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Combine independent MLEs for the same parameter.

Source: R/combine.R
combine.Rd

Given multiple independent MLEs that estimate the same parameter \(\theta\), produces an optimally weighted combination using inverse-variance (Fisher information) weighting.

Usage

combine(x, ...)

# S3 method for class 'list'
combine(x, ...)

# S3 method for class 'mle'
combine(x, ...)

Arguments

x

An mle object, or a list of mle objects.

...

Additional mle objects to combine.

Value

An mle object representing the optimally weighted combination.

Details

The combined estimator has:

  • theta.hat: \((\sum I_i)^{-1} \sum I_i \hat\theta_i\)

  • sigma: \((\sum I_i)^{-1}\)

  • info: \(\sum I_i\)

  • nobs: sum of individual sample sizes

When the Fisher information matrix is not directly available but the variance-covariance matrix is, the FIM is computed as ginv(vcov).

For the legacy interface that accepts a list, see mle_weighted.

See also

mle_weighted, joint

Examples

# Three independent estimates of the same rate
fit1 <- mle(theta.hat = c(lambda = 2.1), sigma = matrix(0.04), nobs = 50L)
fit2 <- mle(theta.hat = c(lambda = 1.9), sigma = matrix(0.02), nobs = 100L)
fit3 <- mle(theta.hat = c(lambda = 2.0), sigma = matrix(0.03), nobs = 70L)

comb <- combine(fit1, fit2, fit3)
params(comb)
#>   lambda 
#> 1.976923 
se(comb)
#> [1] 0.09607689