fk: A function to fit break points within GAMLSS
In gamlss.add: Extra Additive Terms for Generalized Additive Models for Location Scale and Shape
Description
Usage
Arguments
Details
Value
Author(s)
References
See Also
Examples
Description
The fk() function is a additive function to be used for GAMLSS models.
It is an interface for the fitFreeKnots() function of package
gamlss.util. The functions fitFreeKnots() was first based on the curfit.free.knot() function of package DierckxSpline of Sundar Dorai-Raj and Spencer Graves. The function fk() allows the user to use the free knots function fitFreeKnots() within gamlss.
The great advantage of course comes from the fact GAMLSS models provide a variety of distributions and diagnostics.
Usage
1
2
Arguments
x
the x-variable
start
starting values for the breakpoints. If are set the number of break points is also determined by the length of start
control
the degree of the spline function fitted
...
for extra arguments
degree
the degree of the based function
all.fixed
whether to fix all parameter
fixed
the fixed break points
base
Which base should be used
Details
Note that fk itself does no smoothing; it simply sets things up for the function gamlss()
which in turn uses the function additive.fit() for backfitting which in turn uses gamlss.fk().
Note that, finding the break points is not a trivial problem and therefore multiple maximum points can occur.
More details about the free knot splines can be found in package Dierckx, (1991).
The gamlss algorithm used a modified backfitting in this case, that is, it fits the linear part fist.
Note that trying to predict outside the x-range can be dangerous as the example below shows.
Value
The gamlss object saved contains the last fitted object which can be accessed using
obj$par.coefSmo where obj is the fitted gamlss object par is the relevant distribution
parameter.
Author(s)
Mikis Stasinopoulos mikis.stasinopoulos@gamlss.org, Bob Rigby
References
Dierckx, P. (1991) Curve and Surface Fitting with Splines, Oxford Science Publications
Stasinopoulos D. M., Rigby R.A. and Akantziliotou C. (2006) Instructions on how to use the GAMLSS package in R.
Accompanying documentation in the current GAMLSS help files, (see also http://www.gamlss.org/).
Stasinopoulos D. M. Rigby R.A. (2007) Generalized additive models for location scale and shape (GAMLSS) in R.
Journal of Statistical Software, Vol. 23, Issue 7, Dec 2007, http://www.jstatsoft.org/v23/i07.
See Also
Examples
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
## creating a linear + linear function
x <- seq(0,10, length.out=201)
knot <- 5
set.seed(12543)
mu <- ifelse(x<=knot,5+0.5*x,5+0.5*x+1.5*(x-knot))
y <- rNO(201, mu=mu, sigma=.5)
## plot the data
plot(y~x, xlim=c(-1,13), ylim=c(3,23))
## fit model using curfit
m1 <- fitFreeKnots(y, x, knots=3, degree=1)
knots(m1)
## fitted values
lines(fitted(m1)~x, col="red", lwd="3")
## predict
pm1<-predict(m1, newdata=-1:12)
points(-1:12,pm1, col="red",pch = 21, bg="blue")
#------------------------------------------------
## now gamlss
#------------------------------------------------
## now negative binomial data
knot=4
eta1 <- ifelse(x<=knot,0.8+0.08*x,.8+0.08*x+.3*(x-knot))
plot(eta1~x)
set.seed(143)
y <- rNBI(201, mu=exp(eta1), sigma=.1)
da <- data.frame(y=y,x=x)
plot(y~x, data=da)
## getting the break point using profile deviance
n1 <- quote(gamlss(y ~ x+I((x>this)*(x-this)), family=NBI, data=da))
prof.term(n1, min=1, max=9, criterion="GD", start.prev=FALSE)
## now fit the model using fk
g1 <- gamlss(y~fk(x, degree=1, start=c(4)), data=da, family=NBI)
## get the breakpoint
knots(getSmo(g1))
## summary of the gamlss object FreeBreakPointsReg object
getSmo(g1)
## plot fitted model
plot(y~x, data=da)
lines(fitted(g1)~x, data=da, col="red")
#------------------------------------------------
## the aids data as example where things can go wrong
## using fk()
data(aids)
a1<-gamlss(y~x+fk(x, degree=1, start=25)+qrt, data=aids, family=NBI)
knots(getSmo(a1))
# using profile deviance
aids.1 <- quote(gamlss(y ~ x+I((x>this)*(x-this))+qrt,family=NBI,data=aids))
prof.term(aids.1, min=16, max=21, step=.1, start.prev=FALSE)
## The Maximum Likelihood estimator is 18.33231 not 17.37064
## plotting the fit
with(aids, plot(x,y,pch=21,bg=c("red","green3","blue","yellow")[unclass(qrt)]))
lines(fitted(a1)~aids$x)
#-------------------------------------------------
Example output
Loading required package: gamlss.dist
Loading required package: MASS
Loading required package: gamlss
Loading required package: splines
Loading required package: gamlss.data
Loading required package: nlme
Loading required package: parallel
********** GAMLSS Version 5.1-2 **********
For more on GAMLSS look at http://www.gamlss.org/
Type gamlssNews() to see new features/changes/bug fixes.
Loading required package: mgcv
This is mgcv 1.8-25. For overview type 'help("mgcv-package")'.
