-
Notifications
You must be signed in to change notification settings - Fork 1
/
pffr.R
930 lines (860 loc) · 36.8 KB
/
pffr.R
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
#' Penalized flexible functional regression
#'
#' Implements additive regression for functional and scalar covariates and
#' functional responses. This function is a wrapper for \code{mgcv}'s
#' \code{\link[mgcv]{gam}} and its siblings to fit models of the general form
#' \cr \eqn{E(Y_i(t)) = g(\mu(t) + \int X_i(s)\beta(s,t)ds + f(z_{1i}, t) +
#' f(z_{2i}) + z_{3i} \beta_3(t) + \dots )}\cr with a functional (but not
#' necessarily continuous) response \eqn{Y(t)}, response function \eqn{g},
#' (optional) smooth intercept \eqn{\mu(t)}, (multiple) functional covariates
#' \eqn{X(t)} and scalar covariates \eqn{z_1}, \eqn{z_2}, etc.
#'
#' @section Details: The routine can estimate \enumerate{ \item linear
#' functional effects of scalar (numeric or factor) covariates that vary
#' smoothly over \eqn{t} (e.g. \eqn{z_{1i} \beta_1(t)}, specified as
#' \code{~z1}), \item nonlinear, and possibly multivariate functional effects
#' of (one or multiple) scalar covariates \eqn{z} that vary smoothly over the
#' index \eqn{t} of \eqn{Y(t)} (e.g. \eqn{f(z_{2i}, t)}, specified in the
#' \code{formula} simply as \code{~s(z2)}) \item (nonlinear) effects of scalar
#' covariates that are constant over \eqn{t} (e.g. \eqn{f(z_{3i})}, specified
#' as \code{~c(s(z3))}, or \eqn{\beta_3 z_{3i}}, specified as \code{~c(z3)}),
#' \item function-on-function regression terms (e.g. \eqn{\int
#' X_i(s)\beta(s,t)ds}, specified as \code{~ff(X, yindex=t, xindex=s)}, see
#' \code{\link{ff}}). Terms given by \code{\link{sff}} and \code{\link{ffpc}}
#' provide nonlinear and FPC-based effects of functional covariates,
#' respectively. \item concurrent effects of functional covariates \code{X}
#' measured on the same grid as the response are specified as follows:
#' \code{~s(x)} for a smooth, index-varying effect \eqn{f(X(t),t)}, \code{~x}
#' for a linear index-varying effect \eqn{X(t)\beta(t)}, \code{~c(s(x))} for a
#' constant nonlinear effect \eqn{f(X(t))}, \code{~c(x)} for a constant linear
#' effect \eqn{X(t)\beta}. \item Smooth functional random intercepts
#' \eqn{b_{0g(i)}(t)} for a grouping variable \code{g} with levels \eqn{g(i)}
#' can be specified via \code{~s(g, bs="re")}), functional random slopes
#' \eqn{u_i b_{1g(i)}(t)} in a numeric variable \code{u} via \code{~s(g, u,
#' bs="re")}). Scheipl, Staicu, Greven (2013) contains code examples for
#' modeling correlated functional random intercepts using
#' \code{\link[mgcv]{mrf}}-terms. } Use the \code{c()}-notation to denote
#' model terms that are constant over the index of the functional response.\cr
#'
#' Internally, univariate smooth terms without a \code{c()}-wrapper are
#' expanded into bivariate smooth terms in the original covariate and the
#' index of the functional response. Bivariate smooth terms (\code{s(), te()}
#' or \code{t2()}) without a \code{c()}-wrapper are expanded into trivariate
#' smooth terms in the original covariates and the index of the functional
#' response. Linear terms for scalar covariates or categorical covariates are
#' expanded into varying coefficient terms, varying smoothly over the index of
#' the functional response. For factor variables, a separate smooth function
#' with its own smoothing parameter is estimated for each level of the
#' factor.\cr \cr The marginal spline basis used for the index of the the
#' functional response is specified via the \emph{global} argument
#' \code{bs.yindex}. If necessary, this can be overriden for any specific term
#' by supplying a \code{bs.yindex}-argument to that term in the formula, e.g.
