Package 'gamlss'

Description

Functions for fitting the Generalized Additive Models for Location Scale and Shape introduced by Rigby and Stasinopoulos (2005), <doi:10.1111/j.1467-9876.2005.00510.x>. The models use a distributional regression approach where all the parameters of the conditional distribution of the response variable are modelled using explanatory variables.

Details

The DESCRIPTION file:

Index of help topics:

.binom                  Lists used by GAMLSS
IC                      Gives the GAIC for a GAMLSS Object
LR.test                 Likelihood Ratio test for nested GAMLSS models
Q.stats                 A function to calculate the Q-statistics
Rsq                     Generalised (Pseudo) R-squared for GAMLSS
                        models
VC.test                 Vuong and Clarke tests
acfResid                ACF plot of the residuals
additive.fit            Implementing Backfitting in GAMLSS
bfp                     Functions to fit fractional polynomials in
                        GAMLSS
bp                      Bucket plot
calibration             Calibrating centile curves
centiles                Plots the centile curves for a GAMLSS object
centiles.com            Comparing centiles from different GAMLSS models
centiles.pred           Creating predictive centiles values
centiles.split          Plots centile curves split by x for a GAMLSS
                        object
coef.gamlss             Extract Model Coefficients in a GAMLSS fitted
                        model
cs                      Specify a Smoothing Cubic Spline Fit in a
                        GAMLSS Formula
deviance.gamlss         Global Deviance of a GAMLSS model
devianceIncr            The global deviance increment
dtop                    Detrended transformed Owen's plot
edf                     Effective degrees of freedom from gamlss model
find.hyper              A function to select values of hyper-parameters
                        in a GAMLSS model
fitDist                 Fitting Different Parametric 'gamlss.family'
                        Distributions.
fitted.gamlss           Extract Fitted Values For A GAMLSS Model
fittedPlot              Plots The Fitted Values of a GAMLSS Model
formula.gamlss          Extract the Model Formula in a GAMLSS fitted
                        model
gamlss                  Generalized Additive Models for Location Scale
                        and Shape
gamlss-package          Generalized Additive Models for Location Scale
                        and Shape
gamlss.control          Auxiliary for Controlling GAMLSS Fitting
gamlss.cs               Support for Function cs() and scs()
gamlss.fp               Support for Function fp()
gamlss.lo               Support for Function lo()
gamlss.ps               Support for Functions for smoothers
gamlss.random           Support for Functions random() and re()
gamlss.scope            Generate a Scope Argument for Stepwise GAMLSS
gamlssML                Maximum Likelihood estimation of a simple
                        GAMLSS model
gamlssVGD               A Set of Functions for selecting Models using
                        Validation or Test Data Sets and Cross
                        Validation
gen.likelihood          A function to generate the likelihood function
                        from a GAMLSS object
getPEF                  Getting the partial effect function from a
                        continuous term in a GAMLSS model
getQuantile             Getting the partial quantile function for a
                        term
getSmo                  Extracting Smoother information from a GAMLSS
                        fitted object
glim.control            Auxiliary for Controlling the inner algorithm
                        in a GAMLSS Fitting
histDist                This function plots the histogram and a fitted
                        (GAMLSS family) distribution to a variable
histSmo                 Density estimation using the Poisson trick
lms                     A function to fit LMS curves for centile
                        estimation
lo                      Specify a loess fit in a GAMLSS formula
loglogSurv              Survival function plots for checking the tail
                        behaviour of the data
lpred                   Extract Linear Predictor Values and Standard
                        Errors For A GAMLSS Model
model.frame.gamlss      Extract a model.frame, a model matrix or terms
                        from a GAMLSS object for a given distributional
                        parameter
numeric.deriv           An internal GAMLSS function for numerical
                        derivatives
par.plot                A function to plot parallel plot for repeated
                        measurement data
pcat                    Reduction for the Levels of a Factor.
pdf.plot                Plots Probability Distribution Functions for
                        GAMLSS Family
plot.gamlss             Plot Residual Diagnostics for an GAMLSS Object
plot.histSmo            A Plotting Function for density estimator
                        object histSmo
plot2way                Function to plot two interaction in a GAMLSS
                        model
polyS                   Auxiliary support for the GAMLSS
predict.gamlss          Extract Predictor Values and Standard Errors
                        For New Data In a GAMLSS Model
print.gamlss            Prints a GAMLSS fitted model
prodist.gamlss          Extracting Fitted or Predicted Probability
                        Distributions from gamlss Models
prof.dev                Plotting the Profile Deviance for one of the
                        Parameters in a GAMLSS model
prof.term               Plotting the Profile: deviance or information
                        criterion for one of the terms (or
                        hyper-parameters) in a GAMLSS model
ps                      P-Splines Fits in a GAMLSS Formula
quantSheets             Quantile Sheets
random                  Specify a random intercept model in a GAMLSS
                        formula
refit                   Refit a GAMLSS model
residuals.gamlss        Extract Residuals from GAMLSS model
ri                      Specify ridge or lasso Regression within a
                        GAMLSS Formula
rqres.plot              Creating and Plotting Randomized Quantile
                        Residuals
rvcov                   Robust Variance-Covariance matrix of the
                        parameters from a fitted GAMLSS model
stepGAIC                Choose a model by GAIC in a Stepwise Algorithm
summary.gamlss          Summarizes a GAMLSS fitted model
term.plot               Plot regression terms for a specified parameter
                        of a fitted GAMLSS object
update.gamlss           Update and Re-fit a GAMLSS Model
wp                      Worm plot
z.scores                Z-scores for lms objects

Author(s)

Mikis Stasinopoulos [aut, cre, cph] (<https://orcid.org/0000-0003-2407-5704>), Robert Rigby [aut] (<https://orcid.org/0000-0003-3853-1707>), Vlasios Voudouris [ctb], Calliope Akantziliotou [ctb], Marco Enea [ctb], Daniil Kiose [ctb] (<https://orcid.org/0000-0002-3596-5748>), Achim Zeileis [ctb] (<https://orcid.org/0000-0003-0918-3766>)

Maintainer: Mikis Stasinopoulos <[email protected]>

References

Nelder, J. A. and Wedderburn, R. W. M. (1972). Generalized linear models. J. R. Statist. Soc. A., 135 370-384.

Hastie, T. J. and Tibshirani, R. J. (1990). Generalized Additive Models. Chapman and Hall, London.

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

gamlss.dist

Examples

data(abdom)
mod<-gamlss(y~pb(x),sigma.fo=~pb(x),family=BCT, data=abdom, method=mixed(1,20))
plot(mod)
rm(mod)

Description

Those lists are used in GAMLSS fits.

Usage

".binom"

".counts"

".gamlss.bi.list" 

".gamlss.multin.list"

".gamlss.sm.lis"

".real0to1"

".realAll" 

".realline"

".realplus"

Format

List used by the gamlss() function.

.binom

a character vector showing all the binomial type (finite count) distributions

.counts

a character vector showing all the infinity count distributions

.gamlss.bi.list

a character vector showing all the binomial type (finite count) distributions

.gamlss.multin.list

a character vector showing all the multinomial distributions

.gamlss.sm.list

a character vector showing all the available smooth functions

.real0to1

a character vector showing all real line distributions with range 0 to 1

.realAll

a character vector showing all real line distributions from $-\infty$ to $+\infty$ and from $0$ to $+\infty$

.realline

a character vector showing all all real line distributions from $-\infty$ to $+\infty$

.realplus

a character vector showing all all real line distributions from $0$ to $+\infty$

Details

Those list are internal to help the gamlss() function.

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/).

Examples

.binom
.counts
.gamlss.bi.list
.gamlss.multin.list
.gamlss.sm.list
.real0to1
.realline
.realplus

Description

This plot display the ACF and PACF of the residuals of a gamlss or other fitted model (provided that they have been standardised appropriately. Is is appropriate for time series data.

