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The models in this package fall in two groups: one nice one with the exponential family and canonical links and the more complicated one where the observed information depends on data and isn't ensured to be positive definite. In the former case, a line search shouldn't even be needed.
In the latter case, a line search is required for convergence. The current version halfs the step size which works okay. However, we have seen occasional failures and the current approach can also lead to potentially very slow convergence in situations where the observed information is indefinite while we use the positive definite expected information as an approximation. In this case, the step size can easily become much smaller than it should be.
The models in this package fall in two groups: one nice one with the exponential family and canonical links and the more complicated one where the observed information depends on data and isn't ensured to be positive definite. In the former case, a line search shouldn't even be needed.
In the latter case, a line search is required for convergence. The current version halfs the step size which works okay. However, we have seen occasional failures and the current approach can also lead to potentially very slow convergence in situations where the observed information is indefinite while we use the positive definite expected information as an approximation. In this case, the step size can easily become much smaller than it should be.
I think we should consider using https://github.com/JuliaNLSolvers/LineSearches.jl for the cases that require a line search and maybe completely drop the line search when it's not needed.
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