time(fit2 lmerSummary(fit2, tab.only=TRUE)

VC %Total SD CV[%]

total 15.740239 100.00000 3.967397 32.65847

fac1:fac2:fac3 4.703249 29.88042 2.168697 17.85209

fac1:fac2 3.182545 20.21917 1.783969 14.68512

fac1 5.610805 35.64625 2.368714 19.49857

error 2.243640 14.25416 1.497878 12.33010

attr(,"Mean")

[1] 12.14814