starting on regression generics (so that lists or lisp-matrix input works).
[CommonLispStat.git] / src / stat-models / regression.lisp
blob6ad085bfcc19fda6b64d2508fe37d4a93459c781
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.
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.
17 ;;; This version uses lisp-matrix for underlying numerics.
19 (in-package :lisp-stat-regression-linear)
21 ;;; Regresion Model Prototype
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.
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.
37 (defvar regression-model-proto nil
38 "Prototype for all regression model instances.")
40 (defproto regression-model-proto
41 '(x y intercept sweep-matrix basis weights
42 included
43 total-sum-of-squares
44 residual-sum-of-squares
45 predictor-names
46 response-name
47 case-labels
48 doc)
50 *object*
51 "Normal Linear Regression Model")
54 (defun regression-model
55 (x y &key
56 (intercept T)
57 (print T)
58 (weights nil)
59 (included (repeat t (length y)))
60 predictor-names
61 response-name
62 case-labels
63 (doc "Undocumented Regression Model Instance")
64 (debug T))
65 "Args: (x y &key (intercept T) (print T) (weights nil)
66 included predictor-names response-name case-labels)
67 X - list of independent variables or X matrix
68 Y - dependent variable.
69 INTERCEPT - T to include (default), NIL for no intercept
70 PRINT - if not NIL print summary information
71 WEIGHTS - if supplied should be the same length as Y; error
72 variances are
73 assumed to be inversely proportional to WEIGHTS
74 PREDICTOR-NAMES, RESPONSE-NAME, CASE-LABELS
75 - sequences of strings or symbols.
76 INCLUDED - if supplied should be the same length as Y, with
77 elements nil to skip a in computing estimates (but not
78 in residual analysis).
79 Returns a regression model object. To examine the model further assign the
80 result to a variable and send it messages.
81 Example (data are in file absorbtion.lsp in the sample data directory):
82 (def m (regression-model (list iron aluminum) absorbtion))
83 (send m :help) (send m :plot-residuals)"
84 (let ((x (cond
85 ((typep x 'matrix-like) x)
86 ((or (typep x 'vector)
87 (and (consp x)
88 (numberp (car x))) (make-vector (length x) :initial-contents x)))
89 (t x))) ;; actually, might should barf.
90 (y (cond
91 ((typep y 'vector-like) y)
92 ((and (consp x)
93 (numberp (car x))) (make-vector (length y) :initial-contents y))
94 (t y))) ;; actually, might should barf.
95 (m (send regression-model-proto :new)))
96 (format t "~%")
97 (send m :doc doc)
98 (send m :x x)
99 (send m :y y)
100 (send m :intercept intercept)
101 (send m :weights weights)
102 (send m :included included)
103 (send m :predictor-names predictor-names)
104 (send m :response-name response-name)
105 (send m :case-labels case-labels)
106 (if debug
107 (progn
108 (format t "~%")
109 (format t "~S~%" (send m :doc))
110 (format t "X: ~S~%" (send m :x))
111 (format t "Y: ~S~%" (send m :y))))
112 (if print (send m :display))
116 ;; regression-model is the old API, but regression as a generic will
117 ;; be the new API. We need to distinguish between APIs which enable
118 ;; the user to do clear activities, and APIs which enable developers
119 ;; to do clear extensions and development, and underlying
120 ;; infrastructure to keep everything straight and enabled.
123 (defclass model ()
124 ((type structure)))
126 (defgeneric regression ;; assumes x/y from lisp-matrix -- start of a set of generics.
127 (model dataset)
128 "Args: (x y &key (intercept T) (print T) (weights nil)
129 included predictor-names response-name case-labels)
130 X - list of independent variables or X matrix
131 Y - dependent variable.
132 INTERCEPT - T to include (default), NIL for no intercept
133 PRINT - if not NIL print summary information
134 WEIGHTS - if supplied should be the same length as Y; error
135 variances are
136 assumed to be inversely proportional to WEIGHTS
137 PREDICTOR-NAMES, RESPONSE-NAME, CASE-LABELS
138 - sequences of strings or symbols.
139 INCLUDED - if supplied should be the same length as Y, with
140 elements nil to skip a in computing estimates (but not
141 in residual analysis).
142 Returns a regression model object. To examine the model further assign the
143 result to a variable and send it messages.
