Description Usage Arguments Details Value References See Also Examples
This is the basic function for correspondence regression, i.e. the correspondence analysis of a contingency table formed by the categorical variables Y and X, where X can be in turn made up of the combinations of various categorical variables.
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formula 
A 
data 
The data frame containing the variables specified in the 
part 
Character vector specifying the names of conditional factors (e.g. a factor partioning the levels of the lefthand side 
b 
Number of the bootstrap replications (simulations). If 
xep 
Logical specifying whether to output the separate terms in the righthand side ( 
std 
Logical specifying whether to output the standardized coordinates. Defaults to 
rel 
Logical specifying whether to divide the coordinates by the 
phi 
Logical specifying whether to compute the output on the scale of the Chisquared value of the contingency table or of the Phisquared value
(which is Chisquared divided by N). Reminiscent of 
chr 
Character specifying the separator string for constructing the interaction terms. 
Correspondence regression rests on the idea, described by Gilula and Haberman (1988), of using a correspondence analysis to model a polytomous or multinomial (i.e.
'multicategory') response variable (Y
) in terms of other (possibly interacting) factors (X
) (see also 3.2 in Van der Heijden et al. 1989). These are
specified in the argument formula
, which can be constructed in all the usual ways of specifying a model formula: e.g.
Y ~ X1 + X2 + X1 : X2
or Y ~ X1 * X2
Y ~ (X1 + X2 + X3) ^ 2
Y ~ X1 * X2 * X3  X1 : X2 : X3
...
Correspondence regression then crosstabulates the Y
factor with all the combinations in X
, thus producing a typical contingency table, on which a simple
correspondence analysis is performed (see Greenacre 2017: 121128 for the outline of this approach). The more general effects in X
are obtained by aggregating
the combinations.
Correspondence regression also allows for inferential validation of the effects, which is done by means of the bootstrap (in fact, Monte Carlo simulation). Setting the argument
b
to a number > 0, b
replicates of the contingency table are generated with multinomial sampling. From these, b
new values are derived for the
coordinates in both Y
and X
as well as for the eigenvalues (also called the "principal inertias"). On the basis of the replicate/simulated values,
confidence intervals, ellipses or ellipsoids can be computed. CAUTION: bootstrapping/simulation is computationally quite intensive, so it can take a while to reach
results, especially with a large b
.
The argument parm
can be used when one wants to perform a correspondence regression of Y
onto X
conditional on other factors. These conditioning factors are
therefore equivalent to random factors, and corregp
always conditions on the joint variable of all the specified factors. One such use of conditioning factors is
a socalled lectometric analysis in linguistics, where the levels of Y
are grouped/partitioned/nested into clusters and one wants to exclude the heterogeneity
between the clusters.
An object of class "corregp", i.e. a list with components:

A vector of eigenvalues of the correpondence regression. 

The coordinates (matrix) of the Y levels. 

The coordinates of the X levels. If 

A list of the frequencies of every Y and X level. 

If b>0. A list of bootstrap replicates for the eigenvalues, the coordinates of Y levels, the coordinates of X levels and the frequencies of both the Y levels and the X levels. 

A list of auxiliary information (such as the U and V matrices of the SVD, the specified values for all the arguments) to be passed to other functions and methods. 
Gilula, Z. and S.J. Haberman (1988) The analysis of multivariate contingency tables by restricted canonical and restricted association models. Journal of the American Statistical Association 83 (403), 760–771.
Greenacre, M. (2017) Correspondence analysis in practice, Third edition. Boca Raton: Chapman and Hall/CRC.
Van der Heijden, P.G.M., A. de Falguerolles and J. de Leeuw (1989) A combined approach to contingency table analysis using correspondence analysis and loglinear analysis. Applied Statistics 38 (2), 249–292.
print.corregp
, summary.corregp
, screeplot.corregp
, anova.corregp
, plot.corregp
.
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