Canonical Correspondence Analysis (CCA and partial CCA)

Canonical Correspondence Analysis (CCA and partial CCA) is part of:

ADA Advanced Data Analysis on Multiple tables software
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System configuration
- Windows:
  - 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.

Benefits

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
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
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
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.

What is Canonical Correspondence Analysis

Canonical Correspondence Analysis (CCA) has been developed to allow ecologists to relate the abundance of species to environmental variables. However, this method can be used in other domains. Geomarketing and demographic analyses should be able to take advantage of it.

Canonical Correspondence Analysis allows obtaining a simultaneous representation of the sites, the objects, and the variables describing the sites in two or three dimensions that are optimal for a variance criterion.

Principles of Canonical Correspondence Analysis

Let T1 be a contingency table corresponding to the counts on n sites of p objects. This table can be analyzed using Correspondence Analysis (CA) to obtain a simultaneous map of the sites and objects in two or three dimensions.

Let T2 be a table that contains the measures recorded on the same n sites of corresponding to q quantitative and/or qualitative variables.

Canonical Correspondence Analysis can be divided into two parts:

A constrained analysis in a space which number of dimensions is equal to q. This part is the one of main interest as it corresponds to the analysis of the relation between the two tables T1 and T2.
An unconstrained part, which corresponds to the analysis of the residuals. The number of dimensions for the unconstrained CCA is equal to min(n-1-q, p-1).

Two methods derived from Canonical Correspondence Analysis

Partial Canonical Correspondence Analysis adds a preliminary step. The T2 table is subdivided into two groups of variables: the first group contains conditioning variables which effect we want to remove, as it is either known or without interest for the study. A Canonical Correspondence Analysis is run using these variables. A second Canonical Correspondence Analysis is run using the second group of variables which effect we want to analyze. Partial Canonical Correspondence Analysis allows you to analyze the effect of the second group of variables, after the effect of the first group has been removed.
PLS- Canonical Correspondence Analysis: It is possible to relate discriminant PLS to Canonical Correspondence Analysis. Addinsoft is the first software editor to propose a comprehensive and effective integration between the two methods. Using a restructuring of data, a PLS step is applied to the data, either to create orthogonal PLS components that are optimally designed for the Canonical Correspondence Analysis to avoid the constraints in terms of number of variables that can be used, or to select the most influential variables before running the Canonical Correspondence Analysis. As calculations of the Canonical Correspondence Analysis step and results are identical to what is done with the classical Canonical Correspondence Analysis, users can see this approach as a selection method that identifies the variables of higher interest, either because they are selected in the model, or by looking at the chart of the VIPs. In the case of a partial Canonical Correspondence Analysis, the preliminary step is unchanged.

Results for Canonical Correspondence Analysis in XLSTAT

Inertia: This table displays the distribution of the inertia between the constrained Canonical Correspondence Analysis and the unconstrained Canonical Correspondence Analysis.
Eigenvalues and percentages of inertia: In these tables are displayed for the Canonical Correspondence Analysis and the unconstrained Canonical Correspondence Analysis the eigenvalues, the corresponding inertia, and the corresponding percentages, either in terms of constrained inertia (or unconstrained inertia), or in terms of total inertia.
Weighted averages: This table displays the weighted means as well the global weighted means.
Principal coordinates and standard coordinates: The principal coordinates and standard coordinates of the sites, the objects and the variables are then displayed. These coordinates are used to produce the various charts.
Regression coefficients: This table displays the regression coefficients of the variables in the factor space.
Sites and objects maps:
- Sites and objects / Symmetric chart
- Site / Asymmetric
- Objects / Assymetric
- Sites
- Objects
The charts allow you to visualize the relationship between the sites, the objects and the variables. When qualitative variables have been included, the corresponding categories are displayed with a hollowed red circle.