gm.validation {gmvalid}R Documentation

Validation and variability measures for graphical models.

Description

The bootstrapped graphical models are analyzed and some new uncertainty measures and variance estimators are applied in order to determine the uncertainty of a selected graphical model.

Usage

gm.validation(data, N = 0, program = c("coco", "mim"), Umax = 0.5, conf.level = 0.95, ...)

Arguments

data Either the output list from one of the bootstrap functions gm.boot.coco or gm.boot.mim or data frame or a table (array). Variables should have names, data has to be discrete.
N Number of bootstrap replications. Only needed if data is not yet a bootstrap output.
program If a bootstrap is not yet done, which function should do it: gm.boot.coco or gm.boot.mim.
Umax Defines the maximum uncertainty in the edges. In the validation the selection frequency of every edge in the bootstrap replications is the most important foundation. The default is that an edge is maximally uncertain when it is selected in 50
conf.level Confidence level for the bootstrap percentile interval.
... You may add options to the selection strategy, if a bootstrap is still needed. See gm.boot.coco or gm.boot.mim.

Details

The bootstrap functions bring multivariate output about the uncertainty of a selected graphical model. This function presents some possibilities to reduce the uncertainty to a univariate measure, based either on the edge frequencies of presence in the bootstrapped models or on differences between models measured in edges.

Value

"original model" Character string giving the selected model using the original unsampled data.
"mode model" Character string giving a model that was selected the most as a whole. It can happen that for 100 bootstrap replications there are 100 different models selected. So this is not the best way to validate a graphical model.
"mean model" Character string giving a model that consists of all the edges that had a frequency of selection greater than Umax in the bootstrap replications. This selection promisses the best validation results.
"MEU" Linear measure for the uncertainty of the validated model based on the edge frequency. For each edge the minimum distance to a frequency of 0 or 1 is measured, multiplied by Umax and identified as its uncertainty because with a frequency of 0 or 1 we think of an edge as maximally safe. Then the mean over all edges is calculated to receive an uncertainty measure.
"MSEU" Same as above, only the uncertainty of an edge is squared and normalized so that a frequency of Umax results in a stability of 0 respectively an uncertainty of 1.
"differing edges" List that says by how many edges the bootstrapped models differ from the validated model.
"total possible edges" Number of edges the saturated model would include.
"model std" The validated model is interpreted as mean model and the number of differing edges define the difference between 2 models and so the univariate standard error of the validated model is estimated.
"std/total" Uncertainty measure that relates the standard error (model std) to the value of total possible edges.
"expected edges different" The calculated mean of the differing edges.
"bootstrap percentile 95" The value that includes at least the lower 95 the model uncertainty.
"variable names" Matrix that assigns a letter to each variable that is used in the model formulas.

Note

The question when an edge is maximally uncertain is not yet answered satisfactory. Can we say that an association that is selected in 40 is not present? Or that an edge that is present in 60 randomly? Therefore the argument Umax leaves it up to your opinion.

If you already have run a bootstrap, make sure it was with all the possible calculations.

Author(s)

Ronja Foraita, Fabian Sobotka
Bremen Institute for Prevention Research and Social Medicine
(BIPS) http://www.bips.uni-bremen.de

References

Efron B, Tibshirani RJ (1993) An Introduction to the Bootstrap. Chapman & Hall

See Also

gm.boot.coco, gm.boot.mim

Examples

  ### Standard procedure
  data(wam)
  boot.out <- gm.boot.coco(1000,wam,strategy="f",recursive=TRUE,follow=TRUE,all.significant=FALSE)
  gm.validation(boot.out)



[Package gmvalid version 1.1 Index]