Usage

acfResid(obj = NULL, resid = NULL)

Arguments

Details

The ACF and PACF for the residuals r, squared residuals r^2, r^3 and r^4 are plotted

Value

The relevant plots are displayed

Author(s)

Mikis Stasinopoulos. Bob Rigby. Vlasios Voudouris and Majid Djennad

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

acf

Examples

library(datasets)
data(co2)
m1<- gamlss(co2~pb(as.numeric(time(co2)))+factor(cycle(co2)))
acfResid(m1)

Description

This function is not to be used on its own. It is used for backfitting in the GAMLSS fitting algorithms and it is based on the equivalent function written by Trevor Hastie in the gam() S-plus implementation, (Chambers and Hastie, 1991).

Usage

additive.fit(x, y, w, s, who, smooth.frame, maxit = 30, tol = 0.001, 
             trace = FALSE, se = TRUE, ...)

Arguments

Details

This function should not be used on its own

Value

Returns a list with the linear fit plus the smothers

Author(s)

Mikis Stasinopoulos

References

Chambers, J. M. and Hastie, T. J. (1991). Statistical Models in S, Chapman and Hall, London.

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

gamlss

Description

The function bfp generate a power polynomial basis matrix which (for given powers) can be used to fit power polynomials in one x-variable. The function fp takes a vector and returns it with several attributes. The vector is used in the construction of the model matrix. The function fp() is not used for fitting the fractional polynomial curves but assigns the attributes to the vector to aid gamlss in the fitting process. The function doing the fitting is gamlss.fp() which is used at the backfitting function additive.fit (but never used on its own). The (experimental) function pp can be use to fit power polynomials as in $a+b_1 x^{p_1}+b_2 x^{p_2}$., where p1 and p2 have arbitrary values rather restricted as in the fp function.

Usage

bfp(x, powers = c(1, 2), shift = NULL, scale = NULL)
fp(x, npoly = 2, shift = NULL, scale = NULL)
pp(x, start = list(), shift = NULL, scale = NULL)

Arguments

Details

The above functions are an implementation of the fractional polynomials introduced by Royston and Altman (1994). The three functions involved in the fitting are loosely based on the fractional polynomials implementation in S-plus written by Gareth Amber in 1999, (unfortunately the URL link for his work no longer exist). The function bfp generates the right design matrix for the fitting a power polynomial of the type $a+b_1 x^{p_1}+b_2 x^{p_2}+\ldots+b_k x^p_k$. For given powers $p_1,p_2,\ldots,p_k$ given as the argument powers in bfp() the function can be used to fit power polynomials in the same way as the functions poly() or bs() (of package splines) are used to fit orthogonal or piecewise polynomials respectively. The function fp(), which is working as a smoother in gamlss, is used to fit the best fractional polynomials within a set of power values. Its argument npoly determines whether one, two or three fractional polynomials should used in the fitting. For a fixed number npoly the algorithm looks for the best fitting fractional polynomials in the list c(-2, -1, -0.5, 0, 0.5, 1, 2, 3) . Note that npolu=3 is rather slow since it fits all possible combinations 3-way combinations at each backfitting interaction. The function gamlss.fp() is an internal function of GAMLSS allowing the fractional polynomials to be fitted in the backfitting cycle of gamlss, and should be not used on its own.

Value

The function bfp returns a matrix to be used as part of the design matrix in the fitting.

The function fp returns a vector with values zero to be included in the design matrix but with attributes useful in the fitting of the fractional polynomials algorithm in gamlss.fp.

Warning

Since the model constant is included in both the design matrix X and in the backfitting part of fractional polynomials, its values is wrongly given in the summary. Its true values is the model constant minus the constant from the fractional polynomial fitting ??? What happens if more that one fractional polynomials are fitted?

Author(s)

Mikis Stasinopoulos, Bob Rigby

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/.

Royston, P. and Altman, D. G., (1994). Regression using fractional polynomials of continuous covariates: parsimonious parametric modelling (with discussion), Appl. Statist., 43, 429-467.

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

gamlss, gamlss.family

Examples

data(abdom)
#fits polynomials with power 1 and .5 
mod1<-gamlss(y~bfp(x,c(1,0.5)),data=abdom)
# fit the best of one fractional polynomial
m1<-gamlss(y~fp(x,1),data=abdom)
# fit the best of two fractional polynomials
m2<-gamlss(y~fp(x,2),data=abdom)
# fit the best of three fractional polynomials
m3<-gamlss(y~fp(x,3),data=abdom)
# get the coefficient for the second model 
m2$mu.coefSmo
# now power polynomials using the best 2 fp c()
 m4 <- gamlss(y ~ pp(x, c(1,3)), data = abdom)
# This is not good idea in this case because
# if you look at the fitted values you see what it went wrong
plot(y~x,data=abdom)
lines(fitted(m2,"mu")~abdom$x,col="red")
lines(fitted(m4,"mu")~abdom$x,col="blue")

Description

A bucket plot is a graphical way to check the skewness and kurtosis of a continuous variable or the residuals of a fitted GAMLSS model. It plots the transformed moment skewness and transformed moment kurtosis of the variable (or residuals) together with a cloud of points obtained using a non-parametric bootstrap from the original variable (or residuals). It also provides a graphical way of performing the Jarque-Bera test (JarqueandBera,1980).

There are two different bucket plots specified by the type argument:

i) the moment bucket and ii) the centile bucket which itself can be central or tail one.

Usage

bp(obj = NULL, weights = NULL, 
      type = c("moment", "centile.central", "centile.tail"), 
      xvar = NULL, bootstrap = TRUE, no.bootstrap = 99, 
      col.bootstrap = c("lightblue", "pink", "khaki", 
      "thistle", "tan", "sienna1","steelblue", "coral", "gold", 
      "cyan"), 
      pch.bootstrap = rep(21, 10), asCharacter = TRUE, 
      col.point = rep("black", 10), pch.point = 1:10, 
      lwd.point = 2, text.to.show = NULL, cex.text = 1.5, 
      col.text = "black", show.legend = FALSE, n.inter = 4, 
      xcut.points = NULL, overlap = 0, show.given = TRUE, 
      cex = 1, pch = 21, data = NULL, 
      bar.bg = c(num = "lightblue", fac = "pink"), ...)

Arguments

Value

A plot displaying the transformed moment skewness and transformed moment kurtosis of the sample or residual of a model.

Note

The bucket plot provides an additional residual diagnostic tool that can be used for fitted model checking, alongside other diagnostic tools, for example worm plots, and Q (and Z) statistics.

Author(s)

Mikis Stasinopoulos, Bob Rigby and Fernanda De Bastiani

References

De Bastiani, F., Stasinopoulos, D. M., Rigby, R. A., Heller, G. Z., and Lucas A. (2022) Bucket Plot: A Visual Tool for Skewness and Kurtosis Comparisons. send for publication.

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

wp, Q.stats

Examples

m1 <- gamlss(R~pb(Fl)+pb(A), data=rent, family=GA)
bp(m1)

Description

This function can used when the fitted model centiles do not coincide with the sample centiles.

Usage

calibration(object, xvar, cent = c(0.4, 2, 10, 25, 50, 75, 90, 98, 99.6),
            legend = FALSE, fan = FALSE, ...)

Arguments

Details

The function finds the sample quantiles of the residuals of the fitted model (the z-scores) and use them as sample quantile in the argument cent of the centiles() function. This procedure is appropriate if the fitted model centiles do not coincide with the sample centiles and when this failure is the same in all values of the explanatory variable xvar.

