Redundancy analysis (RDA)

Redundancy analysis (RDA) is part of:

  • ADA Advanced Data Analysis on Multiple tables software

  • 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 Redundancy Analysis

Redundancy Analysis (RDA) was developed by Van den Wollenberg (1977) as an alternative to Canonical Correlation Analysis (CCorA).

Redundancy Analysis allows studying the relationship between two tables of variables Y and X. While the Canonical Correlation Analysis is a symmetric method, Redundancy Analysis is non-symmetric. In Canonical Correlation Analysis, the components extracted from both tables are such that their correlation is maximized. In Redundancy Analysis, the components extracted from X are such that they are as much as possible correlated with the variables of Y. Then, the components of Y are extracted so that they are as much as possible correlated with the components extracted from X.

Principles of Redundancy Analysis

Let Y be a table of response variables with n observations and p variables. This table can be analyzed using Principal Component Analysis (PCA) to obtain a simultaneous map of the observations and the variables in two or three dimensions.

Let X be a table that contains the measures recorded for the same n observations on q quantitative and/or qualitative variables.

Redundancy Analysis allows to obtain a simultaneous representation of the observations, the Y variables, and the X variables in two or three dimensions, that is optimal for a covariance criterion (Ter Braak 1986).

Redundancy Analysis can be divided into two parts:

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

It is also possible to use Partial Redundancy Analysis that adds a preliminary step. The X table is subdivided into two groups. The first group X(1) contains conditioning variables which effect we want to remove, as it is either known or without interest for the study. Regressions are run on the Y and X(2) tables and the residuals of the regressions are used for the Redundancy Analysis step. Partial Redundancy Analysis allows you to analyze the effect of the second group of variables, after the effect of the first group has been removed.

Biplot scaling in Redundancy Analysis

XLSTAT offers three different types of scaling. The type of scaling changes the way the scores of the response variables and the observations are computed, and as a matter of fact, their respective position on the plot.

Results for Redundancy Analysis in XLSTAT

If a permutation test was requested, its results are first displayed so that we can check if the relationship between the tables is significant or not.

Eigenvalues and percentages of inertia: In these tables are displayed for the constrained RDA and the unconstrained RDA the eigenvalues, the corresponding inertia, and the corresponding percentages, either in terms of constrained inertia (or unconstrained inertia), or in terms of total inertia.

The scores of the observations, response variables and explanatory variables are displayed. These coordinates are used to produce a summary plot. The chart allows 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.

Screenshots