Loading required package: nnet
Attaching package: 'nnet'
The following object is masked from 'package:mgcv':
multinom
Loading required package: rpart
BP1
5.011936
GAMLSS-RS iteration 1: Global Deviance = 1032.275
GAMLSS-RS iteration 2: Global Deviance = 1030.958
GAMLSS-RS iteration 3: Global Deviance = 1030.957
GAMLSS-RS iteration 4: Global Deviance = 1030.957
GAMLSS-RS iteration 1: Global Deviance = 1021.241
GAMLSS-RS iteration 2: Global Deviance = 1020.682
GAMLSS-RS iteration 3: Global Deviance = 1020.682
GAMLSS-RS iteration 1: Global Deviance = 1012.962
GAMLSS-RS iteration 2: Global Deviance = 1012.919
GAMLSS-RS iteration 3: Global Deviance = 1012.919
GAMLSS-RS iteration 1: Global Deviance = 1013.683
GAMLSS-RS iteration 2: Global Deviance = 1013.649
GAMLSS-RS iteration 3: Global Deviance = 1013.649
GAMLSS-RS iteration 1: Global Deviance = 1020.127
GAMLSS-RS iteration 2: Global Deviance = 1019.822
GAMLSS-RS iteration 3: Global Deviance = 1019.822
GAMLSS-RS iteration 1: Global Deviance = 1027.483
GAMLSS-RS iteration 2: Global Deviance = 1026.827
GAMLSS-RS iteration 3: Global Deviance = 1026.827
GAMLSS-RS iteration 1: Global Deviance = 1034.174
GAMLSS-RS iteration 2: Global Deviance = 1032.899
GAMLSS-RS iteration 3: Global Deviance = 1032.898
GAMLSS-RS iteration 4: Global Deviance = 1032.898
******************************************************************
The Maximum Likelihood estimator is 4.182408
with a Global Deviance equal to 1012.211
A 95 % Confidence interval is: ( 2.990368 , 5.595213 )
******************************************************************
GAMLSS-RS iteration 1: Global Deviance = 1012.078
GAMLSS-RS iteration 2: Global Deviance = 1012.077
GAMLSS-RS iteration 3: Global Deviance = 1012.077
BP1
4.150024
Call: fitFreeKnots(y = y, x = xvar, weights = w, degree = degree,
knots = lambda, fixed = control$fixed, base = control$base)
Coefficients:
(Intercept) x XatBP1
-0.90843 0.07212 0.29733
Estimated Knots:
BP1
4.15
GAMLSS-RS iteration 1: Global Deviance = 381.5559
GAMLSS-RS iteration 2: Global Deviance = 380.1881
GAMLSS-RS iteration 3: Global Deviance = 380.1878
BP1
17.37064
GAMLSS-RS iteration 1: Global Deviance = 394.1451
GAMLSS-RS iteration 2: Global Deviance = 392.7581
GAMLSS-RS iteration 3: Global Deviance = 392.7562
GAMLSS-RS iteration 4: Global Deviance = 392.7557
GAMLSS-RS iteration 1: Global Deviance = 392.9952
GAMLSS-RS iteration 2: Global Deviance = 391.5406
GAMLSS-RS iteration 3: Global Deviance = 391.539
GAMLSS-RS iteration 4: Global Deviance = 391.5384
GAMLSS-RS iteration 1: Global Deviance = 391.8902
GAMLSS-RS iteration 2: Global Deviance = 390.3677
GAMLSS-RS iteration 3: Global Deviance = 390.3655
GAMLSS-RS iteration 4: Global Deviance = 390.3653
GAMLSS-RS iteration 1: Global Deviance = 390.8327
GAMLSS-RS iteration 2: Global Deviance = 389.2424
GAMLSS-RS iteration 3: Global Deviance = 389.24
GAMLSS-RS iteration 4: Global Deviance = 389.2398
GAMLSS-RS iteration 1: Global Deviance = 389.8248
GAMLSS-RS iteration 2: Global Deviance = 388.1668
GAMLSS-RS iteration 3: Global Deviance = 388.1642
GAMLSS-RS iteration 4: Global Deviance = 388.1639
GAMLSS-RS iteration 1: Global Deviance = 388.8692
GAMLSS-RS iteration 2: Global Deviance = 387.1436
GAMLSS-RS iteration 3: Global Deviance = 387.1403
GAMLSS-RS iteration 4: Global Deviance = 387.14
GAMLSS-RS iteration 1: Global Deviance = 387.9669
GAMLSS-RS iteration 2: Global Deviance = 386.1731
GAMLSS-RS iteration 3: Global Deviance = 386.1698
GAMLSS-RS iteration 4: Global Deviance = 386.1696
GAMLSS-RS iteration 1: Global Deviance = 387.12
GAMLSS-RS iteration 2: Global Deviance = 385.2575
GAMLSS-RS iteration 3: Global Deviance = 385.2544
GAMLSS-RS iteration 4: Global Deviance = 385.2543
GAMLSS-RS iteration 1: Global Deviance = 386.3296
GAMLSS-RS iteration 2: Global Deviance = 384.3982
GAMLSS-RS iteration 3: Global Deviance = 384.3952
GAMLSS-RS iteration 4: Global Deviance = 384.3951
GAMLSS-RS iteration 1: Global Deviance = 385.5971
GAMLSS-RS iteration 2: Global Deviance = 383.5956
GAMLSS-RS iteration 3: Global Deviance = 383.5935
GAMLSS-RS iteration 4: Global Deviance = 383.5932
GAMLSS-RS iteration 1: Global Deviance = 384.9225
GAMLSS-RS iteration 2: Global Deviance = 382.8511
