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Abdominal circumference data

Description

Theabdom data frame has 610 rows and 2 columns. The data aremeasurements of abdominal circumference (response variable) taken fromfetuses during ultrasound scans at Kings College Hospital, London, atgestational ages (explanatory variable) ranging between 12 and 42 weeks.

Usage

data(abdom)

Format

This data frame contains the following columns:

y

Abdominal circumference: a numeric vector.

x

Gestational age: a numeric vector.

Details

The data were used to derive reference intervals by Chittyet al.(1994) and also for comparing different reference centile methods byWright and Royston (1997), who also commented that the distribution ofz-scores obtained from the different fitted models "has somewhat longertails than the normal distribution".

Source

Dr. Eileen M. Wright, Department of Medical Statistics and Evaluation,Royal Postgraduate Medical School, Du Cane Road, London, W12 0NN.

Theabdom dataset was copied into thelmls package from thegamlss.data package.gamlss.data is licensed under the GPL 2 and 3.

References

Chitty, L.S., Altman, D.G., Henderson, A. and Campbell, S. (1994). Chartsof fetal size: 3, abdominal measurement.Br. J. Obstet. Gynaec.,101: 125–131.

Wright, E.M. and Royston, P. (1997). A comparison of statisticalmethods for age-related reference intervals.J. R. Statist. Soc. A.,160: 47–69.

Examples

data(abdom)attach(abdom)plot(x, y)detach(abdom)

Parametric bootstrap for LMLS

Description

A simple parametric bootstrap algorithm for location-scale regression modelsfrom thelmls() function.

Usage

boot(m, num_samples = 1000, seed = NULL)

Arguments

Value

Anlmls S3 object, seelmls(). The entryboot with the matrices ofbootstrap samples is added to the object as a list with the nameslocationandscale.

Examples

library(lmls)m <- lmls(y ~ poly(x, 2), ~ x, data = abdom, light = FALSE)m <- boot(m)summary(m, type = "boot")hist(m$boot$scale[, 2])

Gaussian location-scale regression

Description

The location-scale regression model assumes a normally distributed responsevariable with one linear predictor for the mean (= the location) and one forthe standard deviation (= the scale). The standard deviation is mapped tothe linear predictor through a log link.

This function sets up the model object and estimates it with maximumlikelihood.

Usage

lmls(  location,  scale = ~1,  data = environment(location),  light = TRUE,  maxit = 100,  reltol = sqrt(.Machine$double.eps))

Arguments

Value

A fitted linear model for location and scale as anlmls S3 object.The object has at least the following entries:

• y: the response vector

• nobs: the number of observations

• df: the degrees of freedom

• df.residual: the residual degrees of freedom

• coefficients: the regression coefficients as a list with the nameslocation andscale

• fitted.values: the fitted values as a list with the nameslocationandscale

• residuals: the response residuals

• coefficients: the variance-covariance matrices of the regressioncoefficients as a list with the nameslocation andscale

• iterations: the number of iterations the Fisher scoring algorithmtook to converge

Examples

library(lmls)m <- lmls(y ~ poly(x, 2), ~ x, data = abdom)summary(m)plot(m)qqnorm(m)

Methods for LMLS

Description

A couple of methods for location-scale regression models from thelmls()function are provided.

Usage

## S3 method for class 'lmls'coef(object, predictor = c("location", "scale"), ...)## S3 method for class 'lmls'fitted(object, predictor = c("location", "scale"), ...)## S3 method for class 'lmls'predict(  object,  newdata = NULL,  predictor = c("location", "scale"),  type = c("link", "response"),  ...)## S3 method for class 'lmls'residuals(object, type = c("deviance", "pearson", "response"), ...)## S3 method for class 'lmls'vcov(object, predictor = c("location", "scale"), ...)

Arguments

Value

A numeric vector forresiduals(). For the other methods, a numeric vectorif the argumentpredictor is either"location" or"scale", or a listwith the nameslocation andscale if it is both.

MCMC inference for LMLS

Description

A Markov chain Monte Carlo (MCMC) sampler for location-scale regressionmodels from thelmls() function. The sampler uses Gibbs updates for thelocation coefficients and the Riemann manifold Metropolis-adjusted Langevinalgorithm (MMALA) from Girolami and Calderhead (2011) with the Fisher-Raometric tensor for the scale coefficients. The priors for the regressioncoefficients are assumed to be flat.

To find the optimal step size for the MMALA updates, the dual averagingalgorithm from Nesterov (2009) is used during a warm-up phase.

Usage

mcmc(m, num_samples = 1000, num_warmup = 1000, target_accept = 0.8)

Arguments

Value

Anlmls S3 object, seelmls(). The entrymcmc with the matricesof MCMC samples is added to the object as a list with the nameslocationandscale.

References

Girolami, M. and Calderhead, B. (2011), Riemann manifold Langevin andHamiltonian Monte Carlo methods. Journal of the Royal Statistical Society:Series B (Statistical Methodology), 73: 123-214.doi:10.1111/j.1467-9868.2010.00765.x

Nesterov, Y. (2009), Primal-dual subgradient methods for convex problems.Mathematical Programming, 120: 221–259.doi:10.1007/s10107-007-0149-x

Examples

library(lmls)m <- lmls(y ~ poly(x, 2), ~ x, data = abdom, light = FALSE)m <- mcmc(m)summary(m, type = "mcmc")plot(m$mcmc$scale[, 2], type = "l")

Objects exported from other packages

Description

These objects are imported from other packages. Follow the linksbelow to see their documentation.

generics

glance,tidy

Summary for LMLS

Description

Prints a summary for location-scale regression models from thelmls()function.

Usage

## S3 method for class 'lmls'summary(  object,  type = c("ml", "boot", "mcmc"),  digits = max(3, getOption("digits") - 3),  ...)

Arguments

Value

The (unmodified and invisible)lmls S3 object, seelmls().