Check existence and identifiability of the extended MLE

Checks whether a hierarchical log-linear model satisfies both the Fienberg–Rinaldo condition for existence of the extended maximum-likelihood estimate and the rank condition required for identifiable model parameters.

Usage

check_extended_MLE(data, model)

Arguments

data

Capture history data in the standard package format, with one indicator column for each list followed by a count column.

model

A character string specifying a hierarchical model, such as "[12,13,23]".

Value

A single integer status code:

0

Both conditions are satisfied.

1

The Fienberg–Rinaldo condition fails.

2

The model parameters are not identifiable.

3

Both conditions fail.

Details

Two distinct conditions are checked.

The Fienberg–Rinaldo condition determines whether the required extended maximum-likelihood fit exists, allowing for parameters corresponding to sparse interactions to be estimated at minus infinity.

The relevant model matrix is also checked for full column rank. Failure of this condition means that the model parameters are not identifiable.

The two checks are carried out separately, so either one or both may fail.

References

Fienberg, S. E. and Rinaldo, A. (2012). Maximum likelihood estimation in log-linear models. The Annals of Statistics, 40, 996–1023.

Chan, L., Silverman, B. W. and Vincent, K. (2021). Multiple Systems Estimation for Sparse Capture Data: Inferential Challenges When There Are Nonoverlapping Lists. Journal of the American Statistical Association, 116(535), 1297–1306. doi:10.1080/01621459.2019.1708748 .

Examples

data(Artificial_3)

check_extended_MLE(
  Artificial_3,
  "[12,13,23]"
)
#> [1] 2

# The result is 2: the existence condition is satisfied,
# but the model parameters are not identifiable.