Re: small sample-repeated predictors-more

[Rcarlstedt]

In a message dated 10/26/2006 6:42:06 PM Eastern Standard Time,
[hidden email] writes:

Using  some statistical techniques, such as linear regression is no longer
valid,  due to you not having independent observations (within  individual)
....What about linear regression based on scores of pre and post
observations in a single individual? I also ran multiple regression on data from  single
players, looking at how varying HRV on each measurement occasion (prior  to
every at-bat) and it's effect on outcome (each at bat's result)? I then
compared pre and post with intervention differences in how HRV predicted
performance. This was done on every player in the line-up for the entire season  (over
140 measurement occasions pre and post).




__________________________________________
Roland A. Carlstedt,  Ph.D.
Licensed Clinical Psychologist/Licensed Applied  Psychologist
Clinical and Research Director: Integrative Psychological  Services of NYC
Chair and Head Mentor: American Board of Sport  Psychology
Research Fellow in Applied Neuroscience: Brain Resource  Company
_www.americanboardofsportpsychology.org_
(http://www.americanboardofsportpsychology.org/)
[hidden email]
917-680-3994

[peter link]

I guess that is a possibility.  If you used pre- as a covariate, and post-
as your dependent variable (ANCOVA).  Again, sample size is small, which
concerns me.  I guess you might try that.  My one question would be
concerning your sample size.  Maybe others on the list would have imput
about that.

I wouldn't suggest doing linear regression on a single individual using just
pre- and post.  If you would do it this way, why not use all of the data
points, not just pre- and post-?  That would make more sense to me.

I am curious about what you had done in this previous study with baseball
players.  It seems like the way you approached this problem, you could make
inferences about specific players, but not about players in general.

Hopefully someone else will comment about your problem, also.  I guess an
ANCOVA approach may be acceptable, though.  Even though you throw away a lot
of data, it may be the best you can do, given such a small sample.

Peter Link

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]]On Behalf Of
[hidden email]
Sent: Thursday, October 26, 2006 4:41 PM
To: [hidden email]
Subject: Re: small sample-repeated predictors-more


In a message dated 10/26/2006 6:42:06 PM Eastern Standard Time,
[hidden email] writes:

Using  some statistical techniques, such as linear regression is no longer
valid,  due to you not having independent observations (within  individual)
....What about linear regression based on scores of pre and post
observations in a single individual? I also ran multiple regression on data
from  single
players, looking at how varying HRV on each measurement occasion (prior  to
every at-bat) and it's effect on outcome (each at bat's result)? I then
compared pre and post with intervention differences in how HRV predicted
performance. This was done on every player in the line-up for the entire
season  (over
140 measurement occasions pre and post).




__________________________________________
Roland A. Carlstedt,  Ph.D.
Licensed Clinical Psychologist/Licensed Applied  Psychologist
Clinical and Research Director: Integrative Psychological  Services of NYC
Chair and Head Mentor: American Board of Sport  Psychology
Research Fellow in Applied Neuroscience: Brain Resource  Company
_www.americanboardofsportpsychology.org_
(http://www.americanboardofsportpsychology.org/)
[hidden email]
917-680-3994

[Rcarlstedt]

In a message dated 10/26/2006 8:18:01 PM Eastern Standard Time,
[hidden email] writes:

I  wouldn't suggest doing linear regression on a single individual using  just
pre- and post.  If you would do it this way, why not use all of  the data
points, not just pre- and post-?  That would make more sense  to me.


The reason for this was that in the pre-condition HRV was only monitored (5
predictor HRV measures), in the second post condition the player engaged in an
 intervention that manipulated HRV while being monitored. In both cases I
wanted  to find correlations between predictors and outcome measures and variance
 explained through multiple regression and then compare differences (i.e.,
was  more of the variance explained in outcome on the basis of HRV post compared
to  pre-no intervention).