#' \code{~s(x, bs.yindex=list(bs="tp", k=7))} would yield a tensor product
#' spline over \code{x} and the index of the response in which the marginal
#' basis for the index of the response are 7 cubic thin-plate spline functions
#' (overriding the global default for the basis and penalty on the index of
#' the response given by the \emph{global} \code{bs.yindex}-argument).\cr Use
#' \code{~-1 + c(1) + ...} to specify a model with only a constant and no
#' functional intercept. \cr
#'
#' The functional covariates have to be supplied as a \eqn{n} by <no. of
#' evaluations> matrices, i.e. each row is one functional observation. For
#' data on a regular grid, the functional response is supplied in the same
#' format, i.e. as a matrix-valued entry in \code{data}, which can contain
#' missing values.\cr
#'
#' If the functional responses are \emph{sparse or irregular} (i.e., not
#' evaluated on the same evaluation points across all observations), the
#' \code{ydata}-argument can be used to specify the responses: \code{ydata}
#' must be a \code{data.frame} with 3 columns called \code{'.obs', '.index',
#' '.value'} which specify which curve the point belongs to
#' (\code{'.obs'}=\eqn{i}), at which \eqn{t} it was observed
#' (\code{'.index'}=\eqn{t}), and the observed value
#' (\code{'.value'}=\eqn{Y_i(t)}). Note that the vector of unique sorted
#' entries in \code{ydata$.obs} must be equal to \code{rownames(data)} to
#' ensure the correct association of entries in \code{ydata} to the
#' corresponding rows of \code{data}. For both regular and irregular
#' functional responses, the model is then fitted with the data in long
#' format, i.e., for data on a grid the rows of the matrix of the functional
#' response evaluations \eqn{Y_i(t)} are stacked into one long vector and the
#' covariates are expanded/repeated correspondingly. This means the models get
#' quite big fairly fast, since the effective number of rows in the design
#' matrix is number of observations times number of evaluations of \eqn{Y(t)}
#' per observation.\cr
#'
#' Note that \code{pffr} does not use \code{mgcv}'s default identifiability
#' constraints (i.e., \eqn{\sum_{i,t} \hat f(z_i, x_i, t) = 0} or
#' \eqn{\sum_{i,t} \hat f(x_i, t) = 0}) for tensor product terms whose
#' marginals include the index \eqn{t} of the functional response. Instead,
#' \eqn{\sum_i \hat f(z_i, x_i, t) = 0} for all \eqn{t} is enforced, so that
#' effects varying over \eqn{t} can be interpreted as local deviations from
#' the global functional intercept. This is achieved by using
#' \code{\link[mgcv]{ti}}-terms with a suitably modified \code{mc}-argument.
#' Note that this is not possible if \code{algorithm='gamm4'} since only
#' \code{t2}-type terms can then be used and these modified constraints are
#' not available for \code{t2}. We recommend using centered scalar covariates
#' for terms like \eqn{z \beta(t)} (\code{~z}) and centered functional
#' covariates with \eqn{\sum_i X_i(t) = 0} for all \eqn{t} in \code{ff}-terms
#' so that the global functional intercept can be interpreted as the global
#' mean function.
#'
#' The \code{family}-argument can be used to specify all of the response
#' distributions and link functions described in
#' \code{\link[mgcv]{family.mgcv}}. Note that \code{family = "gaulss"} is
#' treated in a special way: Users can supply the formula for the variance by
#' supplying a special argument \code{varformula}, but this is not modified in
#' the way that the \code{formula}-argument is but handed over to the fitter
#' directly, so this is for expert use only. If \code{varformula} is not
#' given, \code{pffr} will use the parameters from argument \code{bs.int} to
#' define a spline basis along the index of the response, i.e., a smooth
#' variance function over $t$ for responses $Y(t)$.
#'
#' @param formula a formula with special terms as for \code{\link[mgcv]{gam}},
#' with additional special terms \code{\link{ff}(), \link{sff}(),
#' \link{ffpc}(), \link{pcre}()} and \code{c()}.
#' @param yind a vector with length equal to the number of columns of the matrix
#' of functional responses giving the vector of evaluation points \eqn{(t_1,
#' \dots ,t_{G})}. If not supplied, \code{yind} is set to
#' \code{1:ncol(<response>)}.
#' @param algorithm the name of the function used to estimate the model.
#' Defaults to \code{\link[mgcv]{gam}} if the matrix of functional responses
#' has less than \code{2e5} data points and to \code{\link[mgcv]{bam}} if not.
#' \code{'\link[mgcv]{gamm}'}, \code{'\link[gamm4]{gamm4}'} and
#' \code{'\link[mgcv]{jagam}'} are valid options as well. See Details for
#' \code{'\link[gamm4]{gamm4}'} and \code{'\link[mgcv]{jagam}'}.
#' @param data an (optional) \code{data.frame} containing the data. Can also be
#' a named list for regular data. Functional covariates have to be supplied as
#' <no. of observations> by <no. of evaluations> matrices, i.e. each row is
#' one functional observation.
#' @param ydata an (optional) \code{data.frame} supplying functional responses
#' that are not observed on a regular grid. See Details.
#' @param method Defaults to \code{"REML"}-estimation, including of unknown
#' scale. If \code{algorithm="bam"}, the default is switched to
#' \code{"fREML"}. See \code{\link[mgcv]{gam}} and \code{\link[mgcv]{bam}} for
#' details.
#' @param bs.yindex a named (!) list giving the parameters for spline bases on
#' the index of the functional response. Defaults to \code{list(bs="ps", k=5,
#' m=c(2, 1))}, i.e. 5 cubic B-splines bases with first order difference
#' penalty.
#' @param bs.int a named (!) list giving the parameters for the spline basis for
#' the global functional intercept. Defaults to \code{list(bs="ps", k=20,
#' m=c(2, 1))}, i.e. 20 cubic B-splines bases with first order difference
#' penalty.