Value

A centile plot is produced and the sample centiles below each centile curve are printed (or saved)

Author(s)

Mikis Stasinopoulos, Bob Rigby and Vlasios Voudouris

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

centiles, centiles.fan

Examples

data(abdom)
m1<-gamlss(y~pb(x), sigma.fo=~pb(x), family=LO, data=abdom)
calibration(m1, xvar=abdom$x, fan=TRUE)

Description

This function centiles() plots centiles curves for distributions belonging to the GAMLSS family of distributions. The function also tabulates the sample percentages below each centile curve (for comparison with the model percentages given by the argument cent.) The function centiles.fan() plots a fan-chart of the centile curves. A restriction of the functions is that it applies to models with one explanatory variable only.

Usage

centiles(obj, xvar, cent = c(0.4, 2, 10, 25, 50, 75, 90, 98, 99.6), 
         legend = TRUE, ylab = "y", xlab = "x", main = NULL, 
         main.gsub = "@", xleg = min(xvar), yleg = max(obj$y), 
         xlim = range(xvar), ylim = range(obj$y), save = FALSE, 
         plot = TRUE, points = TRUE,  pch =  15, cex = 0.5, col =  gray(0.7), 
         col.centiles = 1:length(cent) + 2, lty.centiles = 1, lwd.centiles = 1, ...)
centiles.fan(obj, xvar, cent = c(0.4, 2, 10, 25, 50, 75, 90, 98, 99.6), 
         ylab = "y", xlab = "x", main = NULL, main.gsub = "@", 
         xleg = min(xvar), yleg = max(obj$y), xlim = range(xvar), 
         ylim = range(obj$y), points = FALSE,  median = TRUE, pch =  15, 
         cex = 0.5, col =  gray(0.7),
         colors = c("cm", "gray", "rainbow", "heat", "terrain", "topo"), ...)

Arguments

Details

Centiles are calculated using the fitted values in obj and xvar must correspond exactly to the predictor in obj to plot correctly.

col.centiles, lty.centiles and lwd.centiles may be vector arguments and are recycled to the length cent if necessary.

Value

A centile plot is produced and the sample centiles below each centile curve are printed (or saved)

Warning

This function is appropriate only when one continuous explanatory variable is fitted in the model

Author(s)

Mikis Stasinopoulos, Bob Rigby with contribution from Steve Ellison

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

gamlss, centiles.split , centiles.com

Examples

data(abdom)
h<-gamlss(y~pb(x), sigma.formula=~pb(x), family=BCT, data=abdom) 
# default plot
centiles(h,xvar=abdom$x)
# control of colours and lines
centiles(h, xvar=abdom$x,  col.cent=c(2,3,4,5,1,5,4,3,2,1), 
              lwd.cent=c(1,1,1,1,2,1,1,1,1))
#Control line types
centiles(h, xvar=abdom$x,  col.cent=1, cent=c(.5,2.5,50,97.5,99.5), 
              lty.centiles=c(3,2,1,2,3),lwd.cent=c(1,1,2,1,1))
# control of the main title
centiles(h, xvar=abdom$x,  main="Abdominal data \n @")
# the fan-chart
centiles.fan(h,xvar=abdom$x, colors="rainbow")
rm(h)

Description

This function compares centiles curves for more than one GAMLSS objects.It is based on the centiles function. The function also tabulates the sample percentages below each centile curve (for comparison with the model percentages given by the argument cent.) A restriction of the function is that it applies to models with one explanatory variable only

Usage

centiles.com(obj, ..., xvar, cent = c(0.4, 10, 50, 90, 99.6), 
             legend = TRUE, ylab = "y", xlab = "x", xleg = min(xvar), 
             yleg = max(obj$y), xlim = range(xvar), ylim = NULL, 
             no.data = FALSE, color = TRUE, main = NULL, plot = TRUE)

Arguments

Value

Centile plots are produced for the different fitted models and the sample centiles below each centile curve are printed

Warning

This function is appropriate only when one continuous explanatory variable is fitted in the model

Author(s)

Mikis Stasinopoulos and Bob Rigby

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

gamlss, centiles , centiles.split

Examples

data(abdom)
h1<-gamlss(y~cs(x,df=3), sigma.formula=~cs(x,1),family=BCT, data=abdom)
h2<-gamlss(y~pb(x), sigma.formula=~pb(x), family=BCT, data=abdom )
centiles.com(h1,h2,xvar=abdom$x)
rm(h1,h2)

Description

This function creates predictive centiles curves for new x-values given a GAMLSS fitted model. The function has three options: i) for given new x-values and given percentage centiles calculates a matrix containing the centiles values for y, ii) for given new x-values and standard normalized centile values calculates a matrix containing the centiles values for y, iii) for given new x-values and new y-values calculates the z-scores. A restriction of the function is that it applies to models with only one explanatory variable.

Usage

centiles.pred(obj, type = c("centiles", "z-scores", "standard-centiles"), 
             xname = NULL, xvalues = NULL, power = NULL, yval = NULL, 
             cent = c(0.4, 2, 10, 25, 50, 75, 90, 98, 99.6), 
             dev = c(-4, -3, -2, -1, 0, 1, 2, 3, 4), calibration = FALSE,
             plot = FALSE, legend = TRUE,  ylim = NULL,xlim = NULL,
             ...)

Arguments

Value

a vector (for option type="z-scores") or a matrix for options type="centiles" or type="standard-centiles" containing the appropriate values

Warning

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

Note

The power option should be only used if the model

Author(s)

Mikis Stasinopoulos, based on ideas of Elaine Borghie from the World Health Organization

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

gamlss, centiles, centiles.split

Examples

## bring the data and fit the model
data(abdom)
a<-gamlss(y~pb(x),sigma.fo=~pb(x), data=abdom, family=BCT)
## plot the centiles
centiles(a,xvar=abdom$x)
##-----------------------------------------------------------------------------
## the first use of the function centiles.pred()
## to calculate the centiles at new x values
##-----------------------------------------------------------------------------
newx<-seq(12,40,2)
mat <- centiles.pred(a, xname="x", xvalues=newx )
mat
## now plot the centile curves  
 mat <- centiles.pred(a, xname="x",xvalues=newx, plot=TRUE )
##-----------------------------------------------------------------------------
## the second use of the function centiles.pred()
## to calculate (nornalised) standard-centiles for new x
## values using the fitted model
##-----------------------------------------------------------------------------
newx <- seq(12,40,2)
mat <- centiles.pred(a, xname="x",xvalues=newx, type="standard-centiles" )
mat
## now plot the standard centiles  
mat <- centiles.pred(a, xname="x",xvalues=newx, type="standard-centiles",
       plot = TRUE )
##-----------------------------------------------------------------------------
## the third use of the function centiles.pred()
##  if we have new x and y values what are their z-scores?
##-----------------------------------------------------------------------------
# create new y and x values and plot them in the previous plot
newx <- c(20,21.2,23,20.9,24.2,24.1,25)
newy <- c(130,121,123,125,140,145,150)
for(i in 1:7) points(newx[i],newy[i],col="blue")
## now calculate their z-scores
znewx <- centiles.pred(a, xname="x",xvalues=newx,yval=newy, type="z-scores" )
znewx
## Not run: 
##-----------------------------------------------------------------------------
## What we do if the x variables is transformed?
##----------------------------------------------------------------------------
##  case 1 : transformed x-variable within the formula
##----------------------------------------------------------------------------
## fit model
aa <- gamlss(y~pb(x^0.5),sigma.fo=~pb(x^0.5), data=abdom, family=BCT)
## centiles is working in this case
centiles(aa, xvar=abdom$x, legend = FALSE)
## get predict for values of x at 12, 14, ..., 40
mat <- centiles.pred(aa, xname="x", xvalues=seq(12,40,2), plot=TRUE )
mat
# plot all prediction points
xx <- rep(mat[,1],9)
yy <- unlist(mat[,2:10])
points(xx,yy,col="red")
##----------------------------------------------------------------------------
##  case 2 : the x-variable is previously transformed 
##----------------------------------------------------------------------------
nx <- abdom$x^0.5
aa <- gamlss(y~pb(nx),sigma.fo=~pb(nx), data=abdom, family=BCT)
centiles(aa, xvar=abdom$x)
# equivalent to fitting
newd<-data.frame( abdom, nx=abdom$x^0.5)
aa1 <- gamlss(y~pb(nx),sigma.fo=~pb(nx), family=BCT, data=newd)
centiles(aa1, xvar=abdom$x)
# getting the centiles at x equal to 12, 14, ...40
mat <-  centiles.pred(aa, xname="nx", xvalues=seq(12,40,2), power=0.5, 
         data=newd, plot=TRUE)
# plot all prediction points         
xxx <- rep(mat[,1],9)
yyy <- unlist(mat[,2:10])
points(xxx,yyy,col="red")
# the idea is that if the transformed x-variable is used in the fit
# the power argument has to used in centiles.pred()

