Package 'boxcoxmix' reference manual

Title:	Box-Cox-Type Transformations for Linear and Logistic Models with Random Effects
Description:	Box-Cox-type transformations for linear and logistic models with random effects using non-parametric profile maximum likelihood estimation, as introduced in Almohaimeed (2018) <http://etheses.dur.ac.uk/12831/> and Almohaimeed and Einbeck (2022) <doi:10.1177/1471082X20966919>. The main functions are 'optim.boxcox()' for linear models with random effects and 'boxcoxtype()' for logistic models with random effects.
Authors:	Iago Giné-Vázquez [cre] , Amani Almohaimeed [aut] , Jochen Einbeck [aut]
Maintainer:	Iago Giné-Vázquez <[email protected]>
License:	GPL (>= 3)
Version:	0.46
Built:	2024-10-31 19:46:30 UTC
Source:	https://gitlab.com/iagogv/boxcoxmix

Box-Cox-Type Transformations for Linear and Logistic Models with Random Effects

Description

Box-Cox-type transformations for linear and logistic models with random effects using non-parametric profile maximum likelihood estimation. The main functions are optim.boxcox() for linear models with random effects and boxcoxtype() for logistic models with random effects.

Details

Package:	boxcoxmix
Type:	Package
Version:	0.28
Date:	2020-09-17
License:	GPL (>=3)

Author(s)

Maintainer: Iago Giné-Vázquez [email protected] (ORCID)

Authors:

Amani Almohaimeed [email protected] (ORCID)
Jochen Einbeck [email protected] (ORCID)

References

Box G. and Cox D. (1964). An analysis of transformations. Journal of the Royal Statistical Society. Series B (Methodological), pages 211-252.

Aitkin, M. A., Francis, B., Hinde, J., and Darnell, R. (2009). Statistical modelling in R. Oxford University Press Oxford.

Jochen Einbeck, Ross Darnell and John Hinde (2014). npmlreg: Nonparametric maximum likelihood estimation for random effect models. R package version 0.46-1.

R Core Team (2016). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/.

Box-Cox-type link function for logistic mixed-effects Models

Description

The boxcoxtype() performs a grid search over the parameter Lambda for logistic mixed-effects models and then optimizes over this grid, to calculate the maximum likelihood estimator of the transformation.

Usage

boxcoxtype(
  formula,
  random = ~1,
  k = 3,
  trials = 1,
  data,
  find.in.range = c(-2, 2),
  s = 20,
  plot.opt = 1,
  random.distribution = "np",
  ...
)

boxcoxpower(Lambda = 0)

binomial(link = boxcoxpower(0))
boxcoxtype(
  formula,
  random = ~1,
  k = 3,
  trials = 1,
  data,
  find.in.range = c(-2, 2),
  s = 20,
  plot.opt = 1,
  random.distribution = "np",
  ...
)

boxcoxpower(Lambda = 0)

binomial(link = boxcoxpower(0))

Arguments

`formula`	a formula describing the transformed response and the fixed effect model (e.g. y ~ x).
`random`	a formula defining the random model. Set `random= ~1` to model logistic-type overdispersion model. For a two-level logistic-type model, set `random= ~1\|groups`, where groups are at the upper level.
`k`	the number of mass points.
`trials`	optional prior weights for the data. For Bernoulli distribution, set trials=1.
`data`	a data frame containing variables used in the fixed and random effect models.
`find.in.range`	search in a range of `Lambda`, with default (-2,2) in step of 0.1.
`s`	number of points in the grid search of `Lambda`.
`plot.opt`	Set `plot.opt=1`, to plot the profile log-likelihood against `Lambda`. if `plot.opt=0`, no plot is printed.
`random.distribution`	the mixing distribution, Gaussian Quadrature (gq) or NPML (np) can be set.
`...`	extra arguments will be ignored.
`Lambda`	the power of the transformation
`link`	the link function to be used.

