mdsmat.hlp

是一个经济学管理应用软件 很难找的 但是经济学学生又必须用到

{smcl}
{* 06apr2005}{...}
{cmd:help mdsmat} {right:dialog:  {bf:{dialog mdsmat}}{space 12}}
{right:also see:  {help mds postestimation}}
{hline}

{title:Title}

{p 4 21 2}
{hi:[MV] mdsmat} {hline 2} Multidimensional scaling of proximity data in a matrix


{title:Syntax}

{p 8 24 2}
{cmd:mdsmat} {it:matname}
[{cmd:,} {it:options}]

{synoptset 19 tabbed}{...}
{synopthdr}
{synoptline}
{syntab:Model}
{synopt:{cmdab:sh:ape}{cmd:(}{cmdab:f:ull}{cmd:)}}{it:matname} is a square
	symmetric matrix; the default{p_end}
{synopt:{cmdab:sh:ape}{cmd:(}{cmdab:l:ower}{cmd:)}}{it:matname} is a vector
	with the rowwise lower triangle (with diagonal){p_end}
{synopt:{cmdab:sh:ape}{cmd:(}{cmdab:ll:ower}{cmd:)}}{it:matname} is a vector
	with the rowwise strictly lower triangle (no diagonal){p_end}
{synopt:{cmdab:sh:ape}{cmd:(}{cmdab:u:pper}{cmd:)}}{it:matname} is a vector
	with the rowwise upper triangle (with diagonal){p_end}
{synopt:{cmdab:sh:ape}{cmd:(}{cmdab:uu:pper}{cmd:)}}{it:matname} is a vector
	with the rowwise strictly upper triangle (no diagonal){p_end}
{synopt:{opt nam:es(namelist)}}object names; required with all but
	{cmd:shape(full)}{p_end}
{synopt:{cmd:s2d(}{cmdab:st:andard}{cmd:)}}convert similarity to
	dissimilarity: d(ij) = sqrt(s(ii)+s(jj)-2s(ij)){p_end}
{synopt:{cmd:s2d(}{cmdab:one:minus}{cmd:)}}convert similarity to
	dissimilarity: d(ij) = 1-s(ij){p_end}
{synopt:{opt force}}fix problems in proximity information{p_end}
{synopt:{opt dim:ension(#)}}configuration dimensions; default is
	{cmd:dimension(2)}{p_end}
{synopt:{opt add:constant}}make distance matrix positive definite{p_end}

{syntab:Reporting}
{p2col:{opt neig:en(#)}}maximum number of eigenvalues to display; default is
	{cmd:neigen(10)}{p_end}
{p2col:{opt con:fig}}display table with configuration coordinates{p_end}
{p2col:{opt nopl:ot}}suppress configuration plot{p_end}
{synoptline}
{p2colreset}{...}
{p 4 6 2}
See {help mds postestimation} for features available after estimation.
{p_end}


{title:Description}

{pstd}
{cmd:mdsmat} performs classical metric multidimensional scaling (MDS) for
two-way proximity data with an explicit measure of similarity or dissimilarity
between objects, where the proximities are found in matrix {it:matname}.

{pstd}
If your proximities are stored as variables in long format, see
{helpb mdslong}.  If you are looking for MDS on a data set, based on
dissimilarities between observations over variables, see {helpb mds}.


{title:Options}

{dlgtab:Model}

{phang}{opt shape(shape)}
specifies the storage mode of the existing similarity or dissimilarity matrix
{it:matname}.  The following storage modes are allowed:

{phang2}{opt full}
specifies that {it:matname} is a symmetric n by n matrix.

{phang2}{opt lower}
specifies that {it:matname} is a row or column vector of length n(n+1)/2, with
the rowwise lower triangle of the similarity or dissimilarity matrix
including the diagonal.

{p 16 20 2}
D(11) D(21) D(22) D(31) D(32) D(33) ... D(n1) D(n2) ... D(nn)

{phang2}{opt llower}
specifies that {it:matname} is a row or column vector of length n(n-1)/2, with
the rowwise lower triangle of the similarity or dissimilarity matrix excluding
the diagonal.

{p 16 20 2}
D(21) D(31) D(32) D(41) D(42) D(43) ... D(n1) D(n2) ... D(nn-1)

{phang2}{opt upper}
specifies that {it:matname} is a row or column vector of length n(n+1)/2, with
the rowwise upper triangle of the similarity or dissimilarity matrix including
the diagonal.

{p 16 20 2}
D(11) D(12) ... D(1n) D(22) D(23) ... D(2n) D(33) D(34) ... D(3n) ... D(nn)

{phang2}{opt uupper}
specifies that {it:matname} is a row or column vector of length n(n-1)/2, with
the rowwise upper triangle of the similarity or dissimilarity matrix excluding
the diagonal.

{p 16 20 2}
D(12) D(13) ... D(1n) D(23) D(24) ... D(2n) D(34) D(35) ... D(3n) ... D(n-1n)

{phang}{opt names(namelist)}
is required with all but {cmd:shape(full)}.  The number of
names should equal the number of rows (and columns) of the full similarity or
dissimilarity matrix, and should not contain duplicates.

{phang}{cmd:s2d(standard}|{cmd:oneminus)}
specifies how similarities are converted into dissimilarities, as expected by
{cmd:mdsmat}.  By default {cmd:mdsmat} assumes dissimilarity data.  Specifying
{opt s2d()} indicates that your proximity data are similarities.

