Yes, it's the basic one. You can see the scree plot and mind your theory please.

Muhammed Ashraful Alam Dear,

In scree plot only one point is above the cut point. So, should i go with just first principal component

What is the cumulative proportion of the largest eigenvalue? That is what counts. If the first one, two or three eigenvalues account for up to 95% cumulative, say, then the first one, two or three principal components are relevant respectively.

Several methods have been proposed for determining the number of components that should be kept for further analysis and criteria eigenvalue > 1 is just ones.

Therefore, use the number of components that agrees with the goals of your analysis and balance the variance explained with the noise.

Yes, you can according to the book but you have to think your reality too. You have to compromise between your theory and reality.

How many components do you have? If you have the usual 4, you can decrease the number of component to for example to 3. and then check again their eigenvalues. Also, what is your sampla size?

Dear S. Béatrice Marianne Ewalds-Kvist

I have 200+ samples from two sites and analyzing total 30 characters of these. As there are few morphological variations so I got just one eigenvalue more than 1 explaining 66.024% variance while 2nd eigenvalue was about 0.3 with 8.8% variance.

So, is it possible to explain the data on the basis of loading values of PC1 or may I also consider PC2 (8.8% variance).

Dear Muhammed Ashraful Alam

I have 200+ samples from two sites and analyzing total 30 characters of these. As there are few morphological variations so I got just one eigenvalue more than 1 explaining 66.024% variance while 2nd eigenvalue was about 0.3 with 8.8% variance.

So, is it possible to explain the data on the basis of loading values of PC1 or may I also consider PC2 (8.8% variance).

Dear Roberto Molteni

Thank you so much for your kind response and time

Actually, I have 200+ samples from two sites and analyzing total 30 characters of these. As there are few morphological variations so I got just one eigenvalue more than 1 explaining 66.024% variance while 2nd eigenvalue was about 0.3 with 8.8% variance.

So, is it possible to explain the data on the basis of loading values of PC1 or may I also consider PC2 (8.8% variance).

Dear Muhammad Abrar Yousaf

There are several assumptions to be checked before applying the Principal Components Analysis.

It could be that your 30 variables suffer of multi-collinearity problem. Therefore, collinear terms should be combined or otherwise eliminated prior to factor analysis.

Dear Muhammad Abrar Yousaf,

I emphasize the last Roberto Molteni 's post because it is important to detect redundant information to avoid its influence if any. Among the variables with the highest factor loadings on the first axis, take the most highly correlated, and examine whether they are different ways of measuring the same. When this happens, it is not a latent factor but an artificial one that is better to put right. An axis explaining so much variability of the data suggests a concept that summarizes the information of the variables that make it up. Keep in mind that this concept explains the observed differences between the objects since you apply PCA and not EFA.

D would try to include the second axis and even the third to have a better view of the differences between the objects. With the FactoMineR package, you can take sites as an illustrative variable. D

It is more advisable to perform a confirmatory factorial analysis of the proposed one-dimensional model

If you have got only one eigenvalue above 1, this is clearly suggesting that your scale is one-dimensional. In line with Cristian Ramos-Vera's suggestion, you can test the one-dimensional scale using CFA/SEM which will provide you with an objective fit measure to examine the goodness of your factor solution.

I emphasize the last Molteni 's post because it is important to detect redundant information to avoid its influence if any.

Dear Mehmet Mehmetoglu thank you so much for your kind response and suggestion. I will definitely follow your recommendation.

Dear Jorge Ortiz Pinilla thank you so much for your kind guidance. I will work on it.

Dear Cristian Ramos-Vera thank you for you kind response. I will work on your suggestions.

Only PCs with eigenvalue >1 are taken into consideration (Kaiser 1960).

Kaiser HF (1960) The application of electronic computers to factor analysis. Educ Psychol Measur 20:141–151

Thank you dear F. Bouteldjaoui

Variance is the most important part of PCA. I would take as much PCAs as I need to preserve at least 90% of the main data. Now, again, classification performance has nothing to do with PCA as PCA only reduces the data, it doesn't assure better performance. Having said that, PCA-1 & PCA-2 may have a total variance of 95% but may not classify the data better. Rather, PCA-1 and PCA-100 may classify the data better even if they have a total variance of 85%.

Azmain Yakin Srizon Dear,

thank you so much for such comprehensive details. This really solved my problem.

PCA technique extracts the eigenvalues and eigenvectors from the covariance

matrix of original variables. PCA is designed to transform the original variables into new, uncorrelated variables (axes), called the principal components, which are linear combinations of the original variables. Principal components therefore, means the most important variables in the data set that can explain the important processes taking place in the medium. For the interpretation of any research data

An eigenvalue explains the significance of a factor and the factor that has the maximum eigenvalue is considered the most significant. Eigenvalues of 1.0 or greater are considered significant. Absolute loading values greater than 0.75 correspond to factor loadings classified as ‘strong’ while, loading values between 0.75 and 0.50 corresponds to ‘moderate’, and loading values between 0.50 and 0.30, are ‘weak’. This means that, you do not have to limit your interpretation only to eigenvalues greater than 1. You could combine FA and PCA to determine the most important factors responsible for the interpretation of your data. In this regard, F1 corresponds to PC1, F2 corresponds to PC2............... etc. I agree with Azmain Yakin contribution.