144 Example (data are in file absorbtion.lsp in the sample data directory):
145 (def m (regression-model (list iron aluminum) absorbtion))
146 (send m :help) (send m :plot-residuals)"
147 (let ((m (send regression-model-proto :new)))
148 (format t "~%")
149 (send m :doc doc)
150 (send m :x x)
151 (send m :y y)
152 (send m :intercept intercept)
153 (send m :weights weights)
154 (send m :included included)
155 (send m :predictor-names predictor-names)
156 (send m :response-name response-name)
157 (send m :case-labels case-labels)
158 (if debug
159 (progn
160 (format t "~%")
161 (format t "~S~%" (send m :doc))
162 (format t "X: ~S~%" (send m :x))
163 (format t "Y: ~S~%" (send m :y))))
164 (if print (send m :display))
169 (defmeth regression-model-proto :isnew ()
170 (send self :needs-computing t))
172 (defmeth regression-model-proto :save ()
173 "Message args: ()
174 Returns an expression that will reconstruct the regression model."
175 `(regression-model ',(send self :x)
176 ',(send self :y)
177 :intercept ',(send self :intercept)
178 :weights ',(send self :weights)
179 :included ',(send self :included)
180 :predictor-names ',(send self :predictor-names)
181 :response-name ',(send self :response-name)
182 :case-labels ',(send self :case-labels)))
184 ;;; Computing and Display Methods
186 (defmeth regression-model-proto :compute ()
187 "Message args: ()
188 Recomputes the estimates. For internal use by other messages"
189 (let* ((included (if-else (send self :included) 1 0))
190 (x (send self :x))
191 (y (send self :y))
192 (intercept (send self :intercept))
193 (weights (send self :weights))
194 (w (if weights (* included weights) included))
195 (m (make-sweep-matrix x y w)) ;;; ERROR HERE
196 (n (matrix-dimension x 1))
197 (p (- (matrix-dimension m 0) 1))
198 (tss (mref m p p))
199 (tol (* 0.001
200 (reduce #'* (mapcar #'standard-deviation (list-of-columns x)))))
201 (sweep-result
202 (if intercept
203 (sweep-operator m (iseq 1 n) tol)
204 (sweep-operator m (iseq 0 n) (cons 0.0 tol)))))
205 (format t
206 "~%REMOVEME: regr-mdl-prto :compute~%Sweep= ~A~%x= ~A~%y= ~A~%m= ~A~%tss= ~A~%"
207 sweep-result x y m tss)
208 (setf (slot-value 'sweep-matrix) (first sweep-result))
209 (setf (slot-value 'total-sum-of-squares) tss)
210 (setf (slot-value 'residual-sum-of-squares)
211 (mref (first sweep-result) p p))
212 ;; SOMETHING WRONG HERE! FIX-ME
213 (setf (slot-value 'basis)
214 (let ((b (remove 0 (second sweep-result))))
215 (if b (- (reduce #'- (reverse b)) 1)
216 (error "no columns could be swept"))))))
218 (defmeth regression-model-proto :needs-computing (&optional set)
219 "Message args: ( &optional set )
221 If value given, sets the flag for whether (re)computation is needed to
222 update the model fits."
223 (send self :nop)
224 (if set (setf (slot-value 'sweep-matrix) nil))
225 (null (slot-value 'sweep-matrix)))
227 (defmeth regression-model-proto :display ()
228 "Message args: ()
230 Prints the least squares regression summary. Variables not used in the fit
231 are marked as aliased."
232 (let ((coefs (coerce (send self :coef-estimates) 'list))
233 (se-s (send self :coef-standard-errors))
234 (x (send self :x))
235 (p-names (send self :predictor-names)))
236 (if (send self :weights)
237 (format t "~%Weighted Least Squares Estimates:~2%")
238 (format t "~%Least Squares Estimates:~2%"))
239 (when (send self :intercept)
240 (format t "Constant ~10f ~A~%"
241 (car coefs) (list (car se-s)))
242 (setf coefs (cdr coefs))
243 (setf se-s (cdr se-s)))
244 (dotimes (i (array-dimension x 1))
245 (cond
246 ((member i (send self :basis))
247 (format t "~22a ~10f ~A~%"
248 (select p-names i) (car coefs) (list (car se-s)))
249 (setf coefs (cdr coefs) se-s (cdr se-s)))
250 (t (format t "~22a aliased~%" (select p-names i)))))
251 (format t "~%")
252 (format t "R Squared: ~10f~%" (send self :r-squared))
253 (format t "Sigma hat: ~10f~%" (send self :sigma-hat))
254 (format t "Number of cases: ~10d~%" (send self :num-cases))
255 (if (/= (send self :num-cases) (send self :num-included))
256 (format t "Number of cases used: ~10d~%" (send self :num-included)))
257 (format t "Degrees of freedom: ~10d~%" (send self :df))
258 (format t "~%")))
260 ;;; Slot accessors and mutators
262 (defmeth regression-model-proto :doc (&optional new-doc append)
263 "Message args: (&optional new-doc)
265 Returns the DOC-STRING as supplied to m.
266 Additionally, with an argument NEW-DOC, sets the DOC-STRING to
267 NEW-DOC. In this setting, when APPEND is T, append NEW-DOC to DOC
268 rather than doing replacement."
