SynergyLMM (version 1.1.2)

logLikSubjectDisplacements: Likelihood displacements for the model

Description

logLikSubjectDisplacements allows the user to evaluate the log-likelihood displacement for each subject, indicating the influence of every subject to the model.

Usage

logLikSubjectDisplacements(
  model,
  disp_thrh = NA,
  label_angle = 0,
  var_name = NULL,
  verbose = TRUE,
  ...
)

Value

Returns a plot of the log-likelihood displacement values for each subject, indicating those subjects whose contribution is greater than disp_thrh.

Arguments

model

An object of class "lme" representing the linear mixed-effects model fitted by lmmModel().

disp_thrh

Numeric value indicating the threshold of log-likelihood displacement. If not specified, the threshold is set to three times the mean of the log-likelihood displacement values.

label_angle

Numeric value indicating the angle for the label of subjects with a log-likelihood displacement greater than disp_thrh.

var_name

Name of the variable for the weights of the model in the case that a variance structure has been specified using nlme::varIdent(). (See examples in lmmModel()).

verbose

Logical indicating if subjects with a log-likelihood displacement greater than disp_thrh should be printed to the console.

...

Extra arguments, if any, for lattice::panel.xyplot.

Details

The evaluation of the log-likelihood displacement is based in the analysis proposed in Verbeke and Molenberghs (2009) and Gałecki and Burzykowski (2013). First, a list of models fitted to leave-one-subject-out datasets are obtained. Then, for each model, the maximum likelihood estimate obtained by fitting the model to all data and the maximum likelihood estimate obtained by fitting the model to the data with the \(i\)-th subject removed are obtained and used for the log-likelihood displacement calculation. The likelihood displacement, \(LDi\) , is defined as twice the difference between the log-likelihood computed at a maximum and displaced values of estimated parameters (Verbeke and Molenberghs (2009), Gałecki and Burzykowsk (2013)):

$$LD_i \equiv 2 \times \Bigr[\ell_\textrm{Full}(\widehat{\Theta};\textrm{y})-\ell_\textrm{Full}(\widehat{\Theta}_{(-i)};\textrm{y})\Bigr]$$

where \(\widehat{\Theta}\) is the maximum-likelihood estimate of \(\Theta\) obtained by fitting the model to all data, while \(\widehat{\Theta}_{-i}\) is the maximum-likelihood estimate obtained by fitting the model to the data with the \(i\)-subject excluded.

References

• Andrzej Galecki & Tomasz Burzykowski (2013) Linear Mixed-Effects Models Using R: A Step-by-Step Approach First Edition. Springer, New York. ISBN 978-1-4614-3899-1

• Verbeke, G. & Molenberghs, G. (2000). Linear Mixed Models for Longitudinal Data. Springer New York. https://doi.org/10.1007/978-1-4419-0300-6

Examples

# Load the example data
data(grwth_data)
# Fit the model
lmm <- lmmModel(
  data = grwth_data,
  sample_id = "subject",
  time = "Time",
  treatment = "Treatment",
  tumor_vol = "TumorVolume",
  trt_control = "Control",
  drug_a = "DrugA",
  drug_b = "DrugB",
  combination = "Combination"
  ) 
# Obtain log-likelihood displacement for each subject
logLikSubjectDisplacements(model = lmm)
# Modifying the threshold for log-likelihood displacement
logLikSubjectDisplacements(model = lmm, disp_thrh = 1)

# Calculating the log-likelihood contribution in a model with a variance structure specified
lmm_var <- lmmModel(
  data = grwth_data,
  sample_id = "subject",
  time = "Time",
  treatment = "Treatment",
  tumor_vol = "TumorVolume",
  trt_control = "Control",
  drug_a = "DrugA",
  drug_b = "DrugB",
  combination = "Combination",
  weights = nlme::varIdent(form = ~ 1|SampleID)
  ) 
# Calculate the log-likelihood contribution
logLikSubjectDisplacements(model = lmm, var_name = "SampleID")