The World of Computer Software

home *** CD-ROM | disk | FTP | other *** search

/ The World of Computer Software / World_Of_Computer_Software-02-387-Vol-3of3.iso / r / rxridg93.zip / RXTRACES.DOC < prev next >

Wrap

Text File | 1993-03-01 | 33.7 KB | 632 lines

┌─────────────────────────────────────────────────────────────┐ │ ┌─────────────────────────────────────────────────────────┐ │ │ │ ASCII Documentation File for ... RXtraces.EXE │ │ │ │ │ │ │ │ Version 9103 │ │ │ ├─────────────────────────────────────────────────────────┤ │ │ │ │ │ │ │ a softRX SHAREWARE module from │ │ │ │ │ │ │ │ Bob Obenchain, CompuServe User [72007,467] │ │ │ └─────────────────────────────────────────────────────────┘ │ └─────────────────────────────────────────────────────────────┘ softRX is a trademark of The Software Prescriptions Company. "Personal computing treatments for data analysis infirmities." Copyright(c) 1989-1993 by Bob Obenchain, Ph.D. ALL RIGHTS RESERVED ******************* The author of RXtraces, Bob Obenchain, is a member of the Association of Shareware Professionals <ASP>. ┌───────────────────┐ ─────────────────────────┤ Table-of-Contents ├───────────────────────── └───────────────────┘ softRX User Registration . . . . . . . . . . . . . . . . . . . . . . 1 Introduction to RXtraces . . . . . . . . . . . . . . . . . . . . . . 2 Shrinkage Regression Background Information. . . . . . . . . . . . . 3 Computing System Requirements for RXtraces . . . . . . . . . . . . . 5 softRX Graphical Design Philosophy . . . . . . . . . . . . . . . . . 5 RXtraces File Naming Conventions . . . . . . . . . . . . . . . . . . 6 RXtraces Walk-Through. . . . . . . . . . . . . . . . . . . . . . . . 7 TECHNICAL APPENDIX: "Extent" and "Shape" of Shrinkage. . . . . . . . 9 RXtraces Update History. . . . . . . . . . . . . . . . . . . . . . .11 ASP Hub Network. . . . . . . . . . . . . . . . . . . . . . . . . . .11 ┌─────────────────────┐ ────────────────────────┤ USER REGISTRATION ├──────────────────────── └─────────────────────┘ RXtraces.EXE, its ASCII documentation file [RXtraces.DOC], and the included batch input/output (numerical example) files are user- supported electronic information that we encourage you to examine and to share with others, provided you have not modified them in any way. All softRX SHAREWARE modules are distributed in fully functional form and will remain so without any usage time limits. softRX systems do not display annoying registration "reminder" screens or messages. And no (non-commercial) user who is unable to correspond with softRX in English is expected to register. RXtraces, version 9103 . . . . . . . . . . . . . . . Page 2 of 12 ************************************** ************************************** Only YOU know whether softRX systems are useful to you. And, if you do use them, you must register! ************************************** ************************************** The registration fee for RXtraces is $25 for use either by a single individual or for installation on one single-user-at-a-time system. Three softRX modules (say, RXridge, RXtraces, and PathProj) may be registered together for $50. softRX offers MAIL-IN SUPPORT SERVICES (e.g. answers to questions on the theory, application and/or computation of statistical "shrinkage" regression techniques) only to its REGISTERED users. However, registration fees are mandatory for use of softRX modules in any commercial or government environment. These users must register and pay for their copies within 30 days of first actual use or else their license is withdrawn. Site-License arrangements (of at most $15 per module) may also be made by contacting softRX. Make checks payable to... Bob Obenchain and mail them to... 5261 Woodfield Drive North Carmel, IN 46033-8795, USA !!! Thank You for Supporting the <<<softRX shareware>>> Concept !!! ┌─────────────────────────────┐ ──────────────────┤ INTRODUCTION to RXtraces ├────────────────────── └─────────────────────────────┘ RXtraces does NOT perform generalized ridge regression computations. Rather, RXtraces generates interactive graphical displays of the results