Missing Values

Julia provides support for representing missing values in the statistical sense. This is for situations where no value is available for a variable in an observation, but a valid value theoretically exists. Missing values are represented via themissing object, which is the singleton instance of the typeMissing.missing is equivalent toNULL in SQL andNA in R, and behaves like them in most situations.

Propagation of Missing Values

missing valuespropagate automatically when passed to standard mathematical operators and functions. For these functions, uncertainty about the value of one of the operands induces uncertainty about the result. In practice, this means a math operation involving amissing value generally returnsmissing:

julia> missing + 1missingjulia> "a" * missingmissingjulia> abs(missing)missing

Sincemissing is a normal Julia object, this propagation rule only works for functions which have opted in to implement this behavior. This can be achieved by:

• adding a specific method defined for arguments of typeMissing,
• accepting arguments of this type, and passing them to functions which propagate them (like standard math operators).

Packages should consider whether it makes sense to propagate missing values when defining new functions, and define methods appropriately if this is the case. Passing amissing value to a function which does not have a method accepting arguments of typeMissing throws aMethodError, just like for any other type.

Functions that do not propagatemissing values can be made to do so by wrapping them in thepassmissing function provided by theMissings.jl package. For example,f(x) becomespassmissing(f)(x).

Equality and Comparison Operators

Standard equality and comparison operators follow the propagation rule presented above: if any of the operands ismissing, the result ismissing. Here are a few examples:

julia> missing == 1missingjulia> missing == missingmissingjulia> missing < 1missingjulia> 2 >= missingmissing

In particular, note thatmissing == missing returnsmissing, so== cannot be used to test whether a value is missing. To test whetherx ismissing, useismissing(x).

Special comparison operatorsisequal and=== are exceptions to the propagation rule. They will always return aBool value, even in the presence ofmissing values, consideringmissing as equal tomissing and as different from any other value. They can therefore be used to test whether a value ismissing:

julia> missing === 1falsejulia> isequal(missing, 1)falsejulia> missing === missingtruejulia> isequal(missing, missing)true

Theisless operator is another exception:missing is considered as greater than any other value. This operator is used bysort!, which therefore placesmissing values after all other values:

julia> isless(1, missing)truejulia> isless(missing, Inf)falsejulia> isless(missing, missing)false

Logical operators

Logical (or boolean) operators|,& andxor are another special case since they only propagatemissing values when it is logically required. For these operators, whether or not the result is uncertain, depends on the particular operation. This follows the well-established rules ofthree-valued logic which are implemented by e.g.NULL in SQL andNA in R. This abstract definition corresponds to a relatively natural behavior which is best explained via concrete examples.

Let us illustrate this principle with the logical "or" operator|. Following the rules of boolean logic, if one of the operands istrue, the value of the other operand does not have an influence on the result, which will always betrue:

julia> true | truetruejulia> true | falsetruejulia> false | truetrue

Based on this observation, we can conclude if one of the operands istrue and the othermissing, we know that the result istrue in spite of the uncertainty about the actual value of one of the operands. If we had been able to observe the actual value of the second operand, it could only betrue orfalse, and in both cases the result would betrue. Therefore, in this particular case, missingness doesnot propagate:

julia> true | missingtruejulia> missing | truetrue

On the contrary, if one of the operands isfalse, the result could be eithertrue orfalse depending on the value of the other operand. Therefore, if that operand ismissing, the result has to bemissing too:

julia> false | truetruejulia> true | falsetruejulia> false | falsefalsejulia> false | missingmissingjulia> missing | falsemissing

The behavior of the logical "and" operator& is similar to that of the| operator, with the difference that missingness does not propagate when one of the operands isfalse. For example, when that is the case of the first operand:

julia> false & falsefalsejulia> false & truefalsejulia> false & missingfalse

On the other hand, missingness propagates when one of the operands istrue, for example the first one:

julia> true & truetruejulia> true & falsefalsejulia> true & missingmissing

Finally, the "exclusive or" logical operatorxor always propagatesmissing values, since both operands always have an effect on the result. Also note that the negation operator! returnsmissing when the operand ismissing, just like other unary operators.

