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1 vote

Why my Rho-square on Multinomial Logit Model (McFadden) so small?

$R^2$ measures do not assess goodness of fit. They quantify predictiveness of outcomes. $R^{2}=0$ may be an excellent fit, i.e., every observation may have the same probability of an outcome. Some ...
Frank Harrell's user avatar
0 votes

Weighted likelihood in Bayes' rule

Here's my very personal take on it. I have seen this proposal of weighting the likelihood several times over the years. It's a fairly natural way to extend Bayesian inference, and it comes up from ...
Guillaume Dehaene's user avatar
0 votes

Weighted likelihood in Bayes' rule

While this is beyond statistics, exponential weights can be added to both the likelihood and the prior to introduce (or fix) certain types of biases. $$ P(H|D) \propto P(D|H)^\beta P(H)^\alpha $$ ...
Durden's user avatar
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5 votes
Accepted

Basic question about deriving MAP estimator

If $t$ is a random parameter, for which Bayesian inference is required, then $t$ should have a prior, $p(t)$, so it can have a posterior and a MAP estimate. In the most general case, $t_{MAP}=\arg\...
Johan de Aguas's user avatar
2 votes

Confusion over Fisher-scoring algorithm

TLDR: always use line-search gradient descent or the BFGS algorithm to find the MLE. Fisher scoring is a bad idea. To discuss this method, we need to compare it to other methods to find the MLE. Let's ...
Guillaume Dehaene's user avatar
2 votes
Accepted

Confusion over Fisher-scoring algorithm

Yes, but that matters less than you might think For canonical-link generalised linear models, which are a very popular special case, the algorithm is exactly Newton-Raphson For regression models more ...
Thomas Lumley's user avatar
1 vote

Negative log-likelihood, high BIC, high R-squared, low error, using a difference-in-differences (DiD) methodology

Beyond @PeterFlom's excellent answer about the relative nature of metrics like log-likelihood and BIC, you're missing a critical point: never use a Poisson model without considering the possibility of ...
Ben Bolker's user avatar
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