A dataset demonstrating parameter non-identifiability, where the sum of two parameters is identifiable but individual parameters are not.
Format
A list with 3 elements:
- y
Numeric vector of 100 simulated observations
- spec
A model_spec object with non-identifiable parameters
- true_sum
The true value of a + b used in simulation (5)
Details
The model is: y ~ Normal(a + b, 1)
Only the sum (a + b) affects the likelihood, so infinitely many combinations of (a, b) produce the same likelihood. The Fisher information matrix is singular with rank 1.
Examples
data(nonidentifiable_example)
# Check identifiability
result <- identifiability_check(
nonidentifiable_example$spec,
nonidentifiable_example$y,
par = c(a = 2, b = 3)
)
print(result)
# Fisher information shows rank deficiency
info <- fisher_information(
nonidentifiable_example$spec,
nonidentifiable_example$y,
par = c(a = 2, b = 3)
)
print(info)