I conducted a distance based redundancy analysis (dbRDA) to explore the relevance of some environmental variables in explaining the patterns of the distribution (i.e., spatial and temporal) of two organisms. I used a Bray-Curtis resemblance matrix based on the abundance of both organisms and the environmental variables were used as predictors. Results showed that along Axis 1 (along this axis seasons were separated) the "% of fitted" was 81.3% and the "% of total variation" was 38.5%. I do not understand the difference between "% of fitted" versus "% of total variation" in this analysis.
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$\begingroup$ I suspect you are referring to a particular implementation of the method, but this is actually a more general question related to constrained ordination. $\endgroup$– Gavin SimpsonCommented May 6, 2015 at 22:56
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$\begingroup$ You question needs more context and detail to explain what it is you are showing, where it came from, and what the setting is. Not everyone (in fact few people) here will be familiar with dbRDA or even multivariate analyses of thius type. $\endgroup$– Gavin SimpsonCommented May 6, 2015 at 23:04
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$\begingroup$ Thank you for your prompt answer @GavinSimpson. I conducted a dbRDA using a Bray-Curtis resemblance matrix based on the daily, spatial and seasonal abundance of two organisms and with with environmental variables used as predictors. Results showed that along Axis 1 (along this axis seasons were separated) the "% of fitted" was 81.3% and the "% of total variation" was 38.5% $\endgroup$– BrendaCommented May 7, 2015 at 0:12
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1$\begingroup$ @StasK dbRDA is distance-based RDA and RDA is Redundancy Analysis (reduced rank regression sensu Rao), essentially a reduced-rank multivariate multiple regression. In dbRDA, one embeds a distance matrix in a Euclidean space using principal coordinates analysis, and then take the principal coordinates and use them as the response matrix in in the RDA. $\endgroup$– Gavin SimpsonCommented May 7, 2015 at 2:18
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1$\begingroup$ @StasK Bray-Curtis is the name of a distance/dissimilarity metric: en.wikipedia.org/wiki/Bray%E2%80%93Curtis_dissimilarity This is the distance matrix that is to be embedded in principal coordinates & then ordinated using dbRDA. It's popular in ecology for measuring dissimilarity between samples/assemblages. In RDA, the abundance is measured as a set of $m$ orthogonal linear combinations of the predictor variables. It all starts to get messy when transformations & the distance-based version is being used. $\endgroup$– Gavin SimpsonCommented May 7, 2015 at 2:21
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In a constrained ordination such as dbRDA, axes are extracted that are linear combinations of predictor variables that best explain "variance" in the multivariate response matrix. We can explain the "variance" explained by these linear combinations of the predictors in two ways:
- The first way, which you label as "% of fitted", is simply what proportion of the total "variance" explained by the set of linear combinations (constrained axes) is accounted for by each separate linear combination (or axis). This tells you, of the "variance" explained, which axes account for most of this total.
- The information in 1. above is restricted to an assessment of the explained variance. But this is not the total "variance" in the multivariate response matrix. How much of the "variance" explained by each constrained axis as a proportion of the total "variance" in the response matrix is what is given by "% of total variation"
You don't say where this information came from, but it may well be that the information is provided in terms of the predictors themselves and not the axes, but the distinction above holds; how much of the explain "variance" is contributed by each axis (variable), and how much of the total "variance" is explained by each axis (variable.
answered May 6, 2015 at 23:03