from other softRX shareware systems...like RXridge.EXE, RelaxR.EXE, or the RXridge procedures distributed as source code for the GAUSS, SAS/IML, and S matrix-language interpreters. RXtraces generates INTERACTIVE graphical displays on IBM-compatible personal computers in CGA (medium resolution, 320x200 pixel) mode. RXtraces helps users interpret the results of a generalized ridge regression analysis by displaying... TRACES of fitted regression coefficients, scaled mean squared error estimates, excess (OLS-ridge) eigenvalues, inferior direction cosines, and shrinkage factor patterns. RXtraces, version 9103 . . . . . . . . . . . . . . . Page 3 of 12 RXtraces is designed for ridge "training" applications, allowing students to quickly review output files written by RXridge.EXE or RelaxR.EXE across a wide spectrum of previously computed numerical examples. You do not need to read this documentation before trying RXtraces out. There is very little damage you can do by giving "wrong" choices for menu items and responses to prompts. However, first of all, please > > > MAKE BACK-UP COPIES < < < of the distribution files and/or of the original softRX shareware archives. RXtraces does not modify its input files, which are output files created by RXridge or RelaxR. And RXtraces does not write output files (or make screen prints) unless you first press the "S" key and then press a second, "special" key. Each RXtraces prompt has a [default] value that you may accept simply by pressing the ENTER key; RXtraces menus require you to press a single key, where any differences between upper and lower case are ignored. You can view a "help" screen by pressing the SpaceBar; function key F1 is also a "help" key, but F1 can't be used when you are being prompted for input. And you can always return to the "Main Menu" by repeated pressing of the ENTER or Escape keys. ┌─────────────────────────────────────────────┐ ────────────┤ Shrinkage Regression Background Information ├──────────── └─────────────────────────────────────────────┘ RXtraces interactively displays results of ridge regression computations via "trace" plots. In a trace, P quantities (several estimated coefficients, risks, shrinkage factors, etc.) are plotted vertically against a horizontal indicator of the extent of shrinkage (from "no" shrinkage at the left-hand, least squares estimates all the way to "total" shrinkage at the right-hand extreme, where all coefficient estimates are zero.) Here, P denotes the number of non-constant predictor variables in the regression model; RXtraces accepts values of P from 2 to 20. RXtraces uses a measure of the extent of shrinkage called the "Multicollinearity Allowance," MCAL. See the APPENDIX to this documentation for the definitions of MCAL and Q, the parameter that controls the "shape" or curvature of the ridge path. *** Interpretation of Ridge Trace Plots *** Menu Choice 1: Ridge Coefficient Trace This trace shows how regression coefficient point estimates change as shrinkage (along a path of shape Q) occurs. Any coefficient estimate that is numerically "stable" will plot close to the straight line from its least-squares estimate at MCAL=0 to zero at MCAL=P. Unstable coefficient estimates will change more quickly, possibly switching numerical sign, as RXtraces, version 9103 . . . . . . . . . . . . . . . Page 4 of 12 soon as MCAL starts increasing from zero. Super-stable estimates will change only very little initially, finally approaching zero only as MCAL approaches P. Menu Choice 2: Estimated "Scaled" Risk (Mean-Squared-Error) Trace This trace gives normal distribution theory, "modified" maximum likelihood estimates of "scaled" risk (mean-squared-error loss) as shrinkage of shape Q occurs. The risk is "scaled" by dividing it by an estimate of the error (disturbance term) variance. In other words, scaled risk expresses imprecision in fitted coefficients as a multiple of the variance of a single observation. Maximum likelihood scaled risk estimates are "modified," first of all, so as to be unbiased. Then they are adjusted upward, if necessary, to have correct range relative to a known