Yes, computing covariance with pairwise comparison will be troublesome.
The more general way of computing a covariance matrix for multi-column data
is, (for example in STATA) to only keep all the rows that have no missing
value across all columns and compute a covariance matrix for that
data-frame with no missing values at all.
With cov(), I can do something like for the existing dataframe called "df"
the following:
# Create new dataframe with no missing values at all
df_new = df
for col in names(df)
df_new = df_new[!isna(df_new[col]), :]
end
# Compute covariance matrix for new dataframe
cov(Array(df_new))
Although this is a short code, I still think it will be nice if "cov"
function automatically drops the rows with missing values and compute
covariance, rather than returning "NA" as covariance if there is any NA
value.
Putting "pairwise" option can be the next step!
On Saturday, June 25, 2016 at 8:38:36 AM UTC-5, Milan Bouchet-Valat wrote:
>
> Le vendredi 24 juin 2016 à 23:09 -0700, Jessica Koh a écrit :
> > I actually really agree with this! Does it mean we need to change the
> > existing function's source code to deal with the problem as you
> > suggest?
> The code for cov() will have to be more complex that the sum()
> illustration Andreas gave: to compute the covariance, you need to skip
> all observations for which one of the two variables is missing. This
> gets even more complex when computing covariances between columns of
> matrices, since you need to decide whether to skip rows with at least
> one missing value, or to use different row subsets depending on the
> pairs of columns involved.
>
> Alternatively, I wonder whether this problem could be solved using
> special pseudo-weights types. This could allow sharing the code with
> the weighted covariance function. A special weights type would simply
> be passed, with weight 1 for non-missing observations, and 0 for
> missing ones. These values could be a custom (internal) number type for
> which 0 * NULL would return 0, in order to skip these observations.
>
> Anyway, one will need to experiment with these approaches in practice
> to see whether that would work.
>
>
> Regards
>
> > > It would be great if we could come up with a solution where the
> > > NA/Nullable handling wouldn't have to be hard coded in a specific
> > > statistical function, say cov. It's early and I haven't had coffee
> > > yet so the idea is probably flawed but, in general, it might be
> > > useful to use a dedicated `Accumulator` type when doing
> > > accumulations, e.g. a sum would be something like
> > >
> > > function sum(x::AbstractVector)
> > > acc = Acc{eltype(x) + eltype(x)}(0)
> > > for xx in x
> > > acc !+ xx
> > > end
> > > end
> > >
> > > then instead of specifying the NA handling for every statistical
> > > function. It would be a matter of defining something like
> > > `(!+)(x::Acc, y::Nullable) = x` to "remove" the effect of NAs in
> > > the accumulation. Of course, you don't always want to remove NAs so
> > > this would have to be adjustable. What kind of functionality exists
> > > in NullableArrays for handling Nullable is different ways?
> > >
> > > The original reason I've started to consider the accumulator type
> > > is to have a way of handling memory reuse, e.g. for BigFloats and
> > > JuMP expressions but maybe it could also be useful for NA/Nullable
> > > handling.
> > >
> > >
> > > On Wed, Jun 8, 2016 at 4:42 AM, Milan Bouchet-Valat
> > > wrote:
> > > > Le mardi 07 juin 2016 à 17:23 -0700, Jessica Koh a écrit :
> > > > > Hello Andreas,
> > > > >
> > > > > Sorry I deleted the post before you commented on this. Thank
> > > > you so
> > > > > much for your comment!
> > > > >
> > > > > Yes, I have already tried that, and that works great with 2
> > > > > variables. However, I am dealing with multiple variables with
> > > > missing
> > > > > values, and the location of missing values differ across
> > > > different
> > > > > variables. I want the covariance function to handle missing
> > > > values by
> > > > > pairwise deletion; all available observations should be used to
> > > > > calculate each pairwise covariance without regard to whether
> > > > > variables outside that pair are missing.
> > > > >
> > > > > I can technically write up the function from scratch to do
> > > > this. But
> > > > > this seems like a basic problem, so I was guessing there might
> > > > be
> > > > > some library already written that handle this. Do you suggest
> > > > writing
> > > > > the function from scratch, or are you aware of the existing
> > > > functions
> > > > > to solve this?
> > > > You're right that it's an essential function. I think we should
> > > > write
> > > > one based on the Nullable framework instead of on the
> > > > NA/DataArrays one
> > > > (which is on its way out). That function could either live in
> > > > StatsBase.jl or in NullableArrays.jl.
> > > >
> > > >
> > > > Regards
> > > >
> > > > > > I think you'd have to remove them first. E.g. something like
> > > > > >
> > > > > > julia> X = DataArray(randn(10,2));
> > > > > >
> > > > > > julia> X[2,1] = X[3,2] = NA;
> > > > > >
> > > > > > julia> cov(X[!vec(any(isna(X), 2)),:])
> > > > > > 2×2 DataArrays.DataArray{Float64,2}:
> > > > > > 1.19373 0.236507
> > > > > > 0.236507 0.524404
> > > > > >
> > > > > >
> > > > > > On Tue, Jun 7, 2016 at 6:26 PM, Jessica Koh
> > > >
> > > > > > > wrote:
> > > > > > > Hi all,
> > > > > > >
> > > > > > > Is there a way to create a covariance matrix of matrix that
> > > > > > > contains NA values, using "cov()" function from StatsBase?
> > > > > > >
> > > >
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