GAMLSS-RS iteration 3: Global Deviance = 382.8483
GAMLSS-RS iteration 4: Global Deviance = 382.8481
GAMLSS-RS iteration 1: Global Deviance = 384.194
GAMLSS-RS iteration 2: Global Deviance = 382.0384
GAMLSS-RS iteration 3: Global Deviance = 382.0356
GAMLSS-RS iteration 4: Global Deviance = 382.0355
GAMLSS-RS iteration 1: Global Deviance = 383.5353
GAMLSS-RS iteration 2: Global Deviance = 381.2952
GAMLSS-RS iteration 3: Global Deviance = 381.2926
GAMLSS-RS iteration 4: Global Deviance = 381.2925
GAMLSS-RS iteration 1: Global Deviance = 382.9474
GAMLSS-RS iteration 2: Global Deviance = 380.6226
GAMLSS-RS iteration 3: Global Deviance = 380.62
GAMLSS-RS iteration 4: Global Deviance = 380.6199
GAMLSS-RS iteration 1: Global Deviance = 382.4312
GAMLSS-RS iteration 2: Global Deviance = 380.0215
GAMLSS-RS iteration 3: Global Deviance = 380.0186
GAMLSS-RS iteration 4: Global Deviance = 380.0184
GAMLSS-RS iteration 1: Global Deviance = 381.9868
GAMLSS-RS iteration 2: Global Deviance = 379.4907
GAMLSS-RS iteration 3: Global Deviance = 379.4879
GAMLSS-RS iteration 4: Global Deviance = 379.4877
GAMLSS-RS iteration 1: Global Deviance = 381.6142
GAMLSS-RS iteration 2: Global Deviance = 379.0304
GAMLSS-RS iteration 3: Global Deviance = 379.0277
GAMLSS-RS iteration 4: Global Deviance = 379.0275
GAMLSS-RS iteration 1: Global Deviance = 381.3128
GAMLSS-RS iteration 2: Global Deviance = 378.6399
GAMLSS-RS iteration 3: Global Deviance = 378.6372
GAMLSS-RS iteration 4: Global Deviance = 378.6371
GAMLSS-RS iteration 1: Global Deviance = 381.0821
GAMLSS-RS iteration 2: Global Deviance = 378.3177
GAMLSS-RS iteration 3: Global Deviance = 378.3153
GAMLSS-RS iteration 4: Global Deviance = 378.3152
GAMLSS-RS iteration 1: Global Deviance = 380.9202
GAMLSS-RS iteration 2: Global Deviance = 378.0629
GAMLSS-RS iteration 3: Global Deviance = 378.0604
GAMLSS-RS iteration 4: Global Deviance = 378.0603
GAMLSS-RS iteration 1: Global Deviance = 380.8259
GAMLSS-RS iteration 2: Global Deviance = 377.8733
GAMLSS-RS iteration 3: Global Deviance = 377.8707
GAMLSS-RS iteration 4: Global Deviance = 377.8706
GAMLSS-RS iteration 1: Global Deviance = 380.7194
GAMLSS-RS iteration 2: Global Deviance = 377.6608
GAMLSS-RS iteration 3: Global Deviance = 377.6579
GAMLSS-RS iteration 4: Global Deviance = 377.6578
GAMLSS-RS iteration 1: Global Deviance = 380.6919
GAMLSS-RS iteration 2: Global Deviance = 377.5254
GAMLSS-RS iteration 3: Global Deviance = 377.5222
GAMLSS-RS iteration 4: Global Deviance = 377.5222
GAMLSS-RS iteration 1: Global Deviance = 380.7412
GAMLSS-RS iteration 2: Global Deviance = 377.4651
GAMLSS-RS iteration 3: Global Deviance = 377.4618
GAMLSS-RS iteration 4: Global Deviance = 377.4618
GAMLSS-RS iteration 1: Global Deviance = 380.8655
GAMLSS-RS iteration 2: Global Deviance = 377.4779
GAMLSS-RS iteration 3: Global Deviance = 377.4746
GAMLSS-RS iteration 4: Global Deviance = 377.4745
GAMLSS-RS iteration 1: Global Deviance = 381.0621
GAMLSS-RS iteration 2: Global Deviance = 377.5616
GAMLSS-RS iteration 3: Global Deviance = 377.558
GAMLSS-RS iteration 4: Global Deviance = 377.558
GAMLSS-RS iteration 1: Global Deviance = 381.3283
GAMLSS-RS iteration 2: Global Deviance = 377.7133
GAMLSS-RS iteration 3: Global Deviance = 377.7095
GAMLSS-RS iteration 4: Global Deviance = 377.7095
GAMLSS-RS iteration 1: Global Deviance = 381.6609
GAMLSS-RS iteration 2: Global Deviance = 377.9302
GAMLSS-RS iteration 3: Global Deviance = 377.9262
GAMLSS-RS iteration 4: Global Deviance = 377.9261
GAMLSS-RS iteration 1: Global Deviance = 382.0564
GAMLSS-RS iteration 2: Global Deviance = 378.2087
GAMLSS-RS iteration 3: Global Deviance = 378.2049
GAMLSS-RS iteration 4: Global Deviance = 378.2049
GAMLSS-RS iteration 1: Global Deviance = 382.5117
GAMLSS-RS iteration 2: Global Deviance = 378.5468
GAMLSS-RS iteration 3: Global Deviance = 378.5426
GAMLSS-RS iteration 4: Global Deviance = 378.5426
GAMLSS-RS iteration 1: Global Deviance = 383.0228
GAMLSS-RS iteration 2: Global Deviance = 378.9407
GAMLSS-RS iteration 3: Global Deviance = 378.9361
GAMLSS-RS iteration 4: Global Deviance = 378.936
GAMLSS-RS iteration 1: Global Deviance = 383.5725
GAMLSS-RS iteration 2: Global Deviance = 379.4074