#' @param tensortype which typ of tensor product splines to use. One of
#' "\code{\link[mgcv]{ti}}" or "\code{\link[mgcv]{t2}}", defaults to
#' \code{ti}. \code{t2}-type terms do not enforce the more suitable special
#' constraints for functional regression, see Details.
#' @param ... additional arguments that are valid for \code{\link[mgcv]{gam}},
#' \code{\link[mgcv]{bam}}, \code{'\link[gamm4]{gamm4}'} or
#' \code{'\link[mgcv]{jagam}'}. \code{subset} is not implemented.
#' @return A fitted \code{pffr}-object, which is a
#' \code{\link[mgcv]{gam}}-object with some additional information in an
#' \code{pffr}-entry. If \code{algorithm} is \code{"gamm"} or \code{"gamm4"},
#' only the \code{$gam} part of the returned list is modified in this way.\cr
#' Available methods/functions to postprocess fitted models:
#' \code{\link{summary.pffr}}, \code{\link{plot.pffr}},
#' \code{\link{coef.pffr}}, \code{\link{fitted.pffr}},
#' \code{\link{residuals.pffr}}, \code{\link{predict.pffr}},
#' \code{\link{model.matrix.pffr}}, \code{\link{qq.pffr}},
#' \code{\link{pffr.check}}.\cr If \code{algorithm} is \code{"jagam"}, only
#' the location of the model file and the usual
#' \code{\link[mgcv]{jagam}}-object are returned, you have to run the sampler
#' yourself.\cr
#' @author Fabian Scheipl, Sonja Greven
#' @seealso \code{\link[mgcv]{smooth.terms}} for details of \code{mgcv} syntax
#' and available spline bases and penalties.
#' @references Ivanescu, A., Staicu, A.-M., Scheipl, F. and Greven, S. (2015).
#' Penalized function-on-function regression. Computational Statistics,
#' 30(2):539--568. \url{https://biostats.bepress.com/jhubiostat/paper254/}
#'
#' Scheipl, F., Staicu, A.-M. and Greven, S. (2015). Functional Additive Mixed
#' Models. Journal of Computational & Graphical Statistics, 24(2): 477--501.
#' \url{ https://arxiv.org/abs/1207.5947}
#'
#' F. Scheipl, J. Gertheiss, S. Greven (2016): Generalized Functional Additive Mixed Models,
#' Electronic Journal of Statistics, 10(1), 1455--1492.
#' \url{https://projecteuclid.org/journals/electronic-journal-of-statistics/volume-10/issue-1/Generalized-functional-additive-mixed-models/10.1214/16-EJS1145.full}
#' @export
#' @importFrom mgcv ti jagam gam gam.fit bam gamm
#' @importFrom gamm4 gamm4
#' @importFrom lme4 lmer
#' @examples
#' ###############################################################################
#' # univariate model:
#' # Y(t) = f(t) + \int X1(s)\beta(s,t)ds + eps
#' set.seed(2121)
#' data1 <- pffrSim(scenario="ff", n=40)
#' t <- attr(data1, "yindex")
#' s <- attr(data1, "xindex")
#' m1 <- pffr(Y ~ ff(X1, xind=s), yind=t, data=data1)
#' summary(m1)
#' plot(m1, pages=1)
#'
#' \dontrun{
#' ###############################################################################
#' # multivariate model:
#' # E(Y(t)) = \beta_0(t) + \int X1(s)\beta_1(s,t)ds + xlin \beta_3(t) +
#' # f_1(xte1, xte2) + f_2(xsmoo, t) + \beta_4 xconst
#' data2 <- pffrSim(scenario="all", n=200)
#' t <- attr(data2, "yindex")
#' s <- attr(data2, "xindex")
#' m2 <- pffr(Y ~ ff(X1, xind=s) + #linear function-on-function
#' xlin + #varying coefficient term
#' c(te(xte1, xte2)) + #bivariate smooth term in xte1 & xte2, const. over Y-index
#' s(xsmoo) + #smooth effect of xsmoo varying over Y-index
#' c(xconst), # linear effect of xconst constant over Y-index
#' yind=t,
#' data=data2)
#' summary(m2)
#' plot(m2)
#' str(coef(m2))
#' # convenience functions:
#' preddata <- pffrSim(scenario="all", n=20)
#' str(predict(m2, newdata=preddata))
#' str(predict(m2, type="terms"))
#' cm2 <- coef(m2)
#' cm2$pterms
#' str(cm2$smterms, 2)
#' str(cm2$smterms[["s(xsmoo)"]]$coef)
#'
#' #############################################################################
#' # sparse data (80% missing on a regular grid):
#' set.seed(88182004)
#' data3 <- pffrSim(scenario=c("int", "smoo"), n=100, propmissing=0.8)
#' t <- attr(data3, "yindex")
#' m3.sparse <- pffr(Y ~ s(xsmoo), data=data3$data, ydata=data3$ydata, yind=t)
#' summary(m3.sparse)
#' plot(m3.sparse,pages=1)
#' }
pffr <- function(
formula,
yind,
data=NULL,
ydata=NULL,
algorithm = NA,
method="REML",
tensortype = c("ti", "t2"),
bs.yindex = list(bs="ps", k=5, m=c(2, 1)), # only bs, k, m are propagated...
bs.int = list(bs="ps", k=20, m=c(2, 1)), # only bs, k, m are propagated...
