[R-sig-ME] Profiling the likelihood of repeatability

[Mike Lawrence]

Hi folks,

Nakagawa & Schielzeth's 2010 paper "Repeatability for Gaussian and
non-Gaussian data: a practical guide for biologists" was recently
discussed on this list. They suggest that the reliability of a
measurement may be computed via mixed effects modelling by the
following:

    #compute the model and extract variance estimates
    fit = lmer(
        formula = dv ~ (1|rand)
        , data = my_data
        , REML = TRUE
    )
    vc = VarCorr(fit)
    residual_var = attr(vc,'sc')^2
    intercept_var = attr(vc$rand,'stddev')^2

    #compute raw repeatability
    R = intercept_var/(intercept_var+residual_var)

    #compute correction for measurement effort
    n = data.frame(table(a$rand))
    k = nrow(n)
    N = sum(n$Freq)
    n0 = (N-(sum(n$V1^2)/N))/(k-1)

    #compute effort-corrected repeatability
    Rn = R/(R+(1-R)/n0)

Nakagawa & Schielzeth mention that it is possible to profile the
likelihood of Rn, however I'm not sure how to go about this. Any
suggestions? (I am aware that they provide code to compute Bayesian
credible intervals, but I'd prefer a likelihood profile)

Cheers,

Mike

--
Mike Lawrence
Graduate Student
Department of Psychology
Dalhousie University

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~ Certainty is folly... I think. ~