Details

The Box-Cox transformation (Box & Cox, 1964) is applied to the logistic mixed-effects models with an unspecified mixing distribution. The NPML estimate of the mixing distribution is known to be a discrete distribution involving a finite number of mass-points and corresponding masses (Aitkin et al., 2009). An Expectation-Maximization (EM) algorithm is used for fitting the finite mixture distribution, one needs to specify the number of components k of the finite mixture in advance. This algorithm can be implemented using the npmlreg function alldist for the logistic-type overdispersion model and the npmlreg function allvc for the two-level logistic-type model, setting family = binomial(link = boxcoxpower(Lambda)) where Lambda is the value of the power transformation. When k=1, the npmlreg function alldist() fits the logistic regression model without random effects.

boxcoxtype() performs a grid search over the parameter Lambda and then optimizes over this grid, to calculate the maximum likelihood estimator of the transformation. It produces a plot of the profile likelihood function that summarises information concerning Lambda, including a vertical line indicating the best value of Lambda that maximizes the profile log-likelihood.

Value

List with class boxcoxmix containing:

`Maximum`	the best estimate of `Lambda` found.
`objective`	the value of the profile log-likelihood corresponding to Maximum.
`coef`	the vector of coefficients.
`profile.loglik`	the profile log-likelihood of the fitted regression model.
`fit`	the fitted alldist object from the last EM iteration.
`aic`	the Akaike information criterion of the fitted regression model.
`bic`	the Bayesian information criterion of the fitted regression model.

The other outcomes are not relevant to users and they are intended for internal use only.

Author(s)

Amani Almohaimeed and Jochen Einbeck

References

Box G. and Cox D. (1964). An analysis of transformations. Journal of the Royal Statistical Society. Series B (Methodological), pages 211-252.

Aitkin, M. A., Francis, B., Hinde, J., and Darnell, R. (2009). Statistical modelling in R. Oxford University Press Oxford.

Jochen Einbeck, Ross Darnell and John Hinde (2014). npmlreg: Nonparametric maximum likelihood estimation for random effect models. R package version 0.46-1.

Examples

#Beta blockers data
data("betablocker", package = "flexmix")
library(npmlreg)
betavc <-allvc(cbind(Deaths, Total - Deaths) ~ Treatment, data = betablocker,random=~1|Center,
 k=3,random.distribution='np',family = binomial(link = boxcoxpower(0)))
betavc$disparity
#[1] 318.7211
betavc3 <-boxcoxtype(cbind(Deaths, Total - Deaths) ~ Treatment,random=~1|Center, 
data = betablocker, find.in.range = c(-2,0.4),s=40,k=3,random.distribution='np')
#Maximum Profile Log-likelihood: -158.6025 at lambda= -0.56
betavc3$fit$disparity
#[1] 317.2049
betavc3$aic
#[1] 331.2049
betavc3$bic
#[1] 343.6942

#Beta blockers data
data("betablocker", package = "flexmix")
library(npmlreg)
betavc <-allvc(cbind(Deaths, Total - Deaths) ~ Treatment, data = betablocker,random=~1|Center,
 k=3,random.distribution='np',family = binomial(link = boxcoxpower(0)))
betavc$disparity
#[1] 318.7211
betavc3 <-boxcoxtype(cbind(Deaths, Total - Deaths) ~ Treatment,random=~1|Center, 
data = betablocker, find.in.range = c(-2,0.4),s=40,k=3,random.distribution='np')
#Maximum Profile Log-likelihood: -158.6025 at lambda= -0.56
betavc3$fit$disparity
#[1] 317.2049
betavc3$aic
#[1] 331.2049
betavc3$bic
#[1] 343.6942

Grid search over K for NPML estimation of random effect and variance component models

Description

A grid search over the parameter K, to set the best number of mass-points.

