Velicer's MAP Test results in 0 factors for Dynamic Factor Model notebook

[martinvonk]

David and I get different results dependent on our machines. They get 0 factors with Velicer's MAP test while I get 1 (as intended originally). Velicer's MAP test code:

metran/metran/factoranalysis.py

Lines 220 to 312 in d8aef35

	def _maptest(cov, eigvec, eigval):
	"""Internal method to run Velicer's MAP test.
	Determines the number of factors to be used. This method includes
	two variations of the MAP test: the orginal and the revised MAP test.
	Parameters
	----------
	cov : numpy.ndarray
	Covariance matrix.
	eigvec : numpy.ndarray
	Matrix with columns eigenvectors associated with eigenvalues.
	eigval : numpy.ndarray
	Vector with eigenvalues in descending order.
	Returns
	-------
	nfacts : integer
	Number factors according to MAP test.
	nfacts4 : integer
	Number factors according to revised MAP test.
	References
	----------
	The original MAP test:
	Velicer, W. F. (1976). Determining the number of components
	from the matrix of partial correlations. Psychometrika, 41, 321-327.
	The revised (2000) MAP test i.e., with the partial correlations
	raised to the 4rth power (rather than squared):
	Velicer, W. F., Eaton, C. A., and Fava, J. L. (2000). Construct
	explication through factor or component analysis: A review and
	evaluation of alternative procedures for determining the number
	of factors or components. Pp. 41-71 in R. D. Goffin and
	E. Helmes, eds., Problems and solutions in human assessment.
	Boston: Kluwer.
	"""
	nvars = len(eigval)
	fm = np.array([np.arange(nvars, dtype=float), np.arange(nvars, dtype=float)]).T
	np.put(
	fm,
	[0, 1],
	((np.sum(np.sum(np.square(cov))) - nvars) / (nvars * (nvars - 1))),
	)
	fm4 = np.copy(fm)
	np.put(
	fm4,
	[0, 1],
	(
	(np.sum(np.sum(np.square(np.square(cov)))) - nvars)
	/ (nvars * (nvars - 1))
	),
	)
	for m in range(nvars - 1):
	biga = np.atleast_2d(eigvec[:, : m + 1])
	partcov = cov - np.dot(biga, biga.T)
	# exit function with nfacts=1 if diag partcov contains negatives
	if np.amin(np.diag(partcov)) < 0:
	return 1, 1
	d = np.diag((1 / np.sqrt(np.diag(partcov))))
	pr = np.dot(d, np.dot(partcov, d))
	np.put(
	fm,
	[m + 1, 1],
	((np.sum(np.sum(np.square(pr))) - nvars) / (nvars * (nvars - 1))),
	)
	np.put(
	fm4,
	[m + 1, 1],
	(
	(np.sum(np.sum(np.square(np.square(pr)))) - nvars)
	/ (nvars * (nvars - 1))
	),
	)
	minfm = fm[0, 1]
	nfacts = 0
	minfm4 = fm4[0, 1]
	nfacts4 = 0
	for s in range(nvars):
	fm[s, 0] = s
	fm4[s, 0] = s
	if fm[s, 1] < minfm:
	minfm = fm[s, 1]
	nfacts = s
	if fm4[s, 1] < minfm4:
	minfm4 = fm4[s, 1]
	nfacts4 = s
	return nfacts, nfacts4

On my device:

eigvec = array([[ 0.96750358, -0.25285732],  [ 0.96750358,  0.25285732]])
eigvec[0,0] = 0.9675035797467857
eigvec[0,1] = -0.25285731782401605
eigvec[1,0] = 0.9675035797467855
eigvec[1,1] = 0.2528573178240161

Later on this results in:

minfm = 1.000000000000007
minfm4 = 1.0000000000000142

which yields True for (if s = 1):

if fm[s, 1] < minfm:`

with fm[s, 1] = 1.0

[martinvonk]

Resolved. Reinstalling the environment on Davíd's machine solved the issue.