plot_lambda {smurf}

Plot Goodness-of-Fit Statistics or Information Criteria

Description

Function to plot the goodness-of-fit statistics or information criteria as a function of lambda when lambda is selected in-sample, out-of-sample or using cross-validation.

Usage

plot_lambda(x, ...)

## S3 method for class 'glmsmurf'
plot_lambda(
  x,
  xlab = NULL,
  ylab = NULL,
  lambda.opt = TRUE,
  cv1se = TRUE,
  log.lambda = TRUE,
  ...
)

Arguments

x

An object for which the extraction of goodness-of-fit statistics or information criteria is meaningful. E.g. an object of class 'glmsmurf', typically the result of a call to glmsmurf or glmsmurf.fit.

...

Additional arguments for the plot function.

xlab

Label for the x-axis. The default value is NULL which means that substitute(log(lambda)) is used when log.lambda=TRUE and substitute(lambda) when log.lambda=FALSE.

ylab

Label for the y-axis. The default value is NULL which means that the y-axis label is determined based on method that was used to select lambda.

lambda.opt

Logical indicating if the optimal value of lambda should be indicated on the plot by a vertical dashed line. Default is TRUE.

cv1se

Logical indicating if the standard errors should be indicated on the plot when cross-validation with the one standard error rule is performed (e.g. "cv1se.dev"). Default is TRUE.

log.lambda

Logical indicating if the logarithm of lambda is plotted on the x-axis, default is TRUE.

Details

This plot can only be made when lambda is selected in-sample, out-of-sample or using cross-validation (possibly with the one standard error rule), see the lambda argument of glmsmurf.

See Also

glmsmurf, glmsmurf-class

Examples

# Munich rent data from catdata package
data("rent", package = "catdata")

# The considered predictors are the same as in 
# Gertheiss and Tutz (Ann. Appl. Stat., 2010).
# Response is monthly rent per square meter in Euro

# Urban district in Munich
rent$area <- as.factor(rent$area)

# Decade of construction
rent$year <- as.factor(floor(rent$year / 10) * 10)

# Number of rooms
rent$rooms <- as.factor(rent$rooms)

# Quality of the house with levels "fair", "good" and "excellent"
rent$quality <- as.factor(rent$good + 2 * rent$best)
levels(rent$quality) <- c("fair", "good", "excellent")

# Floor space divided in categories (0, 30), [30, 40), ...,  [130, 140)
sizeClasses <- c(0, seq(30, 140, 10))
rent$size <- as.factor(sizeClasses[findInterval(rent$size, sizeClasses)])

# Is warm water present?
rent$warm <- factor(rent$warm, labels = c("yes", "no"))

# Is central heating present?
rent$central <- factor(rent$central, labels = c("yes", "no"))

# Does the bathroom have tiles?
rent$tiles <- factor(rent$tiles, labels = c("yes", "no"))

# Is there special furniture in the bathroom?
rent$bathextra <- factor(rent$bathextra, labels = c("no", "yes"))

# Is the kitchen well-equipped?
rent$kitchen <- factor(rent$kitchen, labels = c("no", "yes"))



# Create formula with 'rentm' as response variable,
# 'area' with a Generalized Fused Lasso penalty,
# 'year', 'rooms', 'quality' and 'size' with Fused Lasso penalties,
# and the other predictors with Lasso penalties.
formu <- rentm ~ p(area, pen = "gflasso") + 
  p(year, pen = "flasso") + p(rooms, pen = "flasso") + 
  p(quality, pen = "flasso") + p(size, pen = "flasso") +
  p(warm, pen = "lasso") + p(central, pen = "lasso") + 
  p(tiles, pen = "lasso") + p(bathextra, pen = "lasso") + 
  p(kitchen, pen = "lasso") 

# Fit a multi-type regularized GLM using the SMuRF algorithm and select the optimal value of lambda 
# using cross-validation (with the deviance as loss measure and the one standard error rule).
# We use standardization adaptive penalty weights based on an initial GLM fit.
# The number of values of lambda to consider in cross-validation is
# set to 10 using the control argument (default is 50).
munich.fit.cv <- glmsmurf(formula = formu, family = gaussian(), data = rent, 
                          pen.weights = "glm.stand", lambda = "cv1se.dev",
                          control = list(lambda.length = 10L, ncores = 1L))


# Plot average deviance over cross-validation folds as a function of the logarithm of lambda
plot_lambda(munich.fit.cv)
# Zoomed plot
plot_lambda(munich.fit.cv, xlim = c(-7, -3.5), ylim = c(1575, 1750))