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SAS/STAT Topics

SAS/STAT Software

Nonlinear Regression

The SAS/STAT nonlinear regression procedures include the following:

NLIN Procedure


The NLIN procedure fits nonlinear regression models and estimates the parameters by nonlinear least squares or weighted nonlinear least squares. You specify the model with programming statements. This gives you great flexibility in modeling the relationship between the response variable and independent (regressor) variables. It does, however, require additional coding compared to model specifications in linear modeling procedures such as the REG, GLM, and MIXED procedures. The following are highlights of the NLIN procedure's features:

  • provides a high-quality automatic differentiator so that you do not need to specify first and second derivatives. You can, however, specify the derivatives if you wish.
  • solves the nonlinear least squares problem by one of the following four algorithms (methods):
    • steepest-descent or gradient method
    • Newton method
    • modified Gauss-Newton method
    • Marquardt method
  • enables you to confine the estimation procedure to a certain range of values of the parameters by imposing bounds on the estimates
  • computes Hougaard's measure of skewness
  • provides bootstrap estimates of confidence intervals for parameters and the covariance/correlation matrices of the parameter estimates
  • performs weighted estimation
  • creates an output data set that contains statistics that are calculated for each observation
  • creates a data set that contains the parameter estimates at each iteration
  • performs BY group processing, which enables you to obtain separate analyses on grouped observations
  • creates a SAS data set that corresponds to any output table
  • automatically created graphs by using ODS Graphics
For further details, see NLIN Procedure

TRANSREG Procedure


The TRANSREG (transformation regression) procedure fits linear models, optionally with smooth, spline, Box-Cox, and other nonlinear transformations of the variables. The following are highlights of the TRANSREG procedure's features:

  • enables you to fit linear models including:
    • ordinary regression and ANOVA
    • metric and nonmetric conjoint analysis (Green and Wind 1975; de Leeuw, Young, and Takane 1976)
    • linear models with Box-Cox (1964) transformations of the dependent variables
    • regression with a smooth (Reinsch 1967), spline (de Boor 1978; van Rijckevorsel 1982), monotone spline (Winsberg and Ramsay 1980), or penalized B-spline (Eilers and Marx 1996) fit function
    • metric and nonmetric vector and ideal point preference mapping (Carroll 1972)
    • simple, multiple, and multivariate regression with variable transformations (Young, de Leeuw, and Takane 1976; Winsberg and Ramsay 1980; Breiman and Friedman 1985)
    • redundancy analysis (Stewart and Love 1968) with variable transformations (Israels 1984)
    • canonical correlation analysis with variable transformations (van der Burg and de Leeuw 1983)
    • response surface regression (Meyers 1976; Khuri and Cornell 1987) with variable transformations
  • enables you to use a data set that can contain variables measured on nominal, ordinal, interval, and ratio scales; you can specify any mix of these variable types for the dependent and independent variables
  • transform nominal variables by scoring the categories to minimize squared error (Fisher 1938), or treat nominal variables as classification variables
  • enables you to transform ordinal variables by monotonically scoring the ordered categories so that order is weakly preserved (adjacent categories can be merged) and squared error is minimized. Ties can be optimally untied or left tied (Kruskal 1964). Ordinal variables can also be transformed to ranks.
  • enables you to transform interval and ratio scale of measurement variables linearly or nonlinearly with spline (de Boor 1978; van Rijckevorsel 1982), monotone spline (Winsberg and Ramsay 1980), penalized B-spline (Eilers and Marx 1996), smooth (Reinsch 1967), or Box-Cox (Box and Cox 1964) transformations. In addition, logarithmic, exponential, power, logit, and inverse trigonometric sine transformations are available.
  • fits a curve through a scatter plot or fit multiple curves, one for each level of a classification variable
  • enables you to constrain the functions to be parallel or monotone or have the same intercept
  • enables you to code experimental designs and classification variables prior to their use in other analyses
  • perform sweighted estimation
  • generates output data sets including
    • ANOVA results
    • regression tables
    • conjoint analysis part-worth utilities
    • coefficients
    • marginal means
    • original and transformed variables, predicted values, residuals, scores, and more
  • performs BY group processing, which enables you to obtain separate analyses on grouped observations
  • automatically creates graphs by using ODS Graphics
For further details, see TRANSREG Procedure