📄 ca.hlp
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{smcl}
{* 07apr2005}{...}
{cmd:help ca}{...}{right:dialogs: {bf:{dialog ca} {dialog camat}} }
{right:also see: {help ca postestimation}}
{hline}
{title:Title}
{p 4 17 2}
{bf:[MV] ca} {hline 2} Simple correspondence analysis
{title:Syntax}
{pstd}
Simple correspondence analysis of data
{p 8 16 2}
{cmd:ca} {it:rowvar} {it:colvar} {ifin} {weight} [{cmd:,}
{it:options}]
{pstd}
Simple correspondence analysis of a {it:n_r} by {it:n_c} matrix
{p 8 16 2}
{cmd:camat} {it:matname} [{cmd:,}
{it:options}]
{synoptset 22 tabbed}{...}
{marker options}{...}
{synopthdr}
{synoptline}
{syntab:Model 2}
{synopt:{opt dim:ensions(#)}}number of dimensions (factors, axes);
default is {cmd:dim(2)}{p_end}
{synopt:{opth norm:alize(ca##nopt:nopt)}}normalization of row and column
coordinates{p_end}
{synopt:{opt rows:upp(matname_r)}}matrix of supplementary rows{p_end}
{synopt:{opt cols:upp(matname_c)}}matrix of supplementary columns{p_end}
{synopt:{opt mis:sing}}treat missing values as ordinary values
({cmd:ca} only){p_end}
{synopt:{opt rown:ame(str)}}label for rows;
default is {cmd:rowname(rows)} ({cmd:camat} only){p_end}
{synopt:{opt coln:ame(str)}}label for columns;
default is {cmd:colname(columns)} ({cmd:camat} only){p_end}
{syntab:Reporting}
{synopt:{opt norowp:oints}}suppress table for row points{p_end}
{synopt:{opt nocolp:oints}}suppress table for column points{p_end}
{synopt:{opt comp:act}}display tables in a compact format{p_end}
{synopt:{opt plot}}plot the row and column coordinates{p_end}
{synopt:{opt max:length(#)}}maximum number of characters for labels;
default is {cmd:maxlength(12)}{p_end}
{synoptline}
{marker nopt}{...}
{synopthdr:nopt}
{synoptline}
{syntab:Model 2}
{synopt:{opt sy:mmetric}}symmetric (= {opt ca:nonical}) coordinates; the
default{p_end}
{synopt:{opt ro:w}}row principal coordinates{p_end}
{synopt:{opt co:lumn}}column principal coordinates{p_end}
{synopt:{opt pr:incipal}}principal coordinates{p_end}
{synopt:#}power 0<=#<=1 for row coordinates; seldom used{p_end}
{synoptline}
{p 4 6 2}
{cmd:bootstrap}, {cmd:by}, {cmd:jackknife}, {cmd:rolling}, and {cmd:statsby}
may be used with {cmd:ca}; see {help prefix}.
{p_end}
{p 4 6 2}
{cmd:fweight}s, {cmd:aweight}s, and {cmd:iweight}s are allowed with {cmd:ca};
see {help weight}.
{p_end}
{p 4 6 2}
See {help ca postestimation} for features available after estimation.
{p_end}
{title:Description}
{pstd}
{cmd:ca} performs a simple correspondence analysis (CA) of the
cross-tabulation of the integer-valued variables {it:rowvar} and {it:colvar}
with {it:n_r} and {it:n_c} categories, {it:n_r} and {it:n_c} {ul:>} 2. CA is formally equivalent to
various other geometric approaches, including "dual scaling", "reciprocal
averaging", and "canonical correlation analysis of contingency tables".
{pstd}
{cmd:camat} performs a simple correspondence analysis of a {it:n_r} x {it:n_c} matrix
{it:matname} with non-negative entries with strictly positive margins. The
correspondence table need not contain frequencies. The labels for the row and
column categories are obtained from the matrix name stripes.
{pstd}
Results may be replayed using {cmd:ca}; one may also type {cmd:camat}, there is
no difference.
