Factor analysis

[Promises]

1. What do I do if the Principal Components Aanalysis factors (clusters of variables) do not produce common underlying themes that can be explained as a real world construct? The variables are more or less all over the place...
 
2. Could I remove variables/items prior to conducting PCA, if for example I find that they're outliers, following descriptive analysis?
 

I will be grateful for any guidance you can offer. Thanks in advance.

[Art Kendall]

What is the goal of your factor analysis?
Are you trying to create summative scales?

Are you interested in accounting for the variance that is common to the variables or are you interested in accounting for the unique variance also?

Did you use parallel analysis to determine the number of factors to retain? If not how did you decide how many factors to retain?

What constitutes a case in you data? how many cases do you have?

How many variables were input to the PCA?

How many factors did you retain?

Did you use varimax rotation? if not, how did you choose the rotation method?

On 1/5/2014 4:50 PM, Promises [via SPSSX Discussion] wrote:

1. What do I do if the Principal Components Aanalysis factors (clusters of variables) do not produce common underlying themes that can be explained as a real world construct? The variables are more or less all over the place...
 
2. Could I remove variables/items prior to conducting PCA, if for example I find that they're outliers, following descriptive analysis?
 

I will be grateful for any guidance you can offer. Thanks in advance.

---

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NAML

[Rich Ulrich]

[no original message seen yet.]

I would restate Art's initial paragraph -
If these are items that are suppose to make up scales,
then you *ought* to be using PFA, not PCA. So:  What
do the variables measure?

Also - You will not see structure if there are too many
variables for the number of cases.  (And remember that any
case with a missing value will be dropped, by default.)

Ten times the number of variables is usually enough cases,
but that multiplier depends thoroughly on the typical
correlations between variables that will make up a factor.
So you could hint at the r's, too, if you want fuller advice.

 - I always look at the univariate data first, to see that
the coding is what I expected ... no weird values, no non-varying
variables.

--
Rich Ulrich



________________________________

> Date: Sun, 5 Jan 2014 14:10:51 -0800
> From: [hidden email]
> Subject: Re: Factor analysis
> To: [hidden email]
>
> What is the goal of your factor analysis?
> Are you trying to create summative scales?
>
> Are you interested in accounting for the variance that is common to the
> variables or are you interested in accounting for the unique variance
> also?
>
> Did you use parallel analysis to determine the number of factors to
> retain? If not how did you decide how many factors to retain?
>
> What constitutes a case in you data? how many cases do you have?
>
> How many variables were input to the PCA?
>
> How many factors did you retain?
>
> Did you use varimax rotation? if not, how did you choose the rotation method?
>
>
> Art Kendall
> Social Research Consultants
>
> On 1/5/2014 4:50 PM, Promises [via SPSSX Discussion] wrote:
> 1. What do I do if the Principal Components Aanalysis factors (clusters
> of variables) do not produce common underlying themes that can be
> explained as a real world construct? The variables are more or less all
> over the place...
>
> 2. Could I remove variables/items prior to conducting PCA, if for
> example I find that they're outliers, following descriptive analysis?
>
>
> I will be grateful for any guidance you can offer. Thanks in advance.
>

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[Promises]

Thank you, let me try to respond to some of your questions.
1. The goal of the PCA is item reduction to create a questionnaire with fewer items;
2. In this instance I didn't use parallel analysis, I decided on the number of factors based on those suggested from the scree plot +/- 1.
3. There are 267 cases (210 after PCA)
4. The questionnaire has 40 items/variables;
5. I retained 33;
6. Yes, I used varimax rotation.

I look forward to your further feedback or questions if you have any.

[Promises]

Thanks Ulrich,
As I understand it, 5-10 cases per item should sufficen and up to 200-250 cases overall is also fine for PCA. So, in this case there are 211 cases down from the initial 267 after PCA is run (using listwise option)...

The correlation matix is fine, most items are well correlated .3 and over. As for your third point, cleaning was done just after data entry to remove any entry errors as well as examine floor and ceiling effect. I should point out though that given the nature of the items (asking people to state how important a list of goal items are to them), majority of the responses were near to the top of the 5 point scale.

I hope this provides enough additional information.

[Art Kendall]

Is the questionnaire designed to create scales? If so how many?

How were the items generated? Were they used in previous research?

Why did you eliminate the 7 items if you are not yet comfortable with the factor analysis? or do you mean that you retained 33 factors?
do all of your items have nontrivial variance?

Why is there missing data?

On 1/5/2014 5:38 PM, Promises [via SPSSX Discussion] wrote:

Thank you, let me try to respond to some of your questions.
1. The goal of the PCA is item reduction to create a questionnaire with fewer items;
2. In this instance I didn't use parallel analysis, I decided on the number of factors based on those suggested from the scree plot +/- 1.
3. There are 267 cases (210 after PCA)
4. The questionnaire has 40 items/variables;
5. I retained 33;
6. Yes, I used varimax rotation.

