src/stat-models/regression-lispmat.lisp

   1 ;;; -*- mode: lisp -*-
   2 ;;;
   3 ;;; Copyright (c) 2008--, by A.J. Rossini <blindglobe@gmail.com>
   4 ;;; See COPYRIGHT file for any additional restrictions (BSD license).
   5 ;;; Since 1991, ANSI was finally finished.  Modified to match ANSI
   6 ;;; Common Lisp.
   7
   8 ;;;; Originally from:
   9 ;;;; regression.lsp XLISP-STAT regression model proto and methods
  10 ;;;; XLISP-STAT 2.1 Copyright (c) 1990, by Luke Tierney
  11 ;;;; Additions to Xlisp 2.1, Copyright (c) 1989 by David Michael Betz
  12 ;;;; You may give out copies of this software; for conditions see the file
  13 ;;;; COPYING included with this distribution.
  14 ;;;;
  15 ;;;; Incorporates modifications suggested by Sandy Weisberg.
  16
  17 ;;; This version uses lisp-matrix for underlying numerics.
  18
  19 (in-package :lisp-stat-regression-linear)
  20
  21 ;;; Regresion Model Prototype
  22
  23 ;; The general strategy behind the fitting of models using prototypes
  24 ;; is that we need to think about want the actual fits are, and then
  25 ;; the fits can be used to recompute as components are changes.  One
  26 ;; catch here is that we'd like some notion of trace-ability, in
  27 ;; particular, there is not necessarily a fixed way to take care of the
  28 ;; audit trail.  save-and-die might be a means of recording the final
  29 ;; approach, but we are challenged by the problem of using advice and
  30 ;; other such features to capture stages and steps that are considered
  31 ;; along the goals of estimating a model.
  32
  33 ;; Note that the above is a stream-of-conscience response to the
  34 ;; challenge of reproducibility in the setting of prototype "on-line"
  35 ;; computation.
  36
  37 (defvar regression-model-proto nil
  38   "Prototype for all regression model instances.")
  39 (defproto regression-model-proto
  40     '(x y intercept sweep-matrix basis weights
  41       included
  42       total-sum-of-squares
  43       residual-sum-of-squares
  44       predictor-names
  45       response-name
  46       case-labels
  47       doc)
  48   ()
  49   *object*
  50   "Normal Linear Regression Model")
  51
  52
  53 (defun regression-model (x y &key
  54                          (intercept T)
  55                          (print T)
  56                          (weights nil)
  57                          (included (repeat t (length y)))
  58                          predictor-names
  59                          response-name
  60                          case-labels
  61                          (doc "Undocumented Regression Model Instance")
  62                          (debug T))
  63   "Args: (x y &key (intercept T) (print T) (weights nil)
  64           included predictor-names response-name case-labels)
  65 X           - list of independent variables or X matrix
  66 Y           - dependent variable.
  67 INTERCEPT   - T to include (default), NIL for no intercept
  68 PRINT       - if not NIL print summary information
  69 WEIGHTS     - if supplied should be the same length as Y; error
  70               variances are
  71               assumed to be inversely proportional to WEIGHTS
  72 PREDICTOR-NAMES, RESPONSE-NAME, CASE-LABELS
  73             - sequences of strings or symbols.
  74 INCLUDED    - if supplied should be the same length as Y, with
  75               elements nil to skip a in computing estimates (but not
  76               in residual analysis).
  77 Returns a regression model object. To examine the model further assign the
  78 result to a variable and send it messages.
  79 Example (data are in file absorbtion.lsp in the sample data directory):
  80   (def m (regression-model (list iron aluminum) absorbtion))
  81   (send m :help) (send m :plot-residuals)"
  82   (let ((x (cond
  83              ((typep x 'matrix-like) x)
  84              ((or (typep x 'vector)
  85                   (and (consp x)
  86                        (numberp (car x))) (make-vector (length x) :initial-contents x)))
  87              (t x))) ;; actually, might should barf.