Usage

Kfind.boxcox(
  formula,
  groups = 1,
  data,
  lambda = 1,
  EMdev.change = 1e-04,
  steps = 500,
  find.k = c(2, 10),
  model.selection = "aic",
  start = "gq",
  find.tol = c(0, 1.5),
  steps.tol = 15,
  ...
)
Kfind.boxcox(
  formula,
  groups = 1,
  data,
  lambda = 1,
  EMdev.change = 1e-04,
  steps = 500,
  find.k = c(2, 10),
  model.selection = "aic",
  start = "gq",
  find.tol = c(0, 1.5),
  steps.tol = 15,
  ...
)

Arguments

`formula`	a formula describing the transformed response and the fixed effect model (e.g. y ~ x).
`groups`	the random effects. To fit overdispersion models , set `groups` = 1.
`data`	a data frame containing variables used in the fixed and random effect models.
`lambda`	a transformation parameter, setting `lambda`=1 means 'no transformation'.
`EMdev.change`	a small scalar, with default 0.0001, used to determine when to stop EM algorithm.
`steps`	maximum number of iterations for the EM algorithm.
`find.k`	search in a range of `K`, with default (2,10) in step of 1.
`model.selection`	Set `model.selection="aic"`, to use Akaike information criterion as model selection criterion or `model.selection="bic"`, to use Bayesian information criterion as model selection criterion.
`start`	a description of the initial values to be used in the fitted model, Quantile-based version "quantile" or Gaussian Quadrature "gq" can be set.
`find.tol`	search in a range of `tol`, with default (0,1.5) in step of 1.
`steps.tol`	number of points in the grid search of `tol`.
`...`	extra arguments will be ignored.

Details

Not only the shape of the distribution causes the skewness it may due to the use of an insufficient number of classes, K. For this, the Kfind.boxcox() function was created to search over a selected range of K and find the best. For each number of classes, a grid search over tol is performed and the tol with the lowest aic or bic value is considered as the optimal. Having the minimal aic or bic values for a whole range of K that have been specified beforehand, the Kfind.boxcox() function can find the best number of the component as the one with the smallest value. It also plots the aic or bic values against the selected range of K, including a vertical line indicating the best value of K that minimizes the model selection criteria. The full range of classes and their corresponding optimal tol can be printed off from the Kfind.boxcox()'s output and used with other boxcoxmix functions as starting points.

Value

List with class boxcoxmix containing:

`MinDisparity`	the minimum disparity found.
`Best.K`	the value of `K` corresponding to `MinDisparity`.
`AllMinDisparities`	a vector containing all minimum disparities calculated on the grid.
`AllMintol`	list of `tol` values used in the grid.
`All.K`	list of `K` values used in the grid.
`All.aic`	the Akaike information criterion of all fitted regression models.
`All.bic`	the Bayesian information criterion of all fitted regression models.

Author(s)

Amani Almohaimeed and Jochen Einbeck

Examples

# Fabric data
data(fabric, package = "npmlreg")
teststr<-Kfind.boxcox(y ~ x, data = fabric,  start = "gq", groups=1, 
find.k = c(2, 3), model.selection = "aic", steps.tol=5)
# Minimal AIC: 202.2114 at K= 2 









# Fabric data
data(fabric, package = "npmlreg")
teststr<-Kfind.boxcox(y ~ x, data = fabric,  start = "gq", groups=1, 
find.k = c(2, 3), model.selection = "aic", steps.tol=5)
# Minimal AIC: 202.2114 at K= 2

Response Transformations for Random Effect and Variance Component Models

Description

The function np.boxcoxmix() fits an overdispersed generalized linear model and variance component models using nonparametric profile maximum likelihood.

