What does all this mean? I’m a factor analysis ‘noob’ and although I’ve read a book, it didn’t tell me everything apparently.
Since the chi square statistic is so high and the p-value so low, it would seem that the data is close to being coplanar (2 dimensions) within the 6-dimensional space. Yet that only accounts for 89.4% of the variance (am I interpreting this right?)
Also, I thought factors were orthogonal to each other, so how can both factors have positive loadings for every variable?
And what do the uniquenesses mean?
> factanal(charges[3:8],2) Call: factanal(x = charges[3:8], factors = 2) Uniquenesses: APT CHELPG Natural AIM Hirshfeld VDD 0.217 0.250 0.082 0.052 0.005 0.033 Loadings: Factor1 Factor2 APT 0.609 0.642 CHELPG 0.657 0.564 Natural 0.571 0.769 AIM 0.382 0.896 Hirshfeld 0.910 0.408 VDD 0.844 0.504 Factor1 Factor2 SS loadings 2.817 2.544 Proportion Var 0.470 0.424 Cumulative Var 0.470 0.894 Test of the hypothesis that 2 factors are sufficient. The chi square statistic is 77.1 on 4 degrees of freedom. The p-value is 7.15e-16 >
The chi-square statistic and p-value in factanal are testing the hypothesis that the model fits the data perfectly. When the p value is low, as it is here, we can reject this hypothesis – so in this case, the 2-factor model does not fit the data perfectly (this is opposite how it seems you were interpreting the output).
It’s worth noting that 89.4% of the variance explained by two factors is very high, so I’m not sure why the ‘only’.
The factors themselves are uncorrelated (orthogonal) but that doesn’t mean individual measures cannot correlate with both factors. Think about the directions North and East on a compass – they’re uncorrelated, but North-East would ‘load’ onto both of them positively.
Uniquenesses are the variance in each item that is not explained by the two factors.
This link might be useful to your interpretation.