Rotating a Principle Component Analysis Error

[Ricky Gettys]

Hi, I am running Stata SE 15.1 (August 7th update) on Windows 10.
I am doing a PCA on 29 variables,

pca var1-var29

but when I rotate only 4 components using the command:

rotate, comp(4)

or

rotate, f(4)

it runs as if I just input

rotate

meaning it outputs 29 components (see sample output below)

. rotate, comp(4)

Principal components/correlation        Number of obs    =    130,053
        Number of comp.    =         29
        Trace    =         29
Rotation: orthogonal varimax    (Kaiser off)    Rho    =     1.0000

            
Component      Variance    Difference    Proportion    Cumulative
            
Comp1       6.44883    1.12733    0.2224    0.2224
Comp2       5.32149    1.92512    0.1835    0.4059
Comp3       3.39637    1.41976    0.1171    0.5230
Comp4       1.97661    1.06077    0.0682    0.5911
Comp5        .91584    .0945092    0.0316    0.6227
Comp6       .821331    .0857374    0.0283    0.6511
Comp7       .735593    .0278702    0.0254    0.6764
Comp8       .707723    .0658892    0.0244    0.7008
Comp9       .641834    .0432065    0.0221    0.7230
Comp10       .598627    .051037    0.0206    0.7436

Any suggestions? Am I inputting this wrong or is it an error in Stata?

Is anyone else having this issue?

[Phil Bromiley]

You didn't get a quick answer. You'll increase your chances of a helpful answer by following the FAQ on asking questions - provide Stata code in code delimiters, readable Stata output [what you posted is extremely hard to read], and sample data using dataex.

When I played with it (I couldn't replicate your numbers since you didn't provide data), I do get slightly different numbers with the factor option on rotate. The command line documentation says:

factors(#), and synonym components(#), specifies the number of factors or components (columns of the loading matrix) to be rotated,
counted "from the left", that is, with the lowest column index. The other columns are left unrotated. All columns are rotated
by default.

It may be that this means it keeps all the factors but only rotates the number you select.

[William Lisowski]

I commonly see "principal component analysis" used as shorthand for "factor analysis using principal component analysis for factor extraction", but the two are not the same. This confusion is enhanced by SPSS's apparent lack of a separate command for doing principal component analysis other than as the first step of a factor analysis. Wikipedia's discussions of principal component analysis and factor analysis help clarify the distinction. In particular, from the article on principal component analysis,

PCA is generally preferred for purposes of data reduction (i.e., translating variable space into optimal factor space) but not when the goal is to detect the latent construct or factors. ... Factor analysis is generally used when the research purpose is detecting data structure (i.e., latent constructs or factors) or causal modeling.

It is possible that a more appropriate initial command for your objective than

pca var1-var29

would have been

factor var1-var29, pcf

I will also note that the Stata Multivariate Statistics PDF included in your Stata installation and accessible from Stata's Help menu has much more to say about this, including a warning about the inadvisability of rotation after a factor analysis, in the sections on the rotate command and on pca postestimation.

[William Lisowski]

Excuse me, in the final paragraph of post #2, I meant to write "inadvisability of rotation after a principal components analysis".