Re: [ECOLOG-L] fixed vs. random effects in field research

[Bob O'Hara]

On 17/05/16 20:12, Gary Grossman wrote:

I'm having a bit of difficulty getting a clear understanding of what
should be considered a fixed vs. a random effect in a linear mixed model
analysis of field data. Even the statisticians seem to say "it depends
on who's defining it" or "sometimes the same treatment/variable can be
either". Some examples may help, let's say I collected samples annually
in three sites and wanted to test for the effect of daily rainfall,
daily temperature, and density, on recruitment of individuals in the
following year. Using the lmer function in R which of these would be
fixed effects and which would be random? A reference or two would help.
I really couldn't find much in a google search on field studies, but I
didn't go to anything like zoological abstracts. TIA, g2

That's easy! If you only have 3 sites, you don't have enough levels to 
make it worth fitting a random effect.


I look at random effects hierarchically. Basically, the values of random 
effects are assumed to be drawn from a normal distribution, whereas 
fixed effects are assumed to be totally free. What this means is that if 
you have an effect with an unobserved level of the factor, do you think 
the observed levels would tell you something about what values are 
likely for the unobserved level. If you think they do then a random 
effect make make sense.


What you are doing when you have a random effect is estimating the 
variance of the values of the level of the factors. In the example you 
give, I think a random effect would probably make sense if you had (say) 
20 sites, but with three sites you are trying to estimate the variance 
from (in effect) 3 data points. the estimate won't be very good, so as a 
practical matter it's not worth bothering with the extra hassle.


Of course, this is only my opinion: there are other ways of looking at 
random effects, so pick the one which works for you. There will always 
be cases where it's not clear if something should be considered fixed or 
random.


Bob


--
Gary D. Grossman, PhD
Fellow, American Fisheries Soc.

Professor of Animal Ecology
Warnell School of Forestry & Natural Resources
University of Georgia
Athens, GA, USA 30602

Website - Science, Art (G. Grossman Fine Art) and Music
www.garygrossman.net 

Board of Editors - Animal Biodiversity and Conservation
Editorial Board - Freshwater Biology
Editorial Board - Ecology Freshwater Fish

Hutson Gallery Provincetown, MA - www.hutsongallery.net/artists.html






--
Bob O'Hara

Biodiversity and Climate Research Centre
Senckenberganlage 25
D-60325 Frankfurt am Main,
Germany

Tel: +49 69 7542 1863
Mobile: +49 1515 888 5440
WWW:   http://www.bik-f.de/root/index.php?page_id=219
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Re: [ECOLOG-L] fixed vs. random effects in field research

[David Schneider]

Here is a how Quinn  and Keough (2002 Cambridge University 
Press) address the distinction between random and fixed effects.
_
8.1.1 Types of predictor variables (factors)
There are two types of categorical predictor variables
in linear models. The most common type is
a fixed factor, where all the levels of the factor (i.e.
all the groups or treatments) that are of interest
are included in the analysis. We cannot extrapolate
our statistical conclusions beyond these specific
levels to other groups or treatments not in
the study. If we repeated the study, we would
usually use the same levels of the fixed factor
again. Linear models based on fixed categorical
predictor variables (fixed factors) are termed fixed
effects models (or Model 1 ANOVAs). Fixed effect
models are analogous to linear regression models
where X is assumed to be fixed. The other type of
factor is a random factor, where we are only using
a random selection of all the possible levels (or
groups) of the factor and we usually wish to make
inferences about all the possible groups from our
sample of groups. If we repeated the study, we
would usually take another sample of groups
from the population of possible groups. Linear
models based on random categorical predictor
variables (random factors) are termed random
effects models (or Model 2 ANOVAs). 
__

In the Grossman query (below) temperature, rainfall, and
density would likely be fixed because they are of interest -- 
the contrasts would be of interest across  the particular
values of temperature,  rainfall, and density.  Inference
would be only to the measured values and their contrasts.
All three variables become fixed if fitted as a regression
instead of as categorical variables. 
Temperature might be taken as a random variable over a small 
range, but would not be credible as a random variable over 
a wide range, given its profound effect on biological processes. 
Location would be either random or fixed, depending on whether 
the inference was to only those 3 sites at the stated dates of 
measurement (fixed), or to all possible sites in some stated 
area (random),  or to the hypothetical population of a very 
large number of repetitions at those sites (random, as above).
If the locations were known to differ in some salient 
biological way, such that they could be ordered as to
expected effect, location could be legitimately treated as fixed.

The choice of random versus fixed categorical variable lies with 
the judgement and knowledge of the biologist.
A good statistician will demure on demands for hard and fast rules. 
A good  statistician will instead probe the biologist as to the 
scope of inference, then help the biologist form the 
correctly nested (log) likelihood ratio (as in Quinn and 
Keogh or any of many texts).  The likelihood ratio is
key - in either a decision theoretic context (as in Quinn
and Keough) or with inference from a prior to a posterior 
probability, if that is what you want to do. 

