Question about PCA

I am using PCA on a dataset that consists of 141 neurons, with firing rates from every neuron taken at successive time bins (columns are different neurons, rows are different time-points). I am plotting the first three PCA casewise scores to visually express how the neural population is changing across time. I would also like to express the percent of explained variance of each of these 3 PCs, to help interpret this plot.

The Statistitxl PCA analysis gives me the '% of Var' at the top of the results page. However, I believe this is the % of Var for PCs of the column X column covariance matrix, while the casewise score PCs are from a row X row covariance matrix. So I believe the '% of Var' does not apply to the 1st 3 casewise scores PCs, and I should transpose the data and re-run the PCA to get the corrext % of Var calculation. However, I'm not sure. Any insight? Sorry if this is confusing - please ask me to clarify if necessary.

Comments

  • I am not sure I understand you, so my reply may be quite wrong.

    Anyway, in factor analysis, especially before the development of cluster analysis, it was quite common to use the technique as a means of clustering people rather than finding a way of reducing variables. This technique of inverse factor analysis was called "Q" factor analysis (and the more usual one was called "R" factor analysis.

    perhaps you want to carry out an inverted pca something like Q fa? In that case, try looking up Q factor analysis. IIRC it was very popular with political scientists...

    Lance
  • The % of Var as output is the % of the variance of the 141 neuron scores that the first PC explains, and the second PC, and the third PC, etc. This does not directly relate to your plot of the casewise scores other than that the casewise scores for the first PC are for a PC that explains the overall % of Var as indicated.

    If you are trying to illustrate how much of the variability is explained for each case, I am not sure how you could do this. If you transpose the data and re-run the PCA, then your % of Var will refer to how much of the total variability is explained by case 1, case 2, etc - I don't think that this is what you want.

    But, I am not exactly sure what you mean when you say that you "would like to express the percent of explained variance of each of these 3 PCs" - overall, this is the % of Var for the PCA as shown for the original analysis - if you want to somehow do this on a case-by-case basis (i.e. over time) then I am not sure how you could do this.
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