1 ;;;; XLISP-STAT 2.1 Copyright (c) 1990, by Luke Tierney
2 ;;;; Additions to Xlisp 2.1, Copyright (c) 1989 by David Michael Betz
3 ;;;; You may give out copies of this software; for conditions see the file
4 ;;;; COPYING included with this distribution.
11 (in-package 'lisp-stat
)
13 (export '(nreg-model nreg-model-proto mean-function theta-hat epsilon
19 ;;;; Nonlinear Regression Model Prototype
23 (defproto nreg-model-proto
24 '(mean-function theta-hat epsilon count-limit verbose
)
26 regression-model-proto
)
28 (defun nreg-model (mean-function y theta
39 "Args: (mean-function y theta &key (epsilon .0001) (count-limit 20)
40 (print t) parameter-names response-name case-labels
41 weights included (vetbose print))
42 Fits nonlinear regression model with MEAN-FUNCTION and response Y using initial
43 parameter guess THETA. Returns model object."
44 (let ((m (send nreg-model-proto
:new
)))
45 (send m
:mean-function mean-function
)
47 (send m
:new-initial-guess theta
)
48 (send m
:epsilon epsilon
)
49 (send m
:count-limit count-limit
)
50 (send m
:parameter-names parameter-names
)
51 (send m
:response-name response-name
)
52 (send m
:case-labels case-labels
)
53 (send m
:weights weights
)
54 (send m
:included included
)
55 (send m
:verbose verbose
)
56 (if print
(send m
:display
))
59 (defmeth nreg-model-proto
:save
()
61 Returns an expression that will reconstruct the regression model."
62 `(nreg-model ',(send self
:mean-function
)
64 ',(send self
:coef-estimates
)
65 :epsilon
',(send self
:epsilon
)
66 :count-limit
',(send self
:count-limit
)
67 :predictor-names
',(send self
:predictor-names
)
68 :response-name
',(send self
:response-name
)
69 :case-labels
',(send self
:case-labels
)
70 :weights
',(send self
:weights
)
71 :included
',(send self
:included
)
72 :verbose
',(send self
:verbose
)))
78 (defmeth nreg-model-proto
:compute
()
80 Recomputes the estimates. For internal use by other messages"
81 (let* ((y (send self
:y
))
82 (weights (send self
:weights
))
83 (inc (if-else (send self
:included
) 1 0))
84 (w (if weights
(* inc weights
) inc
)))
85 (setf (slot-value 'theta-hat
)
86 (nlreg (send self
:mean-function
)
88 (slot-value 'theta-hat
)
90 (send self
:count-limit
)
92 (send self
:verbose
)))
94 (funcall (make-jacobian (slot-value 'mean-function
)
95 (length (slot-value 'theta-hat
)))
96 (slot-value 'theta-hat
)))
97 (setf (slot-value 'intercept
) nil
)
99 (let ((r (send self
:residuals
)))
100 (setf (slot-value 'residual-sum-of-squares
)
101 (sum (* inc r r
))))))
104 ;;; Slot Accessors and Mutators
107 (defmeth nreg-model-proto
:new-initial-guess
(guess)
108 "Message args: (guess)
109 Sets a new initial uess for parmeters."
110 (setf (slot-value 'theta-hat
) guess
)
111 (send self
:needs-computing t
))
113 (defmeth nreg-model-proto
:theta-hat
()
115 Returns current parameter estimate."
116 (if (send self
:needs-computing
) (send self
:compute
))
117 (coerce (slot-value 'theta-hat
) 'list
))
119 (defmeth nreg-model-proto
:mean-function
(&optional f
)
120 "Message args: (&optional f)
121 With no argument returns the mean function as supplied to m. With an
122 argument F sets the mean function of m to F and recomputes the
124 (when (and f
(functionp f
))
125 (setf (slot-value 'mean-function
) f
)
126 (send self
:needs-computing t
))
127 (slot-value 'mean-function
))
129 (defmeth nreg-model-proto
:epsilon
(&optional eps
)
130 "Message args: (&optional eps)
131 With no argument returns the tolerance as supplied to m. With an argument
132 EPS sets the tolerance of m to EPS and recomputes the estimates."
133 (when (and eps
(numberp eps
))
134 (setf (slot-value 'epsilon
) eps
)
135 (send self
:needs-computing t
))
136 (slot-value 'epsilon
))
138 (defmeth nreg-model-proto
:count-limit
(&optional count
)
139 "Message args: (&optional new-count)
140 With no argument returns the iteration count limit as supplied to m. With
141 an argument COUNT sets the limit to COUNT and recomputes the
143 (when (and count
(numberp count
))
144 (setf (slot-value 'count-limit
) count
)
145 (send self
:needs-computing t
))
146 (slot-value 'count-limit
))
148 (defmeth nreg-model-proto
:parameter-names
(&optional
(names nil set
))
149 "Method args: (&optional names)
