Add calculate_cng_indices

factor_analyzer/factor_analyzer.py

@@ -8,19 +8,21 @@
 """
 
 import warnings
+from typing import Tuple
 
 import numpy as np
 import pandas as pd
 import scipy as sp
 from scipy.optimize import minimize
 from scipy.stats import chi2, pearsonr
 from sklearn.base import BaseEstimator, TransformerMixin
+from sklearn.linear_models import LinearRegression
 from sklearn.utils import check_array
 from sklearn.utils.extmath import randomized_svd
 from sklearn.utils.validation import check_is_fitted
 
 from .rotator import OBLIQUE_ROTATIONS, POSSIBLE_ROTATIONS, Rotator
-from .utils import corr, impute_values, partial_correlations, smc
+from .utils import corr, covariance_to_correlation, impute_values, partial_correlations, smc
 
 POSSIBLE_SVDS = ['randomized', 'lapack']
 
@@ -114,6 +116,70 @@ def calculate_bartlett_sphericity(x):
  return statistic, p_value
 
 
+def calculate_cng_indices(
+ data: np.ndarray, model: str = "components"
+) -> Tuple[int, pd.DataFrame]:
+ """Calculate the Cattel-Nelson-Gorsuch indices, which are used to determine
+ the appropriate number of factors for a factor analysis.
+
+ Direct port of nCng function from nFactors package:
+ https://rdrr.io/cran/nFactors/man/nCng.html
+
+ Parameters
+ ----------
+ data : array-like
+ The array of samples x observable for which to calculate CNG indices
+ model : str
+ "components" or "factors"
+
+ Returns
+ -------
+ num_factors : int
+ The number of components/factors to retain
+ details : pd.DataFrame
+ The eigenvalues and CNG indices of the dataset
+ """
+ data = corr(data.values)
+ if model == "factors":
+ data -= np.linalg.pinv(np.diag(np.diag(np.linalg.pinv(data))))
+ # TODO: Should this line be here?
+ data = covariance_to_correlation(data)
+
+ values = np.sort(np.linalg.eigvals(data))[::-1]
+
+ num_variables = len(data)
+ if num_variables < 6:
+ raise ValueError("The number of variables must be at least 6")
+
+ fit_size = 3
+ cng = np.diff(
+ [
+ [
+ LinearRegression()
+ .fit(idx_values[:, np.newaxis], values[idx_values])
+ .coef_
+ for idx_values in [
+ np.arange(idx_fit, idx_fit + fit_size),
+ np.arange(idx_fit + fit_size, idx_fit + 2 * fit_size),
+ ]
+ ]
+ for idx_fit in range(num_variables - 2 * fit_size)
+ ],
+ axis=1,
+ ).squeeze(axis=(1, 2))
+
+ num_factors = np.nanargmax(cng) + fit_size
+
+ details = pd.DataFrame(
+ {
+ "data": values[: len(cng)],
+ "cng": cng,
+ }
+ )
+
+ return num_factors, details
+
+
 class FactorAnalyzer(BaseEstimator, TransformerMixin):
  """
  A FactorAnalyzer class, which -