  88         (y (cond
  89              ((typep y 'vector-like) y)
  90              ((and (consp x)
  91                    (numberp (car x))) (make-vector (length y) :initial-contents y))
  92              (t y))) ;; actually, might should barf.
  93         (m (send regression-model-proto :new)))
  94     (format t "~%")
  95     (send m :doc doc)
  96     (send m :x x)
  97     (send m :y y)
  98     (send m :intercept intercept)
  99     (send m :weights weights)
 100     (send m :included included)
 101     (send m :predictor-names predictor-names)
 102     (send m :response-name response-name)
 103     (send m :case-labels case-labels)
 104     (if debug
 105         (progn
 106           (format t "~%")
 107           (format t "~S~%" (send m :doc))
 108           (format t "X: ~S~%" (send m :x))
 109           (format t "Y: ~S~%" (send m :y))))
 110     (if print (send m :display))
 111     m))
 112
 113 (defmeth regression-model-proto :isnew ()
 114   (send self :needs-computing t))
 115
 116 (defmeth regression-model-proto :save ()
 117 "Message args: ()
 118 Returns an expression that will reconstruct the regression model."
 119   `(regression-model ',(send self :x)
 120                      ',(send self :y)
 121                      :intercept ',(send self :intercept)
 122                      :weights ',(send self :weights)
 123                      :included ',(send self :included)
 124                      :predictor-names ',(send self :predictor-names)
 125                      :response-name ',(send self :response-name)
 126                      :case-labels ',(send self :case-labels)))
 127
 128 ;;; Computing and Display Methods
 129
 130 (defmeth regression-model-proto :compute ()
 131 "Message args: ()
 132 Recomputes the estimates. For internal use by other messages"
 133   (let* ((included (if-else (send self :included) 1 0))
 134          (x (send self :x))
 135          (y (send self :y))
 136          (intercept (send self :intercept))
 137          (weights (send self :weights))
 138          (w (if weights (* included weights) included))
 139          (m (make-sweep-matrix x y w)) ;;; ERROR HERE
 140          (n (matrix-dimension x 1))
 141          (p (- (matrix-dimension m 0) 1))
 142          (tss (mref m p p))
 143          (tol (* 0.001 (reduce #'* (mapcar #'standard-deviation (column-list x)))))
 144          (sweep-result
 145           (if intercept
 146               (sweep-operator m (iseq 1 n) tol)
 147               (sweep-operator m (iseq 0 n) (cons 0.0 tol)))))
 148     (format t
 149             "~%REMOVEME: regr-mdl-prto :compute~%Sweep= ~A~%x= ~A~%y= ~A~%m= ~A~%tss= ~A~%"
 150            sweep-result x y m tss)
 151     (setf (slot-value 'sweep-matrix) (first sweep-result))
 152     (setf (slot-value 'total-sum-of-squares) tss)
 153     (setf (slot-value 'residual-sum-of-squares)
 154           (mref (first sweep-result) p p))
 155     ;; SOMETHING WRONG HERE! FIX-ME
 156     (setf (slot-value 'basis)
 157           (let ((b (remove 0 (second sweep-result))))
 158             (if b (- (reduce #'- (reverse b)) 1)
 159                 (error "no columns could be swept"))))))
 160
 161 (defmeth regression-model-proto :needs-computing (&optional set)
 162 "Message args: ( &optional set )
 163
 164 If value given, sets the flag for whether (re)computation is needed to
 165 update the model fits."
 166    (send self :nop)
 167    (if set (setf (slot-value 'sweep-matrix) nil))
 168    (null (slot-value 'sweep-matrix)))
 169
 170 (defmeth regression-model-proto :display ()
 171 "Message args: ()
 172
 173 Prints the least squares regression summary. Variables not used in the fit
 174 are marked as aliased."
