Adding PowerLink link function in GLM

[ayushpatnaikgit]

PowerLink refers to the class of transforms that use a power function (e.g. a logarithm or an exponent) to transform responses into a Gaussian or a Gaussian-like.

The summaries of the changes in the following source files are:

• In docs/src/api.md:
  • Added PowerLink under the “Links and methods applied to them” section
• In docs/src/examples.md
  • Added an example “Linear regression with PowerLink. Choose the best model from a set of λs, based on minimum BIC”
• In docs/src/index.md:
  • Added PowerLink under the “Currently the available Link types are” section
• In src/GLM.jl:
  • Exported PowerLink
• In src/glmfit.jl
  • Added a member variable link to GlmResp structure. This is for storing details of the link function with parameters (if any)
• In GlmResp constructor, added one more argument to pass the link
  • Added updateμ! function specifically for PowerLink. Inside the function, the `inverselink’ function is called with PowerLink with the parameter, as the link function.
  • Added GLM.Link function specifically for PowerLink
• In src/glmtools.jl:
  • Added PowerLink to the docstring under “GLM currently supports the following links:”
  • Defined the Powerlink structure, λ is the parameter for this link function. The user needs to specify the λ.
  • Defined linkfun function for PowerLink
  • Defined linkinv functionfor PowerLink
  • Defined mueta function for PowerLink
  • Defined inverselink function for PowerLink
• In test/runtests.jl:
  • Added a set of test cases, which consisted of individual tests of all new functions related to PowerLink
  • Added a test case to compare against the R glm()
  • Added 3 test cases to check PowerLink with some special cases of PowerLink like LogLink, SqrtLink and IdentityLink.

[codecov-commenter]

Codecov Report

Merging #474 (634ece5) into master (429bd7c) will increase coverage by 1.81%. The diff coverage is 100.00%.

:exclamation: Current head 634ece5 differs from pull request most recent head 06d6a59. Consider uploading reports for the commit 06d6a59 to get more accurate results

@@            Coverage Diff             @@
##           master     #474      +/-   ##
==========================================
+ Coverage   85.12%   86.94%   +1.81%     
==========================================
  Files           7        7              
  Lines         827      835       +8     
==========================================
+ Hits          704      726      +22     
+ Misses        123      109      -14     

Impacted Files	Coverage Δ
src/GLM.jl	50.00% <ø> (ø)
src/glmfit.jl	79.29% <100.00%> (+0.55%)	:arrow_up:
src/glmtools.jl	92.30% <100.00%> (+9.60%)	:arrow_up:

---

Continue to review full report at Codecov.

Legend - Click here to learn more Δ = absolute <relative> (impact), ø = not affected, ? = missing data Powered by Codecov. Last update 429bd7c...06d6a59. Read the comment docs.

[ayushpatnaikgit]

@ViralBShah

We are testing:

 GLM.mueta(InverseLink(), 10) == GLM.mueta(PowerLink(-1), 10)

While this is passing in Julia 1.0, it is failing in Julia nightly, and we are getting the following error:

 Evaluated: -0.01 == -0.010000000000000002

I have done rounding, so this test passes.

[ViralBShah]

Look at some of the tests in Julia's LinearAlgebra or other numerical packages on how to handle this in tests.

[mousum-github]

Look at some of the tests in Julia's LinearAlgebra or other numerical packages on how to handle this in tests.

Instead of GLM.mueta(InverseLink(), 10) == GLM.mueta(PowerLink(-1), 10) (or equality checking of two real values) we should use isapprox(GLM.mueta(InverseLink(), 10), GLM.mueta(PowerLink(-1), 10)) or isapprox(GLM.mueta(InverseLink(), 10), GLM.mueta(PowerLink(-1), 10); atol=1.0e-08).

[ayushpatnaikgit]

We can use isapprox, but in this case, rounding seems more apt. I wanted to point out if there is a possible bug in Julia nightly that we should isolate and report.

[ViralBShah]

This is not indicative of a bug in Julia nightly. @mousum-github 's suggestion to use isapprox is the right one.

[ViralBShah]

cc @dmbates

[ViralBShah]

Good to merge?

[ViralBShah]

Bump again. @nalimilan Is this good to merge?

[nalimilan]

Thanks!