lower bound on scaled risk, which re-introduces bias. Menu Choice 3: Excess EigenValues Trace This trace plots the EigenValues of the estimated difference in Mean Squared Error matrices, ordinary least squares minus ridge. As long as all EigenValues are zero or positive, there is good reason to hope that the corresponding ridge estimators yield smaller MSE risk than Least Squares for all directions in P-space (i.e. all possible linear combinations.) As shrinkage continues, at most one negative EigenValue will appear. Menu Choice 4: Inferior Direction-Cosine Trace This trace plots the Direction Cosines (normalized EigenVector) corresponding to any negative EigenValue of the difference in MeanSquaredError matrices, OLS - ridge. This direction gives that single linear combination of ridge regression coefficients that not only fails to benefit from ridge shrinkage of shape Q but probably actually suffers increased risk due to shrinkage. Menu Choice 5: Shrinkage Factor Pattern Trace This trace plots the Delta Shrinkage-Factor Pattern as shrinkage of shape Q occurs. All deltas are equal when Q=1; the trailing deltas are small when Q < 1; and the leading deltas are small when Q > 1. RXtraces, version 9103 . . . . . . . . . . . . . . . Page 5 of 12 ┌───────────────────────────────┐ ────────────────────┤ Computing System Requirements ├────────────────── └───────────────────────────────┘ RXtraces.EXE requires your personal computer to be fully IBM-compatible and to be running IBM PC-DOS or Microsoft MS-DOS version 2.0 or higher. RXtraces uses the screen handling capabilities of a CGA, EGA, or VGA graphics card/monitor. If you system has only a Monochrome Graphics Adapter (MGA) card or Hercules Graphics Card (HGC), you could "simulate" CGA graphics capabilities in order to view trace displays. For example, if you have SIMCGA.COM (version 4.0, July 1987) by C. P. Guzis, you could make the SIMCGA system "memory resident" before invoking RXtraces. DOS Prompt> simcga 3 WARNING: Your CONFIG.SYS file should specify at least... files=20 ┌─────────────────────────────┐ ────────────────────┤ Graphical Design Philosophy ├──────────────────── └─────────────────────────────┘ RXtraces uses CGA (medium resolution, 320x200 pixel) graphics because all true graphics hardware for IBM-compatible personal computers has at least this (minimum) capability. Besides, the (8x8) text font for this resolution resides in ROM within your system. But using CGA also means that there isn't enough resolution to draw "nice" labels, tick marks, and numerical values along axes without greatly reducing the size of the TRACE plot window. I certainly did not want to use any sort of reduced-size plot; rather, I decided to emphasize INTERACTIVE (dynamic, on-screen annotation) methods for high-lighting / reading numerical values directly off of shrinkage TRACE screen displays. [See information below for usage of the V, H, and N keys.] Once in RXtraces graphics mode, you can view a "help" screen by pressing either the SpaceBar or function key F1. The resulting HELP screen tells you which keys to press to activate and move the on-screen cursor and/or how to dynamically annotate, save, or print the screen display. And you can always return to the Menus simply by repeated pressing of the ENTER or Escape keys. RXtraces, version 9103 . . . . . . . . . . . . . . . Page 6 of 12 ┌─────────────────────────┐ ───────────────────────┤ File Naming Conventions ├───────────────────── └─────────────────────────┘ RXtraces assumes that you have (or someone else has) already performed ridge calculations using one of our softRX systems, each of which writes its output to a series of eight (or more) ASCII files. These files have a common FILENAME (of at most 8 characters) and a 3-character DOS extension, ending with the two letters "RX". By convention, the filename should not only indicate which set of regressor and response data are being analyzed but also which numerical value of the shrinkage path "shape" parameter, Q, was used in the computations. For example, the filename "mpg0" labels files associated with analysis of "gas mileage