Re: Principal Component Analysis & Longitudinal Comparison?

[Hans Chen]

I do not know how to answer the following question of my friend's, Any suggestion would be appreciated!

Han Chen

--------------------------------

As we know, we have standardized the data   in order to eliminate the effect of dimensions and scale before we conducted principal component analysis. I just wonder whether we can conduct longitudinal comparison using the standardized data. If not, how can we deal with it?

--

[David Marso]

IMNSHO: You are heading down the wrong track.
Need to update your methodological toolkit.
Here is the results of a quick search I fired off on
"longitudinal structural equation modeling methodology in the social sciences"
Really need to carefully specify what you mean by comparisons.

https://www.google.com/search?q=longitudinal+structural+equation+modeling+methodology+in+the+social+sciences&ie=utf-8&oe=utf-8&aq=t&rls=org.mozilla:en-US:official&client=firefox-a&channel=sb

Hans Chen wrote

I do not know how to answer the following question of my friend's, Any
suggestion would be appreciated!

Han Chen
--------------------------------

As we know, we have standardized the data   in order to eliminate the
effect of dimensions and scale before we conducted principal component
analysis. I just wonder whether we can conduct longitudinal comparison
using the standardized data. If not, how can we deal with it?

--

[Rich Ulrich]

Why is there a concern about "standardized data"?  What does your
friend mean by that?

- Principal components can be performed on (a) covariances or (b)
correlations.  A PCA is performed on (a) covariances in order to take
advantage of a larger importance to be given to variables with more
variance.  Off hand, I don't think I have ever seen that option used in
the social sciences.

If you perform the PCA on (b) correlations, you get the same results
for factors as if you had used covariances on the standard-normal
transformed version of the data.  There is a minor advantage of having
on hand those transformed data -- In my experience, I needed those
transformed data in order to score up the theoretical factors using the
factor-scoring coefficients.

You don't ordinarily perform PCA on a longitudinal collection of data.

Using the PCA from the "base" period is something that is sometimes
done -- In that instance, you *would* standardize all the data for all
periods by using the mean and SD for the baseline period, when you
get around to scoring factors on all data.  "DO REPEAT" is useful for that.
(Or -- Is there a way to get FACTOR to score up data that are to be omitted
from the analysis? - I never knew one.)

If there is some other question arising around longitudinal and standardized
data.... someone will need to be more specific.

--
Rich Ulrich

---

Date: Fri, 28 Mar 2014 12:58:55 -0500
From: [hidden email]
Subject: Re: Principal Component Analysis & Longitudinal Comparison?
To: [hidden email]

I do not know how to answer the following question of my friend's, Any suggestion would be appreciated!

Han Chen

--------------------------------

As we know, we have standardized the data   in order to eliminate the effect of dimensions and scale before we conducted principal component analysis. I just wonder whether we can conduct longitudinal comparison using the standardized data. If not, how can we deal with it?

--

[David Marso]

Looks like Rich needs an update too.
People have been doing such analyses using SEM for decades!
It provides a nice framework for testing all sorts of hypotheses about "change".
Standard traditional FA is incredibly WEAK in such regards.


To answer the query:
"(Or -- Is there a way to get FACTOR to score up data that are to be omitted
from the analysis? - I never knew one.)"

From the FM:
"SELECT Subcommand (FACTOR command)


SELECT limits cases used in the analysis phase to those with a specified value for any one variable.

•Only one SELECT subcommand is allowed. If more than one is specified, the last is in effect.

•The specification is a variable name and a valid value in parentheses. A string value must be specified within quotes. Multiple variables or values are not permitted.

•The selection variable does not have to be specified on the VARIABLES subcommand.

•Only cases with the specified value for the selection variable are used in computing the correlation or covariance matrix. You can compute and save factor scores for the unselected cases as well as the selected cases.

• SELECT is not valid if MATRIX = IN is specified.

Rich Ulrich wrote

Why is there a concern about "standardized data"?  What does your
friend mean by that?

- Principal components can be performed on (a) covariances or (b)
correlations.  A PCA is performed on (a) covariances in order to take
advantage of a larger importance to be given to variables with more
variance.  Off hand, I don't think I have ever seen that option used in
the social sciences.

If you perform the PCA on (b) correlations, you get the same results
for factors as if you had used covariances on the standard-normal
transformed version of the data.  There is a minor advantage of having
on hand those transformed data -- In my experience, I needed those
transformed data in order to score up the theoretical factors using the
factor-scoring coefficients.

You don't ordinarily perform PCA on a longitudinal collection of data.

Using the PCA from the "base" period is something that is sometimes
done -- In that instance, you *would* standardize all the data for all
periods by using the mean and SD for the baseline period, when you
get around to scoring factors on all data.  "DO REPEAT" is useful for that.
(Or -- Is there a way to get FACTOR to score up data that are to be omitted
from the analysis? - I never knew one.)

If there is some other question arising around longitudinal and standardized
data.... someone will need to be more specific.

--
Rich Ulrich

Date: Fri, 28 Mar 2014 12:58:55 -0500
From: [hidden email]
Subject: Re: Principal Component Analysis & Longitudinal Comparison?
To: [hidden email]

I do not know how to answer the following question of my friend's, Any suggestion would be appreciated!
Han Chen--------------------------------


As we know, we have standardized the data   in
order to eliminate the effect of dimensions and scale before we conducted principal
component analysis. I just wonder whether we can conduct longitudinal comparison using the standardized data. If not, how can we deal with it?


--

[Art Kendall]

Please describe in detail what you are trying to do.

Are the items you are thinking of factoring from a pre-existing validated scale such as SATs, GREs etc?

Is is possible that SEM will be what you need or it may be repeated measures GLM or some variant of repeated measures as times series or scale construction.
On 3/28/2014 2:05 PM, Hans Chen [via SPSSX Discussion] wrote:

I do not know how to answer the following question of my friend's, Any suggestion would be appreciated!

Han Chen

--------------------------------

As we know, we have standardized the data   in order to eliminate the effect of dimensions and scale before we conducted principal component analysis. I just wonder whether we can conduct longitudinal comparison using the standardized data. If not, how can we deal with it?

--

---

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