...
){
# TODO: subset args!
call <- match.call()
tensortype <- as.symbol(match.arg(tensortype))
# make sure we use values for the args that were defined as close to the
# actual function call as possible:
lapply(names(head(call, -1))[-1], function(nm)
try(assign(nm, eval(nm, parent.frame()))))
## TODO: does this make sense? useful if pffr is called from a function that
## supplies args as variables that are also defined differently in GlobalEnv:
## this should then ensure that the args as defined in the calling function,
## and not in GlobalEnv get used....
## warn if entries in ... aren't arguments for gam/gam.fit/jagam or gamm4/lmer
## check for special case of gaulss family
dots <- list(...)
gaulss <- FALSE
if(length(dots)){
validDots <- if(!is.na(algorithm) && algorithm=="gamm4"){
c(names(formals(gamm4)), names(formals(lmer)))
} else {
c(names(formals(gam)), names(formals(bam)), names(formals(gam.fit)),
names(formals(jagam)))
}
if(!is.null(dots$family) && dots$family == "gaulss") {
validDots <- c(validDots, "varformula")
gaulss <- TRUE
}
notUsed <- names(dots)[!(names(dots) %in% validDots)]
if(length(notUsed))
warning("Arguments <", paste(notUsed, collapse=", "), "> supplied but not used." )
}
sparseOrNongrid <- !is.null(ydata)
if(sparseOrNongrid){
stopifnot(ncol(ydata)==3)
stopifnot(c(".obs", ".index", ".value") == colnames(ydata))
}
pffrspecials <- c("s", "te", "ti", "t2", "ff", "c", "sff", "ffpc", "pcre")
tf <- terms.formula(formula, specials=pffrspecials)
trmstrings <- attr(tf, "term.labels")
terms <- sapply(trmstrings, function(trm) as.call(parse(text=trm))[[1]], simplify=FALSE)
#ugly, but getTerms(formula)[-1] does not work for terms like I(x1:x2)
frmlenv <- environment(formula)
#which terms are which type:
where.specials <- sapply(pffrspecials, function(sp) attr(tf, "specials")[[sp]]-1)
if(length(trmstrings)) {
where.specials$par <- which(!(1:length(trmstrings) %in%
(unlist(attr(tf, "specials")) - 1)))
# indices of linear/factor terms with functional coefficients over yind
} else where.specials$par <- numeric(0)
responsename <- attr(tf,"variables")[2][[1]]
#start new formula
newfrml <- paste(responsename, "~", sep="")
newfrmlenv <- new.env()
evalenv <- if("data" %in% names(call)) eval.parent(call$data) else NULL
if(sparseOrNongrid){
nobs <- length(unique(ydata$.obs))
stopifnot(all(ydata$.obs %in% rownames(data)))
# FIXME: allow for non-1:nobs .obs-formats!
stopifnot(all(ydata$.obs %in% 1:nobs))
#works for data-lists or matrix-valued covariates as well:
nobs.data <- nrow(as.matrix(data[[1]]))
stopifnot(nobs == nobs.data)
ntotal <- nrow(ydata)
#generate yind for estimates/predictions etc
yind <- if(length(unique(ydata$.index))>100){
seq(min(ydata$.index), max(ydata$.index), l=100)
} else {
sort(unique(ydata$.index))
}
nyindex <- length(yind)
} else {
nobs <- nrow(eval(responsename, envir=evalenv, enclos=frmlenv))
nyindex <- ncol(eval(responsename, envir=evalenv, enclos=frmlenv))
ntotal <- nobs*nyindex
}
if(missing(algorithm)||is.na(algorithm)){
algorithm <- ifelse(ntotal > 1e5, "bam", "gam")
}
if(algorithm == "bam" & missing(method)){
call$method <- "fREML"
}
algorithm <- as.symbol(algorithm)
if(as.character(algorithm)=="bam" && !("chunk.size" %in% names(call))){
call$chunk.size <- 10000
#same default as in bam
}
## no te-terms possible in gamm4:
if(as.character(algorithm)=="gamm4"){
stopifnot(length(unlist(where.specials[c("te","ti")]))<1)
}
if(!sparseOrNongrid){
#if missing, define y-index or get it from first ff/sff-term, then assign expanded versions to newfrmlenv
if(missing(yind)){
if(length(c(where.specials$ff, where.specials$sff))){
if(length(where.specials$ff)){
ffcall <- expand.call(ff, as.call(terms[where.specials$ff][1])[[1]])
} else ffcall <- expand.call(sff, as.call(terms[where.specials$sff][1])[[1]])
if(!is.null(ffcall$yind)){
yind <- eval(ffcall$yind, envir=evalenv, enclos=frmlenv)
yindname <- deparse(ffcall$yind)
} else {
yind <- 1:nyindex
yindname <- "yindex"
}
} else {
yind <- 1:nyindex
yindname <- "yindex"
}
