Fw: Unequal no of factor variables

[Rhonda Boorman-2]

Dear Hector

Thank you for your swift reply.

A few clarifications.  Data for the second survey was collected at the same
time and from the same sample group as the first survey.  It was already
sub-scaled so all I had to do was collapse items into the subscales as
specified.  The correlation analyses I ran were between a subscale from the
second survey and a matching first survey 'component'.  Therefore, I
expected that, if there was some consistency of opinion, this would be
reflected in the correlations.  Of course, this is based on the assumption
that the 'components' are reasonably accurate and stable.  My purpose for
doing the correlations was as support for concurrent validity.

Also, I accept your comment about sample size. Finding adequate numbers of
participants is the bane of research.  Much as we would have liked more, we
had to be satisfied when we got > 300.

Our plan is to collect data again using the first survey, and see if there
is a change in attitude.  What you have said about the chance of replicating
a factor structure raises my existing concerns about finding anything useful
or interpretable.  It may be best to not run a PCA on the second round of
data, but just compare the subscales that were identified in the first round
of data.

Kind Regards

Rhonda


----- Original Message -----
From: "Hector Maletta" <[hidden email]>
To: "'Rhonda Boorman'" <[hidden email]>; <[hidden email]>
Sent: Wednesday, April 30, 2008 10:54 AM
Subject: RE: Unequal no of factor variables

> Rhonda,
> You had apparently 320 cases with 22 variables in your first study (number
> of cases and variables not reported for the second study). These figures
> represent quite a low number of cases per variable, which translates into
> large sampling error. Even if the second study is a perfect replication of
> the first, taken almost at the same time (i.e. without any external
> condition having varied), you may expect perceptible variation from one
> sample to the next. If other conditions also varied between the two
> studies
> (number of cases and variables, details about methodology, interview
> technique, etc) the differences may be still larger. If some time elapsed
> between the two, some conditions may have also changed, making subjects
> respond differently.
> All in all, one may expect that the two studies yield significant
> differences in the correlation of variables, and more so in factor
> structure
> when these are based on a different array of variables.
> It is worth repeating here that "factors" or "components" emerging from
> factor analysis are only statistical constructs, mere algebraic
> derivations
> of regression and correlation coefficients, and cannot be construed as
> real
> "objects". Only for studies that are perfect replications of one another,
> with variables that are very stable over time and across subjects, and
> with
> samples large enough to ensure narrow margins of sampling error, you may
> expect that the overall factor structure is more or less the same in both
> studies. Otherwise, I would be rather surprised to find them equal.
>
> Hector
>
>
>
> -----Original Message-----
> From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
> Rhonda Boorman
> Sent: 29 April 2008 21:33
> To: [hidden email]
> Subject: Unequal no of factor variables
>
> This is a conceptual issue, not technical.  I'm hoping I can get some
> opinions.
>
> With data (n = 320) gathered from a survey we are developing to assess
> organisational attitudes (scale of 1-5), I ran a factor analysis and found
> 4
> factors made up of unequal numbers of variables, dropping from 10
> variables
> in factor one, to 6 in factor two, to 4, to 2.  The content of the factors
> was meaningful.
>
> Another survey was also completed at the same time, and I hoped to use
> this
> for concurrent validity.  However, the correlations are all highest (r =
> .4)
> with factor one, followed by factor two etc.
>
> Can I assume that this is an attribute of the unequal number of variables
> in
> the factors, with the larger factors having greater distribution and less
> variance and thus are more likely to have a higher effect size?
>
> With respect to listers who are so generous with their extensive SPSS
> knowledge, if research questions of this nature are better raised in an
> alternative forum, just let me know, and where it is.
>
> Kind Regards
>
> Rhonda
>
>
> To manage your subscription to SPSSX-L, send a message to
> [hidden email] (not to SPSSX-L), with no body text except the
> command. To leave the list, send the command
> SIGNOFF SPSSX-L
> For a list of commands to manage subscriptions, send the command
> INFO REFCARD
>
>
>

=====================
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[Hector Maletta]

Rhonda,
It is likely that factor scores for the first factor in both studies are
well correlated, even if based on a different set of variables and resulting
in a different structure. A scale based on factor scores in a third survey
(if nothing untoward has happened in the meantime) will probably be well
correlated too with the previous factor scores.
This may be consistent with the idea that observed variables are just
imperfect (and to some extent interchangeable) proxies or indicators for the
underlying factors, so that people with high scores for a factor that loads
strongly on those variables will tend also to have high scores in a factor
based on a different selection of variables from the same study, or the same
variables in a simultaneous but parallel study, or in a replication of the
first study taken shortly afterwards.
One thing you may do is generate factor scores in the second study using
factor score coefficients from the first study, and correlate them with
factor scores emerging from the second study. In a recent study of mine, the
details of the structures were different, especially for minor factors, but
the scores thus calculated were highly correlated.

