PCA is based on R2 (coefficient of determination).

Beside some obvious syntactic hints (if two variables are correlated at almost unity (e.g. r= |0.98|) use only one, the most important concern is about the possibility to assign a 'meaning' to the obtained solution. This normally happens by looking at component loading and this requires the original variables refer to an 'homogeneous semantic domain'. iN other words if you have a sub-set of variables (A sub-set) dealing with 'blood cell populations' and a sub-set B dealing with 'heart functionality' measured on the same patients (statistical units) is much more convenient to perform two separate PCAs for A and B variables respectively and then to correlate the obtained A and B components. This will allow a much more robust and meaningful appreciation of what is going on. (see attached for an example).

Firstly, the eogen value more be 1 or greater than 1

Secondly the variance explained must be more than 20% (I. e total amount of variance explained by the factor)

The PCA allows to explore the links between variables and similarities between individuals. Principal component analysis or PCA is an extremely powerful tool for synthesizing and compressing information, very useful when there is a large amount of quantitative data to be processed and interpreted.

It is important to know that PCA is particularly useful when the variables in the dataset are highly correlated. The correlation indicates that there is redundancy in the data. Due to this redundancy, the PCA can be used to reduce the original variables to a smaller number of new variables (= principal components), the latter explaining most of the variance contained in the original variables. .

In the PCA, the search for axes carrying the maximum inertia is equivalent to constructing new variables of maximum variance. Each axis is associated with a variable called the principal component. So first of all, you have to choose the axes to take in consideration. This can be done in two ways, generally the one using Kaiser's criterion that consists in choosing only the axes whose eigenvalues ​​are greater than 1. Then in each axis, one searches for the variables which contribute the most to its formation. Thus, the first axes ( which must explain an acceptable percentage) correspond to the directions carrying the maximum amount of variation contained in the data set. In other worlds, the variables correlated with the first axes (usually with PC1 and PC2) are the most important to explain the variability in the dataset.

In the circle of the projection of the variables ( also called graph of correlations of variables) , it is the variables close to the edge of the circle that contribute the most to the axis information. Thus, the distance between the variables and the origin measures the quality of representation of the variables. Variables that are far from the origin are well represented by the PCA. You have to be sure that the points contributing the most to the axis are well represented on the axis (otherwise they must be put into additional elements). Finally, for more details, here is an interesting link about PCA. At the end of the text, the author has attached several bibliographical references on the subject of PCA. Good luck.

https://towardsdatascience.com/a-one-stop-shop-for-principal-component-analysis-5582fb7e0a9c

and in French version: http://www.sthda.com/french/articles/38-methodes-des-composantes-principales-dans-r-guide-pratique/73-acp-analyse-en-composantes-principales-avec-r-l-essentiel/

Hossem SAHRAOUI

In FDA speak the PCA's are evaluated when they are CQA's (Critical Quality Attributes). See:

https://pqri.org/wp-content/uploads/2015/10/01-How-to-identify-CQA-CPP-CMA-Final.pdf

Are you sure that it is PCA that is wanted and not FA

https://www.theanalysisfactor.com/the-fundamental-difference-between-principal-component-analysis-and-factor-analysis/

https://www.researchgate.net/post/How-can-I-decide-between-using-principal-components-analysis-versus-factor-analysis

The variables selected for PCA analysis should relate to each other in terms of co-variability. Then one can explain the percentage of variability in one variable with respect to other variables with different eigenvectors.

Thank you all for your relevant answers!

I recommend the insight by Kelvyn Jones , please first take note the thin line of the diffs and similarities between PCA and EFA to understand the nature of data suitable for each of the two and procedures involved.

The great statistician David Cox, clearly demonstrated that any kind of data values can eneter multivariate analysis. In the case of categorical variables the only point is that they must be transformed into binary (1/0, i.e yes/no) variables. This is very easily done in the case of multiple categories by splitting the original variable into n binary variables (with n = number of categories) (see attached).