### sas >> difference between fixed effect model and random effect model

Hi,
What is the difference between a fixed effect model and random effect model
when the data have a multilevel structure, individuals within countres (2 level for example)

if I have Y as a continuous depedent variable and X1 a categorical variable representing countries (10 countries for example), and X2,X3 are 2 continuous variables

What will be the difference between Model1 (considering X1 as a set of dummy variables )

Model1: Y= X1 +X2+X3 +X1*X2+X1*X2 + e

e: individuals residulas

Model 2: Y= X2+X3 +v1*X2+w1*X2 + u1+e
u1,v1 and w1 country residual (random intercept and random slope)

Model 2: which includes the random effect of X1 using the proc mixed procedure for example?

---------------------------------
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### sas >> difference between fixed effect model and random effect model

>>> "adel F." < XXXX@XXXXX.COM > 5/18/2006 12:58 pm >>> wrote
<<<
What is the difference between a fixed effect model and random effect
model when the data have a multilevel structure, individuals within
countres (2 level for example) if I have Y as a continuous depedent
variable and X1 a categorical variable representing countries (10
countries for example), and X2,X3 are 2 continuous variables

What will be the difference between Model1 (considering X1 as a set
of dummy variables )

Model1: Y= X1 +X2+X3 +X1*X2+X1*X2 + e
e: individuals residulas

Model 2: Y= X2+X3 +v1*X2+w1*X2 + u1+e
u1,v1 and w1 country residual (random intercept and random slope)

Model 2: which includes the random effect of X1 using the proc mixed
procedure for example?

I was expecting responses from people who know what they are talking
about. I didn't see any, so I will attempt something, blatantly
ignoring Mark Twain's advice that it is better to keep silent and appear
foolish, that to speak, and remove all doubt :-)

One difference is that the assumptions of the first model are violated,
the assumptions of the second are not (at least, if you get the rest
right).

IME, tese differences affect the standard errors much more than the
parameter estimates.

The number of df for the two models will be different.

I don't fully understand your model 2, in particular, I am not sure
what v and w are in there for, or why X1 is not. If v and w are
attempts to get at interactions, then why not include random slopes

Maybe this will start a discussion

Peter

### sas >> difference between fixed effect model and random effect model

Here is a great doc that explains the differences in detail:

http://www.upa.pdx.edu/IOA/newsom/mlrclass/ho_randfixd.doc

### sas >> difference between fixed effect model and random effect model

Thanks to all
Yes Peter
w1 and v1 are the terms for the interactions (random slopes) and u1 is the term for the random intercept

my understanding is if we have individuals within clusters, the first model is not valid, because it doe not take into account the homogeneity of the individuals within a cluster and consider them as independents (when performing the estimation procedure for the parameters )

The second model take into account the association between individual within a cluster and provides the within cluster and between clusters variation

How much variation in the dependent variable is due to individuals and how much variation is due to the clusters

I hope I get it OK

Peter Flom < XXXX@XXXXX.COM > a rit :

>>> "adel F." 5/18/2006 12:58 pm >>> wrote
<<<
What is the difference between a fixed effect model and random effect
model when the data have a multilevel structure, individuals within
countres (2 level for example) if I have Y as a continuous depedent
variable and X1 a categorical variable representing countries (10
countries for example), and X2,X3 are 2 continuous variables

What will be the difference between Model1 (considering X1 as a set
of dummy variables )

Model1: Y= X1 +X2+X3 +X1*X2+X1*X2 + e
e: individuals residulas

Model 2: Y= X2+X3 +v1*X2+w1*X2 + u1+e
u1,v1 and w1 country residual (random intercept and random slope)

Model 2: which includes the random effect of X1 using the proc mixed
procedure for example?

I was expecting responses from people who know what they are talking
about. I didn't see any, so I will attempt something, blatantly
ignoring Mark Twain's advice that it is better to keep silent and appear
foolish, that to speak, and remove all doubt :-)

One difference is that the assumptions of the first model are violated,
the assumptions of the second are not (at least, if you get the rest
right).

