Confirmatory Factor Analysis using brms

Interfaces brms
1

Hi all,

Not a problem, more a little bit of helpful code. brms can already estimate latent variables using the mi() function for missing data. It can also constrain parameters to be constant. This, I think, provides all the means to fit rudimentary confirmatory factor analysis models.

Simulation code below.


library(tidyverse)
library(brms)

N <- 200

dta <- 
  tibble(
    x = rnorm(N, 0, 1),
    y1 = rnorm(N, 2*x, 1),
    y2 = rnorm(N, 1*x, 1),
    y3 = rnorm(N, 0.5*x, 1),
    xo = as.numeric(NA)
  )

m1 <- 
  brm(
    formula =
      bf(y1 ~ 0 + mi(xo)) +
      bf(y2 ~ 0 + mi(xo)) +
      bf(y3 ~ 0 + mi(xo)) +
      bf(xo | mi() ~ 1) + 
      set_rescor(rescor = FALSE),
    family = gaussian(),
    prior =
      prior(constant(1), class = "b", resp = "y1") +
      prior(constant(1), class = "sigma", resp = "y1") +
      prior(normal(0, 10), class = "b", resp = "y2") +
      prior(constant(1), class = "sigma", resp = "y2") +
      prior(normal(0, 10), class = "b", resp = "y3") +
      prior(constant(1), class = "sigma", resp = "y3") +
      prior(normal(0, 10), class = "Intercept", resp = "xo") +
      prior(cauchy(0, 1), class = "sigma", resp = "xo"),
    data = dta,
    backend = "cmdstanr",
    cores = 4,
    chains = 4,
    threads = threading(2),
    refresh = 5
  )

m1
18 Likes
2

really useful, thanks so much!

1 Like
3

Also, the R package blavaan runs Bayesian SEM models, with Stan as the underlying enine. And as it follows the lavaan syntax and familiarity. It includes a bunch useful/common feautures in SEM

4

This is super helpful, thanks for sharing. Any inkling as to how one might rejig this setup to include correlated factors?

5

Can you include them as outcomes in a multivariate model and use set_rescor(TRUE)?

6

Hmm seems like that estimates correlations between all variables, but I’d like the manifest variables to still have 0 correlation. This is actually documented on github issue 957, looks like I’ll need to wait until brms 3.0.

7

Ah yes, of course. Could you maybe fix some of the correlations to zero by using priors? I can’t remember if you can set priors on individual correlations, but if you can, then you could use constant(0) (Prior Definitions for brms Models — set_prior • brms).

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