blob 356391174d7f705825fc726129c844839cdbd023
1 ;;; -*- mode: lisp -*-
2 ;;;
3 ;;; Copyright (c) 2005--2007, by A.J. Rossini <blindglobe@gmail.com>
5 ;;; Since 1991, ANSI was finally finished. Modified to match ANSI
6 ;;; Common Lisp.
8 ;;;;
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 ;;;;
16 ;;;; Incorporates modifications suggested by Sandy Weisberg.
17 ;;;;
19 (in-package :cl-user)
21 (defpackage :lisp-stat-regression-linear
22 (:use :common-lisp
23 :lisp-stat-object-system
24 :lisp-stat-basics
25 :lisp-stat-compound-data
26 :lisp-stat-math
27 :lisp-stat-matrix
28 :lisp-stat-linalg
29 :lisp-stat-descriptive-statistics)
31 slot-value call-method call-next-method)
33 expt + - * / ** mod rem abs 1+ 1- log exp sqrt sin cos tan
34 asin acos atan sinh cosh tanh asinh acosh atanh float random
35 truncate floor ceiling round minusp zerop plusp evenp oddp
36 < <= = /= >= > ;; complex
37 conjugate realpart imagpart phase
38 min max logand logior logxor lognot ffloor fceiling
39 ftruncate fround signum cis)
40 (:export regression-model regression-model-proto x y intercept sweep-matrix
41 basis weights included total-sum-of-squares residual-sum-of-squares
42 predictor-names response-name case-labels))
44 (in-package :lisp-stat-regression-linear)
46 ;;; Regresion Model Prototype
49 ;; The general strategy behind the fitting of models using prototypes
50 ;; is that we need to think about want the actual fits are, and then
51 ;; the fits can be used to recompute as components are changes. One
52 ;; catch here is that we'd like some notion of trace-ability, in
53 ;; particular, there is not necessarily a fixed way to take care of the
54 ;; audit trail. save-nd-die might be a means of recording the final
55 ;; approach, but we are challenged by the problem of using advice and
56 ;; other such features to capture stages and steps that are considered
57 ;; along the goals of estimating a model.
59 (defvar regression-model-proto nil
60 "Prototype for all regression model instances.")
61 (defproto regression-model-proto
62 '(x y intercept sweep-matrix basis weights
63 included
64 total-sum-of-squares
65 residual-sum-of-squares
66 predictor-names
67 response-name
68 case-labels
69 doc)
71 *object*
72 "Normal Linear Regression Model")
74 (defun regression-model (x y &key
75 (intercept T)
76 (print T)
77 (weights nil)
78 (included (repeat t (length y)))
79 predictor-names
80 response-name
81 case-labels
82 (doc "Undocumented Regression Model Instance")
83 (debug T))
84 "Args: (x y &key (intercept T) (print T) (weights nil)
85 included predictor-names response-name case-labels)
86 X - list of independent variables or X matrix
87 Y - dependent variable.
88 INTERCEPT - T to include (default), NIL for no intercept
89 PRINT - if not NIL print summary information
90 WEIGHTS - if supplied should be the same length as Y; error
91 variances are
92 assumed to be inversely proportional to WEIGHTS
93 PREDICTOR-NAMES, RESPONSE-NAME, CASE-LABELS
94 - sequences of strings or symbols.
95 INCLUDED - if supplied should be the same length as Y, with
96 elements nil to skip a in computing estimates (but not
97 in residual analysis).
98 Returns a regression model object. To examine the model further assign the
99 result to a variable and send it messages.
