Package 'lmls'

Abdominal circumference data

Description

The abdom data frame has 610 rows and 2 columns. The data are measurements of abdominal circumference (response variable) taken from fetuses during ultrasound scans at Kings College Hospital, London, at gestational 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 Chitty et al. (1994) and also for comparing different reference centile methods by Wright and Royston (1997), who also commented that the distribution of z-scores obtained from the different fitted models "has somewhat longer tails 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.

The abdom dataset was copied into the lmls package from the gamlss.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). Charts of fetal size: 3, abdominal measurement. Br. J. Obstet. Gynaec., 101: 125–131.

Wright, E.M. and Royston, P. (1997). A comparison of statistical methods 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 models from the lmls() function.

Usage

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

Arguments

m	A location-scale regression model from the lmls() function.
num_samples	The number of bootstrap samples to draw.
seed	Either NULL or an integer that will be used in a call to set.seed() before simulating the response vectors.

Value

An lmls S3 object, see lmls(). The entry boot with the matrices of bootstrap samples is added to the object as a list with the names location and scale.

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 response variable with one linear predictor for the mean (= the location) and one for the standard deviation (= the scale). The standard deviation is mapped to the linear predictor through a log link.

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

Usage

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

Arguments

location	A two-sided formula with the response variable on the LHS and the predictor for the mean on the RHS.
scale	A one-sided formula with the predictor for the standard deviation on the RHS.
data	A data frame (or list or environment) in which to evaluate the location and scale formulas.
light	If TRUE, the design matrices are removed from the estimated model to save some memory.
maxit	The maximum number of iterations of the Fisher scoring algorithm.
reltol	The relative convergence tolerance of the Fisher scoring algorithm.

Value

A fitted linear model for location and scale as an lmls 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 names location and scale

• fitted.values: the fitted values as a list with the names location and scale

• residuals: the response residuals

• coefficients: the variance-covariance matrices of the regression coefficients as a list with the names location and scale

• iterations: the number of iterations the Fisher scoring algorithm took 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 the lmls() 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

object	A location-scale regression model from the lmls() function.
predictor	The predictor to work on. Either "location" or "scale" or both. If both, a list with the names "location" and "scale" is returned.
...	Currently ignored.
newdata	A data frame (or list or environment) with the covariate values at which the predictions are computed. If NULL, the predictions at the original data are returned.
type	Used by predict() and residuals(): For predict(), "link" or "response". If "link" (default), $\mu$ and log($\sigma$) are returned. If "response", $\mu$ and $\sigma$ are returned. For residuals(), "deviance", "pearson" or "response". If "deviance" (default) or "pearson", ($y - \mu$) / $\sigma$ is returned. If "response", $y - \mu$ is returned.

Value

A numeric vector for residuals(). For the other methods, a numeric vector if the argument predictor is either "location" or "scale", or a list with the names location and scale if it is both.

---

MCMC inference for LMLS

Description

A Markov chain Monte Carlo (MCMC) sampler for location-scale regression models from the lmls() function. The sampler uses Gibbs updates for the location coefficients and the Riemann manifold Metropolis-adjusted Langevin algorithm (MMALA) from Girolami and Calderhead (2011) with the Fisher-Rao metric tensor for the scale coefficients. The priors for the regression coefficients are assumed to be flat.

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

Usage

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

Arguments

m	A location-scale regression model from the lmls() function.
num_samples	The number of MCMC samples after the warm-up. Defaults to 1000.
num_warmup	The number of MCMC samples for the warm-up. Defaults to 1000.
target_accept	The target acceptance rate for the dual averaging algorithm used for the warm-up. Defaults to 0.8.

Value

An lmls S3 object, see lmls(). The entry mcmc with the matrices of MCMC samples is added to the object as a list with the names location and scale.

References

Girolami, M. and Calderhead, B. (2011), Riemann manifold Langevin and Hamiltonian 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")

---

Summary for LMLS

Description

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

Usage

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

Arguments

object	A location-scale regression model from the lmls() function.
type	Either "ml" or "boot" or "mcmc": If "ml", the maximum likelihood estimates and the asymptotic standard errors are shown. If "boot", the bootstrap estimates and confidence intervals are shown. If "mcmc", the Markov chain Monte Carlo (MCMC) estimates and credible intervals are shown.
digits	The number of digits to print.
...	Passed on to printCoefmat().

Value

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

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