GAMLSS-RS iteration 3: Global Deviance = 379.4019
GAMLSS-RS iteration 4: Global Deviance = 379.4018
GAMLSS-RS iteration 1: Global Deviance = 384.184
GAMLSS-RS iteration 2: Global Deviance = 379.9371
GAMLSS-RS iteration 3: Global Deviance = 379.931
GAMLSS-RS iteration 4: Global Deviance = 379.9308
GAMLSS-RS iteration 1: Global Deviance = 384.8531
GAMLSS-RS iteration 2: Global Deviance = 380.5264
GAMLSS-RS iteration 3: Global Deviance = 380.5194
GAMLSS-RS iteration 4: Global Deviance = 380.5192
GAMLSS-RS iteration 1: Global Deviance = 385.5752
GAMLSS-RS iteration 2: Global Deviance = 381.1712
GAMLSS-RS iteration 3: Global Deviance = 381.1633
GAMLSS-RS iteration 4: Global Deviance = 381.163
GAMLSS-RS iteration 1: Global Deviance = 386.3461
GAMLSS-RS iteration 2: Global Deviance = 381.8673
GAMLSS-RS iteration 3: Global Deviance = 381.8582
GAMLSS-RS iteration 4: Global Deviance = 381.8582
GAMLSS-RS iteration 1: Global Deviance = 387.1614
GAMLSS-RS iteration 2: Global Deviance = 382.6114
GAMLSS-RS iteration 3: Global Deviance = 382.601
GAMLSS-RS iteration 4: Global Deviance = 382.601
GAMLSS-RS iteration 1: Global Deviance = 388.0167
GAMLSS-RS iteration 2: Global Deviance = 383.3994
GAMLSS-RS iteration 3: Global Deviance = 383.3874
GAMLSS-RS iteration 4: Global Deviance = 383.3874
GAMLSS-RS iteration 1: Global Deviance = 388.9078
GAMLSS-RS iteration 2: Global Deviance = 384.2275
GAMLSS-RS iteration 3: Global Deviance = 384.2138
GAMLSS-RS iteration 4: Global Deviance = 384.2138
GAMLSS-RS iteration 1: Global Deviance = 389.8308
GAMLSS-RS iteration 2: Global Deviance = 385.092
GAMLSS-RS iteration 3: Global Deviance = 385.0764
GAMLSS-RS iteration 4: Global Deviance = 385.0764
GAMLSS-RS iteration 1: Global Deviance = 390.7817
GAMLSS-RS iteration 2: Global Deviance = 385.9893
GAMLSS-RS iteration 3: Global Deviance = 385.9718
GAMLSS-RS iteration 4: Global Deviance = 385.9718
GAMLSS-RS iteration 1: Global Deviance = 391.5393
GAMLSS-RS iteration 2: Global Deviance = 386.6922
GAMLSS-RS iteration 3: Global Deviance = 386.6738
GAMLSS-RS iteration 4: Global Deviance = 386.6738
GAMLSS-RS iteration 1: Global Deviance = 392.3358
GAMLSS-RS iteration 2: Global Deviance = 387.4411
GAMLSS-RS iteration 3: Global Deviance = 387.4204
GAMLSS-RS iteration 4: Global Deviance = 387.4204
GAMLSS-RS iteration 1: Global Deviance = 393.1679
GAMLSS-RS iteration 2: Global Deviance = 388.2305
GAMLSS-RS iteration 3: Global Deviance = 388.2081
GAMLSS-RS iteration 4: Global Deviance = 388.208
GAMLSS-RS iteration 1: Global Deviance = 394.0319
GAMLSS-RS iteration 2: Global Deviance = 389.0582
GAMLSS-RS iteration 3: Global Deviance = 389.0337
GAMLSS-RS iteration 4: Global Deviance = 389.0335
GAMLSS-RS iteration 1: Global Deviance = 394.9245
GAMLSS-RS iteration 2: Global Deviance = 389.9202
GAMLSS-RS iteration 3: Global Deviance = 389.8935
GAMLSS-RS iteration 4: Global Deviance = 389.8933
GAMLSS-RS iteration 1: Global Deviance = 395.8423
GAMLSS-RS iteration 2: Global Deviance = 390.8145
GAMLSS-RS iteration 3: Global Deviance = 390.7846
GAMLSS-RS iteration 4: Global Deviance = 390.7844
GAMLSS-RS iteration 1: Global Deviance = 396.7822
GAMLSS-RS iteration 2: Global Deviance = 391.7366
GAMLSS-RS iteration 3: Global Deviance = 391.7039
GAMLSS-RS iteration 4: Global Deviance = 391.7037
GAMLSS-RS iteration 1: Global Deviance = 397.7413
GAMLSS-RS iteration 2: Global Deviance = 392.683
GAMLSS-RS iteration 3: Global Deviance = 392.6485
GAMLSS-RS iteration 4: Global Deviance = 392.6483
GAMLSS-RS iteration 1: Global Deviance = 398.7167
GAMLSS-RS iteration 2: Global Deviance = 393.6527
GAMLSS-RS iteration 3: Global Deviance = 393.6155
GAMLSS-RS iteration 4: Global Deviance = 393.6152
GAMLSS-RS iteration 1: Global Deviance = 399.7058
GAMLSS-RS iteration 2: Global Deviance = 394.6422
GAMLSS-RS iteration 3: Global Deviance = 394.6018
GAMLSS-RS iteration 4: Global Deviance = 394.6017
******************************************************************
The Maximum Likelihood estimator is 18.33231
with a Global Deviance equal to 377.4579
A 95 % Confidence interval is: ( 17.19903 , 19.42018 )
******************************************************************
gamlss.add documentation built on Feb. 4, 2020, 9:08 a.m.
