VFUNCTION procedure

Calculates functions of variance components from a REML analysis (S.J. Welham).


Options

PRINT = string
Output required (function); default func

RANDOM = formula
Random model (excluding residual stratum) used for the REML analysis

NCONSTANT = scalar
Value to be used as constant in the numerator function; default 0

DCONSTANT = scalar
Value to be used as constant in the denominator function; default 0

SAVE = REML save structure
Specifies the (REML) save structure from which the variance components are to be taken; by default they are taken from the save structure of the most recent REML analysis


Parameters

NUMERATOR = variates
Each variate contains the coefficients multiplying the components in the numerator of a function

DENOMINATOR = variates
Coefficients multiplying the components in the denominator of the function

FUNCTION = scalars
To save the value of the function

SE = scalars
To save the standard error of the function


Description

VFUNCTION calculates linear functions, reciprocals of linear functions, or ratios of linear functions of the estimates of variance components from a REML analysis. The standard error of the function is also produced.

   The components are taken from the structure specified by the SAVE option. If this option is not set, then the SAVE structure from the most recent REML analysis is used. The RANDOM option must be set to be the random formula used by the REML analysis, but excluding the residual term.

   The function is defined by the variates specified by the NUMERATOR and DENOMINATOR parameters; these give the coefficients of the components for the numerator and denominator of the function, respectively. The order of the components is as given by the RANDOM option, with the residual term added at the end. If either variate contains fewer values than the number of components, the final coefficients are taken to be zero. However, random components that were constrained to be fixed in the REML analysis are ignored. If only NUMERATOR is set the function will be linear; conversely if only DENOMINATOR is used it will be a reciprocal function, and if both NUMERATOR and DENOMINATOR are set then the function is the ratio of two linear functions. Options NCONSTANT and DCONSTANT allow a constant to be included in the numerator and denominator functions, respectively.

   Printed output is controlled by the option PRINT; by default the function and its standard error are printed.

   Parameters FUNCTION and SE allow the value of the function and its standard error to be saved.


Options: PRINT, RANDOM, NCONSTANT, DCONSTANT, SAVE.

Parameters: NUMERATOR, DENOMINATOR, FUNCTION, SE.


Method

The components and their variance-covariance matrix are retrieved using VKEEP. The function is calculated as specified and its standard error is calculated using a formula derived from a Taylor expansion (see, for example, Kendall & Stuart 1963, page 232):

 se( f/g ) = (1/g) × √{ var(f) - 2 × (f/g) × cov(f,g) + (f/g) × (f/g) × var(g) }


Reference

Kendall, M. & Stuart, A. (1963). The Advanced Theory of Statistics, Volume 1. Griffin, London.