~ David Schneider




Quoting "Street, Garrett" :

> There is also an excellent section on what constitutes a random or fixed
> effect in Tom Hobbs and Mevin Hooten's "Bayesian Models: a Statistical Primer
> for Ecologists" using fecundity of spotted owls (adapted from Clark's work on
> the subject), and again using hypothetical sampling of aboveground biomass,
> as examples. Both examples are accompanied by clear and concise explanations
> of the implications for the underlying distributions and assumptions of the
> model one might seek to fit, and for the ecology informing the models.
> 
> Garrett Street
> Assistant Professor
> Wildlife, Fisheries, and Aquaculture
> Mississippi State University
> 
> On May 17, 2016, at 4:34 PM, Brian Church
> > wrote:
> 
> There is a fairly detailed discussion of fixed vs. random effects on
> CrossValidated here:
>
http://stats.stackexchange.com/questions/4700/what-is-the-difference-between-fixed-effect-random-effect-and-mixed-effect-mode
> 
> Based on the discussion there, it seems like temperature, rainfall, and
> density could all be considered to be random effects for the following
> reasons:
> 1. You are unlikely to sample the entire populations for those variables.
> 2. They are not being controlled
> 3. They are likely continuous and distributed in some way (e.g., normal)
> rather than discrete values
> 4. You are unlikely to be interested in responses at a specific temperature,
> rainfall, and density; rather, it seems more interesting to understand
> effects relating to the underlying distributions of those variables.
> 
> Those commenting in the CrossValidated forum cite a few sources, though they
> seem to be general/mathematical rather than ecology-specific. Hope that helps
> some.
> 
> -Brian Church
> 
> 
> On Tue, May 17, 2016 at 11:12 AM, Gary Grossman
> 

Re: [ECOLOG-L] fixed vs. random effects in field research

[Street, Garrett]

There is also an excellent section on what constitutes a random or fixed effect 
in Tom Hobbs and Mevin Hooten's "Bayesian Models: a Statistical Primer for 
Ecologists" using fecundity of spotted owls (adapted from Clark's work on the 
subject), and again using hypothetical sampling of aboveground biomass, as 
examples. Both examples are accompanied by clear and concise explanations of 
the implications for the underlying distributions and assumptions of the model 
one might seek to fit, and for the ecology informing the models.

Garrett Street
Assistant Professor
Wildlife, Fisheries, and Aquaculture
Mississippi State University

On May 17, 2016, at 4:34 PM, Brian Church 
> wrote:

There is a fairly detailed discussion of fixed vs. random effects on 
CrossValidated here: 
http://stats.stackexchange.com/questions/4700/what-is-the-difference-between-fixed-effect-random-effect-and-mixed-effect-mode

Based on the discussion there, it seems like temperature, rainfall, and density 
could all be considered to be random effects for the following reasons:
1. You are unlikely to sample the entire populations for those variables.
2. They are not being controlled
3. They are likely continuous and distributed in some way (e.g., normal) rather 
than discrete values
4. You are unlikely to be interested in responses at a specific temperature, 
rainfall, and density; rather, it seems more interesting to understand effects 
relating to the underlying distributions of those variables.

Those commenting in the CrossValidated forum cite a few sources, though they 
seem to be general/mathematical rather than ecology-specific. Hope that helps 
some.

-Brian Church


On Tue, May 17, 2016 at 11:12 AM, Gary Grossman 
> wrote:
I'm having a bit of difficulty getting a clear understanding of what should be 
considered a fixed vs. a random effect in a linear mixed model analysis of 
field data. Even the statisticians seem to say "it depends on who's defining 
it" or "sometimes the same treatment/variable can be either". Some examples may 
help, let's say I collected samples annually in three sites and wanted to test 
for the effect of daily rainfall, daily temperature, and density, on 
recruitment of individuals in the following year. Using the lmer function in R 
which of these would be fixed effects and which would be random? A reference or 
two would help. I really couldn't find much in a google search on field 
studies, but I didn't go to anything like zoological abstracts. TIA, g2

--
Gary D. Grossman, PhD
Fellow, American Fisheries Soc.

Professor of Animal Ecology
Warnell School of Forestry & Natural Resources
University of Georgia
Athens, GA, USA 30602

Website - Science, Art (G. Grossman Fine Art) and Music 
www.garygrossman.net

Board of Editors - Animal Biodiversity and Conservation
Editorial Board - Freshwater Biology
Editorial Board - Ecology Freshwater Fish

Hutson Gallery Provincetown, MA - 
www.hutsongallery.net/artists.html

Re: [ECOLOG-L] fixed vs. random effects in field research

[Brian Church]

There is a fairly detailed discussion of fixed vs. random effects on
CrossValidated here:
http://stats.stackexchange.com/questions/4700/what-is-the-difference-between-fixed-effect-random-effect-and-mixed-effect-mode

Based on the discussion there, it seems like temperature, rainfall, and
density could all be considered to be random effects for the following
reasons:
1. You are unlikely to sample the entire populations for those variables.
2. They are not being controlled
3. They are likely continuous and distributed in some way (e.g., normal)
rather than discrete values
4. You are unlikely to be interested in responses at a specific
temperature, rainfall, and density; rather, it seems more interesting to
understand effects relating to the underlying distributions of those
variables.