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Description Usage Arguments Details Value Author(s) References See Also Examples
Description
The fk() function is a additive function to be used for GAMLSS models.
It is an interface for the fitFreeKnots() function of package
gamlss.util. The functions fitFreeKnots() was first based on the curfit.free.knot() function of package DierckxSpline of Sundar Dorai-Raj and Spencer Graves. The function fk() allows the user to use the free knots function fitFreeKnots() within gamlss.
The great advantage of course comes from the fact GAMLSS models provide a variety of distributions and diagnostics.
Usage
1 2 |
Arguments
x |
the x-variable |
start |
starting values for the breakpoints. If are set the number of break points is also determined by the length of |
control |
the degree of the spline function fitted |
... |
for extra arguments |
degree |
the degree of the based function |
all.fixed |
whether to fix all parameter |
fixed |
the fixed break points |
base |
Which base should be used |
Details
Note that fk itself does no smoothing; it simply sets things up for the function gamlss()
which in turn uses the function additive.fit() for backfitting which in turn uses gamlss.fk().
Note that, finding the break points is not a trivial problem and therefore multiple maximum points can occur.
More details about the free knot splines can be found in package Dierckx, (1991).
The gamlss algorithm used a modified backfitting in this case, that is, it fits the linear part fist.
Note that trying to predict outside the x-range can be dangerous as the example below shows.
Value
The gamlss object saved contains the last fitted object which can be accessed using
obj$par.coefSmo where obj is the fitted gamlss object par is the relevant distribution
parameter.
Author(s)
Mikis Stasinopoulos mikis.stasinopoulos@gamlss.org, Bob Rigby
References
Dierckx, P. (1991) Curve and Surface Fitting with Splines, Oxford Science Publications
Stasinopoulos D. M., Rigby R.A. and Akantziliotou C. (2006) Instructions on how to use the GAMLSS package in R. Accompanying documentation in the current GAMLSS help files, (see also http://www.gamlss.org/).
Stasinopoulos D. M. Rigby R.A. (2007) Generalized additive models for location scale and shape (GAMLSS) in R. Journal of Statistical Software, Vol. 23, Issue 7, Dec 2007, http://www.jstatsoft.org/v23/i07.
See Also
Examples
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 | ## creating a linear + linear function
x <- seq(0,10, length.out=201)
knot <- 5
set.seed(12543)
mu <- ifelse(x<=knot,5+0.5*x,5+0.5*x+1.5*(x-knot))
y <- rNO(201, mu=mu, sigma=.5)
## plot the data
plot(y~x, xlim=c(-1,13), ylim=c(3,23))
## fit model using curfit
m1 <- fitFreeKnots(y, x, knots=3, degree=1)
knots(m1)
## fitted values
lines(fitted(m1)~x, col="red", lwd="3")
## predict
pm1<-predict(m1, newdata=-1:12)
points(-1:12,pm1, col="red",pch = 21, bg="blue")
#------------------------------------------------
## now gamlss
#------------------------------------------------
## now negative binomial data
knot=4
eta1 <- ifelse(x<=knot,0.8+0.08*x,.8+0.08*x+.3*(x-knot))
plot(eta1~x)
set.seed(143)
y <- rNBI(201, mu=exp(eta1), sigma=.1)
da <- data.frame(y=y,x=x)
plot(y~x, data=da)
## getting the break point using profile deviance
n1 <- quote(gamlss(y ~ x+I((x>this)*(x-this)), family=NBI, data=da))
prof.term(n1, min=1, max=9, criterion="GD", start.prev=FALSE)
## now fit the model using fk
g1 <- gamlss(y~fk(x, degree=1, start=c(4)), data=da, family=NBI)
## get the breakpoint
knots(getSmo(g1))
## summary of the gamlss object FreeBreakPointsReg object
getSmo(g1)
## plot fitted model
plot(y~x, data=da)
lines(fitted(g1)~x, data=da, col="red")
#------------------------------------------------
## the aids data as example where things can go wrong
## using fk()
data(aids)
a1<-gamlss(y~x+fk(x, degree=1, start=25)+qrt, data=aids, family=NBI)
knots(getSmo(a1))
# using profile deviance
aids.1 <- quote(gamlss(y ~ x+I((x>this)*(x-this))+qrt,family=NBI,data=aids))
prof.term(aids.1, min=16, max=21, step=.1, start.prev=FALSE)
## The Maximum Likelihood estimator is 18.33231 not 17.37064
## plotting the fit
with(aids, plot(x,y,pch=21,bg=c("red","green3","blue","yellow")[unclass(qrt)]))
lines(fitted(a1)~aids$x)
#-------------------------------------------------
|
Example output
Loading required package: gamlss.dist
Loading required package: MASS
Loading required package: gamlss
Loading required package: splines
Loading required package: gamlss.data
Loading required package: nlme
Loading required package: parallel
********** GAMLSS Version 5.1-2 **********
For more on GAMLSS look at http://www.gamlss.org/
Type gamlssNews() to see new features/changes/bug fixes.
Loading required package: mgcv
This is mgcv 1.8-25. For overview type 'help("mgcv-package")'.