Usage

np.boxcoxmix(
  formula,
  groups = 1,
  data,
  K = 3,
  tol = 0.5,
  lambda = 1,
  steps = 500,
  EMdev.change = 1e-04,
  plot.opt = 1,
  verbose = TRUE,
  start = "gq",
  ...
)
np.boxcoxmix(
  formula,
  groups = 1,
  data,
  K = 3,
  tol = 0.5,
  lambda = 1,
  steps = 500,
  EMdev.change = 1e-04,
  plot.opt = 1,
  verbose = TRUE,
  start = "gq",
  ...
)

Arguments

`formula`	a formula describing the transformed response and the fixed effect model (e.g. y ~ x).
`groups`	the random effects. To fit overdispersion models , set `groups` = 1.
`data`	a data frame containing variables used in the fixed and random effect models.
`K`	the number of mass points.
`tol`	a positive scalar (usually, 0< `tol` <= 2)
`lambda`	a transformation parameter, setting `lambda`=1 means 'no transformation'.
`steps`	maximum number of iterations for the EM algorithm.
`EMdev.change`	a small scalar, with default 0.0001, used to determine when to stop EM algorithm.
`plot.opt`	Set `plot.opt=1`, to plot the disparity against iteration number. Use `plot.opt=2` for `tolfind.boxcox()` and `plot.opt=3` for `optim.boxcox()`.
`verbose`	If set to FALSE, no printed output on progress.
`start`	a description of the initial values to be used in the fitted model, Quantile-based version "quantile" or Gaussian Quadrature "gq" can be set.
`...`	extra arguments will be ignored.

Details

The Box-Cox transformation (Box & Cox, 1964) is applied to the overdispersed generalized linear models and variance component models with an unspecified mixing distribution. The NPML estimate of the mixing distribution is known to be a discrete distribution involving a finite number of mass-points and corresponding masses (Aitkin et al., 2009). An Expectation-Maximization (EM) algorithm is used for fitting the finite mixture distribution, one needs to specify the number of components K of the finite mixture in advance. To stop the EM-algorithm when it reached its convergence point, we need to defined the convergence criteria that is the absolute change in the successive log-likelihood function values being less than an arbitrary parameter such as EMdev.change = 0.0001 (Einbeck et at., 2014). This algorithm can be implemented using the function np.boxcoxmix(), which is designed to account for overdispersed generalized linear models and variance component models using the non-parametric profile maximum likelihood (NPPML) estimation.

The ability of the EM algorithm to locate the global maximum in fewer iterations can be affected by the choice of initial values, the function np.boxcoxmix() allows us to choose from two different methods to set the initial value of the mass points. When option "gq" is set, then Gauss-Hermite masses and mass points are used as starting points in the EM algorithm, while setting start= "quantile" uses the Quantile-based version to select the starting points.

Value

List with class being either boxcoxmix or boxcoxmixpure containing:

`mass.point`	the fitted mass points.
`p`	the masses corresponding to the mixing proportions.
`beta`	the vector of coefficients.
`sigma`	the standard deviation of the mixing distribution (the square root of the variance).
`se`	the standard error of the estimate.
`w`	a matrix of posterior probabilities that element i comes from cluster k.
`loglik`	the log-likelihood of the fitted regression model.
`complete.loglik`	the complete log-likelihood of the fitted regression model.
`disparity`	the disparity of the fitted regression model.
`EMiteration`	provides the number of iterations of the EM algorithm.
`EMconverged`	TRUE means the EM algorithm converged.
`call`	the matched call.
`formula`	the formula provided.
`data`	the data argument.
`aic`	the Akaike information criterion of the fitted regression model.
`bic`	the Bayesian information criterion of the fitted regression model.
`fitted`	the fitted values for the individual observations.
`fitted.transformed`	the fitted values for the individual transformed observations.
`residuals`	the difference between the observed values and the fitted values.
`residuals.transformed`	the difference between the transformed observed values and the transformed fitted values.
`predicted.re`	a vector of predicted residuals.

The other outcomes are not relevant to users and they are intended for internal use only.

Author(s)

Amani Almohaimeed and Jochen Einbeck

References

Box G. and Cox D. (1964). An analysis of transformations. Journal of the Royal Statistical Society. Series B (Methodological), pages 211-252.

