Re: time series and principal components

Posted by Bruce Weaver on Dec 27, 2021; 4:30pm
URL: http://spssx-discussion.165.s1.nabble.com/time-series-and-principal-components-tp5740917p5740918.html

Hi Art.  You ask how time series (TS) deals with having more variables than cases.  This suggests to me that you are using TS in a different manner than economists do.  As I understand it, economists use the following terminology.

TS:  One unit of observation with repeated measures (likely at regular intervals) over time.

Cross-sectional:  Multiple independent units of observation with observations at one point in time.

Panel data:  Multiple cross-sections over time; or multiple time-series over "subjects".

I ~think~ that when you say TS, you may be thinking of what the economists call panel data.  If so, adjusting your search terms to something like <panel data models and factor analysis> may return some useful results.  E.g., I found this book chapter:

https://www.cambridge.org/core/books/abs/advances-in-economics-and-econometrics/panel-data-models-and-factor-analysis/428C00DCD319FB7DCD26904D0CDFC23B#

If it looks useful, you may be able to get a copy from the author via ResearchGate:

https://www.researchgate.net/publication/287399632_Panel_data_models_and_factor_analysis

HTH.

Cheers,
Bruce

Art Kendall wrote

I am reviewing a journal submission that has some elements that are outside my expertise.  The goal of my post are
(1)to be able to suggest to the author from an some ways to relate the approach to an audience that includes social/behavioral scientists and policy makers from different language backgrounds.
(2)suggest to the editor what to look for in reviewers of the econometric aspects,

I have much experience with principal components and principal factors where the "repeated" variables are items for a summative scales to represent constructs like values, attitudes, abilities, achievement, etc.

I no longer have access to journals etc.  Does anybody have a link to a crosswalk between the vocabulary of time series and the vocabulary of factor analysis in the social behavioral (SB) sciences?

How does TS deal with having more variables (repeats) than cases? In SB there is a rule of thumb that fewer than 10 times as many cases as variables is highly questionable.
How does TS deal with accounting for total variance vs common variance?
How does TS deal with corrected item-total correlation, the correlation of each item with the sum of the other correlations?

In social/behavioral sciences one does not include items and their total/mean in the same "factor analysis", what would make it sensible to have 3 variables that are counts plus the total of the three in a PCA?