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Hi Greg. I am not super sure I understand what you mean, but will try to help! The principal components are axes explaining variation in your data (the variables you input). So high variance explained by a principal component indicates higher relatedness between the variables. If PC1 and PC2 cumulatively explain a super high amount like 90% of your variation, the story of your data is super clear! Pretty much all the relationships between your variables is explained by those two axes. Whereas if there are many principal components explaining very little variation, then the relationship is more complicated or the variables may not be related at all. A biplot can be used to visualize the relationships between the variables (the magnitude of a positive/negative relationship). But the PC values are important to add validity to those relationships. Again, if the PC1 and 2 axes explain 90% the relatedness between variables is going to be much more reliable than if they were cumulatively explaining 20%. If you are interested in a deeper dive, you can look at the individual PC scores for each variable individually in the summary output to look the distance between variables along each PC axis. If the visual biplot is not answering your question, then maybe doing this could help. Does any of this answer your question? Apologies if I am misunderstanding.

Hi! The main RDA assumption is linearity between the predictor and response. Besides that checking for those variance inflation factors like I do in my video is really what's important. Hope this is helpful!

Thank you! It's definitely possible to add in categorical data like that - but you'll likely have to do what's called dummy coding. With dummy coding all the categorical factors would become their own columns and be assigned a 0 or a 1. So with the example you gave, rather than vegetation growth habit being the column name, there would be a separate column for herbaceous, shrub, and tree. If observation 1 was in a tree habitat, then herbaceous and shrub would be denoted with a 0 and tree with a 1. You can think of it like a presence-absence matrix for the category. I hope this is helpful! I will definitely add a PCoA video to my list - I am hoping I can be more active with the semester winding down. :)

Thanks! Yes you can, numeric variables are perfectly fine. Although if you end up with a whole bunch of variables consider doing some dimensionality reduction.

Thank you so much! I have a few more similar videos, but am planning on starting up making more soon! I just came back from 5 months of field work so I am just getting back into the groove of things! Those overlapping labels are always the worst! I have trouble doing it with the biplot function because it's a bit limited in the level of customization you can do. An alternative would to use the fviz_pca_biplot() function in the 'factoextra' package. Similarly the first thing you would put in the brackets would be the name of the PCA object. With this function there is an argument you can add in the brackets called repel which can be 'repel = TRUE' or 'repel = FALSE'. If you try setting it to TRUE it might solve your problem. Another option which is a bit of a 'cheat' is what I usually do to be honest because it is much simpler. For some reason I find any text label repel code I find doesn't really do what I want it to. So I save the plot but as a metafile rather than an image or however else you generally save it. I then insert the metafile into PowerPoint. Here, I can right click, go to group, then ungroup. This unconstrains the text and any other discrete plot element so you can edit it. I use it to move around my labels so they aren't on top of each other and sometimes to revise some variable names to make the aesthetic better. Just be careful to not accidentally alter your plot itself! I hope this is helpful but please let me know if you have any questions!!

Hi! Yea sorry about that it was due to a monitor issue. You can find the code on my github as well if that's helpful. github.com/nikkireg1/Redundancy-Analysis

@@justonebirdsopinionMany thanks again 🙂

Hi! Are you referring to the text on the rda biplot? If so, there is some ggplot code to repel overlapping text. But to be honest, I do a much easier perhaps less 'correct' method to fix my plots when stuff like this happens. I save the plot as a metafile and then insert it in powerpoint. Then if you right click and choose 'ungroup' you will be able to modify individual aesthetic elements of the plot. So you would be able to shift around any overlapping text boxes and even change the variable label if you want. Does this answer your question or am I misinterpreting?

@@justonebirdsopinion Exactly ! I had no Idea of this. it is amazing! Thank you. now my graph is way more readable for my propessor to read. Thank you so much ! it is really good explantion .😇

Hi Kendra! I personally still find it relevant to include columns even if all the values are zero. So personally I would keep data where you know a host does not have a disease of interest. It is interesting how it aligns with the other data frame in the procrustes, even if it is absent in the other dataset as well! I think including it creates a more complete story and there’s nothing fundamentally wrong with including it that I can think of. But don’t be afraid to omit if doing so is more relevant to the question you’re asking! Regardless, make sure both data frames line up (whether that means adding columns where everything is absent or omitting data for which you are missing the pair). Thank you and happy coding! Please let me know if this is helpful or if you have any other questions!

Hi Miguel! When you are going through the step that is equivalent to my env_stand, are you including all the variables for the analysis? Make sure to include any variables that may have been transformed; cbind() them with the non-standardized values. When you do your first rda, all the variables should be there. But after the step() function some should be omitted. I guess my first suggestion would be to ensure that env_stand is including all the variables you want before putting it in the first rda analysis. Are you doing that? If so, let's chat some more. Happy coding!