Loading required package: nnet
Attaching package: 'nnet'
The following object is masked from 'package:mgcv':
multinom
Loading required package: rpart
BP1
5.011936
GAMLSS-RS iteration 1: Global Deviance = 1032.275
GAMLSS-RS iteration 2: Global Deviance = 1030.958
GAMLSS-RS iteration 3: Global Deviance = 1030.957
GAMLSS-RS iteration 4: Global Deviance = 1030.957
GAMLSS-RS iteration 1: Global Deviance = 1021.241
GAMLSS-RS iteration 2: Global Deviance = 1020.682
GAMLSS-RS iteration 3: Global Deviance = 1020.682
GAMLSS-RS iteration 1: Global Deviance = 1012.962
GAMLSS-RS iteration 2: Global Deviance = 1012.919
GAMLSS-RS iteration 3: Global Deviance = 1012.919
GAMLSS-RS iteration 1: Global Deviance = 1013.683
GAMLSS-RS iteration 2: Global Deviance = 1013.649
GAMLSS-RS iteration 3: Global Deviance = 1013.649
GAMLSS-RS iteration 1: Global Deviance = 1020.127
GAMLSS-RS iteration 2: Global Deviance = 1019.822
GAMLSS-RS iteration 3: Global Deviance = 1019.822
GAMLSS-RS iteration 1: Global Deviance = 1027.483
GAMLSS-RS iteration 2: Global Deviance = 1026.827
GAMLSS-RS iteration 3: Global Deviance = 1026.827
GAMLSS-RS iteration 1: Global Deviance = 1034.174
GAMLSS-RS iteration 2: Global Deviance = 1032.899
GAMLSS-RS iteration 3: Global Deviance = 1032.898
GAMLSS-RS iteration 4: Global Deviance = 1032.898
******************************************************************
The Maximum Likelihood estimator is 4.182408
with a Global Deviance equal to 1012.211
A 95 % Confidence interval is: ( 2.990368 , 5.595213 )
******************************************************************
GAMLSS-RS iteration 1: Global Deviance = 1012.078
GAMLSS-RS iteration 2: Global Deviance = 1012.077
GAMLSS-RS iteration 3: Global Deviance = 1012.077
BP1
4.150024
Call: fitFreeKnots(y = y, x = xvar, weights = w, degree = degree,
knots = lambda, fixed = control$fixed, base = control$base)
Coefficients:
(Intercept) x XatBP1
-0.90843 0.07212 0.29733
Estimated Knots:
BP1
4.15
GAMLSS-RS iteration 1: Global Deviance = 381.5559
GAMLSS-RS iteration 2: Global Deviance = 380.1881
GAMLSS-RS iteration 3: Global Deviance = 380.1878
BP1
17.37064
GAMLSS-RS iteration 1: Global Deviance = 394.1451
GAMLSS-RS iteration 2: Global Deviance = 392.7581
GAMLSS-RS iteration 3: Global Deviance = 392.7562
GAMLSS-RS iteration 4: Global Deviance = 392.7557
GAMLSS-RS iteration 1: Global Deviance = 392.9952
GAMLSS-RS iteration 2: Global Deviance = 391.5406
GAMLSS-RS iteration 3: Global Deviance = 391.539
GAMLSS-RS iteration 4: Global Deviance = 391.5384
GAMLSS-RS iteration 1: Global Deviance = 391.8902
GAMLSS-RS iteration 2: Global Deviance = 390.3677
GAMLSS-RS iteration 3: Global Deviance = 390.3655
GAMLSS-RS iteration 4: Global Deviance = 390.3653
GAMLSS-RS iteration 1: Global Deviance = 390.8327
GAMLSS-RS iteration 2: Global Deviance = 389.2424
GAMLSS-RS iteration 3: Global Deviance = 389.24
GAMLSS-RS iteration 4: Global Deviance = 389.2398
GAMLSS-RS iteration 1: Global Deviance = 389.8248
GAMLSS-RS iteration 2: Global Deviance = 388.1668
GAMLSS-RS iteration 3: Global Deviance = 388.1642
GAMLSS-RS iteration 4: Global Deviance = 388.1639
GAMLSS-RS iteration 1: Global Deviance = 388.8692
GAMLSS-RS iteration 2: Global Deviance = 387.1436
GAMLSS-RS iteration 3: Global Deviance = 387.1403
GAMLSS-RS iteration 4: Global Deviance = 387.14
GAMLSS-RS iteration 1: Global Deviance = 387.9669
GAMLSS-RS iteration 2: Global Deviance = 386.1731
GAMLSS-RS iteration 3: Global Deviance = 386.1698
GAMLSS-RS iteration 4: Global Deviance = 386.1696
GAMLSS-RS iteration 1: Global Deviance = 387.12
GAMLSS-RS iteration 2: Global Deviance = 385.2575
GAMLSS-RS iteration 3: Global Deviance = 385.2544
GAMLSS-RS iteration 4: Global Deviance = 385.2543
GAMLSS-RS iteration 1: Global Deviance = 386.3296
GAMLSS-RS iteration 2: Global Deviance = 384.3982
GAMLSS-RS iteration 3: Global Deviance = 384.3952
GAMLSS-RS iteration 4: Global Deviance = 384.3951
GAMLSS-RS iteration 1: Global Deviance = 385.5971
GAMLSS-RS iteration 2: Global Deviance = 383.5956
GAMLSS-RS iteration 3: Global Deviance = 383.5935
GAMLSS-RS iteration 4: Global Deviance = 383.5932
GAMLSS-RS iteration 1: Global Deviance = 384.9225
GAMLSS-RS iteration 2: Global Deviance = 382.8511
