The TRANSREG Procedure

Akaike, H. (1973), “Information Theory and an Extension of the Maximum Likelihood Principle,” in B. N. Petrov and F. Csáki, eds., Proceedings of the Second International Symposium on Information Theory, 267–281, Budapest: Akademiai Kiado.

Box, G. E. P. and Cox, D. R. (1964), “An Analysis of Transformations,” Journal of the Royal Statistical Society, Series B, 26, 211–234.

Breiman, L. and Friedman, J. H. (1985), “Estimating Optimal Transformations for Multiple Regression and Correlation,” Journal of the American Statistical Association, 77, 580–619, with discussion.

Brent, R. P. (1973), Algorithms for Minimization without Derivatives, Englewood Cliffs, NJ: Prentice-Hall, chapter 5.

Brinkman, N. D. (1981), “Ethanol Fuel: A Single-Cylinder Engine Study of Efficiency and Exhaust Emissions,” Society of Automotive Engineers Transactions, 90, 1410–1424.

Carroll, J. D. (1972), “Individual Differences and Multidimensional Scaling,” in R. N. Shepard, A. K. Romney, and S. B. Nerlove, eds., Multidimensional Scaling: Theory and Applications in the Behavioral Sciences, volume 1, New York: Seminar Press.

Craven, P. and Wahba, G. (1979), “Smoothing Noisy Data with Spline Functions,” Numerical Mathematics, 31, 377–403.

de Boor, C. (1978), A Practical Guide to Splines, New York: Springer-Verlag.

de Leeuw, J. (1986), Regression with Optimal Scaling of the Dependent Variable, Leiden, Netherlands: Department of Data Theory, University of Leiden.

de Leeuw, J., Young, F. W., and Takane, Y. (1976), “Additive Structure in Qualitative Data: An Alternating Least Squares Approach with Optimal Scaling Features,” Psychometrika, 41, 471–503.

Draper, N. R. and Smith, H. (1981), Applied Regression Analysis, 2nd Edition, New York: John Wiley & Sons.

Eilers, P. H. C. and Marx, B. D. (1996), “Flexible Smoothing with B-Splines and Penalties,” Statistical Science, 11, 89–121, with discussion.

Fisher, R. A. (1938), Statistical Methods for Research Workers, 10th Edition, Edinburgh: Oliver & Boyd.

Gabriel, K. R. (1981), “Biplot Display of Multivariate Matrices for Inspection of Data and Diagnosis,” in V. Barnett, ed., Interpreting Multivariate Data, London: John Wiley & Sons.

Gifi, A. (1990), Nonlinear Multivariate Analysis, New York: John Wiley & Sons.

Green, P. E. and Wind, Y. (1975), “New Way to Measure Consumers’ Judgments,” Harvard Business Review, 53, 107–117.

Hastie, T. J. and Tibshirani, R. J. (1986), “Generalized Additive Models,” Statistical Science, 3, 297–318.

Hurvich, C. M., Simonoff, J. S., and Tsai, C.-L. (1998), “Smoothing Parameter Selection in Nonparametric Regression Using an Improved Akaike Information Criterion,” Journal of the Royal Statistical Society, Series B, 60, 271–293.

Israels, A. Z. (1984), “Redundancy Analysis for Qualitative Variables,” Psychometrika, 49, 331–346.

Judge, G. G., Griffiths, W. E., Hill, R. C., and Lee, T.-C. (1980), The Theory and Practice of Econometrics, New York: John Wiley & Sons.

Khuri, A. I. and Cornell, J. A. (1987), Response Surfaces, New York: Marcel Dekker.

Kruskal, J. B. (1964), “Nonmetric Multidimensional Scaling by Optimizing Goodness of Fit to a Nonmetric Hypothesis,” Psychometrika, 29, 1–27.

Kuhfeld, W. F. (2010), Marketing Research Methods in SAS, Technical report, SAS Institute Inc., http://support.sas.com/resources/papers/tnote/tnote_marketresearch.html.

Myers, R. H. (1976), Response Surface Methodology, Blacksburg: Virginia Polytechnic Institute and State University.

National Institute of Standards and Technology (1998), “Statistical Reference Data Sets,” http://www.itl.nist.gov/div898/strd/general/dataarchive.html, accessed June 6, 2011.

Press, W. H., Flannery, B. P., Teukolsky, S. A., and Vetterling, W. T. (1989), Numerical Recipes in PASCAL, Cambridge: Cambridge University Press.

Reinsch, C. H. (1967), “Smoothing by Spline Functions,” Numerische Mathematik, 10, 177–183.

SAS Institute Inc. (1993), Algorithms for the PRINQUAL and TRANSREG Procedures, Technical Report R-108, SAS Institute Inc., Cary, NC, http://support.sas.com/publishing/pubcat/techreports/59040.pdf.

Schiffman, S. S., Reynolds, M. L., and Young, F. W. (1981), Introduction to Multidimensional Scaling, New York: Academic Press.

Schwarz, G. (1978), “Estimating the Dimension of a Model,” Annals of Statistics, 6, 461–464.

Siegel, S. (1956), Nonparametric Statistics, New York: McGraw-Hill.

Smith, P. L. (1979), “Splines as a Useful and Convenient Statistical Tool,” American Statistician, 33, 57–62.

Stewart, D. K. and Love, W. A. (1968), “A General Canonical Correlation Index,” Psychological Bulletin, 70, 160–163.

van der Burg, E. and de Leeuw, J. (1983), “Non-linear Canonical Correlation,” British Journal of Mathematical and Statistical Psychology, 36, 54–80.

van Rijckevorsel, J. L. (1982), “Canonical Analysis with B-Splines,” in H. Caussinus, P. Ettinger, and R. Tomassone, eds., COMPUSTAT 1982, Part I, Vienna: Physica-Verlag.

Winsberg, S. and Ramsay, J. O. (1980), “Monotonic Transformations to Additivity Using Splines,” Biometrika, 67, 669–674.

Young, F. W. (1981), “Quantitative Analysis of Qualitative Data,” Psychometrika, 46, 357–388.

Young, F. W., de Leeuw, J., and Takane, Y. (1976), “Regression with Qualitative and Quantitative Variables: An Alternating Least Squares Approach with Optimal Scaling Features,” Psychometrika, 41, 505–529.