Hi Laura! Thanks for your comment! The error you are getting is indicating an issue with your explanatory (x) variables. Since your output is only showing RDA1 and PC1, I am thinking that the explanatory variables you are using are highly correlated - which is causing the crash with the step function. The RDA1 output is essentially saying that all the variance explained can be attributed to this one axis, and PC1 is indicating that there is residual noise that cannot be explained by a RDA axis and is likely due to high correlation as well. My suggestion would be to start with assessing for collinearity first using the vif.cca function. This will tell you if there are any variance inflation factors in your explanatory variables that is messing with the model output. You can also check to see if your explanatory variables are highly correlated using a Pearson's r. The R script for this would be "cor(df$vars, method = 'pearson')". Omit variables that are highly correlated. If everything looks good on that front, you may be missing explanatory variables. So if there's anything you omitted from the beginning, perhaps consider adding it back in. Or it is possible that with the data you have a RDA may not be the best method to use. If you want to chat about this in more detail or have me look over your data - feel free to email me as well! If you go to the About section in my channel profile you will find a link to my website which has my contact information. I hope this at least helps you get started with your problem-solving! Good luck!

@@justonebirdsopinion Thank you very much, this was really helpful. Unfortunately I can't use vif.cca because the step function stops before having concluded, due to the error I mentioned in the first comment. I've also found the function redun() that seems to work on my data; anyway I can't find a lot of literature using this one, whereas rda() seems to be much more used. What do you think about it?

Hi! You can find the R Script and data on my GitHub at this link: github.com/nikkireg1/Redundancy-Analysis. Happy coding! Let me know if you have any questions!

@@justonebirdsopinion Thanks so much for your videos. I would like to ask if you could make vidoe on doing a mantel test and also canonical correspondency analysis. One question, is what is the major and underlying assumption for using a redundancy analysis to doing a canonical correspodnign analysis? Thanks for your time.

@@justonebirdsopinion I have different categories of environmental variables such as the biotic factor (temperature, windspeed), spatial factor (longitude and latitude), and soil properties (soil ph) and I would like to perform Canonical Correspondence analysis. I successfully performed the analysis but I don't know how to customize the plot. I want to customize the different categories of environmental variables by allotting them with different colours to differentiate spatial from biotic. In addition to this, how can I group the species based on a variable such as elevation etc? I would also appreciate it if you can give me your email. Thanks

@@farmIntegral Hi! I will work on making a CCA video and Mantel Test video soon and let you know when it's posted (hopefully the first one within a week)!

@@farmIntegral Hi! Here is a link that might be relevant to helping you group environmental variables by color: stackoverflow.com/questions/61348422/how-to-create-ordination-plots-with-different-species-groups. If this isn't what you're looking for I'm happy to help problem solve more than this! You can reach me via email at nicole.regimbal@mail.utoronto.ca. Looking forward to hearing back from you and happy coding!

Hi! You can now find the R script on my GitHub. Here is the link: github.com/nikkireg1/Linear-Regression

Thanks alot 🙂

Hi! Thank you :) I'm glad the video was helpful so far! Oof that sounds frustrating! It sounds like this could be largely due to autocorrelation between your species. You can create a correlation matrix in R and omit anything that is inflating your results (I suggest omitting anything with a value greater than 0.7 or less than -0.7). Here is the code for that (with df being the name of your dataframe): pearson <- round(cor(df, method = 'pearson'), digits = 2 # rounded to 2 decimals ) This will output a table of all pairwise correlations. Since you have 159 species, that may be a lot to sift through (and kinda painfully).... hopefully creating a visual will make this a little easier - you can use the "corrplot" package to do this. corrplot(pearson, method="circle") So if there's a high correlation between two values, omit one from the analysis. If taking out correlated variables doesn't help, then yes try to take out variables that you think are less important. Removing variables from PCAs have pros and cons, but really there's no right or wrong answer as long as you think through how it will affect your PCA. Here is a link to a post on StackExchange that goes into that a bit more: stats.stackexchange.com/questions/50537/should-one-remove-highly-correlated-variables-before-doing-pca I hope this helps you out! Let me know if you have any questions or ever need another pair of eyes on the data :)

Thanks so much! You are going to want to do a redundancy analysis (RDA) instead - it is essentially just a PCA with explanatory predictors for the response. I have a video on this on my channel, but let me know if you have any questions :) Good luck with your analysis!

Thanks, Liam!

Responding here with my other account so if you respond I'll get a notification😂

@@liamtaylor7710 Hi Liam! What you are thinking of is a RDA rather than a PCA. An RDA tries to fit the composition (presence-absence) to explanatory variables (environmental predictors). I will for sure make a video on this so stay posted!!

RDA stands for redundancy analysis by the way!

​@@justonebirdsopinion thanks. You're an absolute legend!

@@liamtaylor7710 Haha so glad you think so! The RDA video is posted - I hope it's helpful! If it's not what you were looking to do, just let me know and I'd be happy to chat to come up with the proper analysis. Please don't hesitate to comment if you have any questions!

So glad this could be helpful for your ciliate data! Good luck with your project!!