 175   (let ((coefs (coerce (send self :coef-estimates) 'list))
 176         (se-s (send self :coef-standard-errors))
 177         (x (send self :x))
 178         (p-names (send self :predictor-names)))
 179     (if (send self :weights)
 180         (format t "~%Weighted Least Squares Estimates:~2%")
 181         (format t "~%Least Squares Estimates:~2%"))
 182     (when (send self :intercept)
 183           (format t "Constant               ~10f   ~A~%"
 184                   (car coefs) (list (car se-s)))
 185           (setf coefs (cdr coefs))
 186           (setf se-s (cdr se-s)))
 187     (dotimes (i (array-dimension x 1))
 188              (cond
 189                ((member i (send self :basis))
 190                 (format t "~22a ~10f   ~A~%"
 191                         (select p-names i) (car coefs) (list (car se-s)))
 192                 (setf coefs (cdr coefs) se-s (cdr se-s)))
 193                (t (format t "~22a    aliased~%" (select p-names i)))))
 194     (format t "~%")
 195     (format t "R Squared:             ~10f~%" (send self :r-squared))
 196     (format t "Sigma hat:             ~10f~%" (send self :sigma-hat))
 197     (format t "Number of cases:       ~10d~%" (send self :num-cases))
 198     (if (/= (send self :num-cases) (send self :num-included))
 199         (format t "Number of cases used:  ~10d~%" (send self :num-included)))
 200     (format t "Degrees of freedom:    ~10d~%" (send self :df))
 201     (format t "~%")))
 202
 203 ;;; Slot accessors and mutators
 204
 205 (defmeth regression-model-proto :doc (&optional new-doc append)
 206 "Message args: (&optional new-doc)
 207
 208 Returns the DOC-STRING as supplied to m.
 209 Additionally, with an argument NEW-DOC, sets the DOC-STRING to
 210 NEW-DOC.  In this setting, when APPEND is T, append NEW-DOC to DOC
 211 rather than doing replacement."
 212   (send self :nop)
 213   (when (and new-doc (stringp new-doc))
 214     (setf (slot-value 'doc)
 215           (if append
 216               (concatenate 'string
 217                            (slot-value 'doc)
 218                            new-doc)
 219               new-doc)))
 220   (slot-value 'doc))
 221
 222
 223 (defmeth regression-model-proto :x (&optional new-x)
 224 "Message args: (&optional new-x)
 225
 226 With no argument returns the x matrix as supplied to m. With an
 227 argument, NEW-X sets the x matrix to NEW-X and recomputes the
 228 estimates."
 229   (when (and new-x (typep new-x 'matrix-like))
 230     (setf (slot-value 'x) new-x)
 231     (send self :needs-computing t))
 232   (slot-value 'x))
 233
 234 (defmeth regression-model-proto :y (&optional new-y)
 235 "Message args: (&optional new-y)
 236
 237 With no argument returns the y sequence as supplied to m. With an
 238 argument, NEW-Y sets the y sequence to NEW-Y and recomputes the
 239 estimates."
 240   (when (and new-y
 241              (or (typep new-y vector-like)
 242                  (typep  new-y 'sequence)))
 243     (setf (slot-value 'y) new-y)
 244     (send self :needs-computing t))
 245   (slot-value 'y))
 246
 247 (defmeth regression-model-proto :intercept (&optional (val nil set))
 248 "Message args: (&optional new-intercept)
 249
 250 With no argument returns T if the model includes an intercept term,
 251 nil if not. With an argument NEW-INTERCEPT the model is changed to
 252 include or exclude an intercept, according to the value of
 253 NEW-INTERCEPT."
 254   (when set
 255     (setf (slot-value 'intercept) val)
 256     (send self :needs-computing t))
 257   (slot-value 'intercept))
 258
 259 (defmeth regression-model-proto :weights (&optional (new-w nil set))
 260 "Message args: (&optional new-w)
 261
 262 With no argument returns the weight sequence as supplied to m; NIL
 263 means an unweighted model. NEW-W sets the weights sequence to NEW-W
 264 and recomputes the estimates."
