Evaluating a FittedModel over a list of values

Question

Simplified version Using the simpler version suggested by @ulrich-neumann :

data1 = Table[{i, i + 2}, {i, 1, 10}]
data2 = Table[3 i + 2, {i, 1, 10}]
fd = LinearModelFit[{data1, data2}]
testData = Table[{i, i + 2}, {i, 1, 3}](*{{1, 3}, {2, 4}, {3, 5}}*)

Map[Apply[fd, #] &, testData] (* {5., 8., 11.} WORKS AS EXPECTED *)

`

Now I want to embed this in a function :

testFunc1[f1_, data_] := Map[Apply[f1, #] &, data]
testFunc2[f1_, data_] := Table[Apply[f1, data[[i]]] , {i, 1, Length[data]}]
 
testFunc3[f1_, data_] := f1 @@@ data (* as suggested by @MarcoB *)
testFunc4[f1_, data_] := {#, f1 @@ #} & /@ data 

I expect the results to be the same for testFunc1,2,3 but they aren't:

testFunc2[fd, testData]  (* {5., 8., 11.} *)
testFunc3[fd, testData]  (* {5., 8., 11.} *)

but

testFunc1[fd, testData]  (* error messages plus {{{1, 3}, {2., 1.}.{{1, 3}, 3}}, .... *)
testFunc4[fd, testData]  (* error messages plus {{{1, 3}, {2., 1.}.{{1, 3}, 3}}, .... *)

Question : Why do these not give the same output ?

original question I am generating a FittedModel and want to evaluate it on a list of data. This works fine when I use Table to generate the results, but not when I try to use Map. The simple example below takes two inputs x and x+2, and produces the output 3x+2. The fitted model works as expected, until I try to Map it over a list of inputs.

    With[{data1 = Table[{i, i + 2}, {i, 1, 10}], 
      data2 = Table[3 i + 2, {i, 1, 10}]}, 
     With[{fd = LinearModelFit[{data1, data2}], 
       testData = Table[{i, i + 2}, {i, 1, 3}]}, Print["function is ", fd];
(* check it works *)      
      Print["function applied to {4,6} is ", fd[4, 6]]; 
      
(* explicitly generate input data *)      
      Print[Grid[
        Table[{"apply ", fd, " to args ", {i, i + 2}, " result:", 
          Apply[fd, {i, i + 2}]}, {i, 1, Length[testData]}], 
        Frame -> True]];
    
(* Use Table to find the value over test data *)
      Print[Grid[
        Table[{"apply ", fd, " to args ", testData[[k]], " result:", 
          Apply[fd, testData[[k]]]}, {k, 1, Length[testData]}], 
        Frame -> True]];
     
(* Try to map over test data *)      
      Print[Grid[
        Map[{"apply ", fd, " to args ", #, " result:", Apply[fd, #]} &, 
         testData], Frame -> True]]]]

Output looks like this:

so I am guessing the FittedModel somehow picks up the wrong arguments when I try to use Map. Is there a way to make Map behave the same as Table ?

Answer 1

I think your code should work. Let's get both the FittedModel object as well as the pure function within it:

fd = LinearModelFit[{data1, data2}]
fdFunction = LinearModelFit[{data1, data2}]["Function"]

The first returns the FittedModel object; the second returns the pure function expression obtained from the fit. In my opinion, the two should behave the same way on any input. Indeed:

({#, fd @@ #} & /@ testData ) == ({#, fdFunction @@ #} & /@ testData)
(* True *)

However, the two behave differently when used in your testFunc4:

ClearAll[testFunc4]
testFunc4[f1_, data_] := {#, f1 @@ #} & /@ data

testFunc4[fdFunction, testData]
testFunc4[fd, testData]

The first outputs {{{1, 3}, 5.}, {{2, 4}, 8.}, {{3, 5}, 11.}} as expected. The second returns a mess of errors and an incorrect final expression. I think you are running into some scoping conflict between the pure function inside the FittedModel and the pure function you wrote in your testFunc, but I can't put my finger on it quite yet. I am not even sure if the problem should exist, or if this is buggy behavior.

Answer 2

Your model is ok I think (but somewhat convoluted):

data1 = Table[{i, i + 2}, {i, 1, 10}]
data2 = Table[3 i + 2, {i, 1, 10}] 
fd = LinearModelFit[{data1, data2}]

fd is a pure function of two variables.

Apply the fit to testData

testData = Table[{i, i + 2}, {i, 1, 3}](*{{1, 3}, {2, 4}, {3, 5}}*)
Map[Apply[fd, #] &, testData] (*{5., 8., 11.}*)

The corrected first print command :

Print[Grid[Table[{"apply ", fd[x, y], " to args ", {i, i + 2}, " result:", Apply[fd, testData[[i]]]}, {i, 1, Length[testData]}],Frame -> True]]