Aitkin, M. A., Francis, B., Hinde, J., and Darnell, R. (2009). Statistical modelling in R. Oxford University Press Oxford.

Jochen Einbeck, Ross Darnell and John Hinde (2014). npmlreg: Nonparametric maximum likelihood estimation for random effect models. R package version 0.46-1.

Examples

#Pennsylvanian Hospital Stay Data
data(hosp, package = "npmlreg")
test1 <- np.boxcoxmix(duration ~ age + wbc1, data = hosp, K = 2, tol = 1, 
    start = "quantile", lambda = 1)
round(summary(test1)$w, digits = 3)
# [1,] 1.000 0.000

# Refinery yield of gasoline Data
data(Gasoline, package = "nlme")
test2.vc <- np.boxcoxmix(yield ~ endpoint + vapor, groups = Gasoline$Sample, 
      data = Gasoline, K = 3, tol = 1.7, start = "quantile", lambda = 0)
test2.vc$disparity
# [1] 176.9827








#Pennsylvanian Hospital Stay Data
data(hosp, package = "npmlreg")
test1 <- np.boxcoxmix(duration ~ age + wbc1, data = hosp, K = 2, tol = 1, 
    start = "quantile", lambda = 1)
round(summary(test1)$w, digits = 3)
# [1,] 1.000 0.000

# Refinery yield of gasoline Data
data(Gasoline, package = "nlme")
test2.vc <- np.boxcoxmix(yield ~ endpoint + vapor, groups = Gasoline$Sample, 
      data = Gasoline, K = 3, tol = 1.7, start = "quantile", lambda = 0)
test2.vc$disparity
# [1] 176.9827

Response Transformations for Random Effect and Variance Component Models

Description

The optim.boxcox() performs a grid search over the parameter lambda for overdispersed generalized linear models and variance component models and then optimizes over this grid, to calculate the maximum likelihood estimator of the transformation.

Usage

optim.boxcox(
  formula,
  groups = 1,
  data,
  K = 3,
  steps = 500,
  tol = 0.5,
  start = "gq",
  EMdev.change = 1e-04,
  find.in.range = c(-3, 3),
  s = 60,
  plot.opt = 3,
  verbose = FALSE,
  noformat = FALSE,
  ...
)
optim.boxcox(
  formula,
  groups = 1,
  data,
  K = 3,
  steps = 500,
  tol = 0.5,
  start = "gq",
  EMdev.change = 1e-04,
  find.in.range = c(-3, 3),
  s = 60,
  plot.opt = 3,
  verbose = FALSE,
  noformat = FALSE,
  ...
)

Arguments

`formula`	a formula describing the transformed response and the fixed effect model (e.g. y ~ x).
`groups`	the random effects. To fit overdispersion models, set `groups` = 1.
`data`	a data frame containing variables used in the fixed and random effect models.
`K`	the number of mass points.
`steps`	maximum number of iterations for the EM algorithm.
`tol`	a positive scalar (usually, 0<`tol` <= 2)
`start`	a description of the initial values to be used in the fitted model, Quantile-based version "quantile" or Gaussian Quadrature "gq" can be set.
`EMdev.change`	a small scalar, with default 0.0001, used to determine when to stop EM algorithm.
`find.in.range`	search in a range of `lambda`, with default (-3,3) in step of 0.1.
`s`	number of points in the grid search of `lambda`.
`plot.opt`	Set `plot.opt=3`, to plot the disparity against iteration number and the profile log-likelihood against `lambda`. Use `plot.opt=0`, to only plot the profile log-likelihood against `lambda`.
`verbose`	If set to FALSE, no printed output on progress.
`noformat`	Set `noformat = TRUE`, to change the formatting of the plots.
`...`	extra arguments will be ignored.

