#factor-analysis

Question 1: Single choice

A friend proposes to improve factor analysis by allowing correlated latents: $\mathbf{h} \sim \mathcal{N}(\mathbf{0}, C)$ and $\mathbf{v} \mid \mathbf{h} \sim \mathcal{N}(F \mathbf{h} + \mathbf{c}, \Psi)$ , with $\Psi$ diagonal and $C$ an arbitrary covariance matrix (standard factor analysis has $C = I$ ). Is the model more expressive?

Yes; correlated latents can model correlations between visibles that standard factor analysis cannot1
Yes; $C$ adds $H(H+1)/2$ parameters for $H$ latents, which can be estimated from data2
No; $(F, C)$ and $(F C^{1/2}, I)$ give exactly the same $p(\mathbf{v})$ 3
No, but only because $\Psi$ is diagonal; with a full $\Psi$ the correlated latents would help4

Timed test