100 Example (data are in file absorbtion.lsp in the sample data directory):
101 (def m (regression-model (list iron aluminum) absorbtion))
102 (send m :help) (send m :plot-residuals)"
103 (let ((x (cond
104 ((matrixp x) x)
105 ((typep x 'vector) (list x))
106 ((and (consp x)
107 (numberp (car x))) (list x))
108 (t x)))
109 (m (send regression-model-proto :new)))
110 (format t "~%")
111 (send m :doc doc)
112 (send m :x (if (matrixp x) x (apply #'bind-columns x)))
113 (send m :y y)
114 (send m :intercept intercept)
115 (send m :weights weights)
116 (send m :included included)
117 (send m :predictor-names predictor-names)
118 (send m :response-name response-name)
119 (send m :case-labels case-labels)
120 (if debug
121 (progn
122 (format t "~%")
123 (format t "~S~%" (send m :doc))
124 (format t "X: ~S~%" (send m :x))
125 (format t "Y: ~S~%" (send m :y))))
126 (if print (send m :display))
129 (defmeth regression-model-proto :isnew ()
130 (send self :needs-computing t))
132 (defmeth regression-model-proto :save ()
133 "Message args: ()
134 Returns an expression that will reconstruct the regression model."
135 `(regression-model ',(send self :x)
136 ',(send self :y)
137 :intercept ',(send self :intercept)
138 :weights ',(send self :weights)
139 :included ',(send self :included)
140 :predictor-names ',(send self :predictor-names)
141 :response-name ',(send self :response-name)
142 :case-labels ',(send self :case-labels)))
144 ;;; Computing and Display Methods
146 (defmeth regression-model-proto :compute ()
147 "Message args: ()
148 Recomputes the estimates. For internal use by other messages"
149 (let* ((included (if-else (send self :included) 1 0))
150 (x (send self :x))
151 (y (send self :y))
152 (intercept (send self :intercept))
153 (weights (send self :weights))
154 (w (if weights (* included weights) included))
155 (m (make-sweep-matrix x y w)) ;;; ERROR HERE
156 (n (array-dimension x 1))
157 (p (- (array-dimension m 0) 1))
158 (tss (aref m p p))
159 (tol (* 0.001 (reduce #'* (mapcar #'standard-deviation (column-list x)))))
160 ;; (tol (* 0.001 (apply #'* (mapcar #'standard-deviation (column-list x)))))
161 (sweep-result
162 (if intercept
163 (sweep-operator m (iseq 1 n) tol)
164 (sweep-operator m (iseq 0 n) (cons 0.0 tol)))))
165 (format t
166 "~%REMOVEME: regr-mdl-prto :compute =~A~%~A~%~A~%~A~%~A~%"
167 sweep-result x y m tss)
168 (setf (slot-value 'sweep-matrix) (first sweep-result))
169 (setf (slot-value 'total-sum-of-squares) tss)
170 (setf (slot-value 'residual-sum-of-squares)
171 (aref (first sweep-result) p p))
172 (setf (slot-value 'basis)
173 (let ((b (remove 0 (second sweep-result))))
174 (if b (- (reduce #'- (reverse b)) 1)
175 (error "no columns could be swept"))))))
177 (defmeth regression-model-proto :needs-computing (&optional set)
178 "Message args: ( &optional set )
180 If value given, sets the flag for whether (re)computation is needed to
181 update the model fits."
182 (send self :nop)
183 (if set (setf (slot-value 'sweep-matrix) nil))
184 (null (slot-value 'sweep-matrix)))
186 (defmeth regression-model-proto :display ()
187 "Message args: ()
189 Prints the least squares regression summary. Variables not used in the fit
190 are marked as aliased."
