Local Influence Plot Diagnostics for Mixed Poisson Regression Models

Source: R/4_local_influence.R

Local influence plots for mixed Poisson regression models. Currently the conformal normal and normal curvatures are available under several perturbation schemes. The default is the conformal normal curvature since it takes values on \([0,1]\) and other nice properties (see Zhu and Lee, 2001 and Poon and Poon, 1999 for further details).

# S3 method for mixpoissonreg
local_influence_plot(
  model,
  which = c(1, 2, 3, 4),
  caption = list("Case Weights Perturbation", "Hidden Variable Perturbation",
    "Mean Explanatory Perturbation", "Precision Explanatory Perturbation",
    "Simultaneous Explanatory Perturbation"),
  sub.caption = NULL,
  detect.influential = TRUE,
  n.influential = 5,
  draw.benchmark = FALSE,
  lty.benchmark = 2,
  type_plot = "h",
  curvature = c("conformal", "normal"),
  direction = c("canonical", "max.eigen"),
  parameters = c("all", "mean", "precision"),
  mean.covariates = NULL,
  precision.covariates = NULL,
  main = "",
  ask = prod(graphics::par("mfcol")) < length(which) && grDevices::dev.interactive(),
  labels.id = names(stats::residuals(model)),
  cex.id = 0.75,
  cex.oma.main = 1.25,
  cex.caption = 1,
  include.modeltype = TRUE,
  ...
)

Arguments

model

a mixpoissonreg object.
which

a list or vector indicating which plots should be displayed. If a subset of the plots is required, specify a subset of the numbers 1:5, see caption below (and the 'Details') for the different kinds.
caption

captions to appear above the plots; character vector or list of valid graphics annotations. Can be set to "" or NA to suppress all captions.
sub.caption

common title-above the figures if there are more than one. If NULL, as by default, a possible abbreviated version of deparse(x$call) is used.
detect.influential

logical. Indicates whether the benchmark should be used to detect influential observations and identify them on the plot. If there is no benchmark available, the top 'n.influential' observations will be identified in the plot by their indexes.
n.influential

interger. The maximum number of influential observations to be identified on the plot.
draw.benchmark

logical. Indicates whether a horizontal line identifying the benchmark should be drawn.
lty.benchmark

the line type of the benchmark if drawn.
type_plot

what type of plot should be drawn. The default is 'h'.
curvature

the curvature to be returned, 'conformal' for the conformal normal curvature (see Zhu and Lee, 2001 and Poon and Poon, 1999) or 'normal' (see Zhu and Lee, 2001 and Cook, 1986).
direction

the 'max.eigen' returns the eigenvector associated to the largest eigenvalue of the perturbation matrix. The 'canonical' considers the curvatures under the canonical directions, which is known as "total local curvature" (see Lesaffre and Verbeke, 1998). For conformal normal curvatures both of them coincide. The default is 'canonical'.
parameters

the parameter to which the local influence will be computed. The options are 'all', 'mean' and 'precision'. This argument affects the 'case_weights' and 'hidden_variable' perturbation schemes. The default is 'all'.
mean.covariates

a list or vector of characters containing the mean-explanatory variables to be used in the 'mean-explanatory' and 'simultaneous-explanatory' perturbation schemes. If NULL, the 'mean-explanatory' and 'simultaneous-explanatory' perturbation schemes will be computed by perturbing all mean-related covariates. The default is NULL.
precision.covariates

a list or vector of characters containing the precision-explanatory variables to be used in the 'precision-explanatory' and 'simultaneous-explanatory' perturbation schemes. If NULL, the 'precision-explanatory' and 'simultaneous-explanatory' perturbation schemes will be computed by perturbing all precision-related covariates. The default is NULL.
main

character; title to be placed at each plot additionally (and above) all captions.
ask

logical; if TRUE, the user is asked before each plot.
labels.id

vector of labels, from which the labels for extreme points will be chosen. The default uses the observation numbers.
cex.id

magnification of point labels.
cex.oma.main

controls the size of the sub.caption only if that is above the figures when there is more than one.
cex.caption

controls the size of caption.
include.modeltype

logical. Indicates whether the model type ('NB' or 'PIG') should be displayed on the captions.
...

other graphical arguments to be passed.

Value

Called for its side effects.

Details

local_influence.mixpoissonreg provides local influence diagnostics for mixed Poisson regression models for all perturbation schemes considered in Barreto-Souza and Simas (2016), for normal and conformal normal curvatures. Further, it is also provides results for the canonical directions, which is called the total local influence (see Lesaffre and Verbeke, 1998), as well as for the direction of largest curvature, which is the direction of the eigenvector of the perturbation matrix associated to the largest eigenvalue.

local_influence_plot.mixpoissonreg provides a plot of the local influence diagnostics. Each plot corresponds to a perturbation scheme. The first plot considers the 'case-weights' perturbation; the second plot considers the 'hidden-variable' perturbation (which was introduced in Barreto-Souza and Simas, 2016); the third plot considers the mean-explanatory perturbation; the fourth plot considers the precision-explanatory perturbation; the fifth plot considers the simultanous-explanatory perturbation.

For both local_influence.mixpoissonreg and local_influence_plot.mixpoissonreg, one can select which covariates will be perturbed in the 'mean-explanatory', 'precision-explanatory' and 'simultaneous-explanatory' perturbation schemes. These are chosen in the 'mean.covariates' and 'precision.covariates' arguments.

If one considers the total local influence, then Zhu and Lee (2001) provides benchmark for influential observations for all perturbation schemes. These are returned as attributes in the returned list from local_influence.mixpoissonreg. When using the local_influence_plot.mixpoissonreg, only points above the benchmark will be displayed. One can also set the option 'draw_benchmark' to TRUE to plot the benchmark line.

References

DOI:10.1007/s11222-015-9601-6 doi: 10.1007/s11222-015-9601-6 (Barreto-Souza and Simas; 2016)

Cook, R. D. (1986) Assessment of Local Influence. Journal of the Royal Statistical Society. Series B (Methodological), Vol. 48, pp.133-169. https://rss.onlinelibrary.wiley.com/doi/10.1111/j.2517-6161.1986.tb01398.x

Lesaffre, E. and Verbeke, G. (1998) Local Influence in Linear Mixed Models. Biometrics, 54, pp. 570-582.

Poon, W.-Y. and Poon, Y.S. (1999) Conformal normal curvature and assessment of local influence. Journal of the Royal Statistical Society. Series B (Methodological), Vol. 61, pp.51-61. https://rss.onlinelibrary.wiley.com/doi/abs/10.1111/1467-9868.00162

Zhu, H.-T. and Lee, S.-Y. (2001) Local influence for incomplete data models. Journal of the Royal Statistical Society. Series B (Methodological), Vol. 63, pp.111-126. https://rss.onlinelibrary.wiley.com/doi/abs/10.1111/1467-9868.00279

Examples

# \donttest{
data("Attendance", package = "mixpoissonreg")

daysabs_fit <- mixpoissonreg(daysabs ~ gender + math +
prog | gender + math + prog, data = Attendance)
local_influence_plot(daysabs_fit)


daysabs_fit_ml <- mixpoissonregML(daysabs ~ gender + math +
prog | gender + math + prog, data = Attendance, envelope = 100)
local_influence_plot(daysabs_fit_ml, which = 2)

# }

daysabs_progML <- mixpoissonregML(daysabs ~ prog | prog, data = Attendance)
local_influence_plot(daysabs_progML)