{title:Options}
{dlgtab:Model 2}
{phang}{opt dimensions(#)}
specifies the number of dimensions (= factors = axes) to be extracted. The
default is {cmd:dimensions(2)}. If you specify {cmd:dimensions(1)}, the row
and column categories are placed "on a single dimension". {it:#} should be
strictly smaller than the number of rows and the number of columns, counting
only the active rows and columns, excluding supplementary rows and columns
(see options {opt rowsupp()} and {opt colsupp()}).
{pmore}
CA is a hierarchical method so that extracting additional dimensions does not
affect the coordinates and decomposition of inertia of dimensions already
included. The percentages of inertia accounting for the dimensions are in
decreasing order as indicated by "singular values". The first dimension
accounts for the most inertia, followed by the second dimension, then the
third dimension, etc.
{phang}{opt normalize(nopt)}
specifies the normalization method, i.e., how the row and column coordinates
are obtained from the singular vectors and singular values of the matrix of
standardized residuals. See {hi:Normalization and the interpretation of CA}
in the {hi:Remarks} section for a discussion of these different normalization
methods.
{phang2}{opt symmetric}, the default,
distributes the inertia equally over rows and columns, treating the rows and
columns symmetrically. The symmetric normalization is also known as the
standard or canonical normalization. This is the most common normalization
when making a biplot. {cmd:normalize(symmetric)} is equivalent to
{cmd:normalize(0.5)}.
{phang2}{opt row}
should be chosen if you want to compare row categories. Similarity of column
categories should not be interpreted. The biplot interpretation of the
relationship between row and column categories is appropriate.
{cmd:normalize(row)} is equivalent to {cmd:normalize(1)}.
{phang2}{opt column}
should be chosen if you want to compare column categories. Similarity of row
categories should not be interpreted. The biplot interpretation of the
relationship between row and column categories is appropriate.
{cmd:normalize(column)} is equivalent to {cmd:normalize(0)}.
{phang2}{opt principal}
is the normalization to choose if you want to make comparisons among the row
categories and among the column categories. In this normalization, it is not
appropriate to compare row and column points. Thus, a biplot in this
normalization is best avoided. In the principal normalization, the row and
column coordinates are obtained from the left and right singular vectors,
multiplied by the singular values. This normalization method is not
equivalent to {opt normalize(#)} for any {it:#}.
{phang2}{it:#}, 0{ul:<}{it:#}{ul:<}1,
is seldom used; it specifies that the row coordinates are obtained as the left
singular vectors multiplied by the singular values to the power {it:#}, while
the column coordinates equal the right singular vectors multiplied by the
singular values to the power 1-{it:#}.
{phang}{opt rowsupp(matname_r)}
specifies a matrix of supplementary rows. {it:matname_r} should have {it:n_c}
columns. The row names of {it:matname_r} are used for labeling. Supplementary
rows do not affect the computation of the dimensions and the decomposition of
inertia. They are, however, included in the plots and in the table with
statistics of the row points. Since supplementary points do not contribute to
the dimensions, the {cmd:contrib} entries are left blank.
{phang}{opt colsupp(matname_c)}
specifies a matrix of supplementary columns. {it:matname_c} should have {it:n_r}
rows. The column names of {it:matname_c} are used for labeling.
Supplementary columns do not affect the computation of the dimensions and the
decomposition of inertia. They are, however, included in the plots and in the
table with statistics of the column points. Since supplementary points do not
contribute to the dimensions, the {cmd:contrib} entries are left blank.
{phang}{opt missing}, allowed only with {cmd:ca},
treats missing values of {it:rowvar} and {it:colvar} as ordinary values to be
included in the analysis. Observations with missing values are omitted from
the analysis by default.
{phang}{opt rowname(str)}, allowed only with {cmd:camat},
specifies a label to refer to the rows of the matrix. The default is
{cmd:rowname(rows)}.
{phang}{opt colname(str)}, allowed only with {cmd:camat},
specifies a label to refer to the columns of the matrix. The default is
{cmd:colname(columns)}.
{dlgtab:Reporting}
{phang}{cmd:norowpoints}
suppresses the table with row point (category) statistics.
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