191 (let ((coefs (coerce (send self :coef-estimates) 'list))
192 (se-s (send self :coef-standard-errors))
193 (x (send self :x))
194 (p-names (send self :predictor-names)))
195 (if (send self :weights)
196 (format t "~%Weighted Least Squares Estimates:~2%")
197 (format t "~%Least Squares Estimates:~2%"))
198 (when (send self :intercept)
199 (format t "Constant ~10f ~A~%"
200 (car coefs) (list (car se-s)))
201 (setf coefs (cdr coefs))
202 (setf se-s (cdr se-s)))
203 (dotimes (i (array-dimension x 1))
204 (cond
205 ((member i (send self :basis))
206 (format t "~22a ~10f ~A~%"
207 (select p-names i) (car coefs) (list (car se-s)))
208 (setf coefs (cdr coefs) se-s (cdr se-s)))
209 (t (format t "~22a aliased~%" (select p-names i)))))
210 (format t "~%")
211 (format t "R Squared: ~10f~%" (send self :r-squared))
212 (format t "Sigma hat: ~10f~%" (send self :sigma-hat))
213 (format t "Number of cases: ~10d~%" (send self :num-cases))
214 (if (/= (send self :num-cases) (send self :num-included))
215 (format t "Number of cases used: ~10d~%" (send self :num-included)))
216 (format t "Degrees of freedom: ~10d~%" (send self :df))
217 (format t "~%")))
219 ;;; Slot accessors and mutators
221 (defmeth regression-model-proto :doc (&optional new-doc append)
222 "Message args: (&optional new-doc)
224 Returns the DOC-STRING as supplied to m.
225 Additionally, with an argument NEW-DOC, sets the DOC-STRING to
226 NEW-DOC. In this setting, when APPEND is T, append NEW-DOC to DOC
227 rather than doing replacement."
228 (send self :nop)
229 (when (and new-doc (stringp new-doc))
230 (setf (slot-value 'doc)
231 (if append
232 (concatenate 'string
233 (slot-value 'doc)
234 new-doc)
235 new-doc)))
236 (slot-value 'doc))
239 (defmeth regression-model-proto :x (&optional new-x)
240 "Message args: (&optional new-x)
242 With no argument returns the x matrix as supplied to m. With an
243 argument, NEW-X sets the x matrix to NEW-X and recomputes the
244 estimates."
245 (when (and new-x (matrixp new-x))
246 (setf (slot-value 'x) new-x)
247 (send self :needs-computing t))
248 (slot-value 'x))
250 (defmeth regression-model-proto :y (&optional new-y)
251 "Message args: (&optional new-y)
253 With no argument returns the y sequence as supplied to m. With an
254 argument, NEW-Y sets the y sequence to NEW-Y and recomputes the
255 estimates."
256 (when (and new-y
257 (or (matrixp new-y)
258 (typep new-y 'sequence)))
259 (setf (slot-value 'y) new-y)
260 (send self :needs-computing t))
261 (slot-value 'y))
263 (defmeth regression-model-proto :intercept (&optional (val nil set))
264 "Message args: (&optional new-intercept)
266 With no argument returns T if the model includes an intercept term,
267 nil if not. With an argument NEW-INTERCEPT the model is changed to
268 include or exclude an intercept, according to the value of
269 NEW-INTERCEPT."
270 (when set
271 (setf (slot-value 'intercept) val)
272 (send self :needs-computing t))
273 (slot-value 'intercept))
275 (defmeth regression-model-proto :weights (&optional (new-w nil set))
276 "Message args: (&optional new-w)
278 With no argument returns the weight sequence as supplied to m; NIL
279 means an unweighted model. NEW-W sets the weights sequence to NEW-W
280 and recomputes the estimates."
281 (when set
282 (setf (slot-value 'weights) new-w)
283 (send self :needs-computing t))
284 (slot-value 'weights))
286 (defmeth regression-model-proto :total-sum-of-squares ()
287 "Message args: ()
289 Returns the total sum of squares around the mean."
290 (if (send self :needs-computing) (send self :compute))
291 (slot-value 'total-sum-of-squares))
293 (defmeth regression-model-proto :residual-sum-of-squares ()
294 "Message args: ()
296 Returns the residual sum of squares for the model."
297 (if (send self :needs-computing) (send self :compute))
298 (slot-value 'residual-sum-of-squares))
300 (defmeth regression-model-proto :basis ()
301 "Message args: ()
303 Returns the indices of the variables used in fitting the model, in a
304 sequence."
