All Hierarchical or Graphical Models for Generalized Linear Model

Description

Find all hierarchical models of specified GLM with information criterion (AIC, BIC, or AICc) within specified cutoff of minimum value. Alternatively, all such graphical models. Use branch and bound algorithm so we do not have to fit all models.

Usage

1
2
3
glmbb(big, little = ~ 1, family = poisson, data,
    criterion = c("AIC", "AICc", "BIC"), cutoff = 10,
    trace = FALSE, graphical = FALSE, ...)

Arguments

big

an object of class "formula" specifying the largest model to be considered. Model specified must be hierarchical. (See also glm and formula and ‘Details’ section below.)

little

a formula specifying the smallest model to be considered. The response may be omitted and if not omitted is ignored (the response is taken from big). Default is ~ 1. Model specified must be nested within the model specified by big.

family

a description of the error distribution and link function to be used in the model. This can be a character string naming a family function, a family function or the result of a call to a family function. (See family for details of family functions.)

data

an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the models. If not found in data, the variables are taken from environment(big), typically the environment from which glmbb is called.

criterion

a character string specifying the information criterion, must be one of "AIC" (Akaike Information Criterion, the default), "BIC" (Bayes Information Criterion) or "AICc" (AIC corrected for sample size).

cutoff

a nonnegative real number. This function finds all hierarchical models that are submodels of big and supermodels of little with information criterion less than or equal to the cutoff plus the minimum information criterion over all these models.

trace

logical. Emit debug info if TRUE.

graphical

logical. If TRUE search only over graphical models rather than hierarchical models.

...

additional named or unnamed arguments to be passed to statsglm.

Details

Typical value for big is something like foo ~ bar * baz * qux where foo is the response variable (or matrix when family is binomial or quasibinomial, see glm) and bar, baz, and qux are all the predictors that are considered for inclusion in models.

A model is hierarchical if it includes all lower-order interactions for each term. This is automatically what formulas with all variables connected by stars (*) do, like the example above. But other specifications are possible. For example, foo ~ (bar + baz + qux)^2 specifies the model with all main effects, and all two-way interactions, but no three-way interaction, and this is hierarchical.

A model m1 is nested within a model m2 if all terms in m1 are also terms in m_2. The default little model ~ 1 is nested within every model except those specified to have no intercept by 0 + or some such (see link[stats]{formula}).

The interaction graph of a model is the undirected graph whose node set is the predictor variables in the model and whose edge set has one edge for each pair of variables that are in an interaction term. A clique in a graph is a maximal complete subgraph. A model is graphical if it is hierarchical and has an interaction term for the variables in each clique. When graphical = TRUE only graphical models are considered.

Value

An object of class "glmbb" containing at least the following components:

data

the model frame, a data frame containing all the variables.

little

the argument little.

big

the argument big.

criterion

the argument criterion.

cutoff

the argument cutoff.

envir

an R environment object containing all of the fits done.

min.crit

the minimum value of the criterion.

graphical

the argument graphical.

References

Hand, D. J. (1981) Branch and bound in statistical data analysis. The Statistician, 30, 1–13.

See Also

link[stats]{family}, link[stats]{formula}, link[stats]{glm}, isGraphical, isHierarchical

Examples

1
2
3
4
data(crabs)
gout <- glmbb(satell ~ (color + spine + width + weight)^3,
    criterion = "BIC", data = crabs)
summary(gout)