ararslan/betaregression.jl

Regression models for beta distributed responses in Julia

betaregression.jl's Issues

Convergence failures where R betareg succeeds

Convergence can fail for models of the form y ~ 1 when y is a random sample from one of the following beta distributions. In each case, the cause of convergence failure has to do with the precision estimate. The particular failure mode regarding the precision is included.

• Beta(0.5, 0.5): Initial estimate from initialize! is invalid (EDIT: Fixed by #4)
• Beta(0.2, 0.2): Estimate becomes negative during fitting
• Beta(0.5, 10): Estimate becomes negative during fitting
• Beta(10, 0.3): Estimate becomes negative during fitting

For invalid initialization of the precision, we can follow suit with the R package betareg and set the starting value to 1 (see #4). Doing so allows this model to be fit, and the estimates obtained match those obtained from betareg.

The negative precision currently causes an issue in weightdiag due to what seemed like an obvious simplification at the time (but in retrospect is obviously incorrect): the simplification assumes sqrt(ϕ^2) == ϕ, which is only true if ϕ ≥ 0. (In my defense, ϕ is supposed to be positive!) Undoing this simplification causes fitting to throw a ConvergenceException from fit rather than a DomainError from sqrt.

However, betareg actually succeeds in fitting these models on the same data. My very scientific means of determining this:

y = rand(Beta(0.2, 0.2), 10)
fit(BetaRegressionModel, ones(10, 1), y)
clipboard(strip(sprint(show, y), ['[', ']']))

betareg(y ~ 1, data.frame(y=c(...)), link="logit", link.phi="identity", type="ML")

where ... is the contents of my clipboard.

The betareg documentation notes that fitting is performed using R's optim with the default method set to BFGS. Fitting in this package is performed by Fisher scoring (i.e. Newton's method). I'm not sure what effect that difference could have in practice but it's worth noting.

Model the precision parameter with predictors?

Hi there,
Is there an intention to enable the precision parameter to be modelled with predictors?
Cheers

Upstream `dmueta` to GLM

Seems like some nice functionality to share. 😄

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Implement user-defined weights

Some stubs are currently in place but we deliberately throw an error when weights are actually specified. The Ferrari 2004 paper makes no mention of weights and I haven't yet bothered to work out the math myself. Off the top of my head, I think what's needed is to account for it in the linear predictor updates, score vector, and expected Fisher information.

Looking at the R documentation for betareg, it appears they only accept case weights. It would likely be easiest to follow suit and use FrequencyWeights from StatsBase (and just wrap any plain input vector with that type). That makes testing against output from R easier.

I almost surely won't block an initial package release on having this feature.