What is CORExpress?

• CORExpress® develops improved regression and classification models for:
• linear regression
• logistic regression
• linear discriminant analysis
• survival models (Cox regression)
• CORExpress handles multicolinearity due to correlated predictors effectively even with high dimensional data (more variables than cases).

What Features of Regression Models are Improved?

CORExpress improves:

• interpretation of regression coefficients (see Tutorial 1)
• out-of-sample prediction (see Tutorial 2)
• classification (see Tutorial 3)
• variable selection (see Tutorials 1-3)

How does CORExpress Work?

• CORExpress (patent pending) develops regression models using Correlated Component Regression (CCR) methods. CCR was developed by Dr. Jay Magidson for simultaneously estimating regression models and selecting predictors from a potentially large number of candidate predictors. Reliable models are obtained using a fast algorithm that incorporates M-fold cross-validation to optimize tuning parameters (amount of regularization K and # predictor variables P).
• Final models may even include more predictors than cases!!! (impossible with traditional regression methods)

Where can I learn more about CORExpress?

• Technical Documentation
  • Upcoming Chapter
  • Magidson (2013) This chapter in the upcoming Springer Verlager book series New perspectives in Partial Least Squares and Related Methods introduces the Correlated Component Regression (CCR) -- which provides reliable predictions even with near multi-collinear data.
  • Articles
  • Magidson (2010) This article introduces the Correlated Component Regression (CCR) Approach and compares it with other methods, including penalized regression and principal components regression.
  • Magidson and Wassmann (2010) This article introduces suppressor variables, captured by CCR, and the importance of including them in regression models.
  • Conference Presentations
    • 2011 Modern Modeling Methods (M3) Conference (1 hour presentation)
    • 5th ESSEC-SUPELEC Statistical Workshop on “PLS (Partial Least Squares) Developments”, 2011. (Featured presentation)
  • CORExpress User's Guide
  • Tutorials
• Training
• 2-day workshop in Boston (Statistical Modeling Week)
• 1-day workshop in Orlando (Sponsored by American Statistical Association)
• Online Course (January 2012)

Can CORExpress Improve Latent Class Regression Models?

Yes. Latent GOLD® can be used to obtain segments, and CORExpress can be used to predict segment membership or to develop separate regression models for each segment. CORExpress allows many more predictor variables to be included in the model than possible previously.

General Overview

Regression modeling is undergoing a revolution precipitated by the availability of hundreds and even thousands of candidate predictor variables in genomics, but increasingly vast amounts of data are becoming available in all other fields as well. Problems in traditional regression modeling occur when the number of predictors P included in a model approaches or exceeds the sample size N. In this type of situation, involving the presence of ‘high-dimensional data’, traditional regression methods become unreliable and regression coefficients may even be impossible to estimate. Recent advances with high-dimensional data show how such problems can be resolved (see: Cai and Shen (2011)). This important new field continues to evolve at a rapid pace.

Statistical Innovations is pleased to announce our first new software innovation since Latent GOLD in 2000! CORExpress focuses on regression analysis (linear regression, logistic regression, etc.) where large numbers of correlated predictors may be available. On many data sets, it has been shown to outperform penalized regression techniques such as Lasso, and other methods such as Naive Bayes and PLS regression.

Learn more about Correlated Component Regression (CCR) modeling

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Program Features

• Full windows implementation - point and click
• Interactive graphics provide new insights into data and powerful model diagnostic capabilities
• Automatic model scoring of training and validation (holdout) records
• Fast step-down algorithm to simultaneously select the most important predictors and estimate the models.
• CCR-Linear – Continuous dependent variable
• CCR-Logistic – Dichotomous dependent variable
• CCR-LDA – Dichotomous dependent and continuous predictors satisfying assumptions of linear discriminant analysis (LDA)

Tutorials

All sample datasets and sample .spp files used in the tutorial below are downloaded to your computer when you install the demo version of CORExpress. To download individual datasets and .spp files, please refer to our Sample Datasets Page. Download articles here. Take our Online Course to learn more!

Tutorial 1: Getting Started with Correlated Component Regression (CCR) in CORExpress download PDF          + overview - overview This tutorial introduces Key Driver Regression using CCR-LM in CORExpress.

Tutorial 2: CCR for a Continuous Dependent Variable with Many Predictors download PDF          + overview - overview This tutorial introduces the use of CCR-Linear in CORExpress with many predictors.

Tutorial 3: Correlated Component Regression for a Dichotomous Dependent Variable download PDF          + overview - overview This tutorial introduces the use of CCR-LDA in CORExpress.

Tutorial 4: Obtaining Predictions from a 2-class Regression download PDF          + overview - overview This tutorial illustrates a reanalysis of data analyzed by Tenenhaus, et al. (2005): Tenenhaus, M., Pagès, J., Ambroisine L. and & Guinot, C. (2005); PLS methodology for studying relationships between hedonic judgments and product characteristics; Food Quality and Preference. 16, 4, pp 315-325. The data consists of liking ratings on each of 6 different orange juice (OJ) products by 96 judges. Each of the 6 juices is also described by 16 physico-chemical attributes. In addition, the data contains classification information for weighting the judges according to their (posterior membership) probability of being in two different segments which have distinctly different OJ preferences. (click here for details of the random intercept latent class (LC) regression analysis used to obtain these posterior membership probabilities).

Tutorial 5: Prediction with Near Infrared (NIR) Data download PDF          + overview - overview This tutorial shows how a validation sample can be used to compare the performance of different models and methods. In particular, we utilize Cookies NIR data, analyzed earlier by Osbourne, et. al. (1984), Brown et. Al. (2001) and Kraemer and Boulesteix (2011), and show that improved performance can be obtained by removing predictors associated with the highest wavelengths. Use of Cross-validation to determine the number of components based on 700 predictors yields good performance regardless of the particular regression method used. However, we will see that the Correlated Component Regression method (CCR.lm) provides an improvement over the PLS regression method (regardless whether the predictors are standardized) due to the failure of PLS to accurately assess the unreliability of predictors associated with the highest wavelengths.

Tutorial 6: Estimation of Naive Bayes and Extended Naive Bayes Models (forthcoming) Forthcoming          + overview - overview For an introduction to Naive Bayes and its relationship to Logistic Regression, see: http://www.cs.cmu.edu/~tom/mlbook/NBayesLogReg.pdf