{pmore}
Dissimilarity data should have zeros on the diagonal (i.e., an object is
identical to itself) and non-negative off diagonal values.  It is not enforced
that dissimilarities satisfy the triangular inequality,
D(i,j)^2 {ul:<} D(i,h)^2 + D(h,j)^2.  Similarity data should have ones on the
diagonal (i.e., an object is identical to itself) and have off-diagonal values
between zero and one.  In either case, proximities should be symmetric.  See
option {cmd:force} if your data violate these assumptions.

{pmore}
The available {cmd:s2d()} options, {cmd:standard} and {cmd:oneminus}, are
defined as:

{p2colset 13 25 27 2}{...}
{p2col:{cmd:standard}}d(ij) = sqrt(s(ii)+s(jj)-2s(ij)) = sqrt(2(1-s(ij))){p_end}
{p2col:{cmd:oneminus}}d(ij) = 1-s(ij){p_end}
{p2colreset}{...}

{phang}
{opt force} corrects problems with the supplied proximity information.
{opt force} specifies that the dissimilarity matrix is to be symmetrized; the
mean of D(i,j) and D(j,i) is used.  Also, problems on the diagonal
(similarities:  D(i,i)!= 1; dissimilarities: D(i,i)!=0) are fixed.
{cmd:force} does not fix missing values or out of range values (i.e.,
D(i,j)<0; or similarities with D(i,j)>1.)

{phang}{opt dimension(#)}
specifies the dimension of the approximating configuration.  {it:#} defaults
to 2 and should not exceed the number of positive eigenvalues of the centered
distance matrix.

{phang}{cmd:addconstant},
specifies that if the double-centered distance matrix is not positive
semi-definite (psd), a constant should be added to the squared distances to
make it psd, and, hence, Euclidean.

{dlgtab:Reporting}

{phang}{opt neigen(#)}
specifies the number of eigenvalues to be included in the table.  The default
is {cmd:neigen(10)}.  Specifying {cmd:neigen(0)} suppresses the table.

{phang}{opt config}
displays the table with the coordinates of the approximating configuration.
This table may also be displayed by the postestimation command
{cmd:estat config}; see {help mds postestimation}.

{phang}{opt noplot}
suppresses the graph of the approximating configuration.  Note that the graph
can still be produced later via {cmd:mdsconfig} which also allows the standard
graphics options for fine tuning the plot; see {help mds postestimation}.


{title:Remarks}

{pstd}
The purpose of multidimensional scaling (MDS) is to produce a
representation of a dissimilarity relation between a set of n objects by
Euclidean distances between a constructed configuration of points in a
low-dimensional Euclidean space, typically two-dimensional.  If this
low-dimensional representation offers a good enough approximation, we may plot
the points in this low dimensional space, and interpret the (Euclidean,
straight-line) distance between the points as the dissimilarity between the
original objects.  Points mapped close together are similar, points mapped
widely apart are dissimilar.

{pstd}
{cmd:mdsmat} performs MDS on a similarity or dissimilarity matrix
{it:matname}.  You may enter the matrix as a symmetric square matrix or as a
vector (matrix with one row or column) with only the upper or lower triangle;
see option {cmd:shape()} for details.  {it:matname} should not contain missing
values.  The diagonal elements should be 0 (dissimilarities) or 1
(similarities).  If you provide a square matrix (i.e., {cmd:shape(full)}),
names of the objects are obtained from the matrix row and column names.
The row names should all
be distinct, and the column names should equal the row names.  Equation names,
if any, are ignored.  In any of the vectorized shapes, names are specified
with option {cmd:names()}, and the matrix row and column names are ignored.

{pstd}
See option {cmd:force} if your matrix violates these assumptions.


{title:Example}

{pstd}
A famous example in the MDS literature is the data on the percentage of times
that pairs of Morse code signals for two numbers (1,..,9,0) were declared the
same by 598 subjects.  We enter the lower triangle of the data matrix,
excluding the diagonal.  This is called the {cmd:llower} shape (notice the
extra "l" to tell it apart from {cmd:lower} that includes the diagonal).  For
clarity, we enter each row on a separate line; we could have typed the numbers
as one long row as well.

{cmd}{...}
{tab}. matrix input Morse = (     ///
{tab}    62                       ///
{tab}    16 59                    ///
{tab}     6 23 38                 ///
{tab}    12  8 27 56              ///
{tab}    12 14 33 34 30           ///
{tab}    20 25 17 24 18 65        ///
{tab}    37 25 16 13 10 22 65     ///
{tab}    57 28  9  7  5  8 31 58  ///
{tab}    52 18  9  7  5 18 15 39 79 )
{txt}{...}

{pstd}
These are proximity data in similarity format, but in the range [0,100] rather
than [0,1] as required by {cmd:mdsmat}.

{tab}{cmd:. matrix Morse = 0.01 * Morse}

{phang2}
{cmd:. mdsmat Morse, shape(llower) s2d(st) names(1 2 3 4 5 6 7 8 9 0)}


{title:Also see}

{psee}
Manual:  {bf:[MV] mdsmat}
{p_end}

{psee}
Online:  {help mds postestimation};{break}
{helpb mds}, {helpb mdslong};{break}
{helpb ca},
{helpb canon},
{helpb factor},
{helpb pca}
{p_end}