Those commenting in the CrossValidated forum cite a few sources, though
they seem to be general/mathematical rather than ecology-specific. Hope
that helps some.

-Brian Church


On Tue, May 17, 2016 at 11:12 AM, Gary Grossman 
wrote:

> I'm having a bit of difficulty getting a clear understanding of what
> should be considered a fixed vs. a random effect in a linear mixed model
> analysis of field data. Even the statisticians seem to say "it depends on
> who's defining it" or "sometimes the same treatment/variable can be
> either". Some examples may help, let's say I collected samples annually in
> three sites and wanted to test for the effect of daily rainfall, daily
> temperature, and density, on recruitment of individuals in the following
> year. Using the lmer function in R which of these would be fixed effects
> and which would be random? A reference or two would help. I really couldn't
> find much in a google search on field studies, but I didn't go to anything
> like zoological abstracts. TIA, g2
>
> --
> Gary D. Grossman, PhD
> Fellow, American Fisheries Soc.
>
> Professor of Animal Ecology
> Warnell School of Forestry & Natural Resources
> University of Georgia
> Athens, GA, USA 30602
>
> Website - Science, Art (G. Grossman Fine Art) and Music
> www.garygrossman.net
>
> Board of Editors - Animal Biodiversity and Conservation
> Editorial Board - Freshwater Biology
> Editorial Board - Ecology Freshwater Fish
>
> Hutson Gallery Provincetown, MA - www.hutsongallery.net/artists.html
>
>
>

Re: [ECOLOG-L] fixed vs. random effects in field research

[Gabriel Barros]

Hi Dr. Grossman,

The definition of fixed and random independent variables is really an
eternal struggle.
I believe the book of Tony Underwood might help you someway.

Underwood, A.J. Experiments in ecology: their logical design and
interpretation using analysis of variance, xviii, 504p. Cambridge
University Press, 1996.

Best regards,

Gabriel

*Gabriel Barros Gonçalves de Souza*
Biologist - M.Sc. in Ecology and Biomonitoring
PhD Candidate in Ecology at Federal University of Rio de Janeiro (UFRJ)
Laboratory of Fishery Biology and Technology
CRBio: 59.707/05-D
Cel: +55 (71) 99187-9065
CV Lattes: http://lattes.cnpq.br/4012374701934609

2016-05-17 15:12 GMT-03:00 Gary Grossman :

> I'm having a bit of difficulty getting a clear understanding of what
> should be considered a fixed vs. a random effect in a linear mixed model
> analysis of field data. Even the statisticians seem to say "it depends on
> who's defining it" or "sometimes the same treatment/variable can be
> either". Some examples may help, let's say I collected samples annually in
> three sites and wanted to test for the effect of daily rainfall, daily
> temperature, and density, on recruitment of individuals in the following
> year. Using the lmer function in R which of these would be fixed effects
> and which would be random? A reference or two would help. I really couldn't
> find much in a google search on field studies, but I didn't go to anything
> like zoological abstracts. TIA, g2
>
> --
> Gary D. Grossman, PhD
> Fellow, American Fisheries Soc.
>
> Professor of Animal Ecology
> Warnell School of Forestry & Natural Resources
> University of Georgia
> Athens, GA, USA 30602
>
> Website - Science, Art (G. Grossman Fine Art) and Music
> www.garygrossman.net
>
> Board of Editors - Animal Biodiversity and Conservation
> Editorial Board - Freshwater Biology
> Editorial Board - Ecology Freshwater Fish
>
> Hutson Gallery Provincetown, MA - www.hutsongallery.net/artists.html
>
>
>

[ECOLOG-L] fixed vs. random effects in field research

[Gary Grossman]

I'm having a bit of difficulty getting a clear understanding of what should
be considered a fixed vs. a random effect in a linear mixed model analysis
of field data. Even the statisticians seem to say "it depends on who's
defining it" or "sometimes the same treatment/variable can be either". Some
examples may help, let's say I collected samples annually in three sites
and wanted to test for the effect of daily rainfall, daily temperature, and
density, on recruitment of individuals in the following year. Using the
lmer function in R which of these would be fixed effects and which would be
random? A reference or two would help. I really couldn't find much in a
google search on field studies, but I didn't go to anything like zoological
abstracts. TIA, g2

-- 
Gary D. Grossman, PhD
Fellow, American Fisheries Soc.

Professor of Animal Ecology
Warnell School of Forestry & Natural Resources
University of Georgia
Athens, GA, USA 30602

Website - Science, Art (G. Grossman Fine Art) and Music www.garygrossman.net

Board of Editors - Animal Biodiversity and Conservation
Editorial Board - Freshwater Biology
Editorial Board - Ecology Freshwater Fish

Hutson Gallery Provincetown, MA - www.hutsongallery.net/artists.html