small sample-repeated predictors

[Rcarlstedt]

I need some feedback regarding data points (i.e., repeated predictor
measures used as constants ) versus sample size.

I did a longitudinal study with a sample of 9 (tennis  players) and 59
measurement occasions (ca. 7 matches per player). Constants  that were entered into
a regression formula were heart rate  variability (HRV), neurocognition (44
measures) and 3 CSARCS-A (personality  inventory) measures (corresponding to
each measurement occasion-match/outcome  measure; obtained as part of a
pre-competition assessment of the players).  These predictor variables are considered
trait measures (stable).  By contrast, the outcome measures are dynamic and
varied each measurement  occasion (each match; e.g., games won or lost; or HRV
when HRV was used as a  criterion/outcome measure).

Hence the question, can data points be viewed the same as unique samples?
Essentially, I have circa 7 measurement occasions per player and want to
determine how much of the variance can be attributed to the above mentioned
predictors (as constants/traits they were repeatedly entered corresponding  to each
measurement occasion [match outcome measure or HRV]). Can this be done?  If so,
are any statistical adjustments necessary; what caveats are there? My  model
has generated some very potent findings/predictions, consistent with  previous
research of mine that had very large actual unique samples
(participants/subjects) but only one measurement occasion. One issue  is, what is more
valuable, obtaining measures [predicting outcome/trait  predictors] on a few hundred
athletes ONCE (criterion measure,e.g., won-loss %  for the season), or having
scores to hundreds of measurement occasions [data  points/outcome like games
won or quality of at-bat or HRV] but a very small  sample (9 in my tennis study)?

I also just completed a 4 month baseball study that had 11 players and  about
1400 data points (repeated measures; HRV and batting outcome  measures). The
obtained data are unique, sport statistical  outcome measures and real time
HRV during before, during and after  actual/real games across 4-6 months and
over 40 competitions (matches and  games) analyzed in the context of trait
predictors that are obtained once  (constant/stable).

My concern is, can these data points be see as analogous to a sample  of
unique individuals/participants when using multiple regression? I  posted
previously with less details and received the advice that  indeed, constants/traits
can be entered multiple times for one  subject/participant as part of a data set
that contains changing  outcome/criterion measures (in this case HRV or
performance outcome  measures; Panel Analysis).

I also need to know if such a model with a large amount of data  entry points
(repeated constants/traits and multiple outcome measures) but small  actual
sample needs to be adjusted somehow and if my sample size is  the reason for
some incredible adjusted R squared findings I obtained  (inflated???). Like I
mentioned previously, though, the above studies extend and  quasi-replicate
previous research pertaining to a performance model that I have  been advancing
over the last 8 years, and they make conceptual sense.

Any feedback would be greatly appreciated (alternative analysis
methods???....note, the part of the investigations described above did not  involve
manipulation of variables [no pre-post intervention])


__________________________________________
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 5:45:15 PM Eastern Standard Time, Rcarlstedt
writes:

In a message dated 10/26/2006 4:15:36 PM Eastern Standard Time,
[hidden email] writes:

I am a  little confused by your description. So, I'd like to rephrase it to
see  if you and I understand what you have correctly. It sounds like  you
measured 9 tennis players once before or during a variable number  of
different matches.
They were measured once prior to the study on the personality and
neurocognitive meassures.....

They then had there HRV measured pre and post each match...

Predictors were HRV, personality and neurocognitive measures; outcome
criterion measure was games won, or games lost in a match...

Each data entry point included pre and post HRV values (variable per
measurement occasion) and the personality/neurocognitiv
measures(trait/stable/constant across measurement occasion)

Regression models also looked at HRV measures as criterion  variables...




The  average number of matches per player was 7 but there
was some variability  in that number.
Total matches was 59 distributed among 9 players, most played 8 a few  played
less......



(You  refer to 59. Is that the number of
matches the 9 players played?) It  sounds like each player completed 3
personality measures and 44  neurocognition measures. Each player completed
these measures once. You  also measured hear rate variability for each
player. How many times you  measured that for each player is unclear as well
as when those  measurements were collected, if measured more than once. You
also record  the outcome of each match as won or lost.

