Hi, I don´t understand well, what you want to do, but in the case you want to analyse both data, qualitative and quantitative you should do a PCA or a canonical analysis...but, it deppends on your question, both type of data I think you can use it in the same analysis. Sorry I have not been of great help!

Cheers!

The qualitative characters are scored as follow (1,2,3,4,5,...etc), whereas the quantitative characters are scored using the actual length, width ,... etc. (Um or mm or cm). Can I use these mixed data directly to get a PCA (and/or cluster analysis) , or there is a step (or multiple steps) should be done to get the PCA?

PCA really assumes data are interval or ratio scale. Your qualitative characteristics may be ordinal (e.g. if 2 is greater than one in a meaningful sense). In this case you need to make a judgement call about whether they can be said to approximate an interval or ratio scale.

They may represent distinct groups, i.e. the numbers are arbitrary codes applied to different groups. I cannot tell from your description. In this case you absolutely cannot be doing a PCA with the qualitative variables.

I can possibly help more if you tell me more about what the variables are and the question you are asking.

Harry

Thank you Dr. Harold Matthews for your answer.

For qualitative characters, I usually use arbitrary codes, they don't reflect any evolutionary hypothesis

for example

character (1): Flower color; States: white 1, red 2, yellow 3

character (2): Corolla length .....mm

character (3):seed surface, States: smooth 1,reticulated 2, papillose 3

character (4): seed length.... mm

character (5): seed width ....m

Can I use a data matrix constructed from the previous data to get a PCA

Hi Asma,

Character 2, 4, and 5 are interval scales. You could do PCA on them, if you first standardise their scales.

Characters 1 and 3 are categories and are not suitable for PCA.

What is your research question? Do you really need to do a PCA?

Harry

I am studying the taxonomy of the genus Ononis (Leguminosae),so I am trying to use multivariate tools to assess the similarities (or dissimilarities) between taxa. I want to perform a morphometeric analysis using a large number of herbarium specimens belonging to that genus.

OK.

Firstly, I realise now that some people do use categories in PCA. The categorical data would need to be recoded as "dummy variables".

https://www.analyticsvidhya.com/blog/2015/11/easy-methods-deal-categorical-variables-predictive-modeling/

There are different opinions regarding whether this is valid or not and I think I have not fully understood the issues.

However, I would approach the problem more simply I'd suggest:

a) do a MANOVA with taxa as the independent variable and characteristics 4, 5 and 2 as dependent variables

b) do two separate Chi-squared or Fisher's exact tests testing for differences in characteristics three and one, dependent on the taxa.

You could also frame it as a classification task using (for example) Linear Discriminant Analysis to build a model to predict taxa from the continuous characteristics and (dummy coded) categorical characteristics.

Hope this helps

Harru