I look forward to your further feedback or questions if you have any.

---

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[Bruce Weaver]

Your 2nd point below suggests that you're actually using "Eigenvalues > 1" to determine the number of components.  The usual approach with a Scree plot is determine where the last big drop occurs, and retain all components/factors prior to that.  

http://pic.dhe.ibm.com/infocenter/spssstat/v20r0m0/index.jsp?topic=%2Fcom.ibm.spss.statistics.cs%2Ffac_cars_scree_01.htm

HTH.

Promises wrote

Thank you, let me try to respond to some of your questions.
1. The goal of the PCA is item reduction to create a questionnaire with fewer items;
2. In this instance I didn't use parallel analysis, I decided on the number of factors based on those suggested from the scree plot +/- 1.
3. There are 267 cases (210 after PCA)
4. The questionnaire has 40 items/variables;
5. I retained 33;
6. Yes, I used varimax rotation.

I look forward to your further feedback or questions if you have any.

[Promises]

The point of the current process is to reduce the number of items currently in the instrument.

[Rich Ulrich]

I will re-iterate my assertion -- for questionnaire items
that are supposed to cover a common universe, you should
be using PFA rather than PCA.  That means, "iterate on
the communalities" rather than taking them as 1.0.

From another post, I gather that you have 33 factors with
communalities over 1.0!  That is unusually large, and it
suggests that there are, indeed, near-unique items, which (for
the purposes of defining common factors) should be dropped.

As a common-reliability exercise, you should use PFA on them
all, and then examine the achieved communalities after a FIXED
number of factors.  How many do you expect?  5?  8?  10 would
be a lot.  You might try several numbers, and see which items
are have the lowest achieved communalities.  Those are the
ones that have least in common, at that stage of the factoring.

--
Rich Ulrich


[Here is the Reply that I copied from Nabble ]


                ======
Thanks Ulrich,

As I understand it, 5-10 cases per item should sufficen and up to
200-250 cases overall is also fine for PCA. So, in this case there are
211 cases down from the initial 267 after PCA is run (using listwise
option)...


The correlation matix is fine, most items are well correlated .3
 and over. As for your third point, cleaning was done just after data
entry to remove any entry errors as well as examine floor and ceiling
effect. I should point out though that given the nature of the items
(asking people to state how important a list of goal items are to them),
 majority of the responses were near to the top of the 5 point scale.


I hope this provides enough additional information.




        ======
----------------------------------------

> From: [hidden email]
> To: [hidden email]
> Subject: RE: Factor analysis
> Date: Sun, 5 Jan 2014 17:35:48 -0500
>
> [no original message seen yet.]
>
> I would restate Art's initial paragraph -
> If these are items that are suppose to make up scales,
> then you *ought* to be using PFA, not PCA. So:  What
> do the variables measure?
>
> Also - You will not see structure if there are too many
> variables for the number of cases.  (And remember that any
> case with a missing value will be dropped, by default.)
>
> Ten times the number of variables is usually enough cases,
> but that multiplier depends thoroughly on the typical
> correlations between variables that will make up a factor.
> So you could hint at the r's, too, if you want fuller advice.
>
>  - I always look at the univariate data first, to see that
> the coding is what I expected ... no weird values, no non-varying
> variables.
>
> --
> Rich Ulrich
>
>
>
> ________________________________
>> Date: Sun, 5 Jan 2014 14:10:51 -0800
>> From: [hidden email]
>> Subject: Re: Factor analysis
>> To: [hidden email]
>>
>> What is the goal of your factor analysis?
>> Are you trying to create summative scales?
>>
>> Are you interested in accounting for the variance that is common to the
>> variables or are you interested in accounting for the unique variance
>> also?
>>
>> Did you use parallel analysis to determine the number of factors to
>> retain? If not how did you decide how many factors to retain?
>>
>> What constitutes a case in you data? how many cases do you have?
>>
>> How many variables were input to the PCA?
>>
>> How many factors did you retain?
>>
>> Did you use varimax rotation? if not, how did you choose the rotation method?
>>
>>
>> Art Kendall
>> Social Research Consultants
>>
>> On 1/5/2014 4:50 PM, Promises [via SPSSX Discussion] wrote:
>> 1. What do I do if the Principal Components Aanalysis factors (clusters
>> of variables) do not produce common underlying themes that can be
>> explained as a real world construct? The variables are more or less all
>> over the place...
>>
>> 2. Could I remove variables/items prior to conducting PCA, if for
>> example I find that they're outliers, following descriptive analysis?
>>
>>
>> I will be grateful for any guidance you can offer. Thanks in advance.
>>

=====================
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