Effective sample size
Compute effective sample size based on correlation structure in linear mixed model
ESS(fit, method = "full") ## S4 method for signature 'lmerMod' ESS(fit, method = "full")
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. |
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.
effective sample size for each random effect in the model
library(lme4) data(varPartData) # Linear mixed model fit <- lmer( geneExpr[1,] ~ (1|Individual) + (1|Tissue) + Age, info) # Effective sample size ESS( fit )
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