Computational Intensive Functions within GAMLSS

Description

This package is intended for functions needed parallel computations provided by the package foreach.

At the moment the following functions exist:

centiles.boot(), which is designed get bootstrap confidence intervals for centile curves

fitRolling(), rolling regression which is common in time series analysis when one step ahead forecasts is required.

fitPCR(), for univariate principal component regression. I

Details

The DESCRIPTION file:

Index of help topics:

BayesianBoot            Non parametric and Bayesian Bootstrapping for
                        GAMLSS models
centiles.boot           Bootstrapping centiles curves estimated using
                        GAMLSS
fitPCR                  Function to fit simple Principal Component
                        Regression.
fitRolling              Function to Fit Rolling Regression in gamlss
fitted.PCR              Methods for PCR objects
gamlss.foreach-package
                        Computational Intensive Functions within GAMLSS
pc                      Functions to Fit Principal Component Regression
                        in GAMLSS
which.Data.Corr         Detecting Hight Pair-Wise Correlations in Data

Author(s)

Mikis Stasinopoulos, d.stasinopoulos@londonmet.ac.uk,and Bob Rigby r.rigby@londonmet.ac.uk

Maintainer: Mikis Stasinopoulos, d.stasinopoulos@londonmet.ac.uk

References

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, 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, 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. doi:10.1201/b21973

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

See Also

gamlss,centiles,centiles.pred

Examples

library(gamlss.foreach)
# fixed degrees of freedom
cl <- makePSOCKcluster(2)
registerDoParallel(2)
data(db)
nage <- with(db, age^0.33)
ndb <- data.frame(db, nage)
m1 <- gamlss(head~cs(nage, 12), sigma.fo=~cs(nage,4), nu.fo=~nage, 
             tau.fo=~nage, family=BCT, data=ndb)
test1 <- centiles.boot(m1, xname="nage", xvalues=seq(0.01,20,0.2),B=10, power=0.33)
test1
plot(test1)
# degrees of freedom varying
m2 <- gamlss(head~pb(nage), sigma.fo=~pb(nage), nu.fo=~pb(nage), 
             tau.fo=~pb(nage), family=BCT, data=ndb)
test2 <- centiles.boot(m2, xname="nage", xvalues=seq(0.01,20,0.2),B=10, power=0.33)
stopImplicitCluster()
test2
plot(test2)

Non parametric and Bayesian Bootstrapping for GAMLSS models

Description

The function takes a GAMLSS fitted model and bootstrap it to create B bootstrap samples.

Usage

NonParametricBoot(obj, data = NULL, B = 100, newdata = NULL)

BayesianBoot(obj, data = NULL, B = 100, newdata = NULL)

Arguments

Details

The function NonParametric() perform non-parametric bootstraping, Efron and Tibshirani (1993) while the function BayesianBoot() perform Bayesian bootstrap Rubin (1981)

Value

An Bayesian.boot object with elements

Author(s)

Mikis Stasinopoulos, d.stasinopoulos@londonmet.ac.uk

References

Efron, B. and Tibshirani, R, (1993), An introduction to the bootstrap, Chapman and Hall New York, Monographs on statistics and applied probability, vulume 57.

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, doi:10.1201/9780429298547. An older version can be found in https://www.gamlss.com/.

Rubin, D. B. (1981) the bayesian bootstrap. The annals of statistics, pp. 130-134.

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, 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. 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. doi:10.1177/1471082X18759144

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

See Also

gamlss

Examples

m1 <-gamlss(y~x+qrt, data=aids, family=NBI())
registerDoParallel(cores = 2)
B1 <- BayesianBoot(m1)
summary(B1)
plot(B1)
B2 <- NonParametricBoot(m1)
stopImplicitCluster()
summary(B2)
plot(B2)

Bootstrapping centiles curves estimated using GAMLSS

Description

This is a function designed for non-parametric bootstrapping centile curves (growth curves) when the fitted model is fitted using GAMLSS with a single explanatory variable (usually age). Non parametric bootstrapping resample the data with replacement. The model is refitted for each bootstraps sample. Notes that if smoothing is used in the model, it is advisable (but not necessary) that the smoothing degree of freedom are fixed throughout.