Hector

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
Rhonda Boorman
Sent: 29 April 2008 22:53
To: [hidden email]
Subject: Fw: Unequal no of factor variables

Dear Hector

Thank you for your swift reply.

A few clarifications.  Data for the second survey was collected at the same
time and from the same sample group as the first survey.  It was already
sub-scaled so all I had to do was collapse items into the subscales as
specified.  The correlation analyses I ran were between a subscale from the
second survey and a matching first survey 'component'.  Therefore, I
expected that, if there was some consistency of opinion, this would be
reflected in the correlations.  Of course, this is based on the assumption
that the 'components' are reasonably accurate and stable.  My purpose for
doing the correlations was as support for concurrent validity.

Also, I accept your comment about sample size. Finding adequate numbers of
participants is the bane of research.  Much as we would have liked more, we
had to be satisfied when we got > 300.

Our plan is to collect data again using the first survey, and see if there
is a change in attitude.  What you have said about the chance of replicating
a factor structure raises my existing concerns about finding anything useful
or interpretable.  It may be best to not run a PCA on the second round of
data, but just compare the subscales that were identified in the first round
of data.

Kind Regards

Rhonda


----- Original Message -----
From: "Hector Maletta" <[hidden email]>
To: "'Rhonda Boorman'" <[hidden email]>; <[hidden email]>
Sent: Wednesday, April 30, 2008 10:54 AM
Subject: RE: Unequal no of factor variables

> Rhonda,
> You had apparently 320 cases with 22 variables in your first study (number
> of cases and variables not reported for the second study). These figures
> represent quite a low number of cases per variable, which translates into
> large sampling error. Even if the second study is a perfect replication of
> the first, taken almost at the same time (i.e. without any external
> condition having varied), you may expect perceptible variation from one
> sample to the next. If other conditions also varied between the two
> studies
> (number of cases and variables, details about methodology, interview
> technique, etc) the differences may be still larger. If some time elapsed
> between the two, some conditions may have also changed, making subjects
> respond differently.
> All in all, one may expect that the two studies yield significant
> differences in the correlation of variables, and more so in factor
> structure
> when these are based on a different array of variables.
> It is worth repeating here that "factors" or "components" emerging from
> factor analysis are only statistical constructs, mere algebraic
> derivations
> of regression and correlation coefficients, and cannot be construed as
> real
> "objects". Only for studies that are perfect replications of one another,
> with variables that are very stable over time and across subjects, and
> with
> samples large enough to ensure narrow margins of sampling error, you may
> expect that the overall factor structure is more or less the same in both
> studies. Otherwise, I would be rather surprised to find them equal.
>
> Hector
>
>
>
> -----Original Message-----
> From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
> Rhonda Boorman
> Sent: 29 April 2008 21:33
> To: [hidden email]
> Subject: Unequal no of factor variables
>
> This is a conceptual issue, not technical.  I'm hoping I can get some
> opinions.
>
> With data (n = 320) gathered from a survey we are developing to assess
> organisational attitudes (scale of 1-5), I ran a factor analysis and found
> 4
> factors made up of unequal numbers of variables, dropping from 10
> variables
> in factor one, to 6 in factor two, to 4, to 2.  The content of the factors
> was meaningful.
>
> Another survey was also completed at the same time, and I hoped to use
> this
> for concurrent validity.  However, the correlations are all highest (r =
> .4)
> with factor one, followed by factor two etc.
>
> Can I assume that this is an attribute of the unequal number of variables
> in
> the factors, with the larger factors having greater distribution and less
> variance and thus are more likely to have a higher effect size?
>
> With respect to listers who are so generous with their extensive SPSS
> knowledge, if research questions of this nature are better raised in an
> alternative forum, just let me know, and where it is.
>
> Kind Regards
>
> Rhonda
>
>
> To manage your subscription to SPSSX-L, send a message to
> [hidden email] (not to SPSSX-L), with no body text except the
> command. To leave the list, send the command
> SIGNOFF SPSSX-L
> For a list of commands to manage subscriptions, send the command
> INFO REFCARD
>
>
>

=====================
To manage your subscription to SPSSX-L, send a message to
[hidden email] (not to SPSSX-L), with no body text except the
command. To leave the list, send the command
SIGNOFF SPSSX-L
For a list of commands to manage subscriptions, send the command
INFO REFCARD

=====================
To manage your subscription to SPSSX-L, send a message to
[hidden email] (not to SPSSX-L), with no body text except the
command. To leave the list, send the command
SIGNOFF SPSSX-L
For a list of commands to manage subscriptions, send the command
INFO REFCARD