Two-level model for multivariate trace evidence

tlvc() estimates the background of the two-level normal model of Aitken and Lucy (2004) from a reference collection, x_ij = theta_i + e_ij, items theta_i ~ N(mu, C) and measurements within an item e_ij ~ N(0, U): the overall mean, the pooled within-item covariance and the ANOVA between-item covariance (unbiased for any pattern of replication). tlvlr() gives the likelihood ratio of same source against different sources for two items (a control and a recovered fragment, say) from their mean vectors, computed in logarithms from Cholesky factors so that atypical or distant items give a finite value.

Usage

tlvc(x, item)

tlvlr(xa, xb, na, nb, bg)

Arguments

x

The reference measurements: a numeric matrix, one row per observation and one column per variable.

item

The item of each row: labels, every item at least once, some item more than once.

xa, xb

The mean vectors of the two items compared: one number per variable.

na, nb

Their numbers of replicates: positive.

bg

The background, as tlvc() returns it.

Value

tlvc(): a list of mu (the mean), u and c (the within- and between-item covariance matrices; c need not be positive definite, which tlvlr() then refuses). tlvlr(): a named vector, ln and log10, the natural and base-10 logarithms of the ratio.

References

Aitken, C. G. G. and Lucy, D. (2004). Evaluation of trace evidence in the form of multivariate data. Journal of the Royal Statistical Society, Series C, 53(1), 109-122. doi:10.1046/j.0035-9254.2003.05271.x

Examples

set.seed(1)
th <- matrix(rnorm(20, 10, 2), 10, 2)
x <- th[rep(1:10, each = 3), ] + matrix(rnorm(60, 0, 0.2), 30, 2)
bg <- tlvc(x, rep(1:10, each = 3))
tlvlr(th[1, ], th[1, ] + 0.05, 3, 3, bg)
#>       ln    log10 
#> 5.978629 2.596485 
tlvlr(th[1, ], th[2, ], 3, 3, bg)
#>        ln     log10 
#> -387.3127 -168.2078