IME, tese differences affect the standard errors much more than the
parameter estimates.

The number of df for the two models will be different.

I don't fully understand your model 2, in particular, I am not sure
what v and w are in there for, or why X1 is not. If v and w are
attempts to get at interactions, then why not include random slopes

Maybe this will start a discussion

Peter

---------------------------------
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### sas >> difference between fixed effect model and random effect model

XXXX@XXXXX.COM wrote back:

If you have a cluster sample - meaning, you have a survey sample with
known design effects and clustering on at least one stage of your design -
then you may be looking at this the wrong way. If I'm correct, then you
should be looking at this as a survey sample problem, and not as a mixed
models problem.

In this case, you should be using PROC SURVEYREG to analyze the data,
and there is likely to be no issue about fixed vs. random effects at all.
Why, you ask? Because the point of random effects - addressing the fact
that you have a random sample of the possible effects, instead of the
complete population of effects - is already implicitly handled by the
cluster
design.

So, before we go any farther, we need to know about your data, and
you data sources, and your meta-data.

HTH,
David
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```Dale:

I know that I speak for many here when I say thank you for your prompt
and detailed explanations of all things statistical--you're a treasure!

Now that I am done brown-nosing, I have a couple of follow-up/follow-on
questions I'd like to put forth for comment.

You mention that fixed effect model assume that all off-diagonal
covariance terms are zero--but isn't this the same as saying the
observations are independent and have an identity matrix (i.e. no
correlation)?  I had always envisioned the inclusion of fixed terms for
each cluster of observations as having a covariance matrix more akin to
an exchangeable/compound symmetry than identity--a fixed model (in
effect) gives each subject (i.e. cluster) its own intercept, and thus
accounts for the marginal effect of membership in this cluster.  You
continue that if there is some off-diagonal correlation among
observations then using fixed effects are inefficient and the SEs can
be biased--but, again, I thought by including fixed subject effects you
are attempting to account for this correlation.

Staying with fixed effects for the moment, I recall that a key factor
in deciding whether to go with a fixed or random effects model is the
presence of correlation between the subject effect and other
explanatory variables in the model--if there is correlation, but you
use a random effects model, then the estimated correlation coefficients
are biased and inconsistent.  Using a fixed effects model protects
against this type of specification error, but at a cost of reduced
efficiency due to the increased number of parameters.

Now from what you have said and what I have previously gathered, the
decision regarding fixed vs. random puts one on the horns of a
dilemma--if you believe there is correlation within each cluster (and
why else would you try to include it in the model?) you should use a
model that accounts for off-diagonal correlation (marginal or random
effects); however, if there is correlation with other predictors in
your model (highly likely in non or quasi-experimental designs) you're
better off with a fixed effects model.

Now is this the point where you say "using a mixed effects model gets
you the best of both worlds..." or am I just fantasizing about a neat,
tidy solution ;-)

Thanks again for your time and attention, and looking forward to your

Pete

```

```I would like to seek your advice. The data have three waves. I am
analyzing the data with Fixed Effect Method (FEM) using each
individual as a cluster. In the FEM, do I have to be concerned about
multicollinearity among independent variables? Could you give me your

Best,
Sunhee
```

```Hello All,

I am testing analyst forecast error given certain characteristics of
earnings (let's say Earnings and SURPRISE).  My data range from 1980 to
2005, about 100,000 firm-years observations.  Possibly many firms are
duplicated.

I want to run fixed effect model,

Proc Mixed Data=ANALYST;
Class FirmID Year Quarter;
Model ForecastError = FirmID Year Quarter;
Random Earnings SURPRISE;
Run;

Am I correct to run firm and year fixed effect?

Thank you for your comment and help.  I always appreciate your help.

Minsup

```