penLS {gamlss.util} | R Documentation |
The function penLS()
can be used to fit a penalised least square to a response variable y.
There is no explanatory variable here.
The underline model is a random walk.
penLS(y, w = rep(1, length(y)), df = NULL, lambda = NULL, start = 10, order = 1, plot = FALSE, type = c("level", "trend"), method = c("ML", "GAIC", "GCV"), k = 2, ...)
y |
the response variable usually a time series |
w |
prior weights if needed otherwise 1 |
df |
effective degrees of freedom |
lambda |
the smoothing parameter |
start |
the lambda starting value if the local methods are use |
order |
the required difference in the vector of coefficients, see below |
plot |
whether to plot the data and the fitted function |
type |
the type of X matrix, if "level" X is a diagonel matrix of 1's if "trend" X is a diagonal matrix 1:n |
method |
The method used in the estimation of the smoothing parameter |
k |
the penalty used in "GAIC" and "GCV" |
... |
for extra arguments |
The order refers to differences in the penalty matrix, (i) order = 0 : white noise random effects (ii) order = 1 : random walk (iii) order = 2 : random walk of order 2 (iv) order = 3 : random walk of order 3
Returns a fitted object of class penLS
. The object contains
1) the fitted coefficients
2) the fitted.values
3) the response variable y
,
4) the smoothing parameter lambda
, 8) the effective degrees of freedom df
,
5) the estimete for sigma sigma
,
6) the residual sum of squares rss
,
7) the Akaike information criterion aic
,
8) the Bayesian information criterion sbc
and
9) the deviance
The function can be slow for large response variable
Mikis Stasinopoulos d.stasinopoulos@londonmet.ac.uk, Bob Rigby r.rigby@londonmet.ac.uk and Paul Eilers
Eilers, P. H. C. and Marx, B. D. (1996). Flexible smoothing with B-splines and penalties (with comments and rejoinder). Statist. Sci, 11, 89-121.
Rigby, R. A. and Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape,(with discussion), Appl. Statist., 54, part 3, pp 507-554.
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.
set.seed(1234) x<-seq(0,10,length=200); y<-(yt<-1+2*x+.6*x^2-.1*x^3)+rnorm(200,0, 16) yts <- ts(y) plot(yts) #--------------------------------------------------------- #lambda fix m1<-penLS(yts,lambda=1) ; deviance(m1) #--------------------------------------------------------- # fixing df m2<-penLS(yts, df=10) ; deviance(m2) #--------------------------------------------------------- # estimating lambda - ML m3<-penLS(yts) ; deviance(m3) #--------------------------------------------------------- # estimating lambda - GAIC m4<-penLS(yts, method="GAIC", k=3) ; deviance(m4) #--------------------------------------------------------- # different order PPP <- par(mfrow=c(2,2)) penLS(yts, plot=TRUE, order=0, main="order=0") penLS(yts, plot=TRUE, order=1, main="order=1") penLS(yts, plot=TRUE, order=2, main="order=2") penLS(yts, plot=TRUE, order=3, main="order=3") par(PPP)