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Science Forum Index » Space - Consult Forum » factor random and fixed?
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| sue |
 Posted: Thu Jan 11, 2007 7:48 pm |
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Guest
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hi fellow groupies,
I have some data for about 40 subjects. Response is amplitude
(continuous).
Each subject received 5 conditions, each given 10 times to each hand.
(So each received
100 treatments). So factors of interest are condition and hand.
Whether all 50 on the right hand or all 50 on the left hand was done
first was random.
A colleague suggested I put in hand and condition as both random and
fixed effects in the one model.
In fact she seemed to feel that this should be done for any within
subject effects (df permitting).
Does anyone have some references for doing this (with examples)? I in
my ignorance had thought that
factors were fixed or random, and couldnt be both.
I understood fixed factors to be those where the levels in the
experiment were the only levels of interest, while random factors had
levels in the experiment which were a subset of all levels of
interest.Please educate me.
yours in statistical anticipation
sue |
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| Ray Koopman |
| Posted: Fri Jan 12, 2007 12:39 am |
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Guest
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sue wrote:
Quote: hi fellow groupies,
I have some data for about 40 subjects. Response is amplitude
(continuous).
Each subject received 5 conditions, each given 10 times to each hand.
(So each received
100 treatments). So factors of interest are condition and hand.
Whether all 50 on the right hand or all 50 on the left hand was done
first was random.
A colleague suggested I put in hand and condition as both random and
fixed effects in the one model.
In fact she seemed to feel that this should be done for any within
subject effects (df permitting).
Does anyone have some references for doing this (with examples)? I in
my ignorance had thought that
factors were fixed or random, and couldnt be both.
I understood fixed factors to be those where the levels in the
experiment were the only levels of interest, while random factors had
levels in the experiment which were a subset of all levels of
interest.Please educate me.
yours in statistical anticipation
sue
A factor is fixed if you want to make inferences about only those
levels of the factor that appear in your design, regardless of
whether other levels of the factors exist. So any factor can always
be treated as fixed if you are willing to restrict your inferences
to only those levels that are in the design.
A factor is random if the levels in the design are a random sample
of some population of levels, and you want your inferences to apply
to that population. In this case, what counts is the so-called
"sampling fraction" k/K, where k is the number of levels in your
design and K is number of levels in the population. If k = K then
the factor is fixed. If K is so large that k/K is effectively zero
then the factor is random. For intermediate cases, where K is small
enough that k/K not zero, the actual ratio k/K is used; see
Cornfield, J., & Tukey, J. W. (1956). Average values of mean squares
in factorials. Annals of Mathematical Statistics, 27, 907-949.
Also, even though hand-order is balanced, I would analyze the data
with order as a grouping factor, making it a one-between, two-within
design. |
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| sue |
| Posted: Sun Jan 14, 2007 7:50 pm |
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Guest
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perhaps my explanation of my conundrum was a little unclear.
It was suggested that I put condition in the one model as both a fixed
and random factor.
So reponse is a function of b.condition + beta.condition
where sum bi=0 and beta normally distd.
How does one interpret the results? Is it really a valid thing to do?
sue |
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| Ray Koopman |
| Posted: Mon Jan 15, 2007 4:51 am |
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sue wrote:
Quote: perhaps my explanation of my conundrum was a little unclear.
It was suggested that I put condition in the one model as both a fixed
and random factor.
So reponse is a function of b.condition + beta.condition
where sum bi=0 and beta normally distd.
How does one interpret the results? Is it really a valid thing to do?
sue
You can't treat a factor as both fixed and random simultaneously,
in a single analysis, but you can certainly do it sequentially,
in two analyses. They would simply answer two different questions.
Changing a factor from fixed to random affects only tests of effects
that do not involve that factor. In your case, changing Condition from
fixed to random would affect only the tests of the effects of Group,
Hand, and the GH interaction. The expected mean squares of those
sources would change, requiring different denominators in the Fs.
