Skip to main content

Possible Bug in ProbitModelFit when used in a Dataset


Since upgrading to Mathematica 10 on Mac OSX I have come across a number of instances of this error, which occurs using Probit and Logit model fit.


enter image description here



A bit of googling show this is something to do with the estimation algorithm.


But the issue is more complex. When I estimate the model straight from this dataset I get the error, but when I first take the values of the data, then fit the model, I get the expected result.


Here's an example


var = {age, gender, photo6};

mTest = SemanticImport[
   "https://dl.dropboxusercontent.com/u/3997716/test.csv"];

testFit = 
 mTest[ProbitModelFit[#, var, 

    var] &, {#age, #gender, #photo6, #rawM} &]

testFit2 = 
 ProbitModelFit[#, var, 
    var] &@(mTest[All, {"age", "gender", "photo6", "rawM"}] // 
     Normal // Values)

Output of this is


enter image description here


Why the two different results for the same calculation? Is there a workaround that allows the estimation to proceed when directly using the dataset?




Answer



I believe that this is a bug. The rest of this response speculates as to the possible cause.


We start by observing that the test can be made to work by suppressing MissingBehaviour:


mTest[
  ProbitModelFit[#, var, var] &
, {#age, #gender, #photo6, #rawM} &
, MissingBehavior -> None
]

result screenshot



It also works if FailureAction -> None is specified instead, but then the exhibited error message about non-real values is produced (along with the correct result).


As noted elsewhere MissingBehavior is implemented by Dataset`WithOverrides. ??Dataset`WithOverrides reveals that this function temporarily alters the definitions of a number of symbols, namely those in this list:


Dataset`Overrides`PackagePrivate`$AllChangedSymbols

(* { Commonest,First,InterquartileRange,Kurtosis,Last,Mean,Median,Missing,Most,
     Quartiles,Rest,RootMeanSquare,Skewness,StandardDeviation,Total,Variance }
*)

It so happens that ProbitModelFit uses Total. We can verify that fact like this:


$data = mTest[All, {#age, #gender, #photo6, #rawM} &];


On @@ Dataset`Overrides`PackagePrivate`$AllChangedSymbols

ProbitModelFit[$data // Normal, {age, gender, photo6}, {age, gender, photo6}]

Off[]

(* ... produces many trace messages containing Total ... *)

It would appear that the patching performed by Dataset`WithOverrides is interfering with the operation of ProbitModelFit. We can simulate this by engaging in some patching of our own:



Internal`InheritedBlock[{Total}
, Unprotect @ Total
; Total[n___] /; False := Null
; ProbitModelFit[$data // Normal,{age,gender,photo6},{age,gender,photo6}]
]

result screenshot


This patch is even less invasive than the one installed by Dataset`WithOverrides, and yet it generates the same error message (and the same correct output). It would seem that ProbitModelFit is expecting Total to operate exactly as it is shipped -- nothing more, nothing less.


Conclusion


ProbitModelFit does not function properly within a query with default missing- and failure-handling. The missing-handling alters the definition of Total in a manner that causes ProbitModelFit to issue a warning message. The failure-handling sees that message and, by default, fails the whole query operation. Correct operation can be restored by either disabling the missing-handling, the failure-handling, or both.



The missing-handling is implemented by monkey-patching various low-level system components. This patching implements the proper Query semantics, at the cost of disturbing normal non-query system behaviour. Such disturbances are a frequent consequence of monkey-patching. The patching methodology explains not only the issue under discussion, but a number of other erratic Dataset behaviours logged on this site.


Comments

Post a Comment

Popular posts from this blog

mathematical optimization - Minimizing using indices, error: Part::pkspec1: The expression cannot be used as a part specification

I want to use Minimize where the variables to minimize are indices pointing into an array. Here a MWE that hopefully shows what my problem is. vars = u@# & /@ Range[3]; cons = Flatten@ { Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; Minimize[{Total@((vec1[[#]] - vec2[[u[#]]])^2 & /@ Range[1, 3]), cons}, vars, Integers] The error I get: Part::pkspec1: The expression u[1] cannot be used as a part specification. >> Answer Ok, it seems that one can get around Mathematica trying to evaluate vec2[[u[1]]] too early by using the function Indexed[vec2,u[1]] . The working MWE would then look like the following: vars = u@# & /@ Range[3]; cons = Flatten@{ Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; NMinimize[ {Total@((vec1[[#]] - Indexed[vec2, u[#]])^2 & /@ R...
Post a Comment
Read more

functions - Get leading series expansion term?

Given a function f[x] , I would like to have a function leadingSeries that returns just the leading term in the series around x=0 . For example: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x)] x and leadingSeries[(1/x + 2 + (1 - 1/x^3)/4)/(4 + x)] -(1/(16 x^3)) Is there such a function in Mathematica? Or maybe one can implement it efficiently? EDIT I finally went with the following implementation, based on Carl Woll 's answer: lds[ex_,x_]:=( (ex/.x->(x+O[x]^2))/.SeriesData[U_,Z_,L_List,Mi_,Ma_,De_]:>SeriesData[U,Z,{L[[1]]},Mi,Mi+1,De]//Quiet//Normal) The advantage is, that this one also properly works with functions whose leading term is a constant: lds[Exp[x],x] 1 Answer Update 1 Updated to eliminate SeriesData and to not return additional terms Perhaps you could use: leadingSeries[expr_, x_] := Normal[expr /. x->(x+O[x]^2) /. a_List :> Take[a, 1]] Then for your examples: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x), x] leadingSeries[Exp[x], x] leadingSeries[(1/x + 2 + (1 - 1/x...
Post a Comment
Read more

plotting - Plot 4D data with color as 4th dimension

I have a list of 4D data (x position, y position, amplitude, wavelength). I want to plot x, y, and amplitude on a 3D plot and have the color of the points correspond to the wavelength. I have seen many examples using functions to define color but my wavelength cannot be expressed by an analytic function. Is there a simple way to do this? Answer Here a another possible way to visualize 4D data: data = Flatten[Table[{x, y, x^2 + y^2, Sin[x - y]}, {x, -Pi, Pi,Pi/10}, {y,-Pi,Pi, Pi/10}], 1]; You can use the function Point along with VertexColors . Now the points are places using the first three elements and the color is determined by the fourth. In this case I used Hue, but you can use whatever you prefer. Graphics3D[ Point[data[[All, 1 ;; 3]], VertexColors -> Hue /@ data[[All, 4]]], Axes -> True, BoxRatios -> {1, 1, 1/GoldenRatio}]
Post a Comment
Read more