PCA_COMP - Principal Component Values

Returns an array of cells for the i-th principal component (or residuals).

Syntax

PCA_COMP (X, Mask, Standardize, Number, Return)

X

is the independent variables data matrix, so each column represents one variable.

Mask

is the boolean array to select a subset of the input variables in X. If missing, all variables in X are included.

Standardize

is a flag or switch to standardize the input variables before the analysis (i.e., standardize = 1 (default), subtract mean = 2)).

Value	Standardize
1	Standardize (subtract mean and divide by standard deviation) (default).
2	Subtract mean (subtract mean).

Number

is the component number to return. If missing, the first principal component is assumed.

Return

is a switch to select the return output (1 = proportion of variance (default), 2 = variance, 3 = eigenvalue, 4 = loadings, 5 = PC data).

Value	Return
1	Proportion of total variance (default).
2	Variance.
3	Eigenvalue.
4	Loading or weights for input variables.
5	Principal component (PC) data.

Remarks

1. The underlying model is described here.
2. The PCA_COMP function must be entered as an array formula (for return-types greater than 3) in a range that has the rows as the number of variables (return-type = 4) or the number of observations (return-type = 5).
3. The sample data may include data points with missing values.
4. Each column in the input matrix corresponds to a separate variable.
5. Each row in the input matrix corresponds to an observation.
6. Observations (i.e., rows) with missing values are removed.
7. The PCA_COMP function is available starting with version 1.60 APACHE.

Files Examples

Related Links

• Wikipedia - Linear regression.
• Wikipedia - Regression analysis.
• Wikipedia - Ordinary least squares.

References

• J. Edward Jackson; A User's Guide to Principal Components; Wiley-Interscience; (Sep 10, 2003), ISBN: 471471348.
• I.T. Jolliffe; Principal Component Analysis; Springer; 2nd Edition(Oct 01, 2002), ISBN: 0387954422.
• John Y. Campbell, Andrew W. Lo, A. Craig MacKinlay, Andrew Y. Lo; The Econometrics of Financial Markets; Princeton University Press; 2nd edition(Dec 09, 1996), ISBN: 691043019.
• Hamilton, J.D.; Time Series Analysis, Princeton University Press (1994), ISBN 0-691-04289-6.
• Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0-471-690740.