} else {
if (is.symbol(substitute(yind)) | is.character(yind)) {
yindname <- deparse(substitute(yind))
if(!is.null(data) && !is.null(data[[yindname]])){
yind <- data[[yindname]]
}
} else {
yindname <- "yindex"
}
stopifnot(is.vector(yind), is.numeric(yind),
length(yind) == nyindex)
}
#make sure it's a valid name
if(length(yindname)>1) yindname <- "yindex"
# make sure yind is sorted
stopifnot(all.equal(order(yind), 1:nyindex))
yindvec <- rep(yind, times = nobs)
yindvecname <- as.symbol(paste(yindname,".vec",sep=""))
assign(x=deparse(yindvecname), value=yindvec, envir=newfrmlenv)
#assign response in _long_ format to newfrmlenv
assign(x=deparse(responsename), value=as.vector(t(eval(responsename, envir=evalenv,
enclos=frmlenv))),
envir=newfrmlenv)
missingind <- if(any(is.na(get(as.character(responsename), newfrmlenv)))){
which(is.na(get(as.character(responsename), newfrmlenv)))
} else NULL
# repeat which row in <data> how many times
stackpattern <- rep(1:nobs, each=nyindex)
} else {
# sparseOrNongrid:
yindname <- "yindex"
yindvec <- ydata$.index
yindvecname <- as.symbol(paste(yindname,".vec",sep=""))
assign(x=deparse(yindvecname), value=ydata$.index, envir=newfrmlenv)
#assign response in _long_ format to newfrmlenv
assign(x=deparse(responsename), value=ydata$.value, envir=newfrmlenv)
missingind <- NULL
# repeat which row in <data> how many times:
stackpattern <- ydata$.obs
}
##################################################################################
#modify formula terms....
newtrmstrings <- attr(tf, "term.labels")
#if intercept, add \mu(yindex)
if(attr(tf, "intercept")){
# have to jump thru some hoops to get bs.yindex handed over properly
# without having yind evaluated within the call
arglist <- c(name="s", x = as.symbol(yindvecname), bs.int)
intcall <- NULL
assign(x= "intcall", value= do.call("call", arglist, envir=newfrmlenv), envir=newfrmlenv)
newfrmlenv$intcall$x <- as.symbol(yindvecname)
intstring <- deparse(newfrmlenv$intcall)
rm(intcall, envir=newfrmlenv)
newfrml <- paste(newfrml, intstring, sep=" ")
addFint <- TRUE
names(intstring) <- paste("Intercept(",yindname,")",sep="")
} else{
newfrml <-paste(newfrml, "0", sep="")
addFint <- FALSE
}
#transform: c(foo) --> foo
if(length(where.specials$c)){
newtrmstrings[where.specials$c] <- sapply(trmstrings[where.specials$c], function(x){
sub("\\)$", "", sub("^c\\(", "", x)) #c(BLA) --> BLA
})
}
#prep function-on-function-terms
if(length(c(where.specials$ff, where.specials$sff))){
ffterms <- lapply(terms[c(where.specials$ff, where.specials$sff)], function(x){
eval(x, envir=evalenv, enclos=frmlenv)
})
newtrmstrings[c(where.specials$ff, where.specials$sff)] <- sapply(ffterms, function(x) {
safeDeparse(x$call)
})
#apply limits function and assign stacked data to newfrmlenv
makeff <- function(x){
tmat <- matrix(yindvec, nrow=length(yindvec), ncol=length(x$xind))
smat <- matrix(x$xind, nrow=length(yindvec), ncol=length(x$xind),
byrow=TRUE)
if(!is.null(x[["LX"]])){
# for ff: stack weights * covariate
LStacked <- x$LX[stackpattern,]
} else {
# for sff: stack weights, X separately
LStacked <- x$L[stackpattern,]
XStacked <- x$X[stackpattern, ]
}
if(!is.null(x$limits)){
# find int-limits and set weights to 0 outside
use <- x$limits(smat, tmat)
LStacked <- LStacked * use
# find indices for row-wise int-range & maximal occuring width:
windows <- t(apply(use, 1, function(x){
use_this <- which(x)
# edge case: no integration
if(!any(use_this)) return(c(1,1))
range(use_this)
}))
windows <- cbind(windows, windows[,2]-windows[,1]+1)
maxwidth <- max(windows[,3])
# reduce size of matrix-covariates if possible:
if(maxwidth < ncol(smat)){
# all windows have to have same length, so modify windows:
eff.windows <- t(apply(windows, 1, function(window,
maxw=maxwidth,
maxind=ncol(smat)){
width <- window[3]
if((window[2] + maxw - width) <= maxind){
window[1] : (window[2] + maxw -width)
} else {
(window[1] + width - maxw) : window[2]
}
}))
# extract relevant parts of each row and stack'em
shift_and_shorten <- function(X, eff.windows){
