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Since W it is missing, maximizing the marginal likelihood appears to be the most natural estimation approach.
As estimates of α, β, we use the values maximizing the marginal likelihood given the estimates, and.
Model parameters are estimated by maximizing the marginal likelihood which is obtained by integrating out the unobserved random effects b i from the likelihood function [ 16].
Therefore, we instead estimate the parameters by maximizing the marginal probability of the labels as below: (3) The results produced by HLR are still region-level classification.
The hyperparameters, i.e. the variances, are estimated through maximizing the marginal likelihood, and the variables with zero variance estimates are pruned from the model.
The joint log-likelihood of our model is: Since the sequences of { x s, t } are not observed, parameter estimation has to be done via maximizing the marginal log-likelihood logPr({ y s, t }|Θ).
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The more/less concentrated designation is based on the ranking of the 1997 concentration ratio and choosing a break point that maximizes the marginal size of decreases in the concentration numbers in moving from more- to less-concentrated industries.
In step 4 of MAMK CP (Algorithm 3), in order to maximize the marginal gain, we have to compute σ(C i ∪C j ) for all the communities C j ∈ P, thus, MAMK CP requires O ( n 2 τ ) time to obtain a K-VDP when n is large and K is small.
To learn this model, we also need to maximize the marginal likelihood of the labels C n.
Here, we use L-BFGS to maximize the marginal likelihood due to its fast convergence and low-memory consumption.
The marginal logistic regression model was fitted with Stata's xtgee command and multilevel models were fitted using adaptive quadrature with 12 integration points to evaluate and maximize the marginal log likelihood by Stata's xtlogit command.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com