GAMLSS-RS iteration 3: Global Deviance = 382.8483
GAMLSS-RS iteration 4: Global Deviance = 382.8481
GAMLSS-RS iteration 1: Global Deviance = 384.194
GAMLSS-RS iteration 2: Global Deviance = 382.0384
GAMLSS-RS iteration 3: Global Deviance = 382.0356
GAMLSS-RS iteration 4: Global Deviance = 382.0355
GAMLSS-RS iteration 1: Global Deviance = 383.5353
GAMLSS-RS iteration 2: Global Deviance = 381.2952
GAMLSS-RS iteration 3: Global Deviance = 381.2926
GAMLSS-RS iteration 4: Global Deviance = 381.2925
GAMLSS-RS iteration 1: Global Deviance = 382.9474
GAMLSS-RS iteration 2: Global Deviance = 380.6226
GAMLSS-RS iteration 3: Global Deviance = 380.62
GAMLSS-RS iteration 4: Global Deviance = 380.6199
GAMLSS-RS iteration 1: Global Deviance = 382.4312
GAMLSS-RS iteration 2: Global Deviance = 380.0215
GAMLSS-RS iteration 3: Global Deviance = 380.0186
GAMLSS-RS iteration 4: Global Deviance = 380.0184
GAMLSS-RS iteration 1: Global Deviance = 381.9868
GAMLSS-RS iteration 2: Global Deviance = 379.4907
GAMLSS-RS iteration 3: Global Deviance = 379.4879
GAMLSS-RS iteration 4: Global Deviance = 379.4877
GAMLSS-RS iteration 1: Global Deviance = 381.6142
GAMLSS-RS iteration 2: Global Deviance = 379.0304
GAMLSS-RS iteration 3: Global Deviance = 379.0277
GAMLSS-RS iteration 4: Global Deviance = 379.0275
GAMLSS-RS iteration 1: Global Deviance = 381.3128
GAMLSS-RS iteration 2: Global Deviance = 378.6399
GAMLSS-RS iteration 3: Global Deviance = 378.6372
GAMLSS-RS iteration 4: Global Deviance = 378.6371
GAMLSS-RS iteration 1: Global Deviance = 381.0821
GAMLSS-RS iteration 2: Global Deviance = 378.3177
GAMLSS-RS iteration 3: Global Deviance = 378.3153
GAMLSS-RS iteration 4: Global Deviance = 378.3152
GAMLSS-RS iteration 1: Global Deviance = 380.9202
GAMLSS-RS iteration 2: Global Deviance = 378.0629
GAMLSS-RS iteration 3: Global Deviance = 378.0604
GAMLSS-RS iteration 4: Global Deviance = 378.0603
GAMLSS-RS iteration 1: Global Deviance = 380.8259
GAMLSS-RS iteration 2: Global Deviance = 377.8733
GAMLSS-RS iteration 3: Global Deviance = 377.8707
GAMLSS-RS iteration 4: Global Deviance = 377.8706
GAMLSS-RS iteration 1: Global Deviance = 380.7194
GAMLSS-RS iteration 2: Global Deviance = 377.6608
GAMLSS-RS iteration 3: Global Deviance = 377.6579
GAMLSS-RS iteration 4: Global Deviance = 377.6578
GAMLSS-RS iteration 1: Global Deviance = 380.6919
GAMLSS-RS iteration 2: Global Deviance = 377.5254
GAMLSS-RS iteration 3: Global Deviance = 377.5222
GAMLSS-RS iteration 4: Global Deviance = 377.5222
GAMLSS-RS iteration 1: Global Deviance = 380.7412
GAMLSS-RS iteration 2: Global Deviance = 377.4651
GAMLSS-RS iteration 3: Global Deviance = 377.4618
GAMLSS-RS iteration 4: Global Deviance = 377.4618
GAMLSS-RS iteration 1: Global Deviance = 380.8655
GAMLSS-RS iteration 2: Global Deviance = 377.4779
GAMLSS-RS iteration 3: Global Deviance = 377.4746
GAMLSS-RS iteration 4: Global Deviance = 377.4745
GAMLSS-RS iteration 1: Global Deviance = 381.0621
GAMLSS-RS iteration 2: Global Deviance = 377.5616
GAMLSS-RS iteration 3: Global Deviance = 377.558
GAMLSS-RS iteration 4: Global Deviance = 377.558
GAMLSS-RS iteration 1: Global Deviance = 381.3283
GAMLSS-RS iteration 2: Global Deviance = 377.7133
GAMLSS-RS iteration 3: Global Deviance = 377.7095
GAMLSS-RS iteration 4: Global Deviance = 377.7095
GAMLSS-RS iteration 1: Global Deviance = 381.6609
GAMLSS-RS iteration 2: Global Deviance = 377.9302
GAMLSS-RS iteration 3: Global Deviance = 377.9262
GAMLSS-RS iteration 4: Global Deviance = 377.9261
GAMLSS-RS iteration 1: Global Deviance = 382.0564
GAMLSS-RS iteration 2: Global Deviance = 378.2087
GAMLSS-RS iteration 3: Global Deviance = 378.2049
GAMLSS-RS iteration 4: Global Deviance = 378.2049
GAMLSS-RS iteration 1: Global Deviance = 382.5117
GAMLSS-RS iteration 2: Global Deviance = 378.5468
GAMLSS-RS iteration 3: Global Deviance = 378.5426
GAMLSS-RS iteration 4: Global Deviance = 378.5426
GAMLSS-RS iteration 1: Global Deviance = 383.0228
GAMLSS-RS iteration 2: Global Deviance = 378.9407
GAMLSS-RS iteration 3: Global Deviance = 378.9361
GAMLSS-RS iteration 4: Global Deviance = 378.936
GAMLSS-RS iteration 1: Global Deviance = 383.5725
GAMLSS-RS iteration 2: Global Deviance = 379.4074
