Hi Roger

you could handle the problem of insufficient number of non "x" elements like this:

data // Transpose // 
   Map[With[{r = DeleteCases[#, "x"]}, # /. 
       "x" :> If[Length@r >= 2, RandomVariate[NormalDistribution[Mean@r, StandardDeviation@r]], 
         If[Length@r == 1, r[[1]], 0]]] &] // Transpose // TableForm

If a column has just one non "x" element left, return it as rv if it has no elements return 0 as rv.

Robert

That fixed it. Thanks Your last comment is a weakness in my system so far. I have, for simplicity in order to get my head around the problem, assumed at least two non-missing elements in each row. Had not thought about the same affecting columns. Datasets with 19 of the 20 obs missing probably would be eliminated for other reasons before getting this far?

Hi Roger

ok, just replace -> by :>

data// Transpose // 
   Map[With[{r = DeleteCases[#, "x"]}, # /. 
       "x" :> RandomVariate[NormalDistribution[Mean@r, Variance@r]]] &] // 
  Transpose // TableForm

Further you have to take care, that there remain at least two non "x" elements in each column.

Robert

Hi Roger

data//Transpose//
  Map[With[{r = DeleteCases[#, "x"]},
     # /. "x" -> RandomVariate[NormalDistribution[Mean@r, Variance@r]]]&]//
 Transpose

Robert

Right. So now you just need to provide a definition for ColumnBasedFn (and probably change the name :) ). In your first post above, you were using a NormalDistribution to generate a random value, but I realize that that was just an illustration and that in your real situation the function would be different for each column. Just to illustrate, consider this:

ColumnBasedFn[n_] := RandomVariate[UniformDistribution[{n, n + 1}]]

If you added that and ran my code examples above, you'd get all of your "x"s replaced with a random number from within a range defined by the column number.

I noticed that at the bottom of your notebook you're doing this replacement (I assume your colFct is equivalent to my ColumnBasedFn):

Transpose[dataMI1][[#]] /. 
 colFct[#] -> 
  RandomVariate[NormalDistribution[mnstd[[#, 1]], mnstd[[#, 2]]]]

But you don't need to do a replacement, you just need to provide a definition for colFct. Once the colFct expressions are inserted into your data (via either of the methods I demonstrated above), they will get evaluated using whatever definition you provide for colFct. Based on what I see, maybe something like this would work:

colFct[n_] := RandomVariate[NormalDistribution[mnstd[[n, 1]], mnstd[[n, 2]]]]

But I actually haven't carefully analyzed what you're doing, so this is probably not quite right.

Here's another approach:

(*This time we look at the actual value, so we use a function that \
has a special case for "x" and doesn't disturb any other values*)
AnotherReplacer["x", position_] := ColumnBasedFn[Last@position];
AnotherReplacer[value_, _] := value

(*MapIndexed will provide the position info we need.*)
MapIndexed[AnotherReplacer, data, {-1}]

This produces (again)

{{12, 27, 19, 44}, {11, ColumnBasedFn[2], 13, 43}, {ColumnBasedFn[1], 
  56, 23, 60}, {15, 37, 19, 52}, {10, 31, 21, ColumnBasedFn[4]}, {18, 
  40, 22, 43}, {15, 50, 28, 56}, {21, ColumnBasedFn[2], 
  ColumnBasedFn[3], 46}, {20, 39, 25, 51}, {ColumnBasedFn[1], 36, 23, 
  56}, {ColumnBasedFn[1], 27, 21, 39}, {14, 32, 20, 46}, {22, 40, 
  ColumnBasedFn[3], 49}, {ColumnBasedFn[1], 31, ColumnBasedFn[3], 
  44}, {ColumnBasedFn[1], 18, 21, ColumnBasedFn[4]}, {16, 23, 21, 
  34}, {27, 26, 23, 59}, {17, ColumnBasedFn[2], ColumnBasedFn[3], 
  35}, {13, 21, 20, 48}, {11, 51, 18, 54}}