ESS {variancePartition} | R Documentation

## Effective sample size

### Description

Compute effective sample size based on correlation structure in linear mixed model

### Usage

    ESS(fit, method = "full")

    ## S4 method for signature 'lmerMod'
    ESS(fit, method = "full")

### Arguments

`fit` | model fit from lmer()
`method` | "full" uses the full correlation structure of the model. The "approximate" method makes the simplifying assumption that the study has a mean of m samples in each of k groups, and computes m based on the study design. When the study design is evenly balanced (i.e. the assumption is met), this gives the same results as the "full" method.

### Details

Effective sample size calculations are based on:

Liu, G., and Liang, K. Y. (1997). Sample size calculations for studies with correlated observations. Biometrics, 53(3), 937-47.

"full" method: if

V_x = var(Y;x)

is the variance-covariance matrix of Y, the response, based on the covariate x, then the effective sample size corresponding to this covariate is

Σ_{i,j} (V_x^{-1})_{i,j}

. In R notation, this is: `sum(solve(V_x))`. In practice, this can be evaluted as sum(w), where R

"approximate" method: Letting m be the mean number of samples per group,

k

be the number of groups, and

ρ

be the intraclass correlation, the effective sample size is

mk / (1+ρ(m-1))

Note that these values are equal when there are exactly m samples in each group. If m is only an average then this an approximation.

### Value

effective sample size for each random effect in the model

### Examples

    library(lme4)
    data(varPartData)

    # Linear mixed model
    fit <- lmer( geneExpr[1,] ~ (1|Individual) + (1|Tissue) + Age, info)

    # Effective sample size
    ESS( fit )

[Package variancePartition version 1.18.3 Index]