 265   (when (and set
 266              (or (typep new-y vector-like)
 267                  (typep  new-y 'sequence)))
 268     (setf (slot-value 'weights) new-w)
 269     (send self :needs-computing t))
 270   (slot-value 'weights))
 271
 272 (defmeth regression-model-proto :total-sum-of-squares ()
 273 "Message args: ()
 274
 275 Returns the total sum of squares around the mean."
 276   (if (send self :needs-computing) (send self :compute))
 277   (slot-value 'total-sum-of-squares))
 278
 279 (defmeth regression-model-proto :residual-sum-of-squares ()
 280 "Message args: ()
 281
 282 Returns the residual sum of squares for the model."
 283   (if (send self :needs-computing) (send self :compute))
 284   (slot-value 'residual-sum-of-squares))
 285
 286 (defmeth regression-model-proto :basis ()
 287 "Message args: ()
 288
 289 Returns the indices of the variables used in fitting the model, in a
 290 sequence.  Recompute before this, if needed."
 291   (if (send self :needs-computing)
 292       (send self :compute))
 293   ;; This should be silly -- basis MUST be a vector in the new regime.
 294   (if (typep (slot-value 'basis) 'sequence)
 295       (slot-value 'basis)
 296       (list (slot-value 'basis))))
 297
 298
 299 (defmeth regression-model-proto :sweep-matrix ()
 300 "Message args: ()
 301
 302 Returns the swept sweep matrix. For internal use"
 303   (if (send self :needs-computing)
 304       (send self :compute))
 305   (slot-value 'sweep-matrix))
 306
 307 (defmeth regression-model-proto :included (&optional new-included)
 308 "Message args: (&optional new-included)
 309
 310 With no argument, NIL means a case is not used in calculating
 311 estimates, and non-nil means it is used.  NEW-INCLUDED is a sequence
 312 of length of y of nil and t to select cases.  Estimates are
 313 recomputed."
 314   (when (and new-included
 315              (= (nelts new-included) (send self :num-cases)))
 316         (setf (slot-value 'included) (copy-seq new-included))
 317         (send self :needs-computing t))
 318   (if (slot-value 'included)
 319       (slot-value 'included)
 320       (repeat t (send self :num-cases))))
 321
 322 (defmeth regression-model-proto :predictor-names (&optional (names nil set))
 323 "Message args: (&optional (names nil set))
 324
 325 With no argument returns the predictor names. NAMES sets the names."
 326   (if set (setf (slot-value 'predictor-names) (mapcar #'string names)))
 327   (let ((p (matrix-dimension (send self :x) 1))
 328         (p-names (slot-value 'predictor-names)))
 329     (if (not (and p-names (= (length p-names) p)))
 330         (setf (slot-value 'predictor-names)
 331               (mapcar #'(lambda (a) (format nil "Variable ~a" a))
 332                       (iseq 0 (- p 1))))))
 333   (slot-value 'predictor-names))
 334
 335 (defmeth regression-model-proto :response-name (&optional (name "Y" set))
 336    "Message args: (&optional name)
 337
 338 With no argument returns the response name. NAME sets the name."
 339    (send self :nop)
 340    (if set (setf (slot-value 'response-name) (if name (string name) "Y")))
 341    (slot-value 'response-name))
 342
 343 (defmeth regression-model-proto :case-labels (&optional (labels nil set))
 344 "Message args: (&optional labels)
 345 With no argument returns the case-labels. LABELS sets the labels."
 346   (if set (setf (slot-value 'case-labels)
 347                 (if labels
 348                     (mapcar #'string labels)
 349                     (mapcar #'(lambda (x) (format nil "~d" x))
 350                             (iseq 0 (- (send self :num-cases) 1))))))
 351   (slot-value 'case-labels))
 352
 353 ;;;
 354 ;;; Other Methods
 355 ;;; None of these methods access any slots directly.
 356 ;;;
 357
 358 (defmeth regression-model-proto :num-cases ()
 359 "Message args: ()
 360 Returns the number of cases in the model."
 361   (nelts (send self :y)))
 362
 363 (defmeth regression-model-proto :num-included ()
 364 "Message args: ()
 365 Returns the number of cases used in the computations."
 366   (sum (if-else (send self :included) 1 0)))
 367
 368 (defmeth regression-model-proto :num-coefs ()
 369 "Message args: ()
 370 Returns the number of coefficients in the fit model (including the
 371 intercept if the model includes one)."
