rda() function - only one principal component output

[jfloret23]

Dear Jari

I am contacting you regarding your R package RDA. Your package has been very helpful to identify the factors that influence the ecology of Arabidopsis thaliana. However, I have observed that the output shows only one principal component. This seems to never change, regardless of the phenotype I quantified. Do you know what might be causing this? Could it bias the results of the analysis?

My data are structured as follows:

• Y: A single column with either Presence/Absence data (0/1) or Flowering Time (discrete data) — a 1x389 matrix
• X: 26 ecological factors (a 26x389 matrix), standardized and homogenized. I attempted to reduce multicollinearity among the factors, but some correlations remain.

When I run the RDA, the output contains only one principal component (please see the attached code and output).

Thank you in advance
Justine

[gavinsimpson]

At a guess, for the 0/1 responde at least, I would suggest that one or more of the very many variables you included as predictors can perfectly explain the variation left over in the response after extracting 1 RDA axis. If so, this would be an phenomenon called "separation".

[jarioksa]

Your response matrix (Y) is univariate: you have only one response variable in your one-column matrix. You should not use multivariate methods with univariate data. You should regression type methods, such as simple linear model (lm), generalized linear models (glm), generalized additive models (package mgcv), or any other univariate models.

[jfloret23]

Thank you Gavin and Jari for the quick answer !

If I understood correctly your feedback: I should try a second RDA without the factor explaining the variance in RDA1 ?

I have already tried glm model on my data and the output of the RDA and the glm are matching pretty well, same when I am looking at regression between the phenotype and the explanatory variable.

I also try to add the phenotype in the explanatory variable to see if I would have a second axis but no. I would like to understand why ? Is the problem coming from the univariate penotype matrix ? Do the results of the RDA are still valid ?

[jarioksa]

If you have only one column in your dependent data, your data are univariate. With univariate data you have only one axis. In RDA you will have one axis (RDA1) corresponding to the fitted values (RDA1), and a second axis (PC1) corresponding to residual errors. You should use RDA or PCA only if you have several dependent variables. That is, you need to have dependent data with more than one column. For multivariate analysis, you typically need more than two, three or six variables. However, you should not try to craft multivariate data, but you should use methods that are adequate for your problem. I think that in this case regression analysis is the tool you should use.

For univariate data, RDA and linear regression should be equivalent. Even the model coefficients should match. The only difference would be that in RDA the univariate regression would be analysed with permutation tests and in regression with parametric ANOVA.