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Rotation methods for factor analysis and principal component analysis in Julia

Home Page: https://p-gw.github.io/FactorRotations.jl/

License: MIT License

Julia 100.00%

factor-analysis julia psychometrics

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alyst

factorrotations.jl's Issues

Add missing references

add Enzyme compat

Implement Equamax

Implement Parsimax

Add random starts

Some methods converge to local minima, therefore we need to provide a way to start the rotation from random starting points.

Implement Promax

Reflect rotated matrix

Signs in the rotated output matrix should be swapped such that the column sum is always positive.

Implement bifactor rotation

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3253271/

Performance optimisation in Varimax rotation

Means are substracted inefficiently from the loading matrix in varimax rotation leading to a large amount of allocations and performance penalty.

Implement Absolmin

Implement Quartimin

Add `normalize` argument to rotate

I want to be able to provide unnormalized loadings to the rotate function and normalize them during optimisation.

add relative tolerance to optimization routine

Update CompatHelper

Add derivative free rotation methods

Fix documentation for `kaiser_normalize!`

https://p-gw.github.io/FactorRotations.jl/stable/api/#FactorRotations.kaiser_normalize!

Varimax did not converge for echelon-pattern matrix

I'm trying a varimax rotation of a 62x8 matrix A_factors with echelon pattern:

A_rotated = rotate(A_factors, Varimax())

and I am getting

ERROR: ConvergenceError: Algorithm did not converge after 1000 iterations

(also tried 10^4 iterations without success, as well as other rotations, e.g. geomin)

lavaan implementation of varimax works instantly and gives reasonable results:

A_rotated_lav = rcopy(R"lavaan:::lav_matrix_rotate($A_factors, method='varimax', rstarts=10, warn=TRUE, verbose=FALSE)")

Here's the A_factors matrix:

62×8 Array{Float64, 2}:
 -1.8031194480220782   0.0                     0.0                    0.0                     0.0                    0.0                    0.0                   0.0
 -1.780254378158767    0.8320815077043094      0.0                    0.0                     0.0                    0.0                    0.0                   0.0
 -1.8066020073724849   0.6860861819708227      0.23333141990373732    0.0                     0.0                    0.0                    0.0                   0.0
 -1.0884633869922222   1.2078318626461864     -0.014148358570189328  -0.7687259678984802      0.0                    0.0                    0.0                   0.0
 -1.594455847645369    0.5900444638522866      0.3355252683178977     0.13634827579831255     0.1922082926558959     0.0                    0.0                   0.0
 -1.622055937580073    0.8935060997826365      0.46609489031479867    0.22347448650237323     0.11020391952543476   -0.3732211147918004     0.0                   0.0
 -1.3583153251937512   1.1997424103482002      0.6570826080721309    -0.10833691066635939    -0.14042618044854474   -0.33154656943437627    0.4930803720861098    0.0
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 -1.3470176823633673   0.3684993326867659      0.5856812839369648    -0.047102515838819595    0.474095832306008     -0.55577455778375      -0.2788114484550642   -0.044421087141533616
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 -1.391031378168573    0.3629107287699976      0.7020791221911443    -0.2647613112366453      0.10988378615961196   -0.6254972955544791     0.5822135142048368    0.2758399537502801
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 -1.2424729632046516   0.8461973921439498      0.0657763307396866     0.0717710278394688     -0.1338981664668663    -1.0323530943267887     0.4235911317078656    0.15092214620336541
 -1.3375369534732768   0.8922938098944122      0.15457200744660474    0.15051813428289731    -0.06689466377038078   -1.0425235926869274     0.6321727642189441    0.1536553142948441
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 -0.881623507326852   -0.27499536602152386     0.0641009543733715    -0.15758095653368792     0.5149075280617658     0.004028433150330064   1.1724994742917823   -0.00100380468676092
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 -1.2610662476754595   0.48318088901465506     0.8251362419645101    -0.05262493589010914    -0.5401842049351399    -0.8663476756939109     0.41415746845528884   0.6083022361243062
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Add MultivariateStats.jl support

I want to be able to pass objects from MultivariateStats.jl directly to rotate.

using MultivariateStats, FactorRotations

res = fit(FactorAnalysis, X)
rotate(res, Varimax())

Implement tandem criteria

Test rotation against external results

I think it is, it could also be done more consistently for all the methods that the packages have in common.

One general consideration here is if we are comparing the rotation results against some reference, which has limited precision (e.g. the results from 2005 paper) -- that limited precision implies that the corresponding rotation may slightly violate the orthogonality constraints, and the corresponding reference criterion might be accidentally more optimal because the "point" is outside of the domain.
So ideally all reference rotations should contain as many digits after 0 as possible.

Originally posted by @alyst in #58 (comment)

Implement invariant pattern simplicity

Enforce line length in .JuliaFormatter.toml

To keep code consistent we should enforce maximum line length by settings margin = 92 in .JuliaFormatter.toml

Add precompilation

Reorder columns in rotated matrix

Columns in the rotated output matrix should be reordered according to established criteria.

See: Asparouhov, T., & Muthén, B. (2009). Exploratory structural equation modeling. Structural equation modeling: a multidisciplinary journal, 16(3), 397-438.

Implement Promaj

Implement orthogonal rotation methods

Add Kaiser normalization

Add basic documentation

Implement in-place rotation

I want to be able to rotate a factor loading matrix in-place, e.g.

rotate!(L, Varimax(); kwargs...)

correct implementation of initial values

Initial values on _rotate aren't correctly set:

https://github.com/p-gw/FactorRotations.jl/blob/5508889a0304b80aeac6d25a92a0812f8d3744b8/src/rotate.jl#L32C51-L32C51

TagBot does not create tags or releases

TagBot trigger issue

This issue is used to trigger TagBot; feel free to unsubscribe.

If you haven't already, you should update your TagBot.yml to include issue comment triggers.
Please see this post on Discourse for instructions and more details.

If you'd like for me to do this for you, comment TagBot fix on this issue.
I'll open a PR within a few hours, please be patient!

But if in the long run you consider switching to a unified in-place criterion_and_gradient!(grad::Union{AbstractVector, Nothing}, ...), which would skip gradient calculation if grad === nothing, this PR would be irrelevant.
Right now the profiling shows that for a 62x24 matrix rotation ~10% is spent in the array allocation (both gradient calculation and projection).

Disallow epsilon <= 0 in Absolmin

This loss function has `1/(2epsilon)*|x|^2` term, so does not make sense to calculate it at epsilon=0 (perhaps, the ctor should disallow eps=0).
And so with epsilon=0 the gradient if not finite, and it gets caught by `all(isfinite, ∇Q)` check :)

Originally posted by @alyst in #58 (comment)

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