## End(Not run)

Description

This function plots centiles curves for separate ranges of the unique explanatory variable x. It is similar to the centiles function but the range of x is split at a user defined values xcut.point into r separate ranges. The functions also tabulates the sample percentages below each centile curve for each of the r ranges of x (for comparison with the model percentage given by cent) The model should have only one explanatory variable.

Usage

centiles.split(obj, xvar, xcut.points = NULL, n.inter = 4, 
               cent = c(0.4, 2, 10, 25, 50, 75, 90, 98, 99.6), 
               legend = FALSE, main = NULL, main.gsub = "@", 
               ylab = "y", xlab = "x", ylim = NULL, overlap = 0, 
               save = TRUE, plot = TRUE, ...)

Arguments

Value

Centile plots are produced and the sample centiles below each centile curve for each of the r ranges of x can be saved into a matrix.

Warning

This function is appropriate when only one continuous explanatory variable is fitted in the model

Author(s)

Mikis Stasinopoulos, Bob Rigby with contributions from Elaine Borghie

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

gamlss centiles, centiles.com

Examples

data(abdom)
h<-gamlss(y~pb(x), sigma.formula=~pb(x), family=BCT, data=abdom) 
mout <- centiles.split(h,xvar=abdom$x)
mout
rm(h,mout)

Description

coef.gamlss is the GAMLSS specific method for the generic function coef which extracts model coefficients from objects returned by modelling functions. ‘coefficients’ is an alias for coef.

Usage

## S3 method for class 'gamlss'
coef(object, what = c("mu", "sigma", "nu", "tau"), 
                      parameter = NULL, ... )
                      
coefAll(obj, deviance = FALSE, ...)

Arguments

Value

Coefficients extracted from the GAMLSS model object.

Author(s)

Mikis Stasinopoulos

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

gamlss, deviance.gamlss, fitted.gamlss

Examples

data(aids)
h<-gamlss(y~poly(x,3)+qrt, family=NBI, data=aids) # 
coef(h)
coefAll(h)
rm(h)

Description

The functions cs() and scs() are using the cubic smoothing splines function smooth.spline() to do smoothing. They take a vector and return it with several attributes. The vector is used in the construction of the model matrix. The functions do not do the smoothing, but assigns the attributes to the vector to aid gamlss in the smoothing. The function doing the smoothing is gamlss.cs(). This function use the R function smooth.spline() which is then used by the backfitting function additive.fit() which is based on the original GAM implementation described in Chambers and Hastie (1992). The function gamlss.scs() differs from the function cs() in that allows cross validation of the smoothing parameters unlike the cs() which fixes the effective degrees of freedom, df. Note that the recommended smoothing function is now the function pb() which allows the estimation of the smoothing parameters using a local maximum likelihood. The function pb() is based on the penalised beta splines (P-splines) of Eilers and Marx (1996).

The (experimental) function vc is now defunct. For fitting varying coefficient models, Hastie and Tibshirani (1993) use the function pvc().

Usage

cs(x, df = 3, spar = NULL, c.spar = NULL, control = cs.control(...), ...)
scs(x, df = NULL, spar = NULL, control = cs.control(...), ...)
cs.control(cv = FALSE, all.knots = TRUE, nknots = NULL, keep.data = TRUE,
               df.offset = 0, penalty = 1.4, control.spar = list(), ...)

Arguments

Details

Note that cs 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.cs()

Note that cs() and scs() functions behave differently at their default values that is if df and lambda are not specified. cs(x) by default will use 3 extra degrees of freedom for smoothing for x. scs(x) by default will estimate lambda (and the degrees of freedom) automatically using generalised cross validation (GCV). Note that if GCV is used the convergence of the gamlss model can be less stable compared to a model where the degrees of freedom are fixed. This will be true for small data sets.

Value

the vector x is returned, endowed with a number of attributes. The vector itself is used in the construction of the model matrix, while the attributes are needed for the backfitting algorithms additive.fit(). Since smoothing splines includes linear fits, the linear part will be efficiently computed with the other parametric linear parts of the model.

Warning

For a user who wishes to compare the gamlss() results with the equivalent gam() results in S-plus: make sure when using S-plus that the convergence criteria epsilon and bf.epsilon in control.gam() are decreased sufficiently to ensure proper convergence in S-plus. Also note that the degrees of freedom are defined on top of the linear term in gamlss, but on top of the constant term in S-plus, (so use an extra degrees of freedom in S-plus in order to obtain comparable results to those in galmss).

Change the upper limit of spar if you received the warning 'The output df are different from the input, change the control.spar'.

For large data sets do not use expressions, e.g. cs(x^0.5) inside the gamlss function command but evaluate the expression, e.g. nx=$x^0.5$, first and then use cs(nx).

Note

The degrees of freedom df are defined differently from that of the gam() function in S-plus. Here df are the additional degrees of freedom excluding the constant and the linear part of x. For example df=4 in gamlss() is equivalent to df=5 in gam() in S-plus

Author(s)

Mikis Stasinopoulos and Bob Rigby (see also the documentation of the functionsmooth.spline() for the original authors of the cubic spline function.)

References

Chambers, J. M. and Hastie, T. J. (1992) Statistical Models in S, Wadsworth & Brooks/Cole.

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.

Hastie, T. J. and Tibshirani, R. J. (1993), Varying coefficient models (with discussion),J. R. Statist. Soc. B., 55, 757-796.

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

gamlss, gamlss.cs, pb, pvc

Examples

# cubic splines example
data(aids)
# fitting a smoothing cubic spline with 7 degrees of freedom
# plus the a quarterly  effect  
aids1<-gamlss(y~cs(x,df=7)+qrt,data=aids,family=PO) # 
aids2<-gamlss(y~scs(x,df=5)+qrt,data=aids,family=PO) # 
aids3<-gamlss(y~scs(x)+qrt,data=aids,family=PO) # using GCV 
with(aids, plot(x,y))
lines(aids$x,fitted(aids1), col="red")
lines(aids$x,fitted(aids3), col="green")
rm(aids1, aids2, aids3)

Description

Returns the global, -2*log(likelihood), or the penalized, -2*log(likelihood)+ penalties, deviance of a fitted GAMLSS model object.

Usage

## S3 method for class 'gamlss'
deviance(object,  what = c("G", "P"), ...)

Arguments

Details

deviance is a generic function which can be used to extract deviances for fitted models. deviance.gamlss is the method for a GAMLSS object.

Value

The value of the global or the penalized deviance extracted from a GAMLSS object.