150 Sets or returns parameter names."
151 (if set
(setf (slot-value 'predictor-names
) names
))
152 (let ((p-names (slot-value 'predictor-names
))
153 (p (length (slot-value 'theta-hat
))))
154 (if (not (and p-names
(= p
(length p-names
))))
155 (setf (slot-value 'predictor-names
)
156 (mapcar #'(lambda (a) (format nil
"Parameter ~a" a
))
158 (slot-value 'predictor-names
))
160 (defmeth nreg-model-proto
:verbose
(&optional
(val nil set
))
161 "Method args: (&optional val)
162 Sets or retrieves verbose setting. If T iteration info is printed during
164 (if set
(setf (slot-value 'verbose
) val
))
165 (slot-value 'verbose
))
168 ;;; Overrides for Linear Regression Methods
171 (defmeth nreg-model-proto
:x
()
173 Returns the Jacobian matrix at theta-hat."
176 (defmeth nreg-model-proto
:intercept
(&rest args
)
178 Always returns nil. (For compatibility with linear regression.)"
181 (defmeth nreg-model-proto
:fit-values
()
183 Returns the fitted values for the model."
184 (coerce (funcall (send self
:mean-function
) (send self
:theta-hat
))
187 (defmeth nreg-model-proto
:coef-estimates
(&optional guess
)
188 "Message args: (&optional guess)
189 With no argument returns the current parameter estimate. With an
190 argument GUESS takes it as a new initial guess and recomputes
192 (if guess
(send self
:new-initial-guess guess
))
193 (send self
:theta-hat
))
195 (defmeth nreg-model-proto
:predictor-names
() (send self
:parameter-names
))
199 ;;;; Linear Regression Coefficients
203 (defun regression-coefficients (x y
&key
(intercept T
) weights
)
204 "Args: (x y &key (intercept T) weights)
205 Returns the coefficients of the regression of the sequence Y on the columns of
207 (let* ((m (if weights
208 (make-sweep-matrix x y weights
)
209 (make-sweep-matrix x y
)))
210 (n (array-dimension x
1)))
211 (coerce (compound-data-seq
213 (select (car (sweep-operator m
(iseq 1 n
)))
216 (select (car (sweep-operator m
(iseq 0 n
)))
223 ;;;; Nonlinear Regression Functions
226 (defun nlreg1 (f j y initial-beta epsilon count-limit weights verbose
)
227 "Args: (mean-function jacobian y initial-beta
228 epsilon count-limit weights verbose)
229 MEAN-FUNCTION returns the mean response vector for a given parameter vector.
230 JACOBIAN returns the jacobian of MEAN-FUNCTION at a given parameter vector.
231 Y is the observed response vector. Returns the estimated parameter vector
232 obtained by a Gauss-Newton algorithm with backtracking that continues until
233 the COUNT-LIMIT is reached or no component of the parameter vector changes
234 by more than EPSILON."
235 (labels ((rss (beta) ; residual sum of squares
236 (let ((res (- y
(funcall f beta
))))
237 (sum (if weights
(* res res weights
) (* res res
)))))
238 (next-beta (beta delta rss
) ; next beta by backtracking
239 (do* ((lambda 1 (/ lambda
2))
240 (new-rss (rss (+ beta delta
))
241 (rss (+ beta
(* lambda delta
)))))
242 ((or (< new-rss rss
) (< lambda
.0001))
243 (if (>= lambda
.0001)
244 (+ beta
(* lambda delta
))
246 (do* ((delbeta (regression-coefficients
247 (funcall j initial-beta
)
248 (- y
(funcall f initial-beta
))
251 (regression-coefficients
253 (- y
(funcall f beta
))
256 (beta initial-beta
(next-beta beta delbeta rss
))
257 (rss (rss beta
) (rss beta
))
258 (count 0 (1+ count
)))
259 ((or (> count count-limit
) (> epsilon
(max (abs delbeta
))))
260 (if (and verbose
(> count count-limit
))
261 (format t
"Iteration limit exceeded.~%"))
263 (if verbose
(format t
"Residual sum of squares: ~10g~%" rss
)))))
265 (defun make-jacobian (f n
)
267 F is a function of an N-vector. Returns a function that approximates the
268 jacobian function iof F by a symmetric difference."
270 (del (* h
(column-list (identity-matrix n
)))))
272 (let ((b+ (mapcar #'(lambda (x) (+ b x
)) del
))
273 (b- (mapcar #'(lambda (x) (- b x
)) del
)))
274 (apply #'bind-columns
(/ (- (mapcar f b
+) (mapcar f b-
)) (* 2 h
)))))))
276 (defun nlreg (f y guess
&optional
277 (epsilon .0001) (count-limit 20) weights verbose
)
278 "Args: (mean-function y guess &optional
279 (epsilon .0001) (count-limit 20) weights verbose)
280 MEAN-FUNCTION returns the mean response vector for a given parameter vector.
281 Y is the observed response vector. Returns the estimated parameter vector
282 obtained by a Gauss-Newton algorithm that continues until the ITERATION-LIMIT
283 is reached or no component of the parameter vector changes by more than
284 EPSILON. The jacobian of MEAN-FUNCTION is approximated by a symmetric difference."
285 (nlreg1 f
(make-jacobian f
(length guess
)) y guess
286 epsilon count-limit weights verbose
))