data" [ Hocking(1976), "The Analysis and Selection of Variables in Regression," Biometrics 32, 1-51 ] using Hoerl-Kennard "ordinary" ridge regression, Q = 0. The 3-character DOS extensions used by softRX software for generalized ridge regression analysis are: .PRX ...Parameters and variable names, .CRX ...generalized ridge Coefficients, .RRX ...Risk (mean-sq-error) estimates, .ERX ...Excess Eigenvalues (OLS-Ridge), .IRX ...Inferior direction cosines, and .DRX ...shrinkage DELTA factors. .XRX ...regressor matrix coordinates. .YRX ...response vector coordinates. [ NOTE: .XRX and .YRX files are not used by RXtraces. ] RXtraces cannot draw a trace for a data set unless it can find the corresponding .PRX file because it uses the information from the first six lines of this file in drawing all 5 types of trace. For example, "mpg0.PRX" contains... Line 1: 4 = P, number of regressors Line 2: 32 = N, number of observations Line 3: 8 = STEPSPU, steps per unit change in MCAL Line 4: 0 = QSHAPE of the shrinkage path Line 5: XNAM= CYLNDS CUBINS HPOWER WEIGHT Line 6: YNAM= MPG Line 7: 0.8182 0.0000 0.0000 Line 8: 0.7383 0.1618 0.1250 Note: Lines 7 through 39 *** contain a 33 by 3 Line 38: 2.4907 900.7049 3.8750 matrix with columns Line 39: 2.7772 +INF 4.0000 TMSE, K, and MCAL. RXtraces, version 9103 . . . . . . . . . . . . . . . Page 7 of 12 The other 5 files ( .CRX, .RRX, .ERX, .IRX, and .DRX ) will each contain a matrix with P columns and ( 1 + P * STEPSPU ) rows...for MCAL = 0 to MCAL = P. ┌───────────────────────────┐ │ ┌───────────────────────┐ │ ═════════════════════════╡ RXtraces Walk-Through ╞══════════════════════ │ └───────────────────────┘ │ └───────────────────────────┘ To use RXtraces, several RXridge or RelaxR output files (*.PRX, etc.) MUST be located in the current working directory. Furthermore, the RXtraces.EXE file must also either be located in that same directory or else in a some location named in your DOS PATH= environment variable. The first step in use of RXtraces is thus usually to "Change Directories" to the place where your RXridge or RelaxR output files are located. For example, you might need to enter the following three sorts of commands at your DOS> prompt... c: cd \srx\mydata rxtraces The above three commands: (1) make the "C" partition of your hard-disk active, (2) change directories to the "MYDATA" sub-directory of the C:\SRX directory, and (3) launch RXtraces. Next, you must select the filename of a softRX ".PRX" file using the bounce-bar menu on the FILENAME Specification Screen: ┌─────────────────────────────────────────────────────────────┐ │ F I L E N A M E Specification Screen │ │ │ │ │ │ ╔FileNames╗ Arrow Keys: Move Highlight Bar Up / Down. │ │ ║ ║ │ │ ║MPG0█████║ Return Key: Selects the Highlighted File. │ │ ║ ║ │ │ ╚═════════╝ Escape Key: Quit......Terminate PathProj. │ │ │ │ Example FILENAMES... │ │ mpg0 ...Hocking Q = 0 path. │ │ cement-5 ...Hald Q = -5 path. │ └─────────────────────────────────────────────────────────────┘ Let us suppose you highlighted "mpg0" and then selected that filename by pressing the enter key. The next screen will then be... RXtraces, version 9103 . . . . . . . . . . . . . . . Page 8 of 12 ┌───────────────────────────────────────────────────┐ │ │ │ M A I N * M E N U │ │ │ │ FILENAME : mpg0 │ │ │ │ Using RX Parameters... mpg0.prx │ │ │ │ Select one of the 5 types of RXtrace │ │ displays from the following list... │ │ │ │ 1 ...generalized ridge coefficients │ │ 2 ...risk (mean-sq-error) estimates │ │ 3 ...excess eigenvalues (ols-ridge) │ │ 4 ...inferior direction cosines │ │ 5 ...shrinkage delta factors. │ │ C ...change filename (dataset) │ │ │ │ Press a Single Key : 1 2 3 4 5 C Q or Enter │ │ │ │ Use ENTER key for Default Choice. │ │ Press SpaceBar to view HELP screen. │ │ Press Q key to Exit RXtraces now. │ │ │ └───────────────────────────────────────────────────┘ If you selected the default value of 1 on the MainMenu, a ridge trace of shrunken regression coefficient estimates has appeared on your screen. We now list and discuss the "interactive" graphical options you have whenever RXtraces displays a trace