305 (if (send self :needs-computing)
306 (send self :compute))
307 (if (typep (slot-value 'basis) 'sequence)
308 (slot-value 'basis)
309 (list (slot-value 'basis))))
312 (defmeth regression-model-proto :sweep-matrix ()
313 "Message args: ()
315 Returns the swept sweep matrix. For internal use"
316 (if (send self :needs-computing)
317 (send self :compute))
318 (slot-value 'sweep-matrix))
320 (defmeth regression-model-proto :included (&optional new-included)
321 "Message args: (&optional new-included)
323 With no argument, NIL means a case is not used in calculating
324 estimates, and non-nil means it is used. NEW-INCLUDED is a sequence
325 of length of y of nil and t to select cases. Estimates are
326 recomputed."
327 (when (and new-included
328 (= (length new-included) (send self :num-cases)))
329 (setf (slot-value 'included) (copy-seq new-included))
330 (send self :needs-computing t))
331 (if (slot-value 'included)
332 (slot-value 'included)
333 (repeat t (send self :num-cases))))
335 (defmeth regression-model-proto :predictor-names (&optional (names nil set))
336 "Message args: (&optional (names nil set))
338 With no argument returns the predictor names. NAMES sets the names."
339 (if set (setf (slot-value 'predictor-names) (mapcar #'string names)))
340 (let ((p (array-dimension (send self :x) 1))
341 (p-names (slot-value 'predictor-names)))
342 (if (not (and p-names (= (length p-names) p)))
343 (setf (slot-value 'predictor-names)
344 (mapcar #'(lambda (a) (format nil "Variable ~a" a))
345 (iseq 0 (- p 1))))))
346 (slot-value 'predictor-names))
348 (defmeth regression-model-proto :response-name (&optional (name "Y" set))
349 "Message args: (&optional name)
351 With no argument returns the response name. NAME sets the name."
352 (send self :nop)
353 (if set (setf (slot-value 'response-name) (if name (string name) "Y")))
354 (slot-value 'response-name))
356 (defmeth regression-model-proto :case-labels (&optional (labels nil set))
357 "Message args: (&optional labels)
358 With no argument returns the case-labels. LABELS sets the labels."
359 (if set (setf (slot-value 'case-labels)
360 (if labels
361 (mapcar #'string labels)
362 (mapcar #'(lambda (x) (format nil "~d" x))
363 (iseq 0 (- (send self :num-cases) 1))))))
364 (slot-value 'case-labels))
367 ;;; Other Methods
368 ;;; None of these methods access any slots directly.
371 (defmeth regression-model-proto :num-cases ()
372 "Message args: ()
373 Returns the number of cases in the model."
374 (length (send self :y)))
376 (defmeth regression-model-proto :num-included ()
377 "Message args: ()
378 Returns the number of cases used in the computations."
379 (sum (if-else (send self :included) 1 0)))
381 (defmeth regression-model-proto :num-coefs ()
382 "Message args: ()
383 Returns the number of coefficients in the fit model (including the
384 intercept if the model includes one)."
385 (if (send self :intercept)
386 (+ 1 (length (send self :basis)))
387 (length (send self :basis))))
389 (defmeth regression-model-proto :df ()
390 "Message args: ()
391 Returns the number of degrees of freedom in the model."
392 (- (send self :num-included) (send self :num-coefs)))
394 (defmeth regression-model-proto :x-matrix ()
395 "Message args: ()
396 Returns the X matrix for the model, including a column of 1's, if
397 appropriate. Columns of X matrix correspond to entries in basis."