Usage

centiles.boot(obj, data = NULL, xname = NULL, xvalues = NULL, 
  power = NULL, cent = c(2.5, 50, 97.5), B = 100, calibration = FALSE,
  ...)
             
## S3 method for class 'centiles.boot'
print(x, ...) 
## S3 method for class 'centiles.boot'
summary(object, fun = "mean", ...)              
## S3 method for class 'centiles.boot'
plot(x, quantiles = c(0.025, 0.975), 
       ylab = NULL, xlab = NULL, location = "median", original = FALSE, 
       scheme = c("shaded", "lines"), col.cent = "darkred", 
       col.se = "orange", col.shaded = "gray", lwd.center = 1.5, ...)  
             

Arguments

Details

This function is designed for bootstrapping centiles curves. It can be used to provide bootstrap means, standard deviations and quantiles, so the variability of the centile curves can be accessed (eg. by deriving confidence bands for centile curves).

Value

The function returns an object centile.boot which has its own print(), summary(), and plot() functions. The object centile.boot is a list with elements:

Note

See example below of how to use the function when a power transformation is used for the x-variable

Do not forget to use registerDoParallel(cores = NUMBER) or cl <- makeCluster(NUMBER) and registerDoParallel(cl) before calling the function centiles.boot(). Use closeAllConnections() after the fits to close the connections. Where NUMBER depends on the machine used.

Author(s)

Mikis Stasinopoulos, d.stasinopoulos@londonmet.ac.uk, Bob Rigby r.rigby@londonmet.ac.uk and Calliope Akantziliotou

References

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, 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, 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. 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. doi:10.1177/1471082X18759144

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

See Also

gamlss,centiles,centiles.pred

Examples

# bring the data and fit the model
data(abdom) 
m1<-gamlss(y~poly(x,2), sigma.fo=~x, data=abdom, family=BCT)
# perform the bootstrap simulation 
# (only 10 bootstrap samples here)
registerDoParallel(cores = 2)
boC<-centiles.boot(m1,xname="x", xvalues=c(15,20,25,30,35,40,45), B=10)
stopImplicitCluster()
boC
# get summaries
summary(boC, fun="mean")
#summary(boC, "median")
#summary(boC, "quantile", 0.025)
plot(boC)

# with transformation in x within the formula
# unsuitable for large data set since it is slow
m2<-gamlss(y~cs(x^0.5),sigma.fo=~cs(x^0.5), data=abdom, family=BCT) 
boC<-centiles.boot(m2,xname="x", xvalues=c(15,20,25,30,35,40,45), B=10)
summary(boC)
plot(boC)
#
# now with x-variable previously transformed
# better for large data set as it is faster 
nx<-abdom$x^0.5
newd<-data.frame(abdom, nx=abdom$x^0.5)
m3<-gamlss(y~cs(nx),sigma.fo=~cs(nx), data=newd, family=BCT)
boC <- centiles.boot(m3, xname="nx", xvalues=c(15,20,25,30,35,40,45), data=newd, power=0.5, B=10)
summary(boC)
#plot(boC)
# the original variables can be added in
#points(y~x,data=abdom)

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)

Arguments

Details

More details here

Value

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

Author(s)

Mikis Stasinopoulos, Robert Rigby and Fernanda De Bastiani.

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, 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, 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. 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. 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 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]

Function to Fit Rolling Regression in gamlss

Description

Rolling regression is common in time series analysis when one step ahead forecasts is required. The function fitRolling() works as follows: A model is fitted first to the whole data set using gamlss(). Then the function fitRolling() can be used. The function uses a fixed size rolling widow i.e. 365 days. The model is refitted repeatedly for the different windows over time (like a local regression in smoothing). Each time one step ahead forecast of distribution parameters are saved together with the prediction global deviance. The result is presented as a matrix with time as rows and parameters and the prediction deviance as columns.

Usage

fitRolling(obj, data, window = 365, as.time = NULL)

Arguments

Details

If the total observations are N and the window size n then we will need N-n different fits. The parallelization of the fits is achieved using the function foreach() from the package foreach.

Value

Returns a matrix containing as columns the one ahead prediction parameters of the distribution as well as the prediction global deviance.

