Class ImplicitModelPCA
- java.lang.Object
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- dev.nm.stat.factor.implicitmodelpca.ImplicitModelPCA
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public class ImplicitModelPCA extends Object
Given a (de-meaned) time series of vectored observations, we decompose them into a reduced dimension of linear sum of implicit factors. The factors are orthogonal. Specifically, we have \(R = \bar{R} + {B}'F + E\) R is the time series of vectored observation. Its size is N x T. R_bar is the average of each subject's value over time, one entry per subject. It size is N>. We copy the vector T times by columns to form a matrix for computation. F is the time series of factor values. Its size is K x T, where K is the number of implicit factors. B' is the matrix of factor loadings. Its size is N x K. Each row is the factor loadings for each subject. E is the residual matrix. In general, we have: The bigger T is, the more accurate B is. Assuming B is correct, the bigger N is, the more accurate F is; the smaller E (the noise) is, the more accurate F is. Therefore, we first need T big enough to accurately estimate B then need N big enough to accurately F (and E).
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Nested Class Summary
Nested Classes Modifier and Type Class Description static class
ImplicitModelPCA.Result
the regression results
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Constructor Summary
Constructors Constructor Description ImplicitModelPCA(Matrix R)
Constructs an implicit-model that will have one and only one implicit factors.ImplicitModelPCA(Matrix R, double varExplained)
Constructs an implicit-model that will have the number of implicit factors such that the variance explained is bigger than a thresholdImplicitModelPCA(Matrix R, int K)
Constructs an implicit-model that will have K implicit factors.
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Constructor Detail
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ImplicitModelPCA
public ImplicitModelPCA(Matrix R, int K)
Constructs an implicit-model that will have K implicit factors.- Parameters:
R
- the time series of observationsK
- the number of factors
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ImplicitModelPCA
public ImplicitModelPCA(Matrix R)
Constructs an implicit-model that will have one and only one implicit factors.- Parameters:
R
- the time series of observations
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ImplicitModelPCA
public ImplicitModelPCA(Matrix R, double varExplained)
Constructs an implicit-model that will have the number of implicit factors such that the variance explained is bigger than a threshold- Parameters:
R
- the time series of observationsvarExplained
- the percentage of variance explained
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Method Detail
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run
public ImplicitModelPCA.Result run()
Runs the regression.- Returns:
- the regression results
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