398 (let ((m (select (send self :x)
399 (iseq 0 (- (send self :num-cases) 1))
400 (send self :basis))))
401 (if (send self :intercept)
402 (bind-columns (repeat 1 (send self :num-cases)) m)
403 m)))
405 (defmeth regression-model-proto :leverages ()
406 "Message args: ()
407 Returns the diagonal elements of the hat matrix."
408 (let* ((weights (send self :weights))
409 (x (send self :x-matrix))
410 (raw-levs
411 (matmult (* (matmult x (send self :xtxinv)) x)
412 (repeat 1 (send self :num-coefs)))))
413 (if weights (* weights raw-levs) raw-levs)))
415 (defmeth regression-model-proto :fit-values ()
416 "Message args: ()
417 Returns the fitted values for the model."
418 (matmult (send self :x-matrix) (send self :coef-estimates)))
420 (defmeth regression-model-proto :raw-residuals ()
421 "Message args: ()
422 Returns the raw residuals for a model."
423 (- (send self :y) (send self :fit-values)))
425 (defmeth regression-model-proto :residuals ()
426 "Message args: ()
427 Returns the raw residuals for a model without weights. If the model
428 includes weights the raw residuals times the square roots of the weights
429 are returned."
430 (let ((raw-residuals (send self :raw-residuals))
431 (weights (send self :weights)))
432 (if weights (* (sqrt weights) raw-residuals) raw-residuals)))
434 (defmeth regression-model-proto :sum-of-squares ()
435 "Message args: ()
436 Returns the error sum of squares for the model."
437 (send self :residual-sum-of-squares))
439 (defmeth regression-model-proto :sigma-hat ()
440 "Message args: ()
441 Returns the estimated standard deviation of the deviations about the
442 regression line."
443 (let ((ss (send self :sum-of-squares))
444 (df (send self :df)))
445 (if (/= df 0) (sqrt (/ ss df)))))
447 ;; for models without an intercept the 'usual' formula for R^2 can give
448 ;; negative results; hence the max.
449 (defmeth regression-model-proto :r-squared ()
450 "Message args: ()
451 Returns the sample squared multiple correlation coefficient, R squared, for
452 the regression."
453 (max (- 1 (/ (send self :sum-of-squares) (send self :total-sum-of-squares)))
456 (defmeth regression-model-proto :coef-estimates ()
457 "Message args: ()
459 Returns the OLS (ordinary least squares) estimates of the regression
460 coefficients. Entries beyond the intercept correspond to entries in
461 basis."
462 (let ((n (array-dimension (send self :x) 1))
463 (indices (flatten-list
464 (if (send self :intercept)
465 (list 0 (+ 1 (send self :basis))) ;; was cons -- why?
466 (list (+ 1 (send self :basis))))))
467 (m (send self :sweep-matrix)))
468 (format t "~%REMOVEME2: Coef-ests: ~A ~% ~A ~% ~A ~% ~A"
469 m n indices (send self :basis))
470 (coerce (compound-data-seq (select m (+ 1 n) indices)) 'list)))
472 (defmeth regression-model-proto :xtxinv ()
473 "Message args: ()
474 Returns ((X^T) X)^(-1) or ((X^T) W X)^(-1)."
475 (let ((indices (if (send self :intercept)
476 (cons 0 (1+ (send self :basis)))
477 (1+ (send self :basis)))))
478 (select (send self :sweep-matrix) indices indices)))
480 (defmeth regression-model-proto :coef-standard-errors ()
481 "Message args: ()
482 Returns estimated standard errors of coefficients. Entries beyond the
483 intercept correspond to entries in basis."
484 (let ((s (send self :sigma-hat)))
485 (if s (* (send self :sigma-hat) (sqrt (diagonal (send self :xtxinv)))))))
487 (defmeth regression-model-proto :studentized-residuals ()
488 "Message args: ()
489 Computes the internally studentized residuals for included cases and externally studentized residuals for excluded cases."
