Improve consistency of model API

[nalimilan]

Our current StatisticalModel API is heavily inspired from R, adapted to match Julia rules (plus some improvements), but it is not really consistent (since R isn't either). Below is a summary of the situation. Names are considered OK if they are either a standard abbreviation, or are spelled in full (and the name is not too long).

Names consistent with R and OK: coef, nobs, deviance, confint, fitted, residuals, predict, aic, bic, aicc, r2/r², adjr2, adjr², stderr

Names that do not exist in R and are OK: aicc, r2/r², adjr2, adjr², stderr, nulldeviance

Names different from R for good reasons: dof, dof_residual (to avoid two-letter objects, limiting confusion with df = DataFrame(...))

Names not consistent with R for bad reasons, and proposed change:

• loglikelihood -> loglik (shorter, relatively standard abbreviation, and consistent with R)
• nullloglikelihood -> null_loglik (shorter and more readable; if changed, nulldeviance should be called null_deviance)

Names consistent with R which should be changed:

• vcov -> cov
• model_response -> response ("model" is redundant with multiple dispatch)

Name to add and which does not exist in R: params, param or parameters. The choice depends on whether we accept abbreviations, or prefer full names everywhere. Names which should be changed accordingly include potentially coef, loglikelihood/nullloglikelihood, nobs, adjr2/adjr², confint and dof.

[rofinn]

I like all of this except that I'm not a fan of the lik convention in R (maybe like?). Also, seems a little weird to have null_loglik and null_deviance when everything else seems to skip the _. Maybe we could make null a keyword which defaults to false?

[rofinn]

This is probably a separate issue, but would it make sense to merge the StatisticalModel API into StatsModels.jl?

[nalimilan]

I like all of this except that I'm not a fan of the lik convention in R (maybe like?). Also, seems a little weird to have null_loglik and null_deviance when everything else seems to skip the _. Maybe we could make null a keyword which defaults to false?

Yeah. I guess whether to abbreviate loglikelihooddepends on what we decide to do for other abbreviations. Regarding the _, I suggested this mainly because nullloglikelihood is really weird, but OTOH it isn't used that frequently. The idea of replacing it with a parameter is certainly worth considering.

This is probably a separate issue, but would it make sense to merge the StatisticalModel API into StatsModels.jl?

We've discussed this in the past, but I think it's still an open question. I think @kleinschmidt wanted to put only table-related functions in that package, which would mean modeling packages wouldn't even have to depend on it: it would just handle the transformation of formulas + data to a model matrix. Anyway, not really the place to discuss this.

[nalimilan]

See also JuliaStats/Roadmap.jl#4.