# What's the difference between mi() and me() in brms?

I want to understand how to use the mi function to specify a measurement error model that will be the same as that specified by me. Maybe there’s a good reason this might not be possible. If so, I would like to understand the reason.

Here’s an example:

library(brms)
N <- 100
dat <- data.frame(
y = rnorm(N), x1 = rnorm(N),
x2 = rnorm(N), sdx = abs(rnorm(N, 1))
)

# fit a simple error-in-variables model
model1 <- brm(y ~ me(x1, sdx) , data = dat, chains=4, cores=4)

model2 <- brm( bf(y ~ mi(x1)) + bf(x1 | mi(sdx) ~ 0), data=dat, chains=4,cores=4)



What’s the difference between model1 and model2?

From reading the stancode I see thatmodel1 corresponds to the model (ignoring priors):
y \sim N(Bx^* + I, \sigma)
x^* \sim N(x , sd_x)
and estimates B,I and \sigma.

I also see that model2 corresponds to the model (ignoring priors):
y \sim N(Bx^* + I, \sigma_y)
x^* \sim N(x^*_{\mu}, \sigma_x )
x^*_{\mu} \sim N(x, sd_x)

Is it possible to fit model1 using the mi forumla syntax?

Is there some reason to prefer model2 to model1? For what it’s worth, based on my limited statistical knowledge I expect to prefer model1.

• Operating System: Debian 11.1
• brms Version: brms_2.15.6

It’s been a while since I focused on this issue, but I wrote about the se(), me(), and mi() functions in the context of measurement-error models and missing data problems here.