490 (let ((res (send self :residuals))
491 (lev (send self :leverages))
492 (sig (send self :sigma-hat))
493 (inc (send self :included)))
494 (if-else inc
495 (/ res (* sig (sqrt (pmax .00001 (- 1 lev)))))
496 (/ res (* sig (sqrt (+ 1 lev)))))))
498 (defmeth regression-model-proto :externally-studentized-residuals ()
499 "Message args: ()
500 Computes the externally studentized residuals."
501 (let* ((res (send self :studentized-residuals))
502 (df (send self :df)))
503 (if-else (send self :included)
504 (* res (sqrt (/ (- df 1) (- df (^ res 2)))))
505 res)))
507 (defmeth regression-model-proto :cooks-distances ()
508 "Message args: ()
509 Computes Cook's distances."
510 (let ((lev (send self :leverages))
511 (res (/ (^ (send self :studentized-residuals) 2)
512 (send self :num-coefs))))
513 (if-else (send self :included) (* res (/ lev (- 1 lev) )) (* res lev))))
516 (defun plot-points (x y &rest args)
517 "FIXME!!"
518 (declare (ignore x y args))
519 (error "Graphics not implemented yet."))
521 ;; Can not plot points yet!!
522 (defmeth regression-model-proto :plot-residuals (&optional x-values)
523 "Message args: (&optional x-values)
524 Opens a window with a plot of the residuals. If X-VALUES are not supplied
525 the fitted values are used. The plot can be linked to other plots with the
526 link-views function. Returns a plot object."
527 (plot-points (if x-values x-values (send self :fit-values))
528 (send self :residuals)
529 :title "Residual Plot"
530 :point-labels (send self :case-labels)))
532 (defmeth regression-model-proto :plot-bayes-residuals
533 (&optional x-values)
534 "Message args: (&optional x-values)
536 Opens a window with a plot of the standardized residuals and two
537 standard error bars for the posterior distribution of the actual
538 deviations from the line. See Chaloner and Brant. If X-VALUES are not
539 supplied the fitted values are used. The plot can be linked to other
540 plots with the link-views function. Returns a plot object."
542 (let* ((r (/ (send self :residuals)
543 (send self :sigma-hat)))
544 (d (* 2 (sqrt (send self :leverages))))
545 (low (- r d))
546 (high (+ r d))
547 (x-values (if x-values x-values (send self :fit-values)))
548 (p (plot-points x-values r
549 :title "Bayes Residual Plot"
550 :point-labels (send self :case-labels))))
551 (map 'list #'(lambda (a b c d) (send p :plotline a b c d nil))
552 x-values low x-values high)
{"ft_lang_label":"__label__en","ft_lang_prob":0.56955314,"math_prob":0.9248894,"size":18493,"snap":"2019-51-2020-05","text_gpt3_token_len":5469,"char_repetition_ratio":0.20715019,"word_repetition_ratio":0.039644565,"special_character_ratio":0.3447791,"punctuation_ratio":0.11690595,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9913375,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-12-13T13:35:05Z\",\"WARC-Record-ID\":\"<urn:uuid:7daf306c-1947-4e75-8b76-950f4bb73d05>\",\"Content-Length\":\"165111\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:dbd2501d-d551-40aa-b91e-dc54e1b9ec67>\",\"WARC-Concurrent-To\":\"<urn:uuid:1c38888b-96e5-431d-82ec-e8416e39b208>\",\"WARC-IP-Address\":\"195.113.20.142\",\"WARC-Target-URI\":\"https://repo.or.cz/CommonLispStat.git/blob/d61a1ed16197dc232c74d32f9da1e995dd0510db:/regression.lsp\",\"WARC-Payload-Digest\":\"sha1:MG2PXP5U4IS6PVCXQLFY6ALQQVMFP3NF\",\"WARC-Block-Digest\":\"sha1:IVZT342GILKA37VQSK2L4SCMB5CZWT7C\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-51/CC-MAIN-2019-51_segments_1575540555616.2_warc_CC-MAIN-20191213122716-20191213150716-00228.warc.gz\"}"}