Find sigma in regression models on imputed datasets

Question

With a regular lm-object, I can extract sigma like this:

library(mice)
nhanes$group <- as.factor(c(rep("A", 12), rep("B", 13)))
m_1 <- lm(bmi ~ group + age, nhanes)
sigma(m_1)

However, extracting sigma on models conducted on imputed data sets results in an error:

imp <- mice::mice(nhanes, maxit = 2, m = 2)
m_2 <- with(imp, lm(bmi ~ group + age))
sigma(m_2)
# numeric(0)
# Warning message:
#   In nobs.default(object, use.fallback = use.fallback) :
#   no 'nobs' method is available

How would one proceed to extract sigma in the above example?

I have tried various combinations of with() and pool(), but they result in one of two errors:

with(m_2, sigma())
# Error in sigma.default() : argument "object" is missing, with no default


sigma(pool(m_2))
# numeric(0)
# Warning message:
#   In nobs.default(object, use.fallback = use.fallback) :
#   no 'nobs' method is available

Answer 1

Since you chose mice(., m=<m>) (m=2 are very few!), you have m regressions, thus m sigmas,

If we reveal the structure, we see a list of m in the analyses element.

str(m_2, max.level=1)
# List of 4
#  $ call    : language with.mids(data=imp, expr=lm(bmi ~ group + age))
#  $ call1   : language mice::mice(data=nhanes, m=2, maxit=2)
#  $ nmis    : Named int [1:5] 0 9 8 10 0
#   ..- attr(*, "names")= chr [1:5] "age" "bmi" "hyp" "chl" ...
#  $ analyses:List of 42
#  - attr(*, "class")= chr [1:2] "mira" "matrix"

We get the sigmas using lapply.

lapply(m_2$analyses, sigma)
# [[1]]
# [1] 2.711988
# 
# [[2]]
# [1] 2.666487
# 
# [[3]]
# [1] 2.876525
# ...

To get a kind of pooled sigma, you could calculate mean and sd:

sapply(c(mean=mean, sd=sd), \(f) f(sapply(m_2$analyses, sigma)))
#      mean        sd 
# 2.8383536 0.2103296 

---

Data:

data('nhanes', package='mice')
set.seed(42)  ## mice involves stochastic processes!
nhanes$group <- gl(2, 13, labels=LETTERS[1:2])[-1]
imp <- mice::mice(nhanes, maxit=2, m=42, printFlag=F)
m_2 <- with(imp, lm(bmi ~ group + age))