# Calculating principal component scores after PC analysis

I am carrying out a study to find out meteorological patterns using daily met observations including around 30 met parameters (each day is a case with 30 variables). My methodology includes carrying out a PCA:

1. To reduce 30 variables to smaller number of PCs.

2. Find out the PC scores for all days in the ten years.

As first I standardized all 30 variables using SPSS function ANALYSE>>> DESCRIPTIVE. Now that I have got 6 PCs explaining 80% of variance of original data, I have to calculate the PC scores. My questions are as under;

1. Should I use Component Matrix OR Rotated Component Matrix for PC score calculation?

2. Should I multiply the component/Rotated component matrix with original variable matrix (un-standardized) OR i should multiply it with standardized form of original variable matrix?

I think it can be much easier than you realize. In the SPSS Factor Analysis menu click Scores...Save As Variables...(and then I normally choose the Regression method, which simply weights according to component loadings).

• I just went through a document stating that the variables we obtain by following your mentioned procedure are principal "factors" and not principal components. The document also stated that inorder to get PCs from these PFs, we have to go to Transform >>> Compute Variable and multiply the PFs with the square root of the total variance explained by that PF. Need your comments. Commented Jun 28, 2011 at 4:05
• You probably misunderstood the documentation. When you extracted factors by PC method (that is, factors are pr. components) then regression method found under Scores button will save exact component scores for you - same scores you might obtain if calculate yourself by matrix algebra. Commented Jun 28, 2011 at 17:13
• Actually I have calculated the score by; PC Score = SUM WiXi (i=1,2,3...p). where Wi = Component Score coefficient from rotated component matrix and Xi= standardized variables. the resultant scores that i am getting are different from the Extracted Factors from PC method. :( Commented Jun 29, 2011 at 8:20
• Let's be really precise with terms: are the scores you calculate not the same as (or at least correlated at about .99 with) the scores obtained by clicking Scores...Save As Variables...Regression method? Commented Jun 29, 2011 at 22:18
• No. The calculated score are not even near the "obtained" scores. I have tried following steps in a hope to understand the reason but nothing explains why it is so: 1- Standardized the rtated component matrix scores and then multiplied the standardized variable matrix (the scores were even larger). Commented Jun 30, 2011 at 2:43