Hello Jimmy,

this will help

Penn State University (n.d.). Lesson 11: Principal Components Analysis (PCA). STAT 505: Applied Multivariate Statistical Analysis. URL: https://onlinecourses.science.psu.edu/stat505/node/58

Cheers

Dear Jimmy,

The PCA is a multivariate, statistical and exploratory analysis method that can be used in the interpretation of a many-variable data matrix. The objectives of PCA are:

- To discover or to reduce the dimensionality of the data set.

- To identify new meaningful underlying variables.

Your data must meet some assumptions (for valid result) like, continuous variables, linear relationship between variables, sample adequacy, suitable for data reduction, homoscedasticity, multicollinearity, no extreme outliers, normality of residuals etc.

You have to extract the PCs based on eigen values (>1).The first PC accounts for maximum variability in the data, and each succeeding component accounts for less data variability than the previous one.

I have seen your PCA results - Are the bold values indicating prominent loadings? If it is so, the PC1 can be explained by B3. But, in case of PC2 and PC3 there is a little bit of confusion. Both the components show prominent loadings of B1 - examine this. See the link given for understanding the interpretation of PCA outputs.

I have applied PCA in understanding the hydrogeochemical processes. Read the paper published in July, 17 (link given).

Hope you will understand the PCA and its application.

Give your feedback. Good wishes

http://statistics.ats.ucla.edu/stat/spss/output/principal_components.htm

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Dear Anthony,

Thanks for providing the link. I will read this material carefully.

Dear Asit,

Thanks a million for your explanation. And you are right, The bold values indicating prominent loadings. The first PC I can explian well from my knowledge. But I have the same confusion about PC2 and PC3 . So here is the thing.  I don't know how to differentiate the differences between PC2 and PC3. 

Regards

Jimmy

Dear Jimmy,

The result you given - it's not the good output. You run the PCA several times - initially with all variables - examine and see which variable is not suitable for the model (based on statistical parameters - assumptions), exclude that variable and again run and examine - in this way you will get the best result. Already, I told it's an exploratory analysis. So, you have to explore for the best model.

Best wishes - Dr. Asit

Dr. Khalid Hashim - Thanks for recommending the answer. Regards - Dr. Asit

Dear Dr.Asit,

Thanks for your suggestions. I will have a try.

Regards

Jimmy

Dear Researchers,

I recommended Asit Kumar Batabyal explanations about pca. Thanks to asit for beautiful explanations.

THE EXPLORATORY  PROPERTIES OF PCA ARE VERY ATRACTIVE. HOWEVER, IT IS IMPERATIVE THAT IT BE USED ON THE BASIS OF HYPOTHESIS TESTING. YOU GENERATED THE PROBLEM AND YOUR EXPERSTISE AND INSIGHT SHOULD SUGGEST WHAT TO EXPECT AS AN ANSWER, WHICH THE PCA SHOULD BACK UP...OR NOT

Dear Gian,

Thanksfor your recommendation. I will read this paper carefully.

Regards

Jimmy

Dear David,

Thanks for your explaination.

Regards

Jimmy

first see correlation and find the relevant variables then proceed for PCA to see the weightage of each variable