Author(s)

Mikis Stasinopoulos

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

gamlss.family, coef.gamlss, fitted.gamlss

Examples

data(aids)
h<-gamlss(y~poly(x,3)+qrt, family=PO, data=aids) # 
deviance(h)
rm(h)

Description

The global deviance increment is the contribution of each individual observation to the global deviance. The function devianceIncr() can be used to extract the global deviance increment for a fitted gamlss model or for a new (test/validation) data set. Large values for global deviance increment indicate a bad fit and for new data a bad prediction.

Usage

devianceIncr(obj, newdata = NULL)

Arguments

Value

Returns a vector of the global deviance increments for each observation.

Author(s)

Mikis Stasinopoulos

References

Rigby, R. A. and Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape,(with discussion), Appl. Statist., 54, part 3, 1-38.

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

deviance

Examples

#-----------------------------------------------------------------
# Count data set
# fit Poisson model
h1 <- gamlss(Claims~L_Population+L_Accidents+L_KI+L_Popdensity, 
             data=LGAclaims, family=PO)
p1<-devianceIncr(h1)
# fit negative binomial model
h2 <- gamlss(Claims~L_Population+L_Accidents+L_KI+L_Popdensity, 
             data=LGAclaims, family=NBI)
p2<-devianceIncr(h2)
# comparing using boxplots
boxplot(cbind(p1,p2))
# comparing using emphirical cdf
plot(ecdf(p1))
lines(ecdf(p2), col=2)
# comparing agaist the y-values
plot(p1~LGAclaims$Claims, pch=20, col="gray")
points(p2~LGAclaims$Claims, pch="-", col="orange")
#----------------------------------------------------------------
# Continuous data sets
## Not run: 
m1 <- gamlss(head~pb(age), data=db[1:6000,])
p1<-devianceIncr(m1)
m2 <- gamlss(head~pb(age), sigma.fo=~pb(age), nu.fo=~pb(age), 
      tau.fo=~pb(age), data=db[1:6000,], family=BCT)
p2<-devianceIncr(m2)
# comparing using summaries
summary(p1); summary(p2)
# comparing using boxplots
boxplot(cbind(p1,p2))
# comparing using histograms
hist(p1, col=rgb(1,0,0,0.5), xlim=c(0,50), breaks=seq(0,50,2))
hist(p2, col=rgb(0,0,1,0.5), add=T)
# comparing using emphirical cdf
plot(ecdf(p1))
lines(ecdf(p2), col=2)

## End(Not run)
#----------------------------------------------------------------

Description

Provides single or multiple detrended transformed Owen's plot, Owen (1995), for a GAMLSS fitted objects or any other fitted object which has the method resid(). This is a diagnostic tool for checking whether the normalised quantile residuals are coming from a normal distribution or not. This could be true if the horizontal line is within the confidence intervals.

Usage

dtop(object = NULL, xvar = NULL, resid = NULL,
      type = c("Owen", "JW"), 
      conf.level = c("95", "99"), n.inter = 4, 
      xcut.points = NULL, overlap = 0, 
      show.given = TRUE, cex = 1, pch = 21, 
      line = TRUE, ...)

Arguments

Details

If the xvar argument is not specified then a single detrended Owen's plot is used, see Owen (1995). In this case the plot is a detrended nonparametric likelihood confidence band for a distribution function. That is, if the horizontal lines lies within the confidence band then the normalised residuals could have come from a Normal distribution and consequently the assumed response variable distribution is reasonable. If the xvar is specified then we have as many plots as n.iter. In this case the x-variable is cut into n.iter intervals with an equal number observations and detrended Owen's plots for each interval are plotted. This is a way of highlighting failures of the model within different ranges of the explanatory variable.

Value

A plot is returned.

Author(s)

Mikis Stasinopoulos, Bob Rigby and Vlassios Voudouris

References

Jager, L. and Wellner, J. A (2004) A new goodness of fit test: the reversed Berk-Jones statistic, University of Washington, Department of Statistics, Technical report 443.

Owen A. B. (1995) Nonparametric Confidence Bands for a Distribution Function. Journal of the American Statistical Association Vol. 90, No 430, pp. 516-521.

Rigby, R. A. and Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape,(with discussion), Appl. Statist., 54, part 3, 1-38.

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

wp

Examples

data(abdom)
a<-gamlss(y~pb(x),sigma.fo=~pb(x,1),family=LO,data=abdom)
dtop(a)
dtop(a, xvar=abdom$x)
rm(a)

Description

The functions edf() and edfAll() can be used to obtained the effective degrees of freedom for different additive terms for the distribution parameters in a gamlss model.

Usage

edf(obj, what = c("mu", "sigma", "nu", "tau"),
    parameter= NULL, print = TRUE, ...)
edfAll(obj, ...)

Arguments

Value

The function edfAll() re turns a list of edf for all the fitted parameters. The function edf() a vector of edf.

Note

The edf given are the ones fitted in the backfitting so the usually contained (depending on the additive term) the contatnt and the linear part.

Author(s)

Mikis Stasinopoulos

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

gamlss

Examples

library(gamlss.data)
data(usair)
m1<- gamlss(y~pb(x1)+pb(x2)+pb(x6), data=usair)
edfAll(m1)
edf(m1)

Description

This function selects the values of hyper parameters and/or non-linear parameters in a GAMLSS model. It uses the R function optim which then minimises the generalised Akaike information criterion (GAIC) with a user defined penalty.

Usage

find.hyper(model = NULL, parameters = NULL, other = NULL, k = 2,
        steps = c(0.1), lower = -Inf, upper = Inf, method = "L-BFGS-B",
        ...)

Arguments

Details

This historically was an experimental function which worked well for the search of the optimum degrees of freedom and non-linear parameters (e.g. power parameter $\lambda$ used to transform x to $x^\lambda$). With the introduction of the P-Spline smoothing function pb() the function find.hyper() became almost redundant. find.hyper() takes lot longer than pb() to find automatically the hyper parameters while both method produce similar results. See below the examples for a small demonstration.

Value

The function turns the same output as the function optim()

Warning

It may be slow to find the optimum

Author(s)

Mikis Stasinopoulos

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

gamlss, plot.gamlss, optim

Examples

## Not run: 
data(abdom)
# Example estimating the smoothing parameters for mu and 
# the transformation parameters for x
# declare the model
mod1<-quote(gamlss(y~cs(nx,df=p[1]),family=BCT,data=abdom,
                        control=gamlss.control(trace=FALSE)))
# since we want also to find the transformation for x 
# we use the "other"" option
op <- find.hyper(model=mod1, other=quote(nx<-x^p[2]), parameters=c(3,0.5), 
            lower=c(1,0.001), steps=c(0.1,0.001))
op
# the optimum parameters found are 
# p = (p[1],p[2]) = (3.113218 0.001000) = (df for mu, lambda)
# so it needs df = 3 on top of the constant and linear 
# in  the cubic spline model for mu since p[1] is approximately  3
#  and log transformation for x since p[2] is approximately  0 
# here is an example with no data declaration in define the model
# we have to attach the data
attach(abdom)
mod2 <- quote(gamlss(y~cs(nx,df=p[1]),family=BCT,
                control=gamlss.control(trace=FALSE)))
op2<-find.hyper(model=mod2, other=quote(nx<-x^p[2]), parameters=c(3,0.5), 
                lower=c(1,0.001), steps=c(0.1,0.001))
op2
detach(abdom)
#--------------------------------------------------------------
# showing different ways of estimating the smoothing parameter
# get the df using local ML (PQL) 
m0 <- gamlss(y~pb(x), data=abdom)
# get the df using local GAIC 
m1<-gamlss(y~pb(x, method="GAIC", k=2), data=abdom)
# fiiting cubic splines with fixed df's at 3
m2<-gamlss(y~cs(x, df=3), data=abdom)
# fitting cubic splines using find hyper (global GAIC)
mod1 <- quote(gamlss(y~cs(x, df=p[1]),family=BCT,data=abdom,control=gamlss.control(trace=FALSE)))
op <- find.hyper(model=mod1, parameters=c(3), lower=c(1,0.001), steps=c(0.1,0.001))
# now fit final model
m3 <- gamlss(y~cs(x, df=op$par), data=abdom)
# effetive degrees of fredom for the 4 models
edf(m0);edf(m1); m2$mu.df; m3$mu.df
# deviances for the four models
deviance(m0); deviance(m1); deviance(m2); deviance(m3)
# their GAIC
GAIC(m0,m1,m2,m3)
# plotting  the models
plot(y~x, data=abdom, type="n")
lines(fitted(m3)~abdom$x, col="red")
lines(fitted(m1)~abdom$x, col="green")
lines(fitted(m0)~abdom$x, col="blue")
# almost identical

## End(Not run)

Description

The function fitDist() is using the function gamlssML() to fit all relevant parametric gamlss.family distributions, specified by the argument type), to a single data vector (with no explanatory variables). The final marginal distribution is the one selected by the generalised Akaike information criterion with penalty k. The default is k=2 i.e AIC.