Details

The ability of the EM algorithm to locate the global maximum in fewer iterations can be affected by the choice of initial values, the function optim.boxcox() allows us to choose from two different methods to set the initial value of the mass points. When option "gq" is set, then Gauss-Hermite masses and mass points are used as starting points in the EM algorithm, while setting start= "quantile" uses the Quantile-based version to select the starting points.

optim.boxcox() performs a grid search over the parameter lambda and then optimizes over this grid, to calculate the maximum likelihood estimator of the transformation. It produces a plot of the non-parametric profile likelihood function that summarises information concerning lambda, including a vertical line indicating the best value of lambda that maximizes the non-parametric profile log-likelihood.

Value

List with class boxcoxmix containing:

`All.lambda`	list of `lambda` values used in the grid.
`Maximum`	the best estimate of `lambda` found.
`objective`	the value of the profile log-likelihood corresponding to Maximum.
`EMconverged`	1 is TRUE, means the EM algorithm converged.
`EMiteration`	provides the number of iterations of the EM algorithm.
`mass.point`	the fitted mass points.
`p`	the masses corresponding to the mixing proportions.
`beta`	the vector of coefficients.
`sigma`	the standard deviation of the mixing distribution (the square root of the variance).
`se`	the standard error of the estimate.
`w`	a matrix of posterior probabilities that element i comes from cluster k.
`loglik`	the profile log-likelihood of the fitted regression model.
`profile.loglik`	the profile complete log-likelihood of the fitted regression model.
`disparity`	the disparity of the fitted regression model.
`call`	the matched call.
`formula`	the formula provided.
`data`	the data argument.
`aic`	the Akaike information criterion of the fitted regression model.
`fitted`	the fitted values for the individual observations.
`fitted.transformed`	the fitted values for the individual transformed observations.
`residuals`	the difference between the observed values and the fitted values.
`residuals.transformed`	the difference between the transformed observed values and the transformed fitted values.
`predicted.re`	a vector of predicted residuals.

The other outcomes are not relevant to users and they are intended for internal use only.

Author(s)

Amani Almohaimeed and Jochen Einbeck

References

Box G. and Cox D. (1964). An analysis of transformations. Journal of the Royal Statistical Society. Series B (Methodological), pages 211-252.

Aitkin, M. A., Francis, B., Hinde, J., and Darnell, R. (2009). Statistical modelling in R. Oxford University Press Oxford.

Jochen Einbeck, Ross Darnell and John Hinde (2014). npmlreg: Nonparametric maximum likelihood estimation for random effect models. R package version 0.46-1.

Examples

# The strength Data
data(strength, package = "mdscore")
maxlam <- optim.boxcox(y ~ cut*lot, data = strength, K = 3,  
           start = "gq" ,  find.in.range = c(-2, 2), s = 5)
# Maximum profile log-likelihood: 33.6795 at lambda= -0.4  

data(Oxboys, package = "nlme")
Oxboys$boy <- gl(26,9)
maxlamvc <- optim.boxcox(height ~  age, groups = Oxboys$boy,
                         data = Oxboys,   K = 2,  start = "gq",
                         find.in.range=c(-1.2,1), s=6, plot.opt = 0) 
maxlamvc$Maximum
#[1] -0.8333333
plot(maxlamvc,8)





# The strength Data
data(strength, package = "mdscore")
maxlam <- optim.boxcox(y ~ cut*lot, data = strength, K = 3,  
           start = "gq" ,  find.in.range = c(-2, 2), s = 5)
# Maximum profile log-likelihood: 33.6795 at lambda= -0.4  

data(Oxboys, package = "nlme")
Oxboys$boy <- gl(26,9)
maxlamvc <- optim.boxcox(height ~  age, groups = Oxboys$boy,
                         data = Oxboys,   K = 2,  start = "gq",
                         find.in.range=c(-1.2,1), s=6, plot.opt = 0) 
maxlamvc$Maximum
#[1] -0.8333333
plot(maxlamvc,8)

Plot diagnostics for boxcoxmix functions

Description

plot() is a generic function used to produce some useful diagnostic plotting of the functions: np.boxcoxmix(), optim.boxcox() and tolfind.boxcox().

