Canonical Correlation Analysis (CCorA)Canonical Correlation Analysis (CCorA) is part of:
ADA Advanced Data Analysis on Multiple tables software
- Versions: 9x/Me/NT/2000/XP/Vista/Win 7/Win 8
- Excel: 97 and later
- Processor: 32 or 64 bits
- Hard disk: 150 Mb
- Mac OS X:
- OS: OS X
- Excel: X, 2004 and 2011
- Hard disk: 150Mb.
Easy and user-friendly
Easy and user-friendly XLSTAT is flawlessly integrated with Microsoft Excel which is the most popular spreadsheet worldwide. This integration makes it one of the simplest available tools to work with as it utilizes the same philosophy as Microsoft Excel. The program is accessible in a dedicated XLSTAT tab. The analyses are grouped into functional menus. The dialog boxes are user-friendly and setting up an analysis is straightforward.
Data and results shared seamlessly
Data and results shared seamlessly One of the greatest advantages of XLSTAT is the way you can share data and results seamlessly. As the results are stored in Microsoft Excel, anyone can access them. There is no need for the receiver to have an XLSTAT license or any additional viewer which makes your team-work easier and more affordable. In addition, results are easily integrable into other Microsoft Office software such as PowerPoint, so that you can create striking presentation in minutes.
Modular XLSTAT is a modular product. XLSTAT-Pro is a core statistical module of XLSTAT which includes all the mainstream functionalities in statistics and multivariate analysis. More advanced features contained in add-on modules can be added for specific applications. This way you can adapt the software to your needs making the software more cost-efficient.
Didactic The results of XLSTAT are organized by analysis and are easy to navigate. Moreover useful information is provided along with the results to assist you in your interpretation.
Affordable XLSTAT is a complete and modular analytical solution that can suit any analytical business needs. It is very reasonably priced so that the return of your investment is almost immediate. Any XLSTAT license comes with top level support and assistance.
Accessible - Available in many languages
Accessible - Available in many languages We have ensured XLSTAT is accessible to everyone by making the program available in many languages, including Chinese, English, French, German, Italian, Japanese, Polish, Portuguese and Spanish.
Automatable and customizable
Automatable and customizable Most of the statistical functions available in XLSTAT can be called directly from the Visual Basic window of Microsoft Excel. They can be modified and integrated to more code to fit to the specificity of your domain. Adding tables and plots as well as modifying existing outputs becomes easy. Furthermore, XLSTAT includes some special tools on the dialog boxes to generate automatically the VBA code in order to reproduce your analysis using the VBA editor or to simply load pre-set settings. This effortless automation of routine analysis will be a huge time saver on your part.
Origins and aim of Canonical Correlation Analysis
Canonical Correlation Analysis (CCorA, sometimes CCA, but we prefer to use CCA for Canonical Correspondence Analysis) is one of the many statistical methods that allow studying the relationship between two sets of variables.It studies the correlation between two sets of variables and extract from these tables a set of canonical variables that are as much as possible correlated with both tables and orthogonal to each other.
Discovered by Hotelling (1936) this method is used a lot in ecology but is has been supplanted by RDA (Redundancy Analysis) and by CCA (Canonical Correspondence Analysis).
Principles of Canonical Correlation Analysis
This method is symmetrical, contrary to RDA, and is not oriented towards prediction. Let Y1 and Y2 be two tables, with respectively p and q variables. Canonical Correlation Analysis aims at obtaining two vectors a(i) and b(i) such that
ρ(i) = cor[Y1a(i),Y2b(i)] = cov(Y1a(i) Y2b(i)) / [var(Y1a(i)).var(Y2b(i))]
is maximized. Constraints must be introduced so that the solution for a(i) and b(i) is unique. As we are in the end trying to maximize the covariance between Y1a(i) and Y2b(i) and to minimize their respective variance, we might obtain components that are well correlated among each other, but that are not explaining well Y1 and Y2. Once the solution has been obtained for i=1, we look for the solution for i=2 where a(2) and b(2) must respectively be orthogonal to a(1) and b(2), and so on. The number of vectors that can be extracted is to the maximum equal to min(p, q).
Note: The inter-batteries analysis of Tucker (1958) is an alternative where one wants to maximize the covariance between the Y1a(i) and Y2b(i) components.
Results for Canonical Correlation Analysis in XLSTAT
- Similarity matrix: . The matrix that corresponds to the "type of analysis" chosen in the dialog box is displayed.
- Eigenvalues and percentages of inertia: In this table are displayed the eigenvalues, the corresponding inertia, and the corresponding percentages. Note: in some software, the eigenvalues that are displayed are equal to L / (1-L), where L is the eigenvalues given by XLSTAT.
- Wilks Lambda test: This test allows to determine if the two tables Y1 and Y2 are significantly related to each canonical variable.
- Canonical correlations: The canonical correlations, bounded by 0 and 1, are higher when the correlation between Y1 and Y2 is high. However, they do not tell to what extent the canonical variables are related to Y1 and Y2. The squared canonical correlations are equal to the eigenvalues and, as a matter of fact, correspond to the percentage of variability carried by the canonical variable.
The results listed below are computed separately for each of the two groups of input variables.
- Redundancy coefficients: These coefficients allow to measure for each set of input variables what proportion of the variability of the input variables is predicted by the canonical variables.
- Canonical coefficients: These coefficients (also called Canonical weights, or Canonical function coefficients) indicate how the canonical variables were constructed, as they correspond to the coefficients in the linear combine that generates the canonical variables from the input variables. They are standardized if the input variables have been standardized. In that case, the relative weights of the input variables can be compared.
- Correlations between input variables and canonical variables: Correlations between input variables and canonical variables (also called Structure correlation coefficients, or Canonical factor loadings) allow understanding how the canonical variables are related to the input variables.
- Canonical variable adequacy coefficients: The canonical variable adequacy coefficients correspond, for a given canonical variable, to the sum of the squared correlations between the input variables and canonical variables, divided by the number of input variables. They give the percentage of variability taken into account by the canonical variable of interest.
- Square cosines: The squared cosines of the input variables in the space of canonical variables allow to know if an input variable is well represented in the space of the canonical variables. The squared cosines for a given input variable sum to 1. The sum over a reduced number of canonical axes gives the communality.
- Scores: The scores correspond to the coordinates of the observations in the space of the canonical variables.
- Canonical Correlation Analysis: Correlations and redundancy
- Canonical Correlation Analysis: Correlations between input variables and canonical variables
- Canonical Correlation Analysis: General dialog box
- Canonical Correlation Analysis: Options dialog box
- Canonical Correlation Analysis: Outputs dialog box
- Canonical Correlation Analysis: variables plot