`get/find_transformation` with linear transformations

[mattansb]

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1. get/find_transformation should not return identity if an unsupported transformation is present.
2. Should support linear transformations?

m <- lm(I(2 * mpg + 3) ~ hp, mtcars)
insight::find_transformation(m)
#> [1] "identity"

^{Created on 2022-06-27 by the reprex package (v2.0.1)}

[bwiernik]

Is there a context where these concerns arise other than I()?

Generally, we should extract the contents of I() and evaluate that as a function with numerical derivatives

[mattansb]

For (1), a user can use some other unsupported function e.g. foo(y) ~ 1, or datawizard::ranktransform(y) ~ ..

And (2) should also work for functions of linear transformation:

• scale() and datawizard::standardise/standardize() / datawizard::center/centre() (all 3 of which can be inverted with datawizard::unstandardise/unstandardize() https://github.com/easystats/datawizard/pull/191
• datawizard::normalize() anddatawizard::change_scale/data_rescale()which can be inverted withdatawizard::unnormalize()` https://github.com/easystats/datawizard/pull/191

[strengejacke]

The problem is how to detect foo()? cbind(x - y) should return "identity", foo() should return "unknown". Are there any other exceptions?

[mattansb]

The problem is how to detect foo()? cbind(x - y) should return "identity", foo() should return "unknown". Are there any other exceptions?

Perhaps we should just return "identity" if no function or manipulation is detected? All others can be NULL?

---

Here is some working code to make trans/inversetrans functions for linear transformation functions above:

Define functions

as_linear_transform <- function(x, ...) {
  UseMethod("as_linear_transform")
}

as_linear_inverse <- function(x, ...) {
  UseMethod("as_linear_inverse")
}


as_linear_transform.numeric <- function(x, ...) {
  coefs <- .get_ab(x)
  function(x) {
    (x - coefs["a"]) / coefs["b"]
  }
}


as_linear_inverse.numeric <- function(x, ...) {
  coefs <- .get_ab(x)
  function(x) {
    x * coefs["b"] + coefs["a"]
  }
}



.get_ab <- function(x) {
  attr <- attributes(x)
  attr_names <- names(attr)
  
  if (all(c("center", "scale") %in% attr_names)) {
    a <- attr[["center"]]
    b <- attr[["scale"]]
  } else if (all(c("scaled:center", "scaled:scale") %in% attr_names)) {
    a <- attr[["scaled:center"]]
    b <- attr[["scaled:scale"]]
  } else if (all(c("min_value", "range_difference") %in% attr_names)) {
    a <- attr[["min_value"]]
    b <- attr[["range_difference"]]
    
    if ("to_range" %in% attr_names) {
      to_range <- attr[["to_range"]]
      
      b <- (b / diff(to_range)) 
      a <- a - b * to_range[1]
    }
  }
  
  c(a = a, b = b)
}

library(datawizard)
x <- rnorm(4, 40, 13)

Build trans/inverse functions from linear transformation functions in datawizard

foo <- as_linear_transform(standardize(x))
foo(x)
#> [1] -1.39325099  0.09865699  0.32238805  0.97220595
standardize(x)
#> [1] -1.39325099  0.09865699  0.32238805  0.97220595
#> attr(,"center")
#> [1] 40.5878
#> attr(,"scale")
#> [1] 11.42871
#> attr(,"robust")
#> [1] FALSE


foo <- as_linear_transform(scale(x))
foo(x)
#> [1] -1.39325099  0.09865699  0.32238805  0.97220595
scale(x)
#>             [,1]
#> [1,] -1.39325099
#> [2,]  0.09865699
#> [3,]  0.32238805
#> [4,]  0.97220595
#> attr(,"scaled:center")
#> [1] 40.5878
#> attr(,"scaled:scale")
#> [1] 11.42871


foo <- as_linear_transform(change_scale(x, to = c(3, 14.5), range = c(-30, 200)))
foo(x)
#> [1] 5.733237 6.585766 6.713614 7.084943
change_scale(x, to = c(3, 14.5), range = c(-30, 200))
#> [1] 5.733237 6.585766 6.713614 7.084943
#> attr(,"min_value")
#> [1] -30
#> attr(,"range_difference")
#> [1] 230
#> attr(,"to_range")
#> [1]  3.0 14.5

Build inverse trans/inverse functions from linear transformation functions in datawizard

goo <- as_linear_inverse(center(x))
x
#> [1] 24.66474 41.71532 44.27228 51.69886
goo(center(x))
#> [1] 24.66474 41.71532 44.27228 51.69886
#> attr(,"center")
#> [1] 40.5878
#> attr(,"scale")
#> [1] 1
#> attr(,"robust")
#> [1] FALSE


goo <- as_linear_inverse(normalize(x))
x
#> [1] 24.66474 41.71532 44.27228 51.69886
goo(normalize(x))
#> [1] 24.66474 41.71532 44.27228 51.69886
#> attr(,"include_bounds")
#> [1] TRUE
#> attr(,"min_value")
#> [1] 24.66474
#> attr(,"range_difference")
#> [1] 27.03411


goo <- as_linear_inverse(scale(x))
x
#> [1] 24.66474 41.71532 44.27228 51.69886
goo(scale(x))
#>          [,1]
#> [1,] 24.66474
#> [2,] 41.71532
#> [3,] 44.27228
#> [4,] 51.69886
#> attr(,"scaled:center")
#> [1] 40.5878
#> attr(,"scaled:scale")
#> [1] 11.42871

^{Created on 2022-07-05 by the reprex package (v2.0.1)}

[strengejacke]

Perhaps we should just return "identity" if no function or manipulation is detected? All others can be NULL?

But cbind() is a function and should not return "unknown".

[bwiernik]

I'm not following either of your last comments @mattansb

[mattansb]

@bwiernik I gave examples of functions the preform simple linear transformations (scale, center, standardize, normalize and change_scale) that could potentially be used in a formula (e.g., scale(y) ~ x) and how to obtain the transformation functions and their inverse (which is what get_transformation() returns, potentially).

[strengejacke]

I thought when we talk about "transformation" in the meaning of this function, we're talking about a different scale, like normal -> log, or normal -> exp, not standardizing/centering. So you suggest including those as well?

[mattansb]

Hmmm I think it might be useful; having scale(y) ~ x give a transformation of "identity" might be a little misleading, perhaps?

But if this would be too much work / break some stuff, we can save this issue for a later date (:

[DominiqueMakowski]

Perhaps we could add a custom output first and then refine?