t(sapply(1:(nrow(X)),
function(i) X[i, eff.windows[i,]]))
}
smat <- shift_and_shorten(smat, eff.windows)
tmat <- shift_and_shorten(tmat, eff.windows)
LStacked <- shift_and_shorten(LStacked, eff.windows)
if(is.null(x$LX)){ # sff
XStacked <- shift_and_shorten(XStacked, eff.windows)
}
}
}
assign(x=x$yindname,
value=tmat,
envir=newfrmlenv)
assign(x=x$xindname,
value=smat,
envir=newfrmlenv)
assign(x=x$LXname,
value=LStacked,
envir=newfrmlenv)
if(is.null(x[["LX"]])){ # sff
assign(x=x$xname,
value=XStacked,
envir=newfrmlenv)
}
invisible(NULL)
}
lapply(ffterms, makeff)
} else ffterms <- NULL
if(length(where.specials$ffpc)){ ##TODO for sparse
ffpcterms <- lapply(terms[where.specials$ffpc], function(x){
eval(x, envir=evalenv, enclos=frmlenv)
})
lapply(ffpcterms, function(trm){
lapply(colnames(trm$data), function(nm){
assign(x=nm, value=trm$data[stackpattern, nm], envir=newfrmlenv)
invisible(NULL)
})
invisible(NULL)
})
getFfpcFormula <- function(trm) {
frmls <- lapply(colnames(trm$data), function(pc) {
arglist <- c(name="s", x = as.symbol(yindvecname), by= as.symbol(pc),
id=trm$id, trm$splinepars)
call <- do.call("call", arglist, envir=newfrmlenv)
call$x <- as.symbol(yindvecname)
call$by <- as.symbol(pc)
safeDeparse(call)
})
return(paste(unlist(frmls), collapse=" + "))
}
newtrmstrings[where.specials$ffpc] <- sapply(ffpcterms, getFfpcFormula)
ffpcterms <- lapply(ffpcterms, function(x) x[names(x)!="data"])
} else ffpcterms <- NULL
#prep PC-based random effects
if(length(where.specials$pcre)){
pcreterms <- lapply(terms[where.specials$pcre], function(x){
eval(x, envir=evalenv, enclos=frmlenv)
})
#assign newly created data to newfrmlenv
lapply(pcreterms, function(trm){
if(!sparseOrNongrid && all(trm$yind==yind)){
lapply(colnames(trm$efunctions), function(nm){
assign(x=nm, value=trm$efunctions[rep(1:nyindex, times=nobs), nm],
envir=newfrmlenv)
invisible(NULL)
})
} else {
# don't ever extrapolate eigenfunctions:
stopifnot(min(trm$yind)<=min(yind))
stopifnot(max(trm$yind)>=max(yind))
# interpolate given eigenfunctions to observed index values:
lapply(colnames(trm$efunctions), function(nm){
tmp <- approx(x=trm$yind,
y=trm$efunctions[, nm],
xout=yindvec,
method = "linear")$y
assign(x=nm, value=tmp,
envir=newfrmlenv)
invisible(NULL)
})
}
assign(x=trm$idname, value=trm$id[stackpattern], envir=newfrmlenv)
invisible(NULL)
})
newtrmstrings[where.specials$pcre] <- sapply(pcreterms, function(x) {
safeDeparse(x$call)
})
}else pcreterms <- NULL
#transform: s(x, ...), te(x, z,...), t2(x, z, ...) --> <ti|t2>(x, <z,> yindex, ..., <bs.yindex>)
makeSTeT2 <- function(x){
xnew <- x
if(deparse(x[[1]]) %in% c("te", "ti") && as.character(algorithm) == "gamm4") xnew[[1]] <- quote(t2)
if(deparse(x[[1]]) == "s"){
xnew[[1]] <- if(as.character(algorithm) != "gamm4") {
tensortype
} else quote(t2)
#accomodate multivariate s()-terms
xnew$d <- if(!is.null(names(xnew))){
c(length(all.vars(xnew[names(xnew)==""])), 1)
} else c(length(all.vars(xnew)), 1)
} else {
if("d" %in% names(x)){ #either expand given d...
xnew$d <- c(eval(x$d), 1)
} else {#.. or default to univariate marginal bases
xnew$d <- rep(1, length(all.vars(x))+1)
}
}
xnew[[length(xnew)+1]] <- yindvecname
this.bs.yindex <- if("bs.yindex" %in% names(x)){
eval(x$bs.yindex)
} else bs.yindex
xnew <- xnew[names(xnew) != "bs.yindex"]
if(deparse(xnew[[1]]) == "ti"){
# apply sum-to-zero constraints to marginal bases for covariate(s),
# but not to <yindex> to get terms with sum-to-zero-for-each-t constraints
xnew$mc <- c(rep(TRUE, length(xnew$d)-1), FALSE)
}
xnew$bs <- if("bs" %in% names(x)){
if("bs" %in% names(this.bs.yindex)){
c(eval(x$bs), this.bs.yindex$bs)
} else {
c(xnew$bs, "tp")
}
} else {
if("bs" %in% names(this.bs.yindex)){
c(rep("tp", length(xnew$d)-1), this.bs.yindex$bs)
} else {
rep("tp", length(all.vars(x))+1)
}
}
xnew$m <- if("m" %in% names(x)){
if("m" %in% names(this.bs.yindex)){
warning("overriding bs.yindex for m in ", deparse(x))
}
#TODO: adjust length if necessary, m can be a list for bs="ps","cp","ds"!
