Module factor_em

source code

EM algorithm for ML estimation of factor analysis model

Functions

E(Lhat, Phat)
E-step: return delta, D

source code

M(S, delta, D)
M-step: return Lhat, Phat

source code

EM(X, k=2, initial=(), niter=10, compute=False)
EM algorithm source code

logL(Lhat, Phat, S, n)
Log-likelihood for factor analysis model.

source code

simulate()
Generating data from the two-factor model.

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main()
ML factor analysis for scores data

source code

Function Details

E-step: return delta, D

E_{Lhat,Phat}(Z|X) = X * delta.T Cov_{Lhat,Phat}(Z|X) = D

M-step: return Lhat, Phat

Lhat: (delta.T * S * delta + D)^{-1} (S * delta).T Phat: diag((X - Lhat)'(X - Lhat)) / n

Log-likelihood for factor analysis model.

S = X'X/n n = sample size Lhat, Phat = estimators of Lambda, Psi