time series and principal components

[Art Kendall]

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?

[Bruce Weaver]

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?

[jkpeck]

The essence of time series analysis is dealing with various types of correlation over time in the series and the dynamic behavior of series via lagged relationships.  It's pretty far from PC or factor analysis in most cases, so I doubt that there is much commonality between TS concepts and vocabulary and PC etc and, hence, no mapping of terminology between them.

There are some TS procedures in Statistics and a number of TS and econometric extension commands available, but that probably would not get you very far.

[Art Kendall]

Thanks for your feed back.

What the article has would be called panel data then. I just thought of it as multiple time series.
For each case (country) there are several constructs measured for 33 years.

They are trying to use characteristics of some time series to explain other time series.

The writing leaves a lot to be be desired not just in the part about principal components. It takes a lot of "what is the author trying to say here".  When I work face to face with an author, it is often helpful to say "Tell me more about this". or "What are some other words to say this?" Then often I would just say "How about saying it more like that?" Since the review is blind, a great deal of tact is needed.

The well written well reasoned papers are a lot easier to review.

If Jon does not see the role of PC, I don't feel so bad about not being to tell what the author is saying.

[David Marso]

What sort of input is going into the PCA? Perhaps an attempt to reduce the dimensionality of a matrix of cross correlation coefficients?

[Art Kendall]

That is what I wanted to know.  What was the input to PCA?  What was the purpose?

If the article is re-submitted, hopefully those questions will be answered.

When I get a Round Tuit, I'll see if anybody has developed parallel analysis for time series.  YMMV but I have found parallel analysis very useful in ball parking the number of dimensions to retain.  After parallel analysis became available, I went back to several data sets where I had used, Montanelli, scree, and meaning to determine the number of factors (dimensions) to retain.   I then made a new rule of thumb to look at keeping the number of factors around where the eigenvalues from the actual data exceeded those from randomized data by 1.