The function fitDistPred() is using the function gamlssMLpred() to fit all relevant (marginal) parametric gamlss.family distributions to a single data vector (similar to fitDist()) but the final model is selected by the minimum prediction global deviance. The user has to specify the training and validation/test samples.

The function chooseDist() is using the function update.gamlss() to fit all relevant parametric (conditional) gamlss.family distributions to a given fitted gamlss model. The output of the function is a matrix with rows the different distributions (from the argument type) and columns the different GAIC's (). The default argument for k are 2, for AIC, 3.84, for Chi square, and log(n) for BIC. No final model is given by the function like for example in fitDist(). The function getOrder() can be used to rank the columns of the resulting table (matrix). The final model can be refitted using update(), see the examples.

Usage

fitDist(y, k = 2, 
    type = c("realAll", "realline", "realplus", "real0to1", "counts", "binom"), 
    try.gamlss = FALSE, extra = NULL, data = NULL,trace = FALSE, ...)

fitDistPred(y, 
    type = c("realAll", "realline", "realplus", "real0to1", "counts", "binom"), 
    try.gamlss = FALSE, extra = NULL, data = NULL, rand = NULL,
    newdata = NULL, trace = FALSE, ...)    
      
chooseDist(object, k = c(2, 3.84, round(log(length(object$y)), 2)), type = 
    c("realAll", "realline", "realplus", "real0to1", "counts", "binom","extra"), 
    extra = NULL, trace = FALSE, 
    parallel = c("no", "multicore", "snow"), ncpus = 1L, cl = NULL, ...)

chooseDistPred(object, type = c("realAll", "realline", "realplus", 
     "real0to1", "counts", "binom", "extra"), extra = NULL, 
     trace = FALSE, parallel = c("no", "multicore", "snow"), 
     ncpus = 1L, cl = NULL, newdata = NULL, rand = NULL, ...)
      
getOrder(obj, column = 1)

Arguments

Details

The following are the different type argument:

• realAll: All the gamlss.family continuous distributions defined on the real line, i.e. realline and the real positive line i.e. realplus.

• realline: The gamlss.family continuous distributions : "NO", "GU", "RG" ,"LO", "NET", "TF", "TF2", "PE","PE2", "SN1", "SN2", "exGAUS", "SHASH", "SHASHo","SHASHo2", "EGB2", "JSU", "JSUo", "SEP1", "SEP2", "SEP3", "SEP4", "ST1", "ST2", "ST3", "ST4", "ST5", "SST", "GT".

• realplus: The gamlss.family continuous distributions in the positive real line: "EXP", "GA","IG","LOGNO", "LOGNO2","WEI", "WEI2", "WEI3", "IGAMMA","PARETO2", "PARETO2o", "GP", "BCCG", "BCCGo", "exGAUS", "GG", "GIG", "LNO","BCTo", "BCT", "BCPEo", "BCPE", "GB2".

• real0to1: The gamlss.family continuous distributions from 0 to 1: "BE", "BEo", "BEINF0", "BEINF1", "BEOI", "BEZI", "BEINF", "GB1".

• counts: The gamlss.family distributions for counts: "PO", "GEOM", "GEOMo","LG", "YULE", "ZIPF", "WARING", "GPO", "DPO", "BNB", "NBF","NBI", "NBII", "PIG", "ZIP","ZIP2", "ZAP", "ZALG", "DEL", "ZAZIPF", "SI", "SICHEL","ZANBI", "ZAPIG", "ZINBI", "ZIPIG", "ZINBF", "ZABNB", "ZASICHEL", "ZINBF", "ZIBNB", "ZISICHEL".

• binom: The gamlss.family distributions for binomial type data :"BI", "BB", "DB", "ZIBI", "ZIBB", "ZABI", "ZABB".

  The function fitDist() uses the function gamlssML() to fit the different models, the function fitDistPred() uses gamlssMLpred() and the function chooseDist() used update.gamlss().

Value

For the functions fitDist() and fitDistPred() a gamlssML object is return (the one which minimised the GAIC or VDEV respectively) with two extra components:

For the function chooseDist() a matrix is returned, with rows the different distributions and columns the different GAIC's set by k.

Author(s)

Mikis Stasinopoulos, Bob Rigby, Vlasis Voudouris and Majid Djennad.

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

gamlss, gamlssML

Examples

y <- rt(100, df=1)
m1<-fitDist(y, type="realline")
m1$fits
m1$failed
# an example of using  extra
## Not run: 
#---------------------------------------  
# Example of using the argument extra  
library(gamlss.tr)
data(tensile)
gen.trun(par=1,family="GA", type="right")
gen.trun(par=1,"LOGNO", type="right")
gen.trun(par=c(0,1),"TF", type="both")
ma<-fitDist(str, type="real0to1", trace=T,
       extra=c("GAtr", "LOGNOtr", "TFtr"), 
     data=tensile) 
ma$fits
ma$failed
#-------------------------------------
# selecting model using the prediction global deviance
# Using fitDistPred
# creating training data
y <- rt(1000, df=2)
m1 <- fitDist(y, type="realline")
m1$fits
m1$fails
# create validation data
yn <- rt(1000, df=2)
# choose distribution which fits the new data best
p1 <- fitDistPred(y, type="realline", newdata=yn)
p1$fits
p1$failed
#---------------------------------------
# using the function chooseDist()
# fitting normal distribution model
m1 <- gamlss(y~pb(x), sigma.fo=~pb(x), family=NO, data=abdom)
# choose a distribution on the real line 
# and save GAIC(k=c(2,4,6.4),  i.e. AIC, Chi-square and BIC.   
t1 <- chooseDist(m1, type="realline", parallel="snow", ncpus=4)
# the GAIC's
t1
# the distributions which failed are with NA's 
# ordering according to  BIC
getOrder(t1,3)
fm<-update(m1, family=names(getOrder(t1,3)[1]))

## End(Not run)

Description

fitted.gamlss is the GAMLSS specific method for the generic function fitted which extracts fitted values for a specified parameter from a GAMLSS objects. fitted.values is an alias for it. The function fv() is similar to fitted.gamlls() but allows the argument what not to be character

Usage

## S3 method for class 'gamlss'
fitted(object, what = c("mu", "sigma", "nu", "tau"),
                parameter= NULL, ...)
fv(obj, what = c("mu", "sigma", "nu", "tau"), parameter= NULL, ... )

Arguments

Value

Fitted values extracted from the GAMLSS object for the given parameter.

Author(s)

Mikis Stasinopoulos

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

print.gamlss, summary.gamlss, fitted.gamlss, coef.gamlss, residuals.gamlss, update.gamlss, plot.gamlss, deviance.gamlss, formula.gamlss

Examples

data(aids)
h<-gamlss(y~poly(x,3)+qrt, family=PO, data=aids) # 
fitted(h)
rm(h)

Description

This function, applicable only to a models with a single explanatory variable, plots the fitted values for all the parameters of a GAMLSS model against the (one) explanatory variable. It is also useful for comparing the fits for more than one model.

