In greta: Simple and Scalable Statistical Modelling in R

Factor analysis

Factor analysis is a linear latent model used for finding a lower-dimensional probabilistic description of a data set with observations $\mathbf{x}_i \in \mathbb{R}^p$. We assume the data are generated according to $$ \mathbf{x}_i = \mathbf{W} \mathbf{z}_i + \boldsymbol \mu + \epsilon_i $$ where the noise $\epsilon$ is normally distributed with zero mean and diagonal covariance matrix $\Psi = \mathrm{diag}(\psi_1, \dots, \psi_p)$. The goal of factor analysis is to estimate the latent variables $\mathbf{z}_i \mathbb{R}^q$.

In this example we take the mean vector $\boldsymbol \mu$ to be zero.

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W <- normal(0, 1, dim = c(p, q))
Z <- normal(0, 1, dim = c(q, n))
psi <- zeros(p, p)
diag(psi) <- inverse_gamma(1, 1, dim = p)

distribution(X) <- multivariate_normal(t(W %*% Z), psi)

greta documentation built on Sept. 8, 2022, 5:10 p.m.