x$m
} else {
if("m" %in% names(this.bs.yindex)){
this.bs.yindex$m
} else {
NA
}
}
#defaults to 8 basis functions
xnew$k <- if("k" %in% names(x)){
if("k" %in% names(this.bs.yindex)){
c(eval(xnew$k), eval(this.bs.yindex$k))
} else {
c(eval(xnew$k), 8)
}
} else {
if("k" %in% names(this.bs.yindex)){
c(pmax(8, 5^head(eval(xnew$d), -1)), eval(this.bs.yindex$k))
} else {
pmax(8, 5^eval(xnew$d))
}
}
xnew$k <- unlist(xnew$k)
if("xt" %in% names(x)){
# # xt has to be supplied as a list, with length(x$d) entries,
# # each of which is a list or NULL:
# stopifnot(x$xt[[1]]==as.symbol("list") &&
# # =length(x$d)+1, since first element in parse tree is 'list'
# all(sapply(2:length(x$xt), function(i)
# x$xt[[i]][[1]] == as.symbol("list") ||
# is.null(eval(x$xt[[i]][[1]])))))
xnew$xt <- x$xt
}
ret <- safeDeparse(xnew)
return(ret)
}
if(length(c(where.specials$s, where.specials$te, where.specials$t2))){
newtrmstrings[c(where.specials$s, where.specials$te, where.specials$t2)] <-
sapply(terms[c(where.specials$s, where.specials$te, where.specials$t2)],
makeSTeT2)
}
#transform: x --> s(YINDEX, by=x)
if(length(where.specials$par)){
newtrmstrings[where.specials$par] <- sapply(terms[where.specials$par], function(x){
xnew <- bs.yindex
xnew <- as.call(c(quote(s), yindvecname, by=x, xnew))
safeDeparse(xnew)
})
}
#... & assign expanded/additional variables to newfrmlenv
where.specials$notff <- c(where.specials$c, where.specials$par,
where.specials$s, where.specials$te, where.specials$t2)
if(length(where.specials$notff)){
# evalenv below used to be list2env(eval.parent(call$data)), frmlenv),
# but that assigned everything in <data> to the global workspace if frmlenv was the global
# workspace.
evalenv <- if("data" %in% names(call)) {
list2env(eval.parent(call$data))
} else frmlenv
lapply(terms[where.specials$notff],
function(x){
#nms <- all.vars(x)
isC <- safeDeparse(x) %in% sapply(terms[where.specials$c], safeDeparse)
if(isC) {
# drop c()
# FIXME: FUGLY!
x <- formula(paste("~", gsub("\\)$", "",
gsub("^c\\(", "", deparse(x)))))[[2]]
}
## remove names in xt, k, bs, information (such as variable names for MRF penalties etc)
nms <- if(!is.null(names(x))){
all.vars(x[names(x) %in% c("", "by")])
} else all.vars(x)
sapply(nms, function(nm){
var <- get(nm, envir=evalenv)
if(is.matrix(var)){
stopifnot(!sparseOrNongrid || ncol(var) == nyindex)
assign(x=nm,
value=as.vector(t(var)),
envir=newfrmlenv)
} else {
stopifnot(length(var) == nobs)
assign(x=nm,
value=var[stackpattern],
envir=newfrmlenv)
}
invisible(NULL)
})
invisible(NULL)
})
}
newfrml <- formula(paste(c(newfrml, newtrmstrings), collapse="+"))
environment(newfrml) <- newfrmlenv
# variance formula for gaulss
if(gaulss) {
if(is.null(dots$varformula)) {
dots$varformula <- formula(paste("~", safeDeparse(
as.call(c(as.name("s"), x = as.symbol(yindvecname), bs.int)))))
}
environment(dots$varformula) <- newfrmlenv
newfrml <- list(newfrml, dots$varformula)
}
pffrdata <- list2df(as.list(newfrmlenv))
newcall <- expand.call(pffr, call)
newcall$yind <- newcall$tensortype <- newcall$bs.int <-
newcall$bs.yindex <- newcall$algorithm <- newcall$ydata <- NULL
newcall$formula <- newfrml
newcall$data <- quote(pffrdata)
newcall[[1]] <- algorithm
# make sure ...-args are taken from ..., not GlobalEnv:
dotargs <- names(newcall)[names(newcall) %in% names(dots)]
newcall[dotargs] <- dots[dotargs]
if("subset" %in% dotargs){
stop("<subset>-argument is not supported.")