Usage

fittedPlot(object, ..., x = NULL, color = TRUE, line.type = FALSE, xlab = NULL)

Arguments

Value

A plot of the fitted values against the explanatory variable

Author(s)

Mikis Stasinopoulos, Bob Rigby 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. 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

gamlss, centiles, centiles.split

Examples

data(abdom)
h1<-gamlss(y~pb(x), sigma.formula=~x, family=BCT, data=abdom)
h2<-gamlss(y~pb(x), sigma.formula=~pb(x), family=BCT, data=abdom)
fittedPlot(h1,h2,x=abdom$x)
rm(h1,h2)

Description

formula.gamlss is the GAMLSS specific method for the generic function formula which extracts the model formula from objects returned by modelling functions.

Usage

## S3 method for class 'gamlss'
formula(x, what = c("mu", "sigma", "nu", "tau"), 
                parameter= NULL, ... )

Arguments

Value

Returns a model formula

Author(s)

Mikis Stasinopoulos

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

gamlss, deviance.gamlss, fitted.gamlss

Examples

data(aids)
h<-gamlss(y~poly(x,3)+qrt, family=PO, data=aids) # 
formula(h,"mu")
rm(h)

Description

Returns an object of class "gamlss", which is a generalized additive model for location scale and shape (GAMLSS). The function gamlss() is very similar to the gam() function in S-plus (now also in R in package gam), but can fit more distributions (not only the ones belonging to the exponential family) and can model all the parameters of the distribution as functions of the explanatory variables (e.g. using linear, non-linear, smoothing, loess and random effects terms).

This implementation of gamlss() allows modelling of up to four parameters in a distribution family, which are conventionally called mu, sigma, nu and tau.

The function gamlssNews() shows what is new in the current implementation.

Usage

gamlss(formula = formula(data), sigma.formula = ~1, 
        nu.formula = ~1, tau.formula = ~1, family = NO(), 
        data, weights = NULL, 
        contrasts = NULL, method = RS(),  start.from = NULL,  
        mu.start = NULL,  sigma.start = NULL, 
        nu.start = NULL, tau.start = NULL, 
        mu.fix = FALSE, sigma.fix = FALSE, nu.fix = FALSE, 
        tau.fix = FALSE, control = gamlss.control(...), 
        i.control = glim.control(...), ...)
is.gamlss(x)
gamlssNews()

Arguments

Details

The Generalized Additive Model for Location, Scale and Shape is a general class of statistical models for a univariate response variable. The model assumes independent observations of the response variable y given the parameters, the explanatory variables and the values of the random effects. The distribution for the response variable in the GAMLSS can be selected from a very general family of distributions including highly skew and/or kurtotic continuous and discrete distributions, see gamlss.family. The systematic part of the model is expanded to allow modelling not only of the mean (or location) parameter, but also of the other parameters of the distribution of y, as linear parametric and/or additive nonparametric (smooth) functions of explanatory variables and/or random effects terms. Maximum (penalized) likelihood estimation is used to fit the (non)parametric models. A Newton-Raphson/Fisher scoring algorithm is used to maximize the (penalized) likelihood. The additive terms in the model are fitted using a backfitting algorithm.

is.gamlss is a short version is is(object,"gamlss")

Value

Returns a gamlss object with components

Warning

Respect the parameter hierarchy when you are fitting a model. For example a good model for mu should be fitted before a model for sigma is fitted

Note

The following generic functions can be used with a GAMLSS object: print, summary, fitted, coef, residuals, update, plot, deviance, formula

Author(s)

Mikis Stasinopoulos, Bob Rigby, Calliope Akantziliotou and Vlasios Voudouris

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

gamlss.family, pdf.plot, find.hyper

Examples

data(abdom)
mod<-gamlss(y~pb(x),sigma.fo=~pb(x),family=BCT, data=abdom, method=mixed(1,20))
plot(mod)
rm(mod)

Description

Auxiliary function as user interface for gamlss fitting. Typically only used when calling gamlss function with the option control.

Usage

gamlss.control(c.crit = 0.001, n.cyc = 20, mu.step = 1, sigma.step = 1, nu.step = 1, 
               tau.step = 1, gd.tol = Inf, iter = 0, trace = TRUE, autostep = TRUE, 
               save = TRUE, ...)

Arguments

Details

The step length for each of the parameters mu, sigma, nu or tau is very useful to aid convergence if the parameter has a fully parametric model. However using a step length is not theoretically justified if the model for the parameter includes one or more smoothing terms, (even thought it may give a very approximate result).

The c.crit can be increased to speed up the convergence especially for a large set of data which takes longer to fit. When ‘trace’ is TRUE, calls to the function cat produce the output for each outer iteration.

Value

A list with the arguments as components.

Author(s)

Mikis Stasinopoulos, Bob Rigby

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

gamlss

Examples

data(aids)
h<-gamlss(y~poly(x,3)+qrt, family=PO, data=aids) # 
con<-gamlss.control(mu.step=0.1)
h<-gamlss(y~poly(x,3)+qrt, family=PO, data=aids, control=con) # 
rm(h,con)

Description

This is support for the functions cs(), and scs(). It is not intended to be called directly by users. The function gamlss.cs is using the R function smooth.spline

Usage

gamlss.cs(x, y, w, df = NULL, spar = NULL, xeval = NULL, ...)

Arguments

Value

Returns a class "smooth.spline" object with

Author(s)

Mikis Stasinopoulos, Bob Rigby

See Also

gamlss, cs

Description

Those are support for the functions fp() and pp. It is not intended to be called directly by users.

Usage

gamlss.fp(x, y, w, npoly = 2, xeval = NULL)
gamlss.pp(x, y, w)

Arguments

Value

Returns a list with

Author(s)

Mikis Stasinopoulos, Bob Rigby

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

gamlss, fp

Description

This is support for the loess function lo(). It is not intended to be called directly by users. The function gamlss.lo is calling the R function loess.

Usage

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

Arguments

Value

Returns an object

Author(s)

Mikis Stasinopoulos based on Brian Ripley implementation of loess function in R

See Also

gamlss, lo

Description

Those functions are support for the functions pb(), pbo(), ps(), ridge(), ri(), cy(), pvc(), and pbm(). The functions are not intended to be called directly by users.

Usage

gamlss.pb(x, y, w, xeval = NULL, ...)
gamlss.pbo(x, y, w, xeval = NULL, ...)
gamlss.ps(x, y, w, xeval = NULL, ...)
gamlss.ri(x, y, w, xeval = NULL, ...)
gamlss.cy(x, y, w, xeval = NULL, ...)
gamlss.pvc(x, y, w, xeval = NULL, ...)
gamlss.pbm(x, y, w, xeval = NULL, ...)
gamlss.pbz(x, y, w, xeval = NULL, ...)
gamlss.pbc(x, y, w, xeval = NULL, ...)
gamlss.pbp(x, y, w, xeval = NULL, ...)

Arguments

Value

All function return fitted smoothers.

Author(s)

Mikis Stasinopoulos, Bob Rigby

References

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.

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

gamlss, pb, ps, ri,ridge,cy,pvc,pbm

Description

This is support for the functions random() and re() respectively. It is not intended to be called directly by users. .

Usage

gamlss.random(x, y, w, xeval = NULL, ...)
gamlss.re(x, y, w, xeval = NULL, ...)

Arguments

Value

Returns a list with

Author(s)

Mikis Stasinopoulos, based on Trevor Hastie function gam.random

References

Chambers, J. M. and Hastie, T. J. (1991). Statistical Models in S, Chapman and Hall, London.