Note

Do not forget to use registerDoParallel(cores = NUMBER) or cl <- makeCluster(NUMBER) and registerDoParallel(cl) before calling the function fitRolling() and closeAllConnections() after the fits. Where NUMBER depends on the machine used.

Author(s)

Mikis Stasinopoulos, d.stasinopoulos@londonmet.ac.uk

References

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, 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, 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. 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. doi:10.1177/1471082X18759144

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

See Also

gamlss

Examples

# fitting the aids data 45 observations
m1 <- gamlss(formula = y ~ pb(x) + qrt, family = NBI, data = aids) 
# get rolling regression with a window of 30
# there are 45-40=15 fits to do
# declaring cores (not needed for small data like this)
registerDoParallel(cores = 2)
FF <- fitRolling(m1, data=aids, window=30)
FF
stopImplicitCluster()
# check the first prediction
m30_1 <-update(m1, data=aids[1:30,])
predictAll(m30_1, newdata=aids[31,],output="matrix")
FF[1,]
# plot all the data 
plot(y~x, data=aids, xlim=c(0,45), ylim=c(0, 700), col=gray(.8))
# the first 30 observations
points(y~x, data=aids[1:30,], xlim=c(0,45))
# One step ahead forecasts
lines(FF[,"mu"]~as.numeric(rownames(FF)), col="red")
lines(fitted(m1)~aids$x, col="blue")

Methods for PCR objects

Description

The functions below are methods for PCR objects

Usage

## S3 method for class 'PCR'
fitted(object, pc = object$pc, ...)
## S3 method for class 'PCR'
plot(x, type = c("path", "gaic"),
                   labels = TRUE, cex = 0.8, ...)
## S3 method for class 'PCR'
coef(object, param = c("gamma", "beta"), 
              pc = object$pc, ...)
## S3 method for class 'PCR'
predict(object, newdata = NULL, 
                pc = object$pc, ...)
## S3 method for class 'PCR'
vcov(object, pc = object$pc, 
        type = c("vcov", "cor", "se", "all"),
                      ...)

Arguments

Author(s)

Mikis Stasinopoulos d.stasinopoulos@londonmet.ac.uk, Bob Rigby and Fernada De Bastiani

References

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. 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, https://www.jstatsoft.org/v23/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.

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

See Also

fitPCR

Functions to Fit Principal Component Regression in GAMLSS

Description

The functions pcr() and pc() can be use to fit principal component regression (PCR) within a GAMLSS model. They can be used as an extra additive term (together with other additive terms for example pb()) but the idea is mainly to be used on their own as a way of reducing the dimensionality of the the (scaled) x-variables. The functions can be used even when the number of the explanatory variables say p is greater than the number of observations n.

The two functions differ on the way PCR is implemented within the GAMLSS algorithm see for example Stasinopoulos et.al (2021). In the function pc() the singular value decomposition of the scaled x's is done in the beginning and different re-weighted linear models are fitted on the PC scores see algorithm 1 in Stasinopoulos et al. (2021). In the function pcr() at each iteration a new weighted PCR is performed using the function fitPCR() see algorithm 2 in Stasinopoulos et al. (2021).

The functions gamlss.pcr() and gamlss.pc() are supporting functions. The are not intended to be called directly by users. The function gamlss.pc() is using the linear model function lm() to fit the first principal components while the function codegamlss.pcr() uses fitPCR().

The function getSVD() creates a singular value decomposition of a design matrix X using the R function La.svd().

Usage

pc(x.vars = NULL, x = NULL, x.svd = NULL, df = NULL, 
   center = TRUE, scale = TRUE, tol = NULL, 
   max.number = min(p, n), k = log(n), 
   method = c( "t-values","GAIC","k-fold"))

pcr(x.vars = NULL, x = NULL, df = NULL, 
    M = min(p, n), k = log(n), 
    r = 0.2, method = c("GAIC", "t-values", "SPCR"))

gamlss.pc(x, y, w, xeval = NULL, ...)

gamlss.pcr(x, y, w, xeval = NULL, ...)

getSVD(x = NULL, nu = min(n, p), nv = min(n, p))

Arguments

Details

There are three different ways of declaring the list of x-variables (two for the function pcr()):

x.vars: this should be a character vector having the names of the explanatory variables. The names should be contained in the names of variables of the data argument of the function gamlss(), see example below.

x: This should be a design matrix (preferable unscaled since this could create problems when try to predict), see examples.

x.svd: This should be a list created by the function getSVD() which is used as an argument a design matrix, see examples.