269 (send self :nop)
270 (when (and new-doc (stringp new-doc))
271 (setf (slot-value 'doc)
272 (if append
273 (concatenate 'string
274 (slot-value 'doc)
275 new-doc)
276 new-doc)))
277 (slot-value 'doc))
280 (defmeth regression-model-proto :x (&optional new-x)
281 "Message args: (&optional new-x)
283 With no argument returns the x matrix-like as supplied to m. With an
284 argument, NEW-X sets the x matrix-like to NEW-X and recomputes the
285 estimates."
286 (when (and new-x (typep new-x 'matrix-like))
287 (setf (slot-value 'x) new-x)
288 (send self :needs-computing t))
289 (slot-value 'x))
291 (defmeth regression-model-proto :y (&optional new-y)
292 "Message args: (&optional new-y)
294 With no argument returns the y vector-like as supplied to m. With an
295 argument, NEW-Y sets the y vector-like to NEW-Y and recomputes the
296 estimates."
297 (when (and new-y
298 (typep new-y 'vector-like))
299 (setf (slot-value 'y) new-y) ;; fixme -- pls set slot value to a vector-like!
300 (send self :needs-computing t))
301 (slot-value 'y))
303 (defmeth regression-model-proto :intercept (&optional (val nil set))
304 "Message args: (&optional new-intercept)
306 With no argument returns T if the model includes an intercept term,
307 nil if not. With an argument NEW-INTERCEPT the model is changed to
308 include or exclude an intercept, according to the value of
309 NEW-INTERCEPT."
310 (when set
311 (setf (slot-value 'intercept) val)
312 (send self :needs-computing t))
313 (slot-value 'intercept))
315 (defmeth regression-model-proto :weights (&optional (new-w nil set))
316 "Message args: (&optional new-w)
318 With no argument returns the weight vector-like as supplied to m; NIL
319 means an unweighted model. NEW-W sets the weights vector-like to NEW-W
320 and recomputes the estimates."
321 (when (and set
322 (typep new-w 'vector-like))
323 (setf (slot-value 'weights) new-w)
324 (send self :needs-computing t))
325 (slot-value 'weights))
327 (defmeth regression-model-proto :total-sum-of-squares ()
328 "Message args: ()
330 Returns the total sum of squares around the mean.
331 This is recomputed if an update is needed."
332 (if (send self :needs-computing)
333 (send self :compute))
334 (slot-value 'total-sum-of-squares))
336 (defmeth regression-model-proto :residual-sum-of-squares ()
337 "Message args: ()
339 Returns the residual sum of squares for the model.
340 This is recomputed if an update is needed."
341 (if (send self :needs-computing)
342 (send self :compute))
343 (slot-value 'residual-sum-of-squares))
345 (defmeth regression-model-proto :basis ()
346 "Message args: ()
348 Returns the indices of the variables used in fitting the model, in a
349 sequence.
350 This is recomputed if an update is needed."
351 (if (send self :needs-computing)
352 (send self :compute))
353 (slot-value 'basis))
356 (defmeth regression-model-proto :sweep-matrix ()
357 "Message args: ()
359 Returns the swept sweep matrix. For internal use"
360 (if (send self :needs-computing)
361 (send self :compute))
362 (slot-value 'sweep-matrix))
364 (defmeth regression-model-proto :included (&optional new-included)
365 "Message args: (&optional new-included)
367 With no argument, NIL means a case is not used in calculating
368 estimates, and non-nil means it is used. NEW-INCLUDED is a sequence
369 of length of y of nil and t to select cases. Estimates are
370 recomputed."