Esentially, you are saying even if one has hundreds of measures obtained
through hundreds of measurement occasions that are hypothesized to predict and
correspond to specific outcome measures (each HRV data point corresponds to an
outcome [HRV-low frequency and say, batting result]) one should/cannot
validly  use multiple regression to determine variance explained?

Thanks again!

Roland


__________________________________________
Roland A. Carlstedt,  Ph.D.
Licensed Clinical Psychologist/Licensed Applied  Psychologist
Clinical and Research Director: Integrative Psychological  Services of NYC
Chair and Head Mentor: American Board of Sport  Psychology
Research Fellow in Applied Neuroscience: Brain Resource  Company
_www.americanboardofsportpsychology.org_
(http://www.americanboardofsportpsychology.org/)
[hidden email]
917-680-3994

[Rcarlstedt]

In a message dated 10/26/2006 8:18:01 PM Eastern Standard Time,
[hidden email] writes:

I am  curious about what you had done in this previous study with  baseball
players.  It seems like the way you approached this problem,  you could make
inferences about specific players, but not about players in  general.



That was actually the whole point of the investigations, determining
indivdual differences that supposedly exist according to my model and the  Individual
Zone of Optimum Functioning theory (IZOF) that would emerge, but not  in
group data. And, that was the case, but I still am uncertain about  statistical
issues. I'll try to find the post and response about PANEL analysis  that I
received previously that implied that one could use/enter trait constants  each
time other more variable predictor variables are  entered.

__________________________________________
Roland A. Carlstedt,  Ph.D.
Licensed Clinical Psychologist/Licensed Applied  Psychologist
Clinical and Research Director: Integrative Psychological  Services of NYC
Chair and Head Mentor: American Board of Sport  Psychology
Research Fellow in Applied Neuroscience: Brain Resource  Company
_www.americanboardofsportpsychology.org_
(http://www.americanboardofsportpsychology.org/)
[hidden email]
917-680-3994

[Rcarlstedt]

SEE response to similar question that I posed in May. Scroll all the way
down to read how I described the sample size issue then.....thanks!

PS: if anybody remembers having commented on the below matter relative to
PANEL analysis please let me know...thanks!

In a message dated 10/26/2006 8:48:08 P.M. Eastern Standard Time,  Rcarlstedt
writes:

I'll try  to find the post and response about PANEL analysis that I received
previously  that implied that one could use/enter trait constants each time
other  more variable predictor variables are  entered.

Yes, that is by definition a time-invariant variable and that is how  it
is handled in a mixed models approach.


Paul R. Swank,  Ph.D.
Professor, Developmental Pediatrics
Director of Research, Center for  Improving the Readiness of Children for
Learning and Education  (C.I.R.C.L.E.)
Medical School
UT Health Science Center at  Houston

-----Original Message-----
From: SPSSX(r) Discussion  [mailto:[hidden email]] On Behalf Of
[hidden email]
Sent:  Monday, May 15, 2006 1:09 PM
To: [hidden email]
Subject: Sample  Size Issues

I have a methodological question pertaining to sample  size.

If one has a small sample in which specific measures are  considered
TRAITS, that is, they are considered to be stable longitudinal  mediators
of  certain behaviors and outcome measures can they be  seen/used as
repeated  measures in a study that is interested in their  influence on
other outcome  measures?

For example, I have  longitudinal data spanning nine months (a small
sample of athletes). I have  repeated measures (81; ca. 10 per subject)
on heart  rate variability  (HRV) and numerous statistical outcome
measures (e.g.,  games won or  lost)....over ten measurement occasions
(matches) and pre-post  HRV  measurements associated with these matches.
In addition, I have  neuropsychological/cognition measures that are also
considered stable for  the  same sample. I also have intervention
efficacy data obtained in the  context of  an ecologically more valid and
not a controlled  design.

Both cognition and personality/behavioral measures were found to  explain
varying amounts of variance explained in outcome measures  and
vice-versa. Also, among and between variable.