Usage

## S3 method for class 'boxcoxmix'
plot(x, plot.opt = 1, ...)
## S3 method for class 'boxcoxmix'
plot(x, plot.opt = 1, ...)

Arguments

`x`	an object for which a plot is desired.
`plot.opt`	an integer value between 1 and 8.
`...`	additional arguments.

Value

The plots to be printed depend on the number given in plot.opt, for the np.boxcoxmix(), optim.boxcox() and tolfind.boxcox() functions:

`1`	the disparities with the iteration number against the mass points
`2`	the fitted value against the response of the original and the transformed Data.
`3`	probability plot of residuals of the original against the transformed data.
`4`	individual posterior probabilities.
`5`	control charts of residuals of the original against the transformed data.
`6`	The histograms of residuals of the original against the transformed data.
`7`	works only for the `tolfind.boxcox()` function and plots the specified range of `tol` against the disparities
`8`	works only for the `optim.boxcox()` function and gives the profile likelihood function that summarises information concerning `lambda`.
`9`	works only for the `Kfind.boxcox()` function and plots the specified range of `K` against the AIC or BIC information criteria
`10`	works only for the `boxcoxtype()` function and gives the profile likelihood function that summarises information concerning `lambda` for generalized linear Mixed-effects Models.

Summary of boxcoxmix functions

Description

summary() and print() are generic functions used to produce the results of the functions: np.boxcoxmix(), optim.boxcox() and tolfind.boxcox().

Usage

## S3 method for class 'boxcoxmix'
print(x, digits = max(3, getOption("digits") - 3), na.print = "", ...)

## S3 method for class 'boxcoxmixpure'
print(x, digits = max(3, getOption("digits") - 3), na.print = "", ...)

## S3 method for class 'boxcoxmix'
summary(object, digits = max(3, getOption("digits") - 3), ...)

## S3 method for class 'boxcoxmixpure'
summary(object, digits = max(3, getOption("digits") - 3), ...)
## S3 method for class 'boxcoxmix'
print(x, digits = max(3, getOption("digits") - 3), na.print = "", ...)

## S3 method for class 'boxcoxmixpure'
print(x, digits = max(3, getOption("digits") - 3), na.print = "", ...)

## S3 method for class 'boxcoxmix'
summary(object, digits = max(3, getOption("digits") - 3), ...)

## S3 method for class 'boxcoxmixpure'
summary(object, digits = max(3, getOption("digits") - 3), ...)

Arguments

`x`	an object for which a summary is desired.
`digits`	an integer number format.
`na.print`	a character string which is used to indicate NA values output format.
`...`	additional arguments.
`object`	an object for which a summary is desired.

Value

Return invisibly the main object provided, while print a summary of its content.

Grid search over tol for NPPML estimation of random effect and variance component models

Description

A grid search over the parameter tol, to set the initial values of the EM algorithm.

Usage

tolfind.boxcox(
  formula,
  groups = 1,
  data,
  K = 3,
  lambda = 1,
  EMdev.change = 1e-04,
  plot.opt = 2,
  s = 15,
  steps = 500,
  find.in.range = c(0, 1.5),
  start = "gq",
  verbose = FALSE,
  noformat = FALSE,
  ...
)
tolfind.boxcox(
  formula,
  groups = 1,
  data,
  K = 3,
  lambda = 1,
  EMdev.change = 1e-04,
  plot.opt = 2,
  s = 15,
  steps = 500,
  find.in.range = c(0, 1.5),
  start = "gq",
  verbose = FALSE,
  noformat = FALSE,
  ...
)