Control Flow and Short-Circuiting Operators

Control flow operators includingif,while and theternary operatorx ? y : z do not allow for missing values. This is because of the uncertainty about whether the actual value would betrue orfalse if we could observe it. This implies we do not know how the program should behave. In this case, aTypeError is thrown as soon as amissing value is encountered in this context:

julia> if missing           println("here")       endERROR: TypeError: non-boolean (Missing) used in boolean context

For the same reason, contrary to logical operators presented above, the short-circuiting boolean operators&& and|| do not allow formissing values in situations where the value of the operand determines whether the next operand is evaluated or not. For example:

julia> missing || falseERROR: TypeError: non-boolean (Missing) used in boolean contextjulia> missing && falseERROR: TypeError: non-boolean (Missing) used in boolean contextjulia> true && missing && falseERROR: TypeError: non-boolean (Missing) used in boolean context

In contrast, there is no error thrown when the result can be determined without themissing values. This is the case when the code short-circuits before evaluating themissing operand, and when themissing operand is the last one:

julia> true && missingmissingjulia> false && missingfalse

Arrays With Missing Values

Arrays containing missing values can be created like other arrays:

julia> [1, missing]2-element Vector{Union{Missing, Int64}}: 1  missing

As this example shows, the element type of such arrays isUnion{Missing, T}, withT the type of the non-missing values. This reflects the fact that array entries can be either of typeT (here,Int64) or of typeMissing. This kind of array uses an efficient memory storage equivalent to anArray{T} holding the actual values combined with anArray{UInt8} indicating the type of the entry (i.e. whether it isMissing orT).

Arrays allowing for missing values can be constructed with the standard syntax. UseArray{Union{Missing, T}}(missing, dims) to create arrays filled with missing values:

julia> Array{Union{Missing, String}}(missing, 2, 3)2×3 Matrix{Union{Missing, String}}: missing  missing  missing missing  missing  missing

An array with element type allowingmissing entries (e.g.Vector{Union{Missing, T}}) which does not contain anymissing entries can be converted to an array type that does not allow formissing entries (e.g.Vector{T}) usingconvert. If the array containsmissing values, aMethodError is thrown during conversion:

julia> x = Union{Missing, String}["a", "b"]2-element Vector{Union{Missing, String}}: "a" "b"julia> convert(Array{String}, x)2-element Vector{String}: "a" "b"julia> y = Union{Missing, String}[missing, "b"]2-element Vector{Union{Missing, String}}: missing "b"julia> convert(Array{String}, y)ERROR: MethodError: Cannot `convert` an object of type Missing to an object of type String

Skipping Missing Values

Sincemissing values propagate with standard mathematical operators, reduction functions returnmissing when called on arrays which contain missing values:

julia> sum([1, missing])missing

In this situation, use theskipmissing function to skip missing values:

julia> sum(skipmissing([1, missing]))1

This convenience function returns an iterator which filters outmissing values efficiently. It can therefore be used with any function which supports iterators:

julia> x = skipmissing([3, missing, 2, 1])skipmissing(Union{Missing, Int64}[3, missing, 2, 1])julia> maximum(x)3julia> sum(x)6julia> mapreduce(sqrt, +, x)4.146264369941973

Objects created by callingskipmissing on an array can be indexed using indices from the parent array. Indices corresponding to missing values are not valid for these objects, and an error is thrown when trying to use them (they are also skipped bykeys andeachindex):

julia> x[1]3julia> x[2]ERROR: MissingException: the value at index (2,) is missing[...]

This allows functions which operate on indices to work in combination withskipmissing. This is notably the case for search and find functions. These functions return indices valid for the object returned byskipmissing, and are also the indices of the matching entriesin the parent array:

julia> findall(==(1), x)1-element Vector{Int64}: 4julia> findfirst(!iszero, x)1julia> argmax(x)1

Usecollect to extract non-missing values and store them in an array:

julia> collect(x)3-element Vector{Int64}: 3 2 1

Logical Operations on Arrays

The three-valued logic described above for logical operators is also used by logical functions applied to arrays. Thus, array equality tests using the== operator returnmissing whenever the result cannot be determined without knowing the actual value of themissing entry. In practice, this meansmissing is returned if all non-missing values of the compared arrays are equal, but one or both arrays contain missing values (possibly at different positions):

julia> [1, missing] == [2, missing]falsejulia> [1, missing] == [1, missing]missingjulia> [1, 2, missing] == [1, missing, 2]missing

As for single values, useisequal to treatmissing values as equal to othermissing values, but different from non-missing values:

julia> isequal([1, missing], [1, missing])truejulia> isequal([1, 2, missing], [1, missing, 2])false

Functionsany andall also follow the rules of three-valued logic. Thus, returningmissing when the result cannot be determined:

julia> all([true, missing])missingjulia> all([false, missing])falsejulia> any([true, missing])truejulia> any([false, missing])missing