gamlss.foreach (version 1.1-6)

fitPCR: Function to fit simple Principal Component Regression.

Description

This function is a univariate (i.e. one response) version of a principal component regression. It is based on the function svdpc.fit() of package pls but it has been generalised to take prior weights. It gets a (single) response variable y (n x 1) and a matrix of explanatory variables of dimensions n x p and fits different principal component regressions up to principal component M. Note that M can be less or equal to p (if \(n > p\)) or less or equal to n if \(n <p\), that is, when there they are less observations than variables.

The function is used by the GAMLSS additive term function pcr() to fit a principal component regression model within gamlss().

Usage

fitPCR(x = NULL, y = NULL, weights = rep(1, n), 
       M = NULL, df = NULL, supervised = FALSE, 
       k = 2, r = 0.2, plot = TRUE)

Value

It returns a object PCR which can be used with methods print(), summary(), plot(), fitted() and coef(). The object has elements:

coefficients

The beta coefficients for 1 to M principal components

scores

the n x M dimensional matrix T o=f scores

loadings

the p x M dimensional matrix P of loadings

gamma

the first M principal component coefficients

se.gamma

the standard errors of the M principal component coefficients

center

the location parameters used to scale the x's

scale

the scale parameters used to scale the x's

fitted.values

matrix of n x M dimensions

Xvar

sum of squares of the scores i.e. diag(T'T)

gaic

The GAIC values

pc

number of PC i.e. which value of GAIC has the minimum

k

which penalty for GAIC

M

the maximum of PC tried

sigma

The estimated sigma from the M fitted components

residuals

The n x M matrix of the residuals

call

the function call

Arguments

x

a matrix of explanatory variables

y

the response variable

weights

prior weights

M

if set specifies the maximum number of components to be considered

df

if set specifies the number of components

supervised

whether supervised PCR should be used or not, default=FALSE

k

the penalty of GAIC

r

a correlation value (between zero and one) used smoothing parameter when supervised=TRUE

plot

Whether to plot the coefficient path

Author

Mikis Stasinopoulos, Robert Rigby and Fernanda De Bastiani.

Details

More details here

References

Bjorn-Helge Mevik, Ron Wehrens and Kristian Hovde Liland (2019). pls: Partial Least Squares and Principal Component Regression. R package version 2.7-2. https://CRAN.R-project.org/package=pls

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.

Rigby, R. A., Stasinopoulos, D. M., Heller, G. Z., and De Bastiani, F. (2019) Distributions for modeling location, scale, and shape: Using GAMLSS in R, Chapman and Hall/CRC, tools:::Rd_expr_doi("10.1201/9780429298547"). An older version can be found in https://www.gamlss.com/.

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, tools:::Rd_expr_doi("10.18637/jss.v023.i07").

Stasinopoulos D. M., Rigby R.A., Heller G., Voudouris V., and De Bastiani F., (2017) Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC. tools:::Rd_expr_doi("10.1201/b21973")

Stasinopoulos, M. D., Rigby, R. A., and De Bastiani F., (2018) GAMLSS: a distributional regression approach, Statistical Modelling, Vol. 18, pp, 248-273, SAGE Publications Sage India: New Delhi, India. tools:::Rd_expr_doi("10.1177/1471082X18759144")

Stasinopoulos, M. D., Rigby, R. A., Georgikopoulos N., and De Bastiani F., (2021) Principal component regression in GAMLSS applied to Greek-German government bond yield spreads, Statistical Modelling tools:::Rd_expr_doi("10.1177/1471082X211022980").

(see also https://www.gamlss.com/).

See Also

pc

Examples

library(glmnet)
data(QuickStartExample)
attach(QuickStartExample)
hist(y, main="(a)")
if (is.null(rownames(x))) colnames(x) <- paste0("X", 
    seq(1:dim(x)[2]))
############################################################
# fitPCR
############################################################
# fitting
registerDoParallel(cores = 2)
MM<- fitPCR(x,y, k=log(100))
stopImplicitCluster()
points(MM$coef[,16]~rep(16,20))
names(MM)
MM
#----------------------------------------------------------
# plotting
plot(MM)
plot(MM, "gaic")
#----------------------------------------------------------
print(MM)
#----------------------------------------------------------
coef(MM)                        # the gammas
coef(MM, param="beta")          # the betas
coef(MM, param="beta", pc=1)  # at position 1
#----------------------------------------------------------
# plotting y and and fitted balues at different points
plot(y)
points(fitted(MM, pc=3), col=2)
points(fitted(MM, pc=20), col=3)
#----------------------------------------------------------
# variance covariance 
vcov(MM, type="se", pc=1) 
vcov(MM, type="se", pc=2)
vcov(MM, type="se", pc=20)
# library(corrplot)
# corrplot(vcov(MM, type="cor", pc=10))
# corrplot(vcov(MM, type="cor", pc=20))
#----------------------------------------------------------
summary(MM)
summary(MM, param="beta", pc=15)
summary(MM, param ="beta", pc=3) 
summary(MM, param ="beta") # at default
#----------------------------------------------------------
predict(MM, newdata= x[1:5,])
fitted(MM)[1:5]