mds.hlp

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{smcl}
{* 06apr2005}{...}
{cmd:help mds} {right:dialog:  {bf:{dialog mds}}{space 15}}
{right:also see:  {help mds postestimation}}
{hline}

{title:Title}

{p 4 18 2}
{hi:[MV] mds} {hline 2} Multidimensional scaling for two way data


{title:Syntax}

{p 8 12 2}
{cmd:mds} {varlist} {ifin} {cmd:,} {opt id(varname)}
[ {it:options} ]

{synoptset 20 tabbed}{...}
{synopthdr}
{synoptline}
{syntab:Model}
{p2coldent:* {opt id(varname)}}identify observations{p_end}
{synopt:{cmd:unit}[{cmd:(}{it:varlist2}{cmd:)}]}scale variables to min=0 and
	max=1{p_end}
{synopt:{cmd:std}[{cmd:(}{it:varlist3}{cmd:)}]}scale variables to mean=0 and
	sd=1{p_end}
{synopt:{opth mea:sure(measure option:measure)}}similarity or dissimilarity
	measure; default is {cmd:measure(L2)} (Euclidean){p_end}
{synopt:{cmd:s2d(}{cmdab:st:andard}{cmd:)}}convert similarity to
	dissimilarity: d(ij)=sqrt(s(ii)+s(jj)-2s(ij)), the default{p_end}
{synopt:{cmd:s2d(}{cmdab:one:minus}{cmd:)}}convert similarity to
	dissimilarity: d(ij)=1-s(ij){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}
{synopt:{opt neig:en(#)}}maximum number of eigenvalues to display; default is
	{cmd:neigen(10)}{p_end}
{synopt:{opt con:fig}}display table with configuration coordinates{p_end}
{synopt:{opt nopl:ot}}suppress configuration plot{p_end}
{synoptline}
{p2colreset}{...}
{p 4 6 2}
* {opt id()} is required.
{p_end}
{p 4 6 2}
{cmd:bootstrap}, {cmd:by}, {cmd:jackknife}, {cmd:rolling}, {cmd:statsby}, and
{cmd:xi} may be used with {cmd:mds}; see {help prefix}.
{p_end}
{p 4 6 2}
The maximum number of observations allowed in {cmd:mds} is the maximum matrix
size; see {help matsize}.
{p_end}
{p 4 6 2}
See {help mds postestimation} for features available after estimation.
{p_end}


{title:Description}

{pstd}
{cmd:mds} performs classical metric multidimensional scaling (MDS) for
dissimilarity between observations with respect to the variables in
{it:varlist}.  A wide selection of similarity and dissimilarity measures is
available, see the {cmd:measure()} option.

{pstd}
While {cmd:mds} computes dissimilarities from the observations, {cmd:mdslong}
and {cmd:mdsmat} are for when you already have similarity or dissimilarity
information.  {cmd:mdslong} and {cmd:mdsmat} offer the same statistical
features but require different data organizations.  {cmd:mdslong} expects the
proximity information in a "long format" (pairwise or dyadic form), whereas
{cmd:mdsmat} performs MDS on a symmetric dissimilarity matrix; see
{helpb mdslong} and {helpb mdsmat}.


{title:Options}

{dlgtab:Model}

{phang}{opt id(varname)}
is required; it specifies a variable that identifies observations.
A warning message is displayed if {it:varname} has duplicate values.

{phang}{cmd:unit}[{cmd:(}{it:varlist2}{cmd:)}]
specifies variables that are transformed to min=0 and max=1 before entering in
the computation of similarities or dissimilarities.  {cmd:unit} by
itself, without an argument, is a shorthand for {cmd:unit(_all)}.
Variables in {cmd:unit()} should not be included in {cmd:std()}.

{phang}{cmd:std}[{cmd:(}{it:varlist3}{cmd:)}]
specifies variables that are transformed to mean=0 and sd=1 before entering in
the computation of similarities or dissimilarities.  {cmd:std} by
itself, without an argument, is a shorthand for {cmd:std(_all)}.
Variables in {cmd:std()} should not be included in {cmd:unit()}.

{phang}{opt measure(measure)}
specifies the similarity or dissimilarity measure.  The default is
{cmd:measure(L2)}, Euclidean distance.  See {it:{help measure_option}} for
detailed descriptions of the supported measures.

{pmore}
If a similarity measure is selected, the computed similarities will first be
transformed into dissimilarities, before proceeding with scaling; see the
{opt s2d()} option below.

{pmore}
Classical metric MDS with Euclidean distance is equivalent to principal
component analysis (see {helpb pca}); the MDS configuration coordinates are
the principal components.

{phang}{opt s2d(conversion)}
specifies how measures in similarity form are converted to dissimilarities.
The following conversions are available:

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

{pmore}
Obviously, {cmd:s2d()} should only be specified with measures in similarity
form.

{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)}.  Specify {cmd:neigen(0)} to suppress 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:Examples}

    {cmd:. mds price-gear, id(make)}

    {cmd:. mds price-gear, id(make) dim(3) std noplot}

    {cmd:. mds price-gear, id(make) std measure(corr) addconstant}


{title:Also see}

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

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