 372   (if (send self :intercept)
 373       (+ 1 (nelts (send self :basis)))
 374       (nelts (send self :basis))))
 375
 376 (defmeth regression-model-proto :df ()
 377 "Message args: ()
 378 Returns the number of degrees of freedom in the model."
 379   (- (send self :num-included) (send self :num-coefs)))
 380
 381 (defmeth regression-model-proto :x-matrix ()
 382 "Message args: ()
 383 Returns the X matrix for the model, including a column of 1's, if
 384 appropriate. Columns of X matrix correspond to entries in basis."
 385   (let ((m (select (send self :x)
 386                    (iseq 0 (- (send self :num-cases) 1))
 387                    (send self :basis))))
 388     (if (send self :intercept)
 389         (bind2 (repeat 1 (send self :num-cases)) m)
 390         m)))
 391
 392 (defmeth regression-model-proto :leverages ()
 393 "Message args: ()
 394 Returns the diagonal elements of the hat matrix."
 395   (let* ((weights (send self :weights))
 396          (x (send self :x-matrix))
 397          (raw-levs
 398           (matmult (* (matmult x (send self :xtxinv)) x)
 399                    (repeat 1 (send self :num-coefs)))))
 400     (if weights (* weights raw-levs) raw-levs)))
 401
 402 (defmeth regression-model-proto :fit-values ()
 403 "Message args: ()
 404 Returns the fitted values for the model."
 405   (matmult (send self :x-matrix) (send self :coef-estimates)))
 406
 407 (defmeth regression-model-proto :raw-residuals ()
 408 "Message args: ()
 409 Returns the raw residuals for a model."
 410   (- (send self :y) (send self :fit-values)))
 411
 412 (defmeth regression-model-proto :residuals ()
 413 "Message args: ()
 414 Returns the raw residuals for a model without weights. If the model
 415 includes weights the raw residuals times the square roots of the weights
 416 are returned."
 417   (let ((raw-residuals (send self :raw-residuals))
 418         (weights (send self :weights)))
 419     (if weights (* (sqrt weights) raw-residuals) raw-residuals)))
 420
 421 (defmeth regression-model-proto :sum-of-squares ()
 422 "Message args: ()
 423 Returns the error sum of squares for the model."
 424   (send self :residual-sum-of-squares))
 425
 426 (defmeth regression-model-proto :sigma-hat ()
 427 "Message args: ()
 428 Returns the estimated standard deviation of the deviations about the
 429 regression line."
 430   (let ((ss (send self :sum-of-squares))
 431         (df (send self :df)))
 432     (if (/= df 0) (sqrt (/ ss df)))))
 433
 434 ;; for models without an intercept the 'usual' formula for R^2 can give
 435 ;; negative results; hence the max.
 436 (defmeth regression-model-proto :r-squared ()
 437 "Message args: ()
 438 Returns the sample squared multiple correlation coefficient, R squared, for
 439 the regression."
 440   (max (- 1 (/ (send self :sum-of-squares) (send self :total-sum-of-squares)))
 441        0))
 442
 443 (defmeth regression-model-proto :coef-estimates ()
 444 "Message args: ()
 445
 446 Returns the OLS (ordinary least squares) estimates of the regression
 447 coefficients. Entries beyond the intercept correspond to entries in
 448 basis."
