TAILIEUCHUNG - SAS/ETS 9.22 User's Guide 111

SAS/Ets User's Guide 111. Provides detailed reference material for using SAS/ETS software and guides you through the analysis and forecasting of features such as univariate and multivariate time series, cross-sectional time series, seasonal adjustments, multiequational nonlinear models, discrete choice models, limited dependent variable models, portfolio analysis, and generation of financial reports, with introductory and advanced examples for each procedure. You can also find complete information about two easy-to-use point-and-click applications: the Time Series Forecasting System, for automatic and interactive time series modeling and forecasting, and the Investment Analysis System, for time-value of money analysis of a variety of investments | 1092 F Chapter 18 The MODEL Procedure Collinearity diagnostics are also useful when an estimation does not converge. The diagnostics provide insight into the numerical problems and can suggest which parameters need better starting values. These diagnostics are based on the approach of Belsley Kuh and Welsch 1980 . Iteration History The options ITPRINT ITDETAILS XPX I and ITALL specify a detailed listing of each iteration of the minimization process. ITPRINT Option The ITPRINT information is selected whenever any iteration information is requested. The following information is displayed for each iteration N is the number of usable observations. Objective Trace S is the corrected objective function value. is the trace of the S matrix. subit is the number of subiterations required to find a A or a damping factor that reduces the objective function. R is the R convergence measure. The estimates for the parameters at each iteration are also printed. ITDETAILS Option The additional values printed for the ITDETAILS option are Theta is the angle in degrees between A the parameter change vector and the negative gradient of the objective function. Phi is the directional derivative of the objective function in the A direction scaled by the objective function. Stepsize is the value of the damping factor used to reduce A if the Gauss-Newton method is used. Lambda is the value of A if the Marquardt method is used. Rank XPX is the rank of the X0X matrix output if the projected Jacobian crossproducts matrix is singular . The definitions of PPC and R are explained in the section Convergence Criteria on page 1078. When the values of PPC are large the parameter associated with the criteria is displayed in parentheses after the value. Iteration History F 1093 XPX and I Options The XPX and the I options select the printing of the augmented X X matrix and the augmented X X matrix after a sweep operation Goodnight 1979 has been performed on it. An example of the output from the following

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