Timeline for Does it make sense to use criteria from PCA to select the numbers of factors in a factor analysis?
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17 events
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| Mar 17, 2021 at 18:22 | comment | added | ttnphns | A question about the Cattell's scree-plot criterion | |
| Nov 9, 2020 at 22:08 | comment | added | ttnphns | (cont.) (ii) in FA itself, the most genuine criterion for the value of m would be the quality of reconstruction of the off-diagonal elements of the correlation (covariance) matrix, and not the amount of variance the factors explain. That were my main points. | |
| Nov 9, 2020 at 22:08 | comment | added | ttnphns | @RichardDiSalvo, Throughout my numerous comments to this current as well as the other Q, I expressed reasons for my feeling that preliminary criteria (1) Kaiser's, (2) Cattell's scree, and possibly (3) Parallel analysis - should be based on PCA rather than on EFA itself. My main reasons were two: (i) eigenvalues or explained variances corresponding to the m+1, m+2... factors are not "real" or "existing" because only m factors were modeled in the FA; | |
| Nov 9, 2020 at 20:48 | comment | added | Richard DiSalvo | @ttnphns I understand that with a lot of items the differences aren't likely to matter, but I don't I see why gain in explained variance is a bad plot to drop in instead of the eigenvalue plot (when using factor). I think you might be suggesting that there are other analyses in addition to the eigenvalue (or similar) plot for determining number of factors? That makes sense. But you said "the factor variances are only of modest value in judging if m is optimal or not"; if so, and since these will be related to the eigenvalues in some cases, how should we guess at a reasonable number of factors? | |
| Nov 9, 2020 at 20:40 | comment | added | Richard DiSalvo | @gung i don't think the differences are important with many items, but not sure about few items. in my work with 185 items factored into around 5 factors, scree (eigenvalue) plot and the marginal gain in var explained plot (based on a bunch of ML factor models) are nearly identical. i think on this site we have simulation/theoretical evidence that the "with many items this is not important" is true in general stats.stackexchange.com/questions/123063/… | |
| Nov 8, 2020 at 9:27 | vote | accept | user1205901 - Слава Україні | ||
| Nov 7, 2020 at 3:24 | comment | added | ttnphns | (cont.) So, @RichardDiSalvo, the (or at least one) objection to your idea to base the initial (tentative) choice of m on the eigevalues or on variances found in EFA is that the main goal of EFA is not maximizing explained variance - unlike PCA. In PCA, the more PCs you extract the more variance you explain. In FA, you have to find an optimal number of factors m and not m+1, even if m+1 may still enhance the prediction of correlations (e.g. due to overfitting). | |
| Nov 7, 2020 at 2:55 | comment | added | ttnphns | (cont.) But the goal of the modeling is to restore correlations by the m extracted factors, and not quite to give maximized eigenvalues or a nice scree of those. Since the factor extraction has been done, the factor variances are only of modest value in judging if m is optimal or not. | |
| Nov 7, 2020 at 2:55 | comment | added | ttnphns | As I've already mentioned there (see), it is perfectly logical to make the initial estimate of the number of factors in EFA by analysing the eigenvalues of PCA. Because PCA is a descriptive method yet akin to EFA. We need a descriptive method giving us all existing eigenvalues of the total variance in order to correctly appreciate such "rules" as Kaiser's and Cattell's, and, to an extent, the parralel analysis. Eigenvalues of EFA are already the result of modeling. | |
| Nov 7, 2020 at 2:25 | comment | added | ttnphns | A related thread stats.stackexchange.com/q/241032/3277, especially look in the comments. | |
| Nov 6, 2020 at 20:32 | comment | added | gung - Reinstate Monica | It's worth recognizing that FA & PCA perform the same arithmetic over a nearly identical matrix. So while the theory is quite different, and the interpretations are supposed to be different, the output isn't necessarily all that different in practice. As a result, it may be 'good enough for government work'. | |
| Nov 6, 2020 at 20:21 | answer | added | chl | timeline score: 3 | |
| Nov 5, 2020 at 21:58 | comment | added | Richard DiSalvo | @chl ok i did some reading & now I'm thinking, the scree plot of eigenvalues for PCA corresponds to the marginal gain in explained variance from the addition of the factor (component). but this just happens to be so for PCA. the most sensible thing (maybe) to drop into this role for factor analysis would then be the marginal increase in the variance explained by the factors (equivalent to -- and to me more intuitively phrased as since it looks like MSE -- the marginal decline in the sum of the uniquenesses i.e. variances of the errors from the addition of the factor). any thoughts appreciated! | |
| Nov 5, 2020 at 7:47 | comment | added | chl | You can do parallel analysis on FA results as well. For instance, the psych R package offers both ways (PCA and/or FA). It's just that even as a rough approximation PCA works quite well in this case. If you want to learn more about the subtle distinction between those two approaches, look for some of @ttnphns's nice answers related to this topic. | |
| Nov 5, 2020 at 7:22 | history | edited | user1205901 - Слава Україні |
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| Nov 5, 2020 at 3:42 | comment | added | Richard DiSalvo | I too am confused why PCA criteria are being used everywhere in factor analysis. It seems that factor analysis has very natural criteria to analyze, e.g. the mean uniqueness (a form of mean squared error), which is the same as 1 minus the common var explained. Plotting this as a function of the number of factors leads to a production possibilities frontier, and then arguments regarding tradeoffs between explanatory power and the number of factors can be meaningfully discussed. (relatedly, I'm not sure why PCA scree plots use eigenvectors rather than the cumulative sum of eigenvectors) | |
| Mar 27, 2020 at 11:12 | history | asked | user1205901 - Слава Україні | CC BY-SA 4.0 |