plot... ENTER, ESC, or letter M key...will return you to the above menus so you can switch between data sets and/or between the 5 types of trace plot for each data set. V key....Displays an On-Screen Cursor that you can move with the "arrow" keys (on your numeric keypad) as well as an On-Screen Listing of the numeric values at the Cursor (see PgUp and PgDn, below.) Use the up and down arrows to jump between the different curves on each trace. Use the left and right arrows to decrease and increase, respectively, MCAL by one "step", usually 0.125. Use the BackSpace and Tab keys to decrease and increase, respectively, MCAL, by 4 steps, usually 0.500. Finally, press either... S (special key) to Save/Print the annotated screen or....... ENTER key, ESCape key, or space bar ONCE to eliminate the On-Screen Cursor and Values. H key....HIGH-LIGHT one of the curves on the trace plot by changing its color from cyan to magenta and display the NAME of the corresponding regressor variable or principal axis. Use PgUp and PgDn to reveal trace details under the on-screen message. You may Highlight curve "0" to return to a "plain" trace plot. RXtraces, version 9103 . . . . . . . . . . . . . . . Page 9 of 12 N key....Replaces the trace plot with a "NAMES and NUMERICS" screen. Use the right arrow, left arrow, Tab, and BackSpace keys to change MCAL (by 1 or 4 steps)...same as with the V key, above. (Up and down arrow keys are not used here.) Finally, press ENTER just once to return to the trace plot. PgDn key...Move On-Screen Messages to the BOTTOM of the Screen. PgUp key...Move On-Screen Messages to the TOP of the Screen. S key....SPECIAL KEY signal. A message will appear to indicate which keys have been activate for screen saves, dumps, etc. Press any other key to deactivate the special keys... L or F10 dumps screen to HP Laserjet I or F9 dumps to IBM Graphics Matrix E or F8 dumps to Epson FX, JX, or LQ O or F7 dumps to Okidata Microline S = SAVE screen...as filename.PIX Q = QUIT...Immediate Termination!!! NOTE: If you invoke the DOS "graphics" command before entering RXtraces, you could also use the Shift-PrtSc key combination for screen dumps to your printer. With some dot-matrix printers, this will work better than the I, E, O Special Keys. F1 key or SpaceBar...displays a "help" screen that summarizes all of the above "interactive" options you can exercise on each trace plot. ┌────────────────────────────────────────────────────────────────────┐ │ TECHNICAL APPENDIX......"Shape" and "Extent" of Shrinkage in the │ │ Two-Parameter Generalized Ridge Family. │ └────────────────────────────────────────────────────────────────────┘ Q = the ridge parameter that controls the "shape" (or "curvature") of the ridge path through regression coefficient likelihood space. Q = +1 ...yields uniform shrinkage (all Shrinkage Factors equal.) Q = 0 ...yields Hoerl-Kennard "ordinary" ridge regression. Q = -5 ...is usually very close, numerically, to "Principal Components Regression," with exact agreement in the limit as Q approaches minus infinity. MCAL = the "Multicollinearity Allowance" parameter that indexes the "extent" of ridge shrinkage along any ridge path. = P - trace( P x P diagonal matrix of Delta Shrinkage Factors ). MCAL = 0 ...yields zero shrinkage. This is the "starting point" of the ridge path, where the ridge estimator coincides with the Ordinary Least Squares estimator at the left-hand extreme. MCAL = P ...yields "total" shrinkage. This is the right-hand "end point" of the path, where the ridge estimator is all ZEROS. RXtraces, version 9103 . . . . . . . . . . . . . . . Page 10 of 12 where... P = Number of Predictor Variables (non-constant Regressors), N = Number of Observations (or Regressor Combinations), and generalized ridge regression "Shrinkage Factors" are of the form... EigenValue Delta = ---------------------------------- EigenValue + Konstant*EigenValue^Q or, equivalently,... 