371 (when (and new-included
372 (= (nelts new-included) (send self :num-cases)))
373 (setf (slot-value 'included) (copy-seq new-included))
374 (send self :needs-computing t))
375 (if (slot-value 'included)
376 (slot-value 'included)
377 (repeat t (send self :num-cases))))
379 (defmeth regression-model-proto :predictor-names (&optional (names nil set))
380 "Message args: (&optional (names nil set))
382 With no argument returns the predictor names. NAMES sets the names."
383 (if set (setf (slot-value 'predictor-names) (mapcar #'string names)))
384 (let ((p (matrix-dimension (send self :x) 1))
385 (p-names (slot-value 'predictor-names)))
386 (if (not (and p-names (= (length p-names) p)))
387 (setf (slot-value 'predictor-names)
388 (mapcar #'(lambda (a) (format nil "Variable ~a" a))
389 (iseq 0 (- p 1))))))
390 (slot-value 'predictor-names))
392 (defmeth regression-model-proto :response-name (&optional (name "Y" set))
393 "Message args: (&optional name)
395 With no argument returns the response name. NAME sets the name."
396 (send self :nop)
397 (if set (setf (slot-value 'response-name) (if name (string name) "Y")))
398 (slot-value 'response-name))
400 (defmeth regression-model-proto :case-labels (&optional (labels nil set))
401 "Message args: (&optional labels)
402 With no argument returns the case-labels. LABELS sets the labels."
403 (if set (setf (slot-value 'case-labels)
404 (if labels
405 (mapcar #'string labels)
406 (mapcar #'(lambda (x) (format nil "~d" x))
407 (iseq 0 (- (send self :num-cases) 1))))))
408 (slot-value 'case-labels))
411 ;;; Other Methods
412 ;;; None of these methods access any slots directly.
415 (defmeth regression-model-proto :num-cases ()
416 "Message args: ()
417 Returns the number of cases in the model."
418 (nelts (send self :y)))
420 (defmeth regression-model-proto :num-included ()
421 "Message args: ()
422 Returns the number of cases used in the computations."
423 (sum (if-else (send self :included) 1 0)))
425 (defmeth regression-model-proto :num-coefs ()
426 "Message args: ()
427 Returns the number of coefficients in the fit model (including the
428 intercept if the model includes one)."
429 (if (send self :intercept)
430 (+ 1 (nelts (send self :basis)))
431 (nelts (send self :basis))))
433 (defmeth regression-model-proto :df ()
434 "Message args: ()
435 Returns the number of degrees of freedom in the model."
436 (- (send self :num-included) (send self :num-coefs)))
438 (defmeth regression-model-proto :x-matrix ()
439 "Message args: ()
440 Returns the X matrix for the model, including a column of 1's, if
441 appropriate. Columns of X matrix correspond to entries in basis."
442 (let ((m (select (send self :x)
443 (iseq 0 (- (send self :num-cases) 1))
444 (send self :basis))))
445 (if (send self :intercept)
446 (bind2 (repeat 1 (send self :num-cases)) m)
447 m)))
449 (defmeth regression-model-proto :leverages ()
450 "Message args: ()
451 Returns the diagonal elements of the hat matrix."
452 (let* ((weights (send self :weights))
453 (x (send self :x-matrix))
454 (raw-levs
455 (m* (* (m* x (send self :xtxinv)) x)
456 (repeat 1 (send self :num-coefs)))))
457 (if weights (* weights raw-levs) raw-levs)))
459 (defmeth regression-model-proto :fit-values ()
460 "Message args: ()
461 Returns the fitted values for the model."
462 (m* (send self :x-matrix) (send self :coef-estimates)))
464 (defmeth regression-model-proto :raw-residuals ()
465 "Message args: ()
466 Returns the raw residuals for a model."
467 (- (send self :y) (send self :fit-values)))
469 (defmeth regression-model-proto :residuals ()
470 "Message args: ()
471 Returns the raw residuals for a model without weights. If the model
472 includes weights the raw residuals times the square roots of the weights
473 are returned."
474 (let ((raw-residuals (send self :raw-residuals))
475 (weights (send self :weights)))
476 (if weights (* (sqrt weights) raw-residuals) raw-residuals)))
478 (defmeth regression-model-proto :sum-of-squares ()
479 "Message args: ()
480 Returns the error sum of squares for the model."
481 (send self :residual-sum-of-squares))
483 (defmeth regression-model-proto :sigma-hat ()
484 "Message args: ()
485 Returns the estimated standard deviation of the deviations about the
486 regression line."
487 (let ((ss (send self :sum-of-squares))
488 (df (send self :df)))
489 (if (/= df 0) (sqrt (/ ss df)))))
491 ;; for models without an intercept the 'usual' formula for R^2 can give
492 ;; negative results; hence the max.
493 (defmeth regression-model-proto :r-squared ()
494 "Message args: ()
495 Returns the sample squared multiple correlation coefficient, R squared, for
496 the regression."