Arguments

`formula`	a formula describing the transformed response and the fixed effect model (e.g. y ~ x).
`groups`	the random effects. To fit overdispersion models , set `groups` = 1.
`data`	a data frame containing variables used in the fixed and random effect models.
`K`	the number of mass points.
`lambda`	a transformation parameter, setting `lambda`=1 means 'no transformation'.
`EMdev.change`	a small scalar, with default 0.0001, used to determine when to stop EM algorithm.
`plot.opt`	Set `plot.opt=2`, to plot the EM trajectories and the development of the disparity over iteration number. And `plot.opt=0`, for none of them.
`s`	number of points in the grid search of `tol`.
`steps`	maximum number of iterations for the EM algorithm.
`find.in.range`	search in a range of `tol`, with default (0,1.5) in step of 0.1 .
`start`	a description of the initial values to be used in the fitted model, Quantile-based version "quantile" or Gaussian Quadrature "gq" can be set.
`verbose`	If set to FALSE, no printed output on progress.
`noformat`	Set `noformat = TRUE`, to change the formatting of the plots.
`...`	extra arguments will be ignored.

Details

A grid search over tol can be performed using tolfind.boxcox() function, which works for np.boxcoxmix() to find the optimal solution.

Value

List with class boxcoxmix containing:

`MinDisparity`	the minimum disparity found.
`Mintol`	the value of `tol` corresponding to `MinDisparity`.
`AllDisparities`	a vector containing all disparities calculated on the grid.
`Alltol`	list of `tol` values used in the grid.
`AllEMconverged`	1 is TRUE, means the EM algorithm converged.
`aic`	the Akaike information criterion of the fitted regression model.
`bic`	the Bayesian information criterion of the fitted regression model.

Author(s)

Amani Almohaimeed and Jochen Einbeck

Examples

# The Pennsylvanian Hospital Stay Data
data(hosp, package = "npmlreg")
test1 <- tolfind.boxcox(duration ~ age , data = hosp, K = 2, lambda = 0, 
           find.in.range = c(0, 2), s = 10,  start = "gq")
# Minimal Disparity: 137.8368 at tol= 2 
# Minimal Disparity with EM converged: 137.8368 at tol= 2

# Effect of Phenylbiguanide on Blood Pressure
data(PBG, package = "nlme")
test2 <- tolfind.boxcox(deltaBP ~ dose , groups = PBG$Rabbit, find.in.range = c(0, 2),
    data = PBG, K = 2, lambda = -1, s = 15,  start = "quantile", plot.opt = 0)
test2$Mintol
# [1] 1.6
test2$MinDisparity
# [1] 449.5876








# The Pennsylvanian Hospital Stay Data
data(hosp, package = "npmlreg")
test1 <- tolfind.boxcox(duration ~ age , data = hosp, K = 2, lambda = 0, 
           find.in.range = c(0, 2), s = 10,  start = "gq")
# Minimal Disparity: 137.8368 at tol= 2 
# Minimal Disparity with EM converged: 137.8368 at tol= 2

# Effect of Phenylbiguanide on Blood Pressure
data(PBG, package = "nlme")
test2 <- tolfind.boxcox(deltaBP ~ dose , groups = PBG$Rabbit, find.in.range = c(0, 2),
    data = PBG, K = 2, lambda = -1, s = 15,  start = "quantile", plot.opt = 0)
test2$Mintol
# [1] 1.6
test2$MinDisparity
# [1] 449.5876

Package 'boxcoxmix'

Help Index

Box-Cox-Type Transformations for Linear and Logistic Models with Random Effects

Description

Details

Author(s)

References

See Also

Box-Cox-type link function for logistic mixed-effects Models

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Grid search over K for NPML estimation of random effect and variance component models

Description

Usage

Arguments

Details

Value

Author(s)

See Also

Examples

Response Transformations for Random Effect and Variance Component Models

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Response Transformations for Random Effect and Variance Component Models

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Plot diagnostics for boxcoxmix functions

Description

Usage

Arguments

Value

Summary of boxcoxmix functions

Description

Usage

Arguments

Value

Grid search over tol for NPPML estimation of random effect and variance component models

Description

Usage

Arguments

Details

Value

Author(s)

See Also

Examples