Test for the presence of local factors, as in local_factors(), with additional flexibility.

Test for the presence of local factors, as in local_factors(), with additional flexibility.

Usage

test_local_factors(X, r, loadings = NULL)

Arguments

X

A (usually standardized) t by n matrix of observations.

r

An integer denoting the number of factors in X.

loadings

(optional) Matrix that represents a sparse basis of the loading space.

Value

Returns a list with the following components:

• has_local_factors Logical equal to TRUE if local factors are present.

• n_small Integer denoting the number of small loadings in sparse rotation.

• gamma_n Integer denoting the critical value to compare n_small to.

• h_n Number denoting the cutoff used to determine which loadings are small.

• loadings Matrix that is the rotation of the loadings that produces the smallest l1-norm (if not supplied).

Examples

# Minimal example with 2 factors, where X is a 224 by 207 matrix
r <- 2
M <- nrow(example_data)
n <- ncol(example_data)

# Find minimum rotation
rotation_result <- find_local_factors(X = example_data, r)

# Test if sparse basis has local factors
test_result <- test_local_factors(
   X = example_data,
   r = r,
   loadings = rotation_result$rotated_loadings
)

test_result$has_local_factors
#> [1] TRUE