The sample size was  only 8-12. However, data points or repeated measures
for outcome measures  ranged from 52-81. Thus, although I only had a
sample of around 10, I have up  to 81 outcome measures.

My question: if my cognition and  personality/behavioral measures are
considered stable, can they be entered as  predictor variables equivalent
to the amount of measurement occasions  multiple times? For example, if
player  A played 10 matches and 10 HRV  measurements were taken, can one
justifiably  enter his or her  cognition-personality scores ten times to
match the outcome measurements;  under the assumption that these stable
traits are enduring and  will  indeed influence HRV and performance
outcome measures at different  points  in time (the predictor measures
have very  high Test-Retest  reliability)?

This would increase sample size/predictor data points from  8 to 81,
albeit the predictor and outcome measures would be from a  limited
sample?

Is this more a theoretical or methodological issue or  can one justify
such an approach because stable predictor variables will  "always"
influence certain performance (at the intra and inter-individual  level)?
Which my results demonstrated.

What about vice versa when  looking at how HRV and outcome is associated
with cognition/personality  measures (only 8 measures/8 subjects),
whereas the HRV/Outcome measurement  involves 52-81 measurement
occasions.

Any feedback would be  appreciated including statistical considerations,
limitations, alternative  data-analysis suggestions etc.

Thanks!

RC





____________________________________________
Roland A. Carlstedt,  Ph.D.
Licensed Clinical Psychologist/Licensed Applied Psychologist
Chair,  American Board of Sport Psychology
Clinical and Research Director:  Integrative Psychological Services of NYC
Research Fellow in Applied  Neuroscience: Brain Resource Company
_www.americanboardofsportpsychology.org_
(http://www.americanboardofsportpsychology.org/)
[hidden email]
917-680-3994

[peter link]

Roland -

For your hypothetical example of  many people observed many times, I would
recommend MIXED procedure (or some other software for Multilevel Modelling -
HLM, MLwin, MIXOR, SAS Proc Mixed, to name a few).  To reiterate, linear
regression is not advised in this situation due to assumptions not being met
(non-independent observations, [E(ei * ej) does not equal 0].)  If
interested in this approach see Singer & Willett, Applied Longitudinal Data
Analysis, Oxford University Press, 2003.

Peter
  -----Original Message-----
  From: [hidden email] [mailto:[hidden email]]
  Sent: Thursday, October 26, 2006 5:43 PM
  To: Peter Link; [hidden email]
  Subject: Re: small sample-repeated predictors-more


  In a message dated 10/26/2006 8:18:01 PM Eastern Standard Time,
[hidden email] writes:
    I wouldn't suggest doing linear regression on a single individual using
just
    pre- and post.  If you would do it this way, why not use all of the data
    points, not just pre- and post-?  That would make more sense to me.

  The reason for this was that in the pre-condition HRV was only monitored
(5 predictor HRV measures), in the second post condition the player engaged
in an intervention that manipulated HRV while being monitored. In both cases
I wanted to find correlations between predictors and outcome measures and
variance explained through multiple regression and then compare differences
(i.e., was more of the variance explained in outcome on the basis of HRV
post compared to pre-no intervention).

  Esentially, you are saying even if one has hundreds of measures obtained
through hundreds of measurement occasions that are hypothesized to predict
and correspond to specific outcome measures (each HRV data point corresponds
to an outcome [HRV-low frequency and say, batting result]) one should/cannot
validly use multiple regression to determine variance explained?

  Thanks again!

  Roland

  __________________________________________
  Roland A. Carlstedt, Ph.D.
  Licensed Clinical Psychologist/Licensed Applied Psychologist
  Clinical and Research Director: Integrative Psychological Services of NYC
  Chair and Head Mentor: American Board of Sport Psychology
  Research Fellow in Applied Neuroscience: Brain Resource Company
  www.americanboardofsportpsychology.org
  [hidden email]
  917-680-3994