 449   (let ((n (array-dimension (send self :x) 1))
 450         (indices (flatten-list
 451                   (if (send self :intercept)
 452                      (cons 0 (+ 1 (send self :basis)))
 453                      (list (+ 1 (send self :basis))))))
 454         (m (send self :sweep-matrix)))
 455     (format t "~%REMOVEME2: Coef-ests: ~% Sweep Matrix: ~A ~% array dim 1: ~A ~% Swept indices:  ~A ~% basis: ~A"
 456             m n indices (send self :basis))
 457     (coerce (compound-data-seq (select m (+ 1 n) indices)) 'list))) ;; ERROR
 458
 459 (defmeth regression-model-proto :xtxinv ()
 460 "Message args: ()
 461 Returns ((X^T) X)^(-1) or ((X^T) W X)^(-1)."
 462   (let ((indices (if (send self :intercept)
 463                      (cons 0 (1+ (send self :basis)))
 464                      (1+ (send self :basis)))))
 465     (select (send self :sweep-matrix) indices indices)))
 466
 467 (defmeth regression-model-proto :coef-standard-errors ()
 468 "Message args: ()
 469 Returns estimated standard errors of coefficients. Entries beyond the
 470 intercept correspond to entries in basis."
 471   (let ((s (send self :sigma-hat)))
 472     (if s (* (send self :sigma-hat) (sqrt (diagonal (send self :xtxinv)))))))
 473
 474 (defmeth regression-model-proto :studentized-residuals ()
 475 "Message args:  ()
 476 Computes the internally studentized residuals for included cases and externally studentized residuals for excluded cases."
 477   (let ((res (send self :residuals))
 478         (lev (send self :leverages))
 479         (sig (send self :sigma-hat))
 480         (inc (send self :included)))
 481     (if-else inc
 482              (/ res (* sig (sqrt (pmax .00001 (- 1 lev)))))
 483              (/ res (* sig (sqrt (+ 1 lev)))))))
 484
 485 (defmeth regression-model-proto :externally-studentized-residuals ()
 486 "Message args:  ()
 487 Computes the externally studentized residuals."
 488   (let* ((res (send self :studentized-residuals))
 489          (df (send self :df)))
 490     (if-else (send self :included)
 491              (* res (sqrt (/ (- df 1) (- df (^ res 2)))))
 492              res)))
 493
 494 (defmeth regression-model-proto :cooks-distances ()
 495 "Message args: ()
 496 Computes Cook's distances."
 497   (let ((lev (send self :leverages))
 498         (res (/ (^ (send self :studentized-residuals) 2)
 499                 (send self :num-coefs))))
 500     (if-else (send self :included) (* res (/ lev (- 1 lev) )) (* res lev))))
 501
 502
 503 (defun plot-points (x y &rest args)
 504   "need to fix."
 505   (declare (ignore x y args))
 506   (error "Graphics not implemented yet."))
 507
 508 ;; Can not plot points yet!!
 509 (defmeth regression-model-proto :plot-residuals (&optional x-values)
 510 "Message args: (&optional x-values)
 511 Opens a window with a plot of the residuals. If X-VALUES are not supplied
 512 the fitted values are used. The plot can be linked to other plots with the
 513 link-views function. Returns a plot object."
 514   (plot-points (if x-values x-values (send self :fit-values))
 515                (send self :residuals)
 516                :title "Residual Plot"
 517                :point-labels (send self :case-labels)))
 518
 519 (defmeth regression-model-proto :plot-bayes-residuals
 520   (&optional x-values)
 521   "Message args: (&optional x-values)
 522
 523 Opens a window with a plot of the standardized residuals and two
 524 standard error bars for the posterior distribution of the actual
 525 deviations from the line. See Chaloner and Brant. If X-VALUES are not
 526 supplied the fitted values are used. The plot can be linked to other
 527 plots with the link-views function.  Returns a plot object."
 528
 529   (let* ((r (/ (send self :residuals)
 530                (send self :sigma-hat)))
 531          (d (* 2 (sqrt (send self :leverages))))
 532          (low (- r d))
 533          (high (+ r d))
 534          (x-values (if x-values x-values (send self :fit-values)))
 535          (p (plot-points x-values r
 536                          :title "Bayes Residual Plot"
 537                          :point-labels (send self :case-labels))))
 538     (map 'list #'(lambda (a b c d) (send p :plotline a b c d nil))
 539          x-values low x-values high)
 540     (send p :adjust-to-data)
 541     p))