497 (max (- 1 (/ (send self :sum-of-squares) (send self :total-sum-of-squares)))
500 (defmeth regression-model-proto :coef-estimates ()
501 "Message args: ()
503 Returns the OLS (ordinary least squares) estimates of the regression
504 coefficients. Entries beyond the intercept correspond to entries in
505 basis."
506 (let ((n (array-dimension (send self :x) 1))
507 (indices (flatten-list
508 (if (send self :intercept)
509 (cons 0 (+ 1 (send self :basis)))
510 (list (+ 1 (send self :basis))))))
511 (m (send self :sweep-matrix)))
512 (format t "~%REMOVEME2: Coef-ests: ~% Sweep Matrix: ~A ~% array dim 1: ~A ~% Swept indices: ~A ~% basis: ~A"
513 m n indices (send self :basis))
514 (coerce (compound-data-seq (select m (+ 1 n) indices)) 'list))) ;; ERROR
516 (defmeth regression-model-proto :xtxinv ()
517 "Message args: ()
518 Returns ((X^T) X)^(-1) or ((X^T) W X)^(-1)."
519 (let ((indices (if (send self :intercept)
520 (cons 0 (1+ (send self :basis)))
521 (1+ (send self :basis)))))
522 (select (send self :sweep-matrix) indices indices)))
524 (defmeth regression-model-proto :coef-standard-errors ()
525 "Message args: ()
526 Returns estimated standard errors of coefficients. Entries beyond the
527 intercept correspond to entries in basis."
528 (let ((s (send self :sigma-hat)))
529 (if s (* (send self :sigma-hat) (sqrt (diagonalf (send self :xtxinv)))))))
531 (defmeth regression-model-proto :studentized-residuals ()
532 "Message args: ()
533 Computes the internally studentized residuals for included cases and externally studentized residuals for excluded cases."
534 (let ((res (send self :residuals))
535 (lev (send self :leverages))
536 (sig (send self :sigma-hat))
537 (inc (send self :included)))
538 (if-else inc
539 (/ res (* sig (sqrt (pmax .00001 (- 1 lev)))))
540 (/ res (* sig (sqrt (+ 1 lev)))))))
542 (defmeth regression-model-proto :externally-studentized-residuals ()
543 "Message args: ()
544 Computes the externally studentized residuals."
545 (let* ((res (send self :studentized-residuals))
546 (df (send self :df)))
547 (if-else (send self :included)
548 (* res (sqrt (/ (- df 1) (- df (^ res 2)))))
549 res)))
551 (defmeth regression-model-proto :cooks-distances ()
552 "Message args: ()
553 Computes Cook's distances."
554 (let ((lev (send self :leverages))
555 (res (/ (^ (send self :studentized-residuals) 2)
556 (send self :num-coefs))))
557 (if-else (send self :included) (* res (/ lev (- 1 lev) )) (* res lev))))
560 (defun plot-points (x y &rest args)
561 "need to fix."
562 (declare (ignore x y args))
563 (error "Graphics not implemented yet."))
565 ;; Can not plot points yet!!
566 (defmeth regression-model-proto :plot-residuals (&optional x-values)
567 "Message args: (&optional x-values)
568 Opens a window with a plot of the residuals. If X-VALUES are not supplied
569 the fitted values are used. The plot can be linked to other plots with the
570 link-views function. Returns a plot object."
571 (plot-points (if x-values x-values (send self :fit-values))
572 (send self :residuals)
573 :title "Residual Plot"
574 :point-labels (send self :case-labels)))
576 (defmeth regression-model-proto :plot-bayes-residuals
577 (&optional x-values)
578 "Message args: (&optional x-values)
580 Opens a window with a plot of the standardized residuals and two
581 standard error bars for the posterior distribution of the actual
582 deviations from the line. See Chaloner and Brant. If X-VALUES are not
583 supplied the fitted values are used. The plot can be linked to other
584 plots with the link-views function. Returns a plot object."
586 (let* ((r (/ (send self :residuals)
587 (send self :sigma-hat)))
588 (d (* 2 (sqrt (send self :leverages))))
589 (low (- r d))
590 (high (+ r d))
591 (x-values (if x-values x-values (send self :fit-values)))
592 (p (plot-points x-values r
593 :title "Bayes Residual Plot"
594 :point-labels (send self :case-labels))))
595 (map 'list #'(lambda (a b c d) (send p :plotline a b c d nil))
596 x-values low x-values high)
597 (send p :adjust-to-data)