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FNLINEAR procedure

Estimates linear functions of one or more random variables, and calculates their variances and covariances (S.A. Gezan).

Options

PRINT = string token Output required (summary); default summ
CONSTANTVALUE = scalar Constant value for the function; default 0
COEFFICIENTS = scalar Linear coefficients for the random variables in the function; no default – must be set

Parameters

ESTIMATES = variates Estimated values of the random variables
VCOVARIANCE = symmetric matrices Variance-covariance matrix of the random variable estimates
FUNCTIONESTIMATE = scalars Saves the estimated value of the function
SE = scalars Saves the standard error of the function estimate
NEWESTIMATES = variates Saves new vectors of estimates, including the estimated value of the function
NEWVCOVARIANCE = symmetric matrices Saves variance-covariance matrices for the NEWESTIMATES

Description

FNLINEAR estimates linear functions of one or more random variables. The estimated values of the random variables, from which the function value is calculated, are supplied (in a variate) by the ESTIMATES parameter. Their variances and covariances are supplied (in a symmetric matrix) by the VCOVARIANCE parameter. The linear coefficients for the function are supplied (again in a variate) by the COEFFICIENTS, and the constant is supplied (in a scalar) by the CONSTANTVALUE option. So the function value is given by

SUM(ESTIMATES * COEFFICIENTS) + CONSTANTVALUE

The value can be saved by the FUNCTIONESTIMATE parameter, and its standard error can be saved by the SE option (both in scalars). The NEWESTIMATES parameter can save a new variate of estimates, containing the original ESTIMATES variate and then the function value inserted at the end. The corresponding variance-covariance matrix can be saved (in a symmetric matrix) by the NEWVCOVARIANCE parameter.

Options: PRINT, CONSTANTVALUE, COEFFICIENTS.

Parameters: ESTIMATES, VCOVARIANCE, FUNCTIONESTIMATE, SE, NEWESTIMATES, NEWVCOVARIANCE.

Method

The linear function w of the random variables f, g, h etc. is defined by the expression:

w = a0 + a1 × f + a2 × g + a3 × h + …

where a0, a1, a2 etc. are (known) coefficients. The estimated means and variances of the random variables, supplied by the ESTIMATES and VCOVARIANCE parameter, are used to calculate the estimated value of the function w and to calculate its variance. If the original random variables are Normally distributed, the random variable w is also Normally distributed and the variance calculation is exact.

Action with RESTRICT

Any restrictions are ignored.

See also

Procedures: FNCORRELATION, FNPOWER.

Commands for: Calculations and manipulation.

Example

CAPTION  'FNLINEAR example'; STYLE=meta
VARIATE  [VALUES=4.01,19.63,13.65] means
SYMMETRICMATRIX [ROWS=3; VALUES=150.40,-31.85,161.13,0.93,-9.32,23.31] vcov
PRINT    means,vcov
FNLINEAR [PRINT=summary; CONSTANTVALUE=2; COEFFICIENTS=!(1,2,0)]\ 
         ESTIMATES=means; VCOVARIANCE=vcov; FUNCTIONESTIMATE=est; SE=se;\ 
         NEWESTIMATES=newmeans; NEWVCOVARIANCE=newvcov
PRINT    est,se
&        newmeans,newvcov
Updated on March 8, 2019

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