RLFUNCTIONAL procedure

Fits a linear functional relationship model (M.S. Dhanoa).


Options

PRINT = string
Controls printed output (estimates); default esti

CIPROBABILITY = scalar
Defines the size of the confidence interval; default 0.95 i.e. 95%


Parameters

Y = variates
Y-variate for each model

X = variates
X-variate for each model

METHOD = strings
Method to use for each model (bartlett, majoraxis, reducedmajoraxis); default bart

SLOPE = scalars
Saves the estimated slopes

INTERCEPT = scalar
Saves the estimated intercepts

LOWER = scalar
Saves lower values of confidence intervals for the slopes

UPPER = scalar
Saves upper values of confidence intervals for the slopes


Description

RLFUNCTIONAL can be used to estimate the slope and intercept of a linear equation describing the relationship between two variables, when the observations on both variables are subject to error variation. This contrasts with the situation in ordinary linear regression, where we assume that only the y-variate is subject to error (the x-variate is assumed to be observed exactly). For further details see Sokal & Rohlf (1995, Section 14.13) and Bartlett (1949).

   The y- and x-variates must be specified by the Y and X parameters respectively. The slope and intercept can be saved (in scalars) using the SLOPE and INTERCEPT parameters. Lower and upper values from a confidence interval for the SLOPE can be saved (in scalars) using the LOWER and UPPER parameters. The probability for the confidence interval is specified by the CIPROBABILITY option (default 0.95 i.e. 95%).

   The METHOD parameter specifies one of the following strings, to indicate the method of estimation:

    bartlett
Bartlett's three-group method (default);

    majoraxis
takes the major axis from a principal component analysis (this assumes that X and Y are equally variable);

    reducedmajoraxis
estimates the slope as the geometric mean of the regression coefficients from regressions of Y on X and X on Y.

 

Options: PRINT, CIPROBABILITY.

Parameters: Y, X, METHOD, SLOPE, INTERCEPT, LOWER, UPPER.


Method

RLFUNCTIONAL uses the methods described in Section 14.13 of Sokal & Rohlf (1995).


Action with RESTRICT

If either the Y or X variates is restricted, the model is estimated using only the units not excluded by the restriction.


References

Bartlett, M.S. (1949). Fitting a straight line when both variables are subject to error. Biometrics, 5, 207-212.

Sokal, R.R. & Rohlf, F.J. (1995). Biometry (3rd edition). W.H. Freeman & Company, New York.