       cov matrix of sample means, variances and covariances

• To: mathgroup at smc.vnet.net
• Subject: [mg15200] cov matrix of sample means, variances and covariances
• From: Albert Maydeu-Olivares <amaydeu at nil.fut.es>
• Date: Tue, 22 Dec 1998 04:01:33 -0500
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,

Does anyone know how to efficiently compute the covariance matrix of the
sample means, covariances, and variances of a subj x nvars data matrix?

I enclose a notebook with some code I wrote with a 300 x 4 matrix of
binary data.
It's very slow.

I would not like to use use it on a 1000 x 50 matrix!!

In:=
T[matrix_List] := Transpose[matrix]
L[matrix_List] := Length[matrix]
Diag[matrix_List] := Table[If[i == j, matrix[[i,j]], 0], {i, L[matrix]},
{j, L[matrix]}]
VecLow[matrix_List] := Flatten[MapIndexed[Take[#1, First[#2] - 1] & ,
matrix]] VecLowDiag[matrix_List] := Flatten[MapIndexed[Take[#1,
First[#2]] & , matrix]] VecDiag[matrix_List] := Table[matrix[[i,i]],
{i, Length[matrix]}]

In:=
patterns = {{0, 0, 1, 1}, {0, 1, 1, 1}, {1, 0, 0, 0}, {1, 0, 0, 1}, {1,
0, 1, 0}, {1, 0, 1, 1},
{1, 1, 0, 0}, {1, 1, 0, 1}, {1, 1, 1, 0}, {1, 1, 1, 1}}//N;  obsfreq
= {39, 10, 30, 51, 24, 12, 19, 20, 43, 52}; n = L[obsfreq];  data =
Flatten[Table[Table[patterns[[i]], {obsfreq[[i]]}], {i, n}], 1]; subj =
L[data];

nvars = L[T[data]]; l = nvars + Binomial[nvars, 2];

Timing[dmat = Table[dd = {data[[i]]}; mat = T[dd] . dd;
dj = Flatten[{VecDiag[mat], VecLow[mat]}], {i, subj}];

dmean = Table[Table[Sum[dmat[[i,j]], {i, subj}], {j, l}]/subj,
{k, subj}];

w = T[dmat - dmean] . (dmat - dmean)/subj; ]

Out=
{23.95 Second,Null}

N[w,3]//MatrixForm

----------------------------------------------------------------------------
Albert Maydeu-Olivares				Tel. +34 93 4021079 ext. 3099 Faculty of
Psychology 				Fax. +34 93 4021362 University of Barcelona				E-Mail:
amaydeu at tinet.fut.es Passeig de la Vall d'Hebron, 171.
08035 - Barcelona (Spain)
----------------------------------------------------------------------------

```

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