nbfactors {ERP}

Determination of the number of factors in high dimensional factor models.

Description

This function is not supposed to be called directly by users. It implements the variance inflation method proposed by Friguet et al. (2009) to choose the number of factors in high dimensional factor models.

Usage

nbfactors(dta,maxnbfactors=15,diagnostic.plot=FALSE,min.err=0.001,verbose=FALSE,
svd.method=c("fast.svd","irlba"))

Arguments

dta

n x m scaled matrix which rows are multivariate m-profiles for n individuals. n can be much smaller than m. Columns are all centered with standard deviations 1.

maxnbfactors

Maximum number of factors. It has to be a positive integer, smaller than the rank of dta.

diagnostic.plot

Logical value. If TRUE, a plot dispalying the variance inflation curve is produced, with recommendations for the optimal number of factors.

min.err

stopping criterion for the iterative algorithm. Maximum difference between the estimated parameters in the last two iterations.

verbose

logical value. If verbose=TRUE, then some information is printed along the calculation.

svd.method

the EM algorithm starts from an SVD estimation of the factor model parameters. The default option to implement this SVD is fast.svd. An alternative option is an approximate but faster SVD by function irlba.

Details

It is highly recommended to run the function first with diagnostic.plot=TRUE and to choose the number of factors based on the plot that will be produced. Two recommendations are provided: a conservative one obtaned using a kind of elbow criterion, and a liberal one that minimizes the variance inflation curve.

Value

sdt

Variance inflation values for a number of factors going from 0 to maxnbfactors.

nbf

Recommendation for an optimal number of factors (the more liberal, see the details Section for more information).

Author(s)

David Causeur, IRMAR, UMR 6625 CNRS, Agrocampus Ouest, Rennes, France.

References

Friguet, C., Kloareg, M. and Causeur, D. (2009). A factor model approach to multiple testing under dependence. Journal of the American Statistical Association. 104 (488), 1406-1415.

See Also

emfa

Examples

data(impulsivity)
erpdta = as.matrix(impulsivity[,5:505])   # erpdta contains the whole set of ERP curves   
nbf = nbfactors(scale(erpdta),maxnbfactors=10,diagnostic.plot=TRUE)