}
if("weights" %in% dotargs){
wtsdone <- FALSE
if(length(dots$weights) == nobs){
newcall$weights <- dots$weights[stackpattern]
wtsdone <- TRUE
}
if (!is.null(dim(dots$weights)) &&
all(dim(dots$weights) == c(nobs, nyindex))) {
newcall$weights <- as.vector(t(dots$weights))
wtsdone <- TRUE
}
if(!wtsdone){
stop("weights have to be supplied as a vector with length=rows(data) or
a matrix with the same dimensions as the response.")
}
}
if("offset" %in% dotargs){
ofstdone <- FALSE
if(length(dots$offset) == nobs){
newcall$offset <- dots$offset[stackpattern]
ofstdone <- TRUE
}
if(!is.null(dim(dots$offset)) &&
all(dim(dots$offset) == c(nobs, nyindex))){
newcall$offset <- as.vector(t(dots$offset))
ofstdone <- TRUE
}
if(!ofstdone){
stop("offsets have to be supplied as a vector with length=rows(data) or
a matrix with the same dimensions as the response.")
}
}
if(as.character(algorithm) == "jagam"){
newcall <- newcall[names(newcall) %in% c("", names(formals(jagam)))]
if(is.null(newcall$file)) {
newcall$file <- tempfile("pffr2jagam", tmpdir = getwd(), fileext = ".jags")
}
}
# call algorithm to estimate model
m <- eval(newcall)
if(as.character(algorithm) == "jagam"){
m$modelfile <- newcall$file
message("JAGS/BUGS model code written to \n", m$modelfile, ",\n see ?jagam")
return(m)
}
m.smooth <- if(as.character(algorithm) %in% c("gamm4","gamm")){
m$gam$smooth
} else m$smooth
#return some more info s.t. custom predict/plot/summary will work
trmmap <- newtrmstrings
names(trmmap) <- names(terms)
if(addFint) trmmap <- c(trmmap, intstring)
# map labels to terms --
# ffpc are associated with multiple smooths
# parametric are associated with multiple smooths if covariate is a factor
labelmap <- as.list(trmmap)
lbls <- sapply(m.smooth, function(x) x$label)
if(length(c(where.specials$par, where.specials$ffpc))){
if(length(where.specials$par)){
for(w in where.specials$par){
# only combine if <by>-variable is a factor!
if(is.factor(get(names(labelmap)[w], envir=newfrmlenv))){
labelmap[[w]] <- {
#covariates for parametric terms become by-variables:
where <- sapply(m.smooth, function(x) x$by) == names(labelmap)[w]
sapply(m.smooth[where], function(x) x$label)
}
} else {
labelmap[[w]] <- paste0("s(",yindvecname,"):",names(labelmap)[w])
}
}
}
if(length(where.specials$ffpc)){
ind <- 1
for(w in where.specials$ffpc){
labelmap[[w]] <- {
#PCs for X become by-variables:
where <- sapply(m.smooth, function(x) x$id) == ffpcterms[[ind]]$id
sapply(m.smooth[where], function(x) x$label)
}
ind <- ind+1
}
}
labelmap[-c(where.specials$par, where.specials$ffpc)] <- lbls[pmatch(
sapply(labelmap[-c(where.specials$par, where.specials$ffpc)], function(x){
## FUGLY: check whether x is a function call of some sort
## or simply a variable name.
if(length(parse(text=x)[[1]]) != 1){
tmp <- eval(parse(text=x))
return(tmp$label)
} else {
return(x)
}
}), lbls)]
} else{
labelmap[1:length(labelmap)] <- lbls[pmatch(
sapply(labelmap[1:length(labelmap)], function(x){
## FUGLY: check whether x is a function call of some sort
## or simply a variable name.
if(length(parse(text=x)[[1]]) != 1){
tmp <- eval(parse(text=x))
return(tmp$label)
} else {
return(x)
}
}), lbls)]
}
# check whether any parametric terms were left out & add them
nalbls <- sapply(labelmap,
function(x) {
any(is.null(x)) | any(is.na(x[!is.null(x)]))
})
if (any(nalbls)) {
labelmap[nalbls] <- trmmap[nalbls]
}
names(m.smooth) <- lbls
if(as.character(algorithm) %in% c("gamm4","gamm")){
m$gam$smooth <- m.smooth
} else{
m$smooth <- m.smooth
}
ret <- list(
call=call,
formula=formula,
termmap=trmmap,
labelmap=labelmap,
responsename = responsename,
nobs=nobs,
nyindex=nyindex,
yindname = yindname,
yind=yind,
where=where.specials,
ff=ffterms,
ffpc=ffpcterms,
pcreterms=pcreterms,
missingind = missingind,
sparseOrNongrid=sparseOrNongrid,
ydata=ydata)
if(as.character(algorithm) %in% c("gamm4","gamm")){
m$gam$pffr <- ret
class(m$gam) <- c("pffr", class(m$gam))
} else {
m$pffr <- ret
class(m) <- c("pffr", class(m))
}
return(m)
}# end pffr()