IMIFA (version 2.1.5)

Ledermann: Ledermann Bound

Description

Returns the maximum number of latent factors in a factor analysis model for data of dimension P which actually achieves dimension reduction in terms of the number of covariance parameters. This Ledermann bound is given by the largest integer smaller than or equal to the solution \(k\) of \((M - k)^2 \geq M + k\).

Usage

Ledermann(P,
          isotropic = FALSE)

Arguments

P

Integer number of variables in data set. This argument is vectorised.

isotropic

Logical indicating whether uniquenesses are constrained to be isotropic, in which case the bound is simply \(P-1\). Defaults to FALSE.

Value

The Ledermann bound, a non-negative integer, or a vector of length(P) such bounds.

Examples

# NOT RUN {
Ledermann(c(25, 50, 100))

data(olive)
Ledermann(ncol(olive[,-c(1,2)]))
# }