cLMS function

LMS conversion to and from z-scores

LMS conversion to and from z-scores

Routines to handle references constructed with the LMS method. Given a set of LMS values, the functions convert z-scores to measurement centiles and vice versa.

cLMS(z, L = 1, M, S)

zLMS(x, L = 1, M, S)

Arguments

  • z: vector or one-column matrix of z-scores to be converted to measurements.
  • L: vector of Box-Cox transformation (lambda) values, L in the LMS method.
  • M: vector of medians (mu), M in the LMS method.
  • S: vector of coefficients of variation (sigma), S in the LMS method.
  • x: vector or one-column matrix of measurements to be converted to z-scores.

Returns

If x and z are vectors zLMS and cLMS

each return a vector, respectively of z-scores and measurement centiles, with length matching the length of (the longest of) x or z, L, M and S. If x or z are matrices zLMS and cLMS each return a matrix, the number of rows matching the length of (the longest of) L, M and S, and the number of columns matching the length of x or z.

Details

L, M and S -- and if vectors then x and z -- should all be the same length, recycled if necessary. The formulae converting x to z and vice versa are:

z=(x/M)L−1LSz=((x/M)L−1)/L/S z = \frac{(x/M)^L - 1}{L S}z = ((x/M)^L - 1)/L/S x=M(1+LSz)1/L)x=M(1+LSz)(1/L) x = M (1 + L S z)^{1/L})x = M (1 + L S z)^(1/L)

where L is reset to 10^-7 if it is zero. The LMS method is the same as the BCCG family in the gamlss package, except that lambda in LMS is referred to as nu in BCCG.

Examples

cLMS(z = as.matrix(-2:2), L = 1:-1, M = 5:7, S = rep(0.1, 3))
cLMS(z = 0:2, L = 1:-1, M = 7, S = 0.1)
cLMS(z = as.matrix(0:2), L = 1:-1, M = 7, S = 0.1)
zLMS(x = 6.5, L = 1:-1, M = 5:7, S = rep(0.1, 3))

See Also

z2cent, LMS2z, pdLMS

Author(s)

Tim Cole tim.cole@ucl.ac.uk

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