Have a look at https://www.youtube.com/watch?v=KhI3fnS6oJw

StatHand - Interpreting the results of a principal components analysis in SPSS

and

https://stats.oarc.ucla.edu/spss/output/principal_components/

Hello Mohammad,

1. No. Initial communality simply informs you as to what proportion of a variable's score variance is shared with that of other variables in the set. Look at loadings (and/or pattern matrix, depending on whether you use orthogonal or oblique rotation of your chosen solution) to determine what variables are or are not affiliated with a given component, and how strongly.

2. No. Under the variance extracted, this is the proportion of score variance (in principal components analysis, all variance is assumed to be common/shared variance) that is captured by the first component (a linear combination of the variables in your set), not by a specific variable. These numbers can change if you rotate your solution.

If not rotated, component 1 will always account for the largest proportion of total score variance, followed by component 2, and successively lower amounts for the following components.

3. How best to weight component scores to create an ad hoc index depends on how you wish to use that index. If it is to predict scores on some criterion variable, then you'd want to weight the component scores to maximize the correlation between your composite/index score and the criterion variable. Multiple regression would be one simple way to investigate that. If some other goal is more important for you, your method to identify "best weighting" may well be different.

Good luck with your work.

Hello David Morse

Thank you very much for your answer

However, I still do not know which table in the PCA test in SPSS should I use to determine the main component?

and According to which table can I analyze and argue which is my first component and the second component to the end?

explain:

I also uploaded PDF file that is the result of my test

And I do not know which of my five variables is my first, second, third, fourth and fifth component.

Could you please check the attachment?

And help me determine the first to fifth components.

This is meant to be helpful. If you are choosing varimax and oblimin solutions you are not doing a Principal Components Analysis but a factor analysis and that is a completely different model. PCA sensu stricto is a data transformation which produces orthogonal components.

"Like donkeys and zebras. They seem to differ only by colour until you try to ride one"

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

On FA you may find these helpful:

https://www.youtube.com/watch?v=g_3kaSnq-DY

Interpreting SPSS Output for Factor Analysis

https://stats.oarc.ucla.edu/spss/output/factor-analysis/

hello Kelvyn Jones

Thank you for your guidance and submission of links and files

It was very useful and practical, and I used the analysis that was in these files

also want to say

I used the PCA method in EViews software and was able to find the coefficient and weight of each value in each component by PC1 to PC5.

I attached pdf file of this result.

Do you think I can use this result and PC1 as a coefficient and a weight for each variable?

I want to to multiply the coefficient of each variable that exist in PC1 in the original data of that variable and calculate the sum, and create an index based on the coefficients or weights in PC1

Or if it is possible i want to make these coefficients in standard between zero to one And create a set of coefficients with sum one.

Why not use the scores of pc1 or the rank of the values?

Hello Kelvyn Jones

Exactly I want to use the score of PC1 as the weight of each variable.

For example, the value of PC1 for the first variable I mean ZESTEGHRAZ is 0.585271, that I want to use it as the weight of this variable in the model.

it's correct?

the Scores are a ‘weight‘ of each variable using the loadings. To calculate by hand see

https://alexsingleton.files.wordpress.com/2014/09/8-principle-components-analysis.pdf

especially Equation 30

All software that calculates a PCA will allow you to calculate and store the 'Score Vector' as that is the point!

I briefly looked at eviews and found this:

http://blog.eviews.com/2018/11/principal-component-analysis-part-ii.html

See sub head "Score analysis"

Hello Professor Kelvyn Jones

Thank you very much for your explanation. I read the files that you sent for me.

if there is no problem i want ask you the last question

if I want use the scores of PC1 In the "Eigenvectors" table in EViews as weight...

Can I Determine the weight two variables that have a negative coefficient (marked with a red line in the attach file) by removing the negative sign of these two variables?

I mean, I put all the variables on an absolute value and ignore the negative sign. And then I do weighting based on a total of 1.

According to the table 1 attachment.

I know the reason for the negative coefficients, which is the direction of the special vector in the Biplot Figure

But because negative weights are incorrect, can I use this method to calculate weight of variables?

Are the weights in Table 1 correct? Or I have to determine the weights according to Table 2.

Thanks a lot.

No - the negative weights are not incorrect. They are telling you that the associated variable concerned is negatively related to that principal component - your input variables are not all going in "the same direction" in producing this component. The thing you are trying to measure/estimate - the component - is not a unitary concept in terms of the input variables you have specified. That is quite normal, if somewhat inconvenient for a single index.

https://www.theanalysisfactor.com/principal-component-analysis-negative-loadings/

If you want to do something, far better to drop the "offending" variable(s) from the input list if it is conceptually measuring something else.

I am of course presuming that all input variables have been measured in the same “direction“ so that on each one a high value indicates a lot of the underlying concept so that one does not measure wealth and another poverty. If you do then of course you would get meaningful positive and negative loadings.

thank you Professor Kelvyn Jones

allow me explain a little about the research and my question...

I'm researching about "the relationship between liquidity management and banks profitability"

These 5 variables (independent variables) are liquidity ratios extracted from the Banks financial statements. I need to know the weight or effect of each of these variables. Then I put each variable with its own weight (coefficient) in the main equation of my research and test it with EViews software.

the variables are:

loans, Non-current receivables, legal reserve, etc. (all numbers are in billions)

Now that the coefficient (weight) of each variable are specified in PC1, I see two variables have a negative sign. unfortunately I can't use a negative sign in my research equation.

Based on the research I have done and the files you sent:

in the Analysis of the numbers of PC1, it is found that the closer these number are to +1 or -1, they have more weight and effect , And the closer they are to zero, they have less weight .

finally I only want the weight of each variable, not the positive or negative correlation between the variables, and in my research I don't want use the variables with a negative sign weight or delete them.

My question was: can I put these PC1 coefficients (whose their sign is due to the positive and negative correlations between the variables) put in absolute value and use them as weights?

Exactly Like "Table 1" in the attachment named "weight"

Or should I be considerer a negative sign as negative weight?

I am sorry but the answer is the same as the last time you asked: "No". The 5 ratios do not move in a "unified way".

You seem to be wanting to use the resultant index to explain/model something else - if that is the case, there is no need to limit yourself to just one index and there should be no collinearity problems as the PCs are extracted to be orthogonal to each other,

Have a look at

Article Predicting Who Voted for Brexitt Through Ecological Analysis...

And that is me done - over and out.