Like I said HRV was measured pre and post match on each player,  personality
and neurocognition were considered traits and thus hypothesized to  influence
outcome (games won or lost) or pre and/or post HRV.

I realize that the subject N = 9, however, previously I was told trait
measures can be entered repeatedly over time, thus, in this case I looked at 9
players who were measured 6-8 times each for HRV, leading to muliple repeated
measures on the sample of 9 with personality entered repeatedly (they were
different for each player). I was told this was a panel analysis technique and
was acceptable. Variability existed at the inter and intra-individual levels
for all measures, just that at the within/intra level
personality/neurocognition was less variable (trait/constant-based on one test  occasion
pre-study/assessment).

So even though I have a N of 9, I have 59 data points. I want to know if  59
(measurement occasions on HRV and outcome) is considered analogous to a
sample of 59, or how the data should be/can be handled/analyzed.

Hope this clarifies things.

Thanks for your time in pondering this problem.









__________________________________________
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]

Hi Roland -

To answer your last question: even though you have 59 data point, this is
not really analagous to having a sample size of 59.  Your data is of a
hierarchical nature; you have repeated measure nested within individuals.
Using some statistical techniques, such as linear regression is no longer
valid, due to you not having independent observations (within individual).

As for how to analyze the data you have - I would normally suggest looking
into using the MIXED procedure (or some other program for estimating
Multilevel Models), but you have such a small sample with pretty unbalanced
data that that is probably not a viable option.  I don't know that much
about Repeated Measures ANOVA, but that may be an option.  Maybe someone
else on the list could comment about that.

Good luck, Roland.  Ask if you have any follow up questions.

Peter Link
VA San Diego Healthcare System

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]]On Behalf Of
[hidden email]
Sent: Thursday, October 26, 2006 2:49 PM
To: [hidden email]
Subject: Re: small sample-repeated predictors


In a message dated 10/26/2006 5:45:15 PM Eastern Standard Time, Rcarlstedt
writes:

In a message dated 10/26/2006 4:15:36 PM Eastern Standard Time,
[hidden email] writes:

I am a  little confused by your description. So, I'd like to rephrase it to
see  if you and I understand what you have correctly. It sounds like  you
measured 9 tennis players once before or during a variable number  of
different matches.
They were measured once prior to the study on the personality and
neurocognitive meassures.....

They then had there HRV measured pre and post each match...

Predictors were HRV, personality and neurocognitive measures; outcome
criterion measure was games won, or games lost in a match...

Each data entry point included pre and post HRV values (variable per
measurement occasion) and the personality/neurocognitiv
measures(trait/stable/constant across measurement occasion)

Regression models also looked at HRV measures as criterion  variables...




The  average number of matches per player was 7 but there
was some variability  in that number.
Total matches was 59 distributed among 9 players, most played 8 a few
played
less......



(You  refer to 59. Is that the number of
matches the 9 players played?) It  sounds like each player completed 3
personality measures and 44  neurocognition measures. Each player completed
these measures once. You  also measured hear rate variability for each
player. How many times you  measured that for each player is unclear as well
as when those  measurements were collected, if measured more than once. You
also record  the outcome of each match as won or lost.

Like I said HRV was measured pre and post match on each player,  personality
and neurocognition were considered traits and thus hypothesized to
influence
outcome (games won or lost) or pre and/or post HRV.

I realize that the subject N = 9, however, previously I was told trait
measures can be entered repeatedly over time, thus, in this case I looked at
9
players who were measured 6-8 times each for HRV, leading to muliple
repeated
measures on the sample of 9 with personality entered repeatedly (they were
different for each player). I was told this was a panel analysis technique
and
was acceptable. Variability existed at the inter and intra-individual levels
for all measures, just that at the within/intra level
personality/neurocognition was less variable (trait/constant-based on one
test  occasion
pre-study/assessment).

So even though I have a N of 9, I have 59 data points. I want to know if  59
(measurement occasions on HRV and outcome) is considered analogous to a
sample of 59, or how the data should be/can be handled/analyzed.

Hope this clarifies things.

Thanks for your time in pondering this problem.









__________________________________________
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