Effective Number of Independent Measurements per Subject

Compute the effective number of independent measurements per subject for a generalized linear mixed model

Usage

meff(fit)

Arguments

fit: model fit from fastlmm() or fastglmm()

Value

m.mean: mean number of measurements per subject
rho: intra-class correlation within subjects
m.eff: effective number of independent measurements per subject
m.max: maximum value of m.eff for m -> Inf
fraction: m.eff / m.max

Details

In a repeated measures model with multiple correlated measurements per subject, Lui and Liang (1997) define a formula for the effect number of _independent_ measurements per subject (m.eff): $$ m_\text{eff} = m / (1+(m-1)\rho) $$ where $m$ is the mean number of measurements per subjectd, and $\rho$ is the intra-class correlation indicating the correlation between measurements within the same subject.

Increasing $m$ has diminishing returns and as $m$ increases, $m_\text{eff}$ converges to $1/\rho$.

References

Liu, G. and Liang, K.Y., 1997. Sample size calculations for studies with correlated observations. Biometrics, pp.937-947.

Examples

data(PsychAD)

# regression formula
form <- PTPRG ~ (1|SubID) + offset(log(libSize))

# fit NBMM in on PTPRG expression
fit <- fastglmm.nb(form, PsychAD)

# effective number of independent measurements per subject
meff(fit)
#>     m.mean        rho    m.eff    m.max  fraction
#> 1 202.9564 0.03465127 25.37575 28.85897 0.8793019