GAMLSS-RS iteration 3: Global Deviance = 379.4019
GAMLSS-RS iteration 4: Global Deviance = 379.4018
GAMLSS-RS iteration 1: Global Deviance = 384.184
GAMLSS-RS iteration 2: Global Deviance = 379.9371
GAMLSS-RS iteration 3: Global Deviance = 379.931
GAMLSS-RS iteration 4: Global Deviance = 379.9308
GAMLSS-RS iteration 1: Global Deviance = 384.8531
GAMLSS-RS iteration 2: Global Deviance = 380.5264
GAMLSS-RS iteration 3: Global Deviance = 380.5194
GAMLSS-RS iteration 4: Global Deviance = 380.5192
GAMLSS-RS iteration 1: Global Deviance = 385.5752
GAMLSS-RS iteration 2: Global Deviance = 381.1712
GAMLSS-RS iteration 3: Global Deviance = 381.1633
GAMLSS-RS iteration 4: Global Deviance = 381.163
GAMLSS-RS iteration 1: Global Deviance = 386.3461
GAMLSS-RS iteration 2: Global Deviance = 381.8673
GAMLSS-RS iteration 3: Global Deviance = 381.8582
GAMLSS-RS iteration 4: Global Deviance = 381.8582
GAMLSS-RS iteration 1: Global Deviance = 387.1614
GAMLSS-RS iteration 2: Global Deviance = 382.6114
GAMLSS-RS iteration 3: Global Deviance = 382.601
GAMLSS-RS iteration 4: Global Deviance = 382.601
GAMLSS-RS iteration 1: Global Deviance = 388.0167
GAMLSS-RS iteration 2: Global Deviance = 383.3994
GAMLSS-RS iteration 3: Global Deviance = 383.3874
GAMLSS-RS iteration 4: Global Deviance = 383.3874
GAMLSS-RS iteration 1: Global Deviance = 388.9078
GAMLSS-RS iteration 2: Global Deviance = 384.2275
GAMLSS-RS iteration 3: Global Deviance = 384.2138
GAMLSS-RS iteration 4: Global Deviance = 384.2138
GAMLSS-RS iteration 1: Global Deviance = 389.8308
GAMLSS-RS iteration 2: Global Deviance = 385.092
GAMLSS-RS iteration 3: Global Deviance = 385.0764
GAMLSS-RS iteration 4: Global Deviance = 385.0764
GAMLSS-RS iteration 1: Global Deviance = 390.7817
GAMLSS-RS iteration 2: Global Deviance = 385.9893
GAMLSS-RS iteration 3: Global Deviance = 385.9718
GAMLSS-RS iteration 4: Global Deviance = 385.9718
GAMLSS-RS iteration 1: Global Deviance = 391.5393
GAMLSS-RS iteration 2: Global Deviance = 386.6922
GAMLSS-RS iteration 3: Global Deviance = 386.6738
GAMLSS-RS iteration 4: Global Deviance = 386.6738
GAMLSS-RS iteration 1: Global Deviance = 392.3358
GAMLSS-RS iteration 2: Global Deviance = 387.4411
GAMLSS-RS iteration 3: Global Deviance = 387.4204
GAMLSS-RS iteration 4: Global Deviance = 387.4204
GAMLSS-RS iteration 1: Global Deviance = 393.1679
GAMLSS-RS iteration 2: Global Deviance = 388.2305
GAMLSS-RS iteration 3: Global Deviance = 388.2081
GAMLSS-RS iteration 4: Global Deviance = 388.208
GAMLSS-RS iteration 1: Global Deviance = 394.0319
GAMLSS-RS iteration 2: Global Deviance = 389.0582
GAMLSS-RS iteration 3: Global Deviance = 389.0337
GAMLSS-RS iteration 4: Global Deviance = 389.0335
GAMLSS-RS iteration 1: Global Deviance = 394.9245
GAMLSS-RS iteration 2: Global Deviance = 389.9202
GAMLSS-RS iteration 3: Global Deviance = 389.8935
GAMLSS-RS iteration 4: Global Deviance = 389.8933
GAMLSS-RS iteration 1: Global Deviance = 395.8423
GAMLSS-RS iteration 2: Global Deviance = 390.8145
GAMLSS-RS iteration 3: Global Deviance = 390.7846
GAMLSS-RS iteration 4: Global Deviance = 390.7844
GAMLSS-RS iteration 1: Global Deviance = 396.7822
GAMLSS-RS iteration 2: Global Deviance = 391.7366
GAMLSS-RS iteration 3: Global Deviance = 391.7039
GAMLSS-RS iteration 4: Global Deviance = 391.7037
GAMLSS-RS iteration 1: Global Deviance = 397.7413
GAMLSS-RS iteration 2: Global Deviance = 392.683
GAMLSS-RS iteration 3: Global Deviance = 392.6485
GAMLSS-RS iteration 4: Global Deviance = 392.6483
GAMLSS-RS iteration 1: Global Deviance = 398.7167
GAMLSS-RS iteration 2: Global Deviance = 393.6527
GAMLSS-RS iteration 3: Global Deviance = 393.6155
GAMLSS-RS iteration 4: Global Deviance = 393.6152
GAMLSS-RS iteration 1: Global Deviance = 399.7058
GAMLSS-RS iteration 2: Global Deviance = 394.6422
GAMLSS-RS iteration 3: Global Deviance = 394.6018
GAMLSS-RS iteration 4: Global Deviance = 394.6017
******************************************************************
The Maximum Likelihood estimator is 18.33231
with a Global Deviance equal to 377.4579
A 95 % Confidence interval is: ( 17.19903 , 19.42018 )
******************************************************************
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