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

gamlss, random

Description

Generates a scope argument for a stepwise GAMLSS.

Usage

gamlss.scope(frame, response = 1, smoother = "cs", arg = NULL, form = TRUE)

Arguments

Details

Each formula describes an ordered regimen of terms, each of which is eligible on their own for inclusion in the gam model. One of the terms is selected from each formula by step.gam. If a 1 is selected, that term is omitted.

Value

a list of formulas is returned, one for each column in frame (excluding the response). For a numeric variable, say x1, the formula is

~ 1 + x1 + cs(x1)

If x1 is a factor, the last smooth term is omitted.

Author(s)

Mikis Stasinopoulos: a modified function from Statistical Models in S

References

Chambers, J. M. and Hastie, T. J. (1991). Statistical Models in S, Chapman and Hall, London.

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

stepGAIC

Examples

data(usair)
gs1<-gamlss.scope(model.frame(y~x1+x2+x3+x4+x5+x6, data=usair))
gs2<-gamlss.scope(model.frame(usair))
gs1
gs2
gs3<-gamlss.scope(model.frame(usair), smooth="fp", arg="3")
gs3

Description

The function gamlssML() fits a gamlss.family distribution to single data set using a non linear maximisation algorithm in R. This is relevant only when explanatory variables do not exist.

The function gamlssMLpred() is similar to gamlssML() but it saves the predictive global deviance for the newdata. The new data in gamlssMLpred() can be given with the arguments newdata or defining the factor rand. rand should be a binary factor rand splitting the original data set into a training set (value 1) and a validation/test set (values 2), see also gamlssVGD

Usage

gamlssML(formula, family = NO, weights = NULL, mu.start = NULL, 
 sigma.start = NULL, nu.start = NULL, tau.start = NULL, 
 mu.fix = FALSE, sigma.fix = FALSE, nu.fix = FALSE, 
 tau.fix = FALSE, data, start.from = NULL, ...)

gamlssMLpred(response = NULL, data = NULL, family = NO, 
 rand = NULL, newdata = NULL, ...)

Arguments

Details

The function gamlssML() fits a gamlss.family distribution to a single data set is using a non linear maximisation. in fact it uses the internal function MLE() which is a copy of the mle() function of package stat4. The function gamlssML() could be for large data faster than the equivalent gamlss() function which is designed for regression type of models.

The function gamlssMLpred() uses the function gamlssML() to fit the model but then uses predict.gamlssML() to predict for new data and saves the the prediction i) deviance increments, ii) global deviance iii) residuals.

Value

Returns a gamlssML object which behaves like a gamlss fitted objected

Author(s)

Mikis Stasinopoulos, Bob Rigby, Vlasis Voudouris and Majid Djennad

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

gamlss.family, gamlss

Examples

#-------- negative binomial 1000 observations
y<- rNBI(1000)
  system.time(m1<-gamlss(y~1, family=NBI))
  system.time(m1a<-gamlss(y~1, family=NBI, trace=FALSE))
system.time(m11<-gamlssML(y, family=NBI))
AIC(m1,m1a,m11, k=0)
# neg. binomial   n=10000
 y<- rNBI(10000)
 system.time(m1<-gamlss(y~1, family=NBI))
 system.time(m1a<-gamlss(y~1, family=NBI, trace=FALSE))
system.time(m11<-gamlssML(y, family=NBI))
AIC(m1,m1a,m11, k=0)
# binomial type data 
data(aep)
m1 <- gamlssML(aep$y, family=BB) # ok
m2 <- gamlssML(y, data=aep, family=BB) # ok
m3 <- gamlssML(y~1, data=aep, family=BB) # ok 
m4 <- gamlssML(aep$y~1, family=BB) # ok
AIC(m1,m2,m3,m4)
## Not run: 
#-----------------------------------------------------------
# neg. binomial   n=10000
y<- rNBI(10000)
rand <- sample(2, length(y), replace=TRUE, prob=c(0.6,0.4))
table(rand)
   Y <- subset(y, rand==1)
YVal <- subset(y, rand==2) 
length(Y)
length(YVal) 
da1 <- data.frame(y=y)
dim(da1)
da2 <- data.frame(y=Y)
dim(da2)
danew <- data.frame(y=YVal)
# using gamlssVGD to fit the models
g1 <- gamlssVGD(y~1, rand=rand, family=NBI, data=da1)
g2 <- gamlssVGD(y~1, family=NBI, data=da2, newdata=dan)
AIC(g1,g2)
VGD(g1,g2)
# using gamlssMLpred to fit the models
p1 <- gamlssMLpred(y, rand=rand, family=NBI)
p2 <- gamlssMLpred(Y, family=NBI, newdata=YVal)
# AIC and VGD should produce identical results
AIC(p1,p2,g1,g2)
VGD(p1,p2, g1,g2)
# the fitted residuals
wp(p1, ylim.all=1)
# the prediction residuals 
wp(resid=p1$residVal, ylim.all=.5)
#-------------------------------------------------------------
# chossing between distributions
p2<-gamlssMLpred(y, rand=rand, family=PO)
p3<-gamlssMLpred(y, rand=rand, family=PIG)
p4<-gamlssMLpred(y, rand=rand, family=BNB)
AIC(p1, p2, p3, p4)
VGD(p1, p2, p3, p4)
#--------------------------------------------------

## End(Not run)

Description

This is a set of function useful for selecting appropriate models.

The functions gamlssVGD, VGD, getTGD, TGD can be used when a subset of the data is used for validation or testing.

The function stepVGD() is a stepwise procedure for selecting an appropriate model for any of the parameters of the model minimising the test global deviance. The function stepVGDAll.A() can select a model using strategy A for all the parameters.

The functions gamlssCV, CV can be used for a k-fold cross validation.

Usage

gamlssVGD(formula = NULL, sigma.formula = ~1, nu.formula = ~1, 
          tau.formula = ~1, data = NULL, family = NO, 
          control = gamlss.control(trace = FALSE), 
          rand = NULL, newdata = NULL, ...)
          
VGD(object, ...)          

getTGD(object, newdata = NULL, ...)

TGD(object, ...)  

gamlssCV(formula = NULL, sigma.formula = ~1, nu.formula = ~1, 
         tau.formula = ~1, data = NULL, family = NO, 
         control = gamlss.control(trace = FALSE), 
         K.fold = 10, set.seed = 123, rand = NULL, 
         parallel = c("no", "multicore", "snow"), 
         ncpus = 1L, cl = NULL, ...)

CV(object, ...)

drop1TGD(object, scope, newdata, parameter = c("mu", "sigma", "nu", "tau"), 
         sorted = FALSE, trace = FALSE, 
         parallel = c("no", "multicore", "snow"), 
         ncpus = 1L, cl = NULL, ...)
         
add1TGD(object, scope, newdata, parameter = c("mu", "sigma", "nu", "tau"), 
        sorted = FALSE, trace = FALSE, 
        parallel = c("no", "multicore", "snow"), 
        ncpus = 1L, cl = NULL, ...)

stepTGD(object, scope, newdata, 
        direction = c("both", "backward", "forward"),
        trace = TRUE, keep = NULL, steps = 1000, 
        parameter = c("mu", "sigma", "nu", "tau"), 
        parallel = c("no", "multicore", "snow"), 
        ncpus = 1L, cl = NULL, ...)
        
stepTGDAll.A(object, scope = NULL, newdata = NULL, 
        steps = 1000, sigma.scope = NULL, nu.scope = NULL, 
        tau.scope = NULL, mu.try = TRUE, sigma.try = TRUE, 
        nu.try = TRUE, tau.try = TRUE,
        parallel = c("no", "multicore", "snow"), 
        ncpus = 1L, cl = NULL, ...)

Arguments