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.

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

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
]

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}]
]

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.