The usual, but not necessary, result is that it becomes harder to
reject the null, because some of each observed mean square can be
attributed to interaction with the newly-random factors. |
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| Guest |
| Posted: Wed Jan 17, 2007 10:06 am |
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Ray Koopman wrote:
Quote: sue wrote:
perhaps my explanation of my conundrum was a little unclear.
It was suggested that I put condition in the one model as both a fixed
and random factor.
So reponse is a function of b.condition + beta.condition
where sum bi=0 and beta normally distd.
How does one interpret the results? Is it really a valid thing to do?
sue
You can't treat a factor as both fixed and random simultaneously,
in a single analysis, but you can certainly do it sequentially,
in two analyses. They would simply answer two different questions.
Changing a factor from fixed to random affects only tests of effects
that do not involve that factor. In your case, changing Condition from
fixed to random would affect only the tests of the effects of Group,
Hand, and the GH interaction.
It is a but more complicated. A random effect implicitely implies a
compound correlation structure of the observations of the same stratum.
A fixed effects term still assumes independence.
Alain
www.highstat.com
highstat@highstat.com
he expected mean squares of those
Quote: sources would change, requiring different denominators in the Fs.
The usual, but not necessary, result is that it becomes harder to
reject the null, because some of each observed mean square can be
attributed to interaction with the newly-random factors. |
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| Bill H |
| Posted: Wed Jan 17, 2007 11:36 am |
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sue wrote:
Quote: perhaps my explanation of my conundrum was a little unclear.
It was suggested that I put condition in the one model as both a fixed
and random factor.
So reponse is a function of b.condition + beta.condition
where sum bi=0 and beta normally distd.
How does one interpret the results? Is it really a valid thing to do?
sue
It might help to think of the random effect as a model for the variance
and the fixed effect a model for the mean. The magnitude of the random
effect is usually not interpreted, although if it is statistically
significant, that means you are modeling some of the variance within
condition that needs to be modeled, ie. if not modeled would become
part of the general error term and basically screw up your tests of the
fixed effects. |
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| sue |
| Posted: Thu Jan 18, 2007 8:25 pm |
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My reading tells me that what my colleague meant was my factors are
mixed effects.
So the factor does have a random contribution and a fixed contribution.
In effect it is both random and fixed.
A whole new world opens up.......with a whole new language.
sue |
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| Brett Magill |
| Posted: Fri Jan 19, 2007 11:01 am |
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sue wrote:
Quote: My reading tells me that what my colleague meant was my factors are
mixed effects.
So the factor does have a random contribution and a fixed contribution.
In effect it is both random and fixed.
A whole new world opens up.......with a whole new language.
sue
Sue,
Mixed models contain both random and fixed factors, thus they are mixed
in the sense that they are not purely random or purely fixed. However,
each factor is either random or fixed. The levels of a factor are
either a sample of the possible levels to which you intend to infer or
the levels are exhaustive. |
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| klange |
| Posted: Sun Jan 21, 2007 7:02 pm |
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Hi Sue,
This sounds like the kind of language found in multilevel (or
heirarchical) modeling, where effects can indeed have both a fixed and
random component - a different use of the terms as found in ANOVA-type
models. I'd recommend Judith Singer's work for a good introduction to
the terminology etc.
Cheers,
Kylie.
sue wrote:
Quote: My reading tells me that what my colleague meant was my factors are
mixed effects.
So the factor does have a random contribution and a fixed contribution.
In effect it is both random and fixed.
A whole new world opens up.......with a whole new language.
sue |
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| sue |
| Posted: Sun Jan 21, 2007 8:54 pm |
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klange wrote:
Quote: Hi Sue,
This sounds like the kind of language found in multilevel (or
heirarchical) modeling, where effects can indeed have both a fixed and
random component - a different use of the terms as found in ANOVA-type
models. I'd recommend Judith Singer's work for a good introduction to
the terminology etc.
Cheers,
Thanks Kylie,
I am already sorting my way through Judiths paper. It is a different
language that uses the same terms in anova in a different way. But it
certainly seems the way to go. My impression is that almost everything
should be done with multilevel. I've also found some course notes on
the web by carolyn anderson that are helpful. Any other references
gratefully received.
sue |
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