tuneFactors  R Documentation 
Uses Bai and Ng (2002) information criteria approach. Missing data is interpolated using the fillNA
function.
tuneFactors(
X,
type = 2,
standardize = TRUE,
r.max = min(15, ncol(X)  1),
plot = TRUE
)
X 

type 
Character. Option for which information criteria to use. Default is 2. 
standardize 
Logical. Standardize the data before estimating the model. Default is 
r.max 
Integer. Maximum number of factors to search for. Default is min(15,ncol(X)1). 
plot 
Logical. Make a plot showing the IC value for each of the number of factors considered. Default is 
To calculate the number of factors to use in the model, the information criteria approach of Bai and Ng (2002) is used. This can be done before sparseDFM
is fitted to the data to determine r
. Bai and Ng (2002) consider 3 types of information criteria with different penalties of the form:
IC_1(r) = log\left(V_r(\hat{\bm{F}},\hat{\bm{\Lambda}})\right) + r \left( \frac{n+p}{np}\right)log\left( \frac{np}{n+p}\right)
IC_2(r) = log\left(V_r(\hat{\bm{F}},\hat{\bm{\Lambda}})\right) + r \left( \frac{n+p}{np} \right)log\left( min\{n,p\}\right)
IC_3(r) = log\left(V_r(\hat{\bm{F}},\hat{\bm{\Lambda}})\right) + r \frac{log\left( min\{n,p\}\right)}{min\{n,p\}}
The sum of squared residuals for r
factors V_r(\hat{\bm{F}},\hat{\bm{\Lambda}}) = \sum_{i=1}^p\sum_{t=1}^n E[\hat{\epsilon}_{i,t}^2]/np
with \hat{\epsilon}_{i,t} = X_{t,i}\hat{\bm{F}}_t\hat{\bm{\Lambda}}_i
is found using PCA on the standardized data set \bm{X}
. The estimated factors \hat{\bm{F}}
corresponding to the principle components and the estimated loadings \hat{\bm{\Lambda}}
corresponding to the eigenvectors. Should the data contain missing values, then the missing data is interpolated using fillNA
.
The number of factors to use will correspond to argmin_r IC_i(r)
for i=1,2
or 3
. Type 2 is the highest when working in finite samples and therefore is set to default.
The number of factors to use according to Bai and Ng (2002) information criteria.
Bai, J., & Ng, S. (2002). Determining the number of factors in approximate factor models. Econometrica, 70(1), 191221.
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