Value

For the function pc() returns an object pc with elements "coef", "beta", "pc", "edf", "AIC". The object pc has methods plot(), coef() and print().

For the function pcr() returns an object PCR see for the help for function fitPCR.

Note

Do not forget to use registerDoParallel(cores = NUMBER) or cl <- makeCluster(NUMBER) and registerDoParallel(cl) before calling the function pc() without specifying the degrees of freedom. Use closeAllConnections() after the fits to close the connections. The NUMBER depends on the machine used.

Author(s)

Mikis Stasinopoulos d.stasinopoulos@londonmet.ac.uk, Bob Rigby

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, 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, 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. 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. 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 doi:10.1177/1471082X211022980.

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

See Also

centiles.boot, fitRolling

Examples

# the pc() function
# fitting the same model using different arguments
# using x.vars
p1 <- gamlss(y~pc(x.vars=c("x1","x2","x3","x4","x5","x6")), data=usair)
registerDoParallel(cores = 2)
t1 <- gamlss(y~pcr(x.vars=c("x1","x2","x3","x4","x5","x6")), data=usair)
# using x
X <- model.matrix(~x1+x2+x3+x4+x5+x6, data=usair)[,-1]
p2 <- gamlss(y~pc(x=X), data=usair)
t2 <- gamlss(y~pcr(x=X), data=usair)
# using x.svd
svdX <- getSVD(X)
p3 <- gamlss(y~pc(x.svd=svdX), data=usair)
# selecting the componets 
p3 <- gamlss(y~pc(x.svd=svdX, df=3), data=usair)
stopImplicitCluster()
plot(getSmo(t2))
plot(getSmo(t2), "gaic")

Detecting Hight Pair-Wise Correlations in Data

Description

There are two function here.

The function which.Data.Corr() is taking as an argument a data.frame or a data matrix and it reports the pairs of variables which have higher correlation than r.

The function which.yX.Corr() it takes as arguments a continuous response variable, y, and a set of continuous explanatory variables, x, (which may include first order interactions), and it creates a data.frame containing all variables with a pair-wise correlation above r. If the set of the continuous explanatory variables contains first order interactions, then by default, (hierarchical = TRUE), the main effects of the first order interactions will be also included so hierarchy will be preserved.

Usage

which.Data.Corr(data, r = 0.9, digits=3)
which.yX.Corr(y, x, r = 0.5, plot = TRUE, 
              hierarchical = TRUE, print = TRUE, digits=3)

Arguments

Value

The function which.Data.Corr() creates a matrix with three columns. The first two columns contain the names of the variables having pair-wise correlation higher than r and the third column show their correlation.

The function which.yX.Corr() creats a design matrix which containts variables which have

Author(s)

Mikis Stasinopoulos d.stasinopoulos@londonmet.ac.uk, Bob Rigby and Fernada De Bastiani.

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, 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, 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. 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. 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 doi:10.1177/1471082X211022980.

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

See Also

pc

Examples

data(oil, package="gamlss.data")
dim(oil)
# which variables are highly correlated?
CC<- which.Data.Corr(oil, r=0.999)
head(CC)
# 6 of them
# get the explanatory variables
form1 <- as.formula(paste("OILPRICE ~ ",
          paste(names(oil)[-1],collapse='+'))) 
# no interactions
X <- model.matrix(form1, data=oil)[,-1]
dim(X)
sX <- which.yX.Corr(oil$OILPRICE,x=X, r=0.4)
dim(sX)
# first order interactions
form2 <- as.formula(paste("OILPRICE ~ ",
        paste0(paste0("(",paste(names(oil)[-1], 
        collapse='+')), ")^2"))) 
form2
XX <- model.matrix(form2, data=oil)[,-1]
dim(XX)
which.yX.Corr(oil$OILPRICE,x=XX, r=0.4)