Estimate the number of dimensions for the Multiple Correspondence Analysis by cross-validation

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Description

Estimate the number of dimensions for the Multiple Correspondence Analysis by cross-validation

Usage

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estim_ncpMCA(don, ncp.min=0, ncp.max=5,  method = c("Regularized","EM"), 
     method.cv = c("Kfold","loo"), nbsim=100, pNA=0.05, threshold=1e-4)

Arguments

don

a data.frame with categorical variables; with missing entries or not

ncp.min

integer corresponding to the minimum number of components to test

ncp.max

integer corresponding to the maximum number of components to test

method

"Regularized" by default or "EM"

method.cv

"Kfold" for cross-validation or "loo" for leave-one-out

nbsim

number of simulations, useful only if method.cv="Kfold"

pNA

percentage of missing values added in the data set, useful only if method.cv="Kfold"

threshold

the threshold for assessing convergence

Details

For leave-one-out cross-validation (method.cv="loo"), each cell of the data matrix is alternatively removed and predicted with a MCA model using ncp.min to ncp.max dimensions. The number of components which leads to the smallest mean square error of prediction (MSEP) is retained. For the Kfold cross-validation (method.cv="Kfold"), pNA percentage of missing values is inserted at random in the data matrix and predicted with a MCA model using ncp.min to ncp.max dimensions. This process is repeated nbsim times. The number of components which leads to the smallest MSEP is retained. More precisely, for both cross-validation methods, the missing entries are predicted using the imputeMCA function, it means using it means using the regularized iterative MCA algorithm (method="Regularized") or the iterative MCA algorithm (method="EM"). The regularized version is more appropriate to avoid overfitting issues.

Value

ncp

the number of components retained for the MCA

criterion

the criterion (the MSEP) calculated for each number of components

Author(s)

Francois Husson husson@agrocampus-ouest.fr and Julie Josse Julie.Josse@agrocampus-ouest.fr

References

Josse, J., Chavent, M., Liquet, B. and Husson, F. (2010). Handling missing values with Regularized Iterative Multiple Correspondence Analysis, Journal of Clcassification, 29 (1), pp. 91-116.

See Also

imputeMCA

Examples

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## Not run: 
data(vnf)
result <- estim_ncpMCA(vnf,ncp.min=0, ncp.max=5)

## End(Not run)