1 = ----------------------------- 1 + Konstant*EigenValue^(Q-1) Empirical evidence that choice of "shape" as well as "extent" of shrinkage can be rewarding... Min.MeanSqErr Min.MeanSqErr Data Set Number of Number of Amount of Shrinkage Name Observations Predictors Shrinkage Shape ============= ============ ========== ============= ============= FACE data N = 21, P = 10, MCAL = 2.3, Qshape = +.77 Air Pollution N = 60, P = 15, MCAL = 5.4, Qshape = +.07 and Mortality Acetylene N = 16, P = 9, MCAL = 5.2, Qshape = -.35 Ten-Factor N = 36, P = 10, MCAL = 3.6, Qshape = -.78 Stack Loss N = 15, P = 3, MCAL = 0.24, Qshape = -.95 Mantell, Bell N = 25, P = 3, MCAL = 0.95, Qshape = -1.1 Productivity Wood Beam N = 10, P = 2, MCAL = 0.26, Qshape = -1.4 Longley N = 16, P = 6, MCAL = 4.0, Qshape = -1.4 Hocking MPG N = 32, P = 10, MCAL = 8.8, Qshape = -7.6 Diesel data N = 44, P = 9, MCAL = 4.9, Qshape = -20 Portland N = 13, P = 4, MCAL = 3.0, Qshape = -INF. Cement, Hald. ============= ============ ========== ============ ============= Data Set Number of Number of Amount of Shrinkage Name Observations Predictors Shrinkage Shape Min.MeanSqErr Min.MeanSqErr RXtraces, version 9103 . . . . . . . . . . . . . . . Page 11 of 12 ┌────────────────────────────┐ ┌────────────────────┤ RXtraces UpDate History... ├────────────────────┐ │ └────────────────────────────┘ │ │ 8902-06 ...developmental versions │ │ 8907 ...beta test version │ │ 8910 ...cosmetic changes to menus, variable name defaults, etc. │ │ 9002 ...add ability to save\print annotated TRACE displays │ │ 9004 ...detect zero range (max=min) & LZEXE (c) Fabrice Bellard │ │ 9008 ...bounce-bar filename menu; doc. update; change-of-address │ │ 9010 ...change screen save file to .PCX format │ │ 9012 ...fix bounce-bar selection menu for monochrome screens │ │ 9103 ...permanent change of address; documentation update │ │ 9303 ...major documentation revision/update. │ └──────────────────────────────────────────────────────────────────────┘ ┌─────────┐ ┌─────┴───┐ │ (R) ──│ │o │────────────────── │ ┌─────┴╨──┐ │ Association of │ │ │─┘ Shareware └───│ o │ Professionals ──────│ ║ │──────────────────── └────╨────┘ MEMBER ASP wants to make sure that the shareware principle works for you. If you are unable to resolve a shareware-related problem with an ASP member by contacting the member directly, ASP may be able to help. The ASP Ombudsman can help you resolve a dispute or problem with an ASP member, but does not provide technical support for members' products. Please write to the ASP Ombudsman at 545 Grover Road, Muskegon, MI 49442-9427 or send a CompuServe Mail message to 70007,3536. ┌───────────────────────────────────────────────────────────────────┐ │ In an effort to make it easier for you to obtain your favorite │ │ software, the latest updates of many ASP authored programs can be │ │ found on the BBSs listed below. These BBSs are members of the... │ ├───────────────────────────────────────────────────────────────────┤ │ ASP Hub Network (AHN). │ └───────────────────────────────────────────────────────────────────┘ Zone 1 - East Coast USA North-East Coast Mid-East Coast [Site #1] [Site #2] The Consultant BBS The Break RBBS <East> Jay Caplan Bruce Jackson P.O. Box 8571 4660 Whitaker PL New York NY 10116-4655 Dale City, VA 22193-3011 Data1) 718-837-3236 Data1) 703-680-9269 Data2) Data2) 703-551-0000 RXtraces, version 9103 . . . . . . . . . . . . . . . Page 12 of 12 Zone 2 - North Mid-USA Zone 3 - Southern Mid-USA [Site #3] [Site #4] The Twilight Zone The DataExchange BBS John Hrusovszky Don Morris 1119 E. Main St 119 Herring St. Auburndale, WI 54412 Leesville, LA 71446 Data1) 715-652-2758 Data1) 318-239-2122 Data2) Data2) Zone 4 - West Coast USA [Site #5] [Site #6] Attention to Details BBS Space BBS Clint Bradford Owen Hawkins 5085 Trail Canyon Dr PO Box X Mira Loma CA 91752 Menlo Park, CA 94026 Data1) 909-681-6221 Data1) 415-323-4398 (ASP Files) Data2) Data2) 415-323-4193 (Other Files) Zone 5 - Canada [Site #7] Knightec BBS Phil Knight 35 Robb Blvd #6 Orangeville, ONT L9W 3L1 Data1) 519-940-0007 Data2) ┌──────────────────────────────────────────────────────────────┐ │ These BBSs are bound by special agreement with the ASP. │ │ In the case of a dispute contact the ASP Omsbudsman. │ └──────────────────────────────────────────────────────────────┘