multiway (version 1.0-7)

multiway-package: tools:::Rd_package_title("multiway")

Description

tools:::Rd_package_description("multiway")

Author

tools:::Rd_package_author("multiway")

Maintainer: tools:::Rd_package_maintainer("multiway")

Details

The DESCRIPTION file: tools:::Rd_package_DESCRIPTION("multiway") tools:::Rd_package_indices("multiway") cpd computes the N-way Canonical Polyadic Decomposition of a tensor. indscal fits the Individual Differences Scaling model. mcr fits the Multiway Covariates Regression model. parafac fits the 3-way and 4-way Parallel Factor Analysis-1 model. parafac2 fits the 3-way and 4-way Parallel Factor Analysis-2 model. sca fits the four different Simultaneous Component Analysis models. tucker fits the 3-way and 4-way Tucker Factor Analysis model.

References

Bro, R., & De Jong, S. (1997). A fast non-negativity-constrained least squares algorithm. Journal of Chemometrics, 11, 393-401.

Bro, R., & Kiers, H.A.L. (2003). A new efficient method for determining the number of components in PARAFAC models. Journal of Chemometrics, 17, 274-286. tools:::Rd_expr_doi("10.1002/cem.801")

Carroll, J. D., & Chang, J-J. (1970). Analysis of individual differences in multidimensional scaling via an n-way generalization of "Eckart-Young" decomposition. Psychometrika, 35, 283-319. tools:::Rd_expr_doi("10.1007/BF02310791")

Harshman, R. A. (1970). Foundations of the PARAFAC procedure: Models and conditions for an "explanatory" multimodal factor analysis. UCLA Working Papers in Phonetics, 16, 1-84.

Harshman, R. A. (1972). PARAFAC2: Mathematical and technical notes. UCLA Working Papers in Phonetics, 22, 30-44.

Harshman, R. A., & Lundy, M. E. (1994). PARAFAC: Parallel factor analysis. Computational Statistics and Data Analysis, 18, 39-72. tools:::Rd_expr_doi("10.1016/0167-9473(94)90132-5")

Haughwout, S. P., LaVallee, R. A., & Castle, I-J. P. (2015). Surveillance Report #102: Apparent Per Capita Alcohol Consumption: National, State, and Regional Trends, 1977-2013. Bethesda, MD: NIAAA, Alcohol Epidemiologic Data System.

Helwig, N. E. (2013). The special sign indeterminacy of the direct-fitting Parafac2 model: Some implications, cautions, and recommendations, for Simultaneous Component Analysis. Psychometrika, 78, 725-739. tools:::Rd_expr_doi("10.1007/S11336-013-9331-7")

Helwig, N. E. (2017). Estimating latent trends in multivariate longitudinal data via Parafac2 with functional and structural constraints. Biometrical Journal, 59(4), 783-803. tools:::Rd_expr_doi("10.1002/bimj.201600045")

Hitchcock, F. L. (1927). The expression of a tensor or a polyadic as a sum of products. Journal of Mathematics and Physics, 6, 164-189. tools:::Rd_expr_doi("10.1002/sapm192761164")

Kiers, H. A. L., ten Berge, J. M. F., & Bro, R. (1999). PARAFAC2-part I: A direct-fitting algorithm for the PARAFAC2 model. Journal of Chemometrics, 13, 275-294. tools:::Rd_expr_doi("10.1002/(SICI)1099-128X(199905/08)13:3/4<275::aid-cem543>3.0.CO;2-B")

Kroonenberg, P. M., & de Leeuw, J. (1980). Principal component analysis of three-mode data by means of alternating least squares algorithms. Psychometrika, 45, 69-97. tools:::Rd_expr_doi("10.1007/BF02293599")

Moore, E. H. (1920). On the reciprocal of the general algebraic matrix. Bulletin of the American Mathematical Society 26, 394-395.

Nephew, T. M., Yi, H., Williams, G. D., Stinson, F. S., & Dufour, M.C., (2004). U.S. Alcohol Epidemiologic Data Reference Manual, Vol. 1, 4th ed. U.S. Apparent Consumption of Alcoholic Beverages Based on State Sales, Taxation, or Receipt Data. Bethesda, MD: NIAAA, Alcohol Epidemiologic Data System. NIH Publication No. 04-5563.

Penrose, R. (1950). A generalized inverse for matrices. Mathematical Proceedings of the Cambridge Philosophical Society 51, 406-413. tools:::Rd_expr_doi("10.1017/S0305004100030401")

Ramsay, J. O. (1988). Monotone regression splines in action. Statistical Science, 3, 425-441. tools:::Rd_expr_doi("10.1214/ss/1177012761")

Smilde, A. K., & Kiers, H. A. L. (1999). Multiway covariates regression models. Journal of Chemometrics, 13, 31-48. tools:::Rd_expr_doi("10.1002/(SICI)1099-128X(199901/02)13:1<31::aid-cem528>3.0.CO;2-P")

Timmerman, M. E., & Kiers, H. A. L. (2003). Four simultaneous component models for the analysis of multivariate time series from more than one subject to model intraindividual and interindividual differences. Psychometrika, 68, 105-121. tools:::Rd_expr_doi("10.1007/BF02296656")

Tucker, L. R. (1966). Some mathematical notes on three-mode factor analysis. Psychometrika, 31, 279-311. tools:::Rd_expr_doi("10.1007/BF02289464")

See Also

CMLS ~~

Examples

# See examples for... 
#   cpd (Canonical Polyadic Decomposition)
#   indscal (INividual Differences SCALing)
#   mcr (Multiway Covariates Regression)
#   parafac (Parallel Factor Analysis-1)
#   parafac2 (Parallel Factor Analysis-2)
#   sca (Simultaneous Component Analysis)
#   tucker (Tucker Factor Analysis)