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Instant-use add-on functions for the Wolfram Language

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 MissingDataLogLikelihood

Source Notebook

Compute a log-likelihood for data with missing values

Contributed by: Sjoerd Smit

ResourceFunction["MissingDataLogLikelihood"][dist, data]

computes the log-likelihood for obervations data from the distribution dist, assuming that the probabilities that values are Missing is independent of the observed values.

Details

ResourceFunction["MissingDataLogLikelihood"] uses MarginalDistribution to obtain distributions for data rows where elements are Missing.

Examples

Basic Examples (2) 

Compute a log-likelihood from data with missing values:

In[1]:=
ResourceFunction["MissingDataLogLikelihood"][ BernoulliDistribution[p], {0, 1, 1, Missing[], 1, Missing[], 0}]
Out[1]=

Since this is univariate data, this is equivalent to:

In[2]:=
LogLikelihood[BernoulliDistribution[p], DeleteMissing@{0, 1, 1, Missing[], 1, Missing[], 0}]
Out[2]=

Compute a log-likelihood for a multivariate distribution:

In[3]:=
ResourceFunction["MissingDataLogLikelihood"][ DirichletDistribution[{a1, a2, a3, a4}], \!\(\* TagBox[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ InterpretationBox[ StyleBox["\<\"0.450136\"\>", ShowStringCharacters->False, "NodeID" -> 12], 0.45013577777665764`, AutoDelete->True], ",", InterpretationBox[ StyleBox["\<\"0.297068\"\>", ShowStringCharacters->False, "NodeID" -> 13], 0.29706770109764097`, AutoDelete->True], ",", RowBox[{"Missing", "[", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ InterpretationBox[ StyleBox["\<\"0.578003\"\>", ShowStringCharacters->False, "NodeID" -> 14], 0.5780027759958483, AutoDelete->True], ",", InterpretationBox[ StyleBox["\<\"0.0273841\"\>", ShowStringCharacters->False, "NodeID" -> 15], 0.0273840870029496, AutoDelete->True], ",", RowBox[{"Missing", "[", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"Missing", "[", "]"}], ",", RowBox[{"Missing", "[", "]"}], ",", InterpretationBox[ StyleBox["\<\"0.371392\"\>", ShowStringCharacters->False, "NodeID" -> 16], 0.37139167367775067`, AutoDelete->True]}], "}"}], ",", RowBox[{"{", RowBox[{ InterpretationBox[ StyleBox["\<\"0.0115941\"\>", ShowStringCharacters->False, "NodeID" -> 17], 0.011594090904890523`, AutoDelete->True], ",", RowBox[{"Missing", "[", "]"}], ",", InterpretationBox[ StyleBox["\<\"0.350979\"\>", ShowStringCharacters->False, "NodeID" -> 18], 0.3509791338002293, AutoDelete->True]}], "}"}], ",", RowBox[{"{", RowBox[{ InterpretationBox[ StyleBox["\<\"0.0607383\"\>", ShowStringCharacters->False, "NodeID" -> 19], 0.060738304995325135`, AutoDelete->True], ",", InterpretationBox[ StyleBox["\<\"0.32696\"\>", ShowStringCharacters->False, "NodeID" -> 20], 0.32695977786381486`, AutoDelete->True], ",", InterpretationBox[ StyleBox["\<\"0.268544\"\>", ShowStringCharacters->False, "NodeID" -> 21], 0.2685435470656679, AutoDelete->True]}], "}"}], ",", RowBox[{"{", RowBox[{ InterpretationBox[ StyleBox["\<\"0.230961\"\>", ShowStringCharacters->False, "NodeID" -> 22], 0.2309612456768055, AutoDelete->True], ",", RowBox[{"Missing", "[", "]"}], ",", InterpretationBox[ StyleBox["\<\"0.545698\"\>", ShowStringCharacters->False, "NodeID" -> 23], 0.5456982769697271, AutoDelete->True]}], "}"}]}], "}"}], NumberForm]\)]
Out[3]=

Applications (1) 

Find a maximum-likelihood estimate for a BinormalDistribution with randomly missing values:

In[4]:=
SeedRandom[1234]; data = Table[RandomChoice[{1, 1} -> {Missing[], j}], {i, RandomVariate[BinormalDistribution[{-1, 2}, {3, 1}, 0.5], 200]}, {j, i} ];
In[5]:=
dist = BinormalDistribution[{m1, m2}, {s1, s2}, r]; assum = DistributionParameterAssumptions[dist]; vars = DeleteDuplicates@Flatten[List @@ dist]; NMaximize[ {ResourceFunction["MissingDataLogLikelihood"][dist, data], assum}, vars, Method -> "RandomSearch" ]
Out[8]=

Publisher

Sjoerd Smit

Version History

  • 1.0.1 – 21 June 2023
  • 1.0.0 – 07 June 2023

Source Metadata

  • Citation:
    • "Maximum Likelihood from Incomplete Data via the EM Algorithm", A. P. Dempster; N. M. Laird; D. B. Rubin, Journal of the Royal Statistical Society. Series B (Methodological), Vol. 39, No. 1. (1977), pp. 1-38. https://doi.org/10.1111/j.2517-6161.1977.tb01600.x

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