This message has been cross posted to the following eGroups: Young Professionals Group and Statistical Consulting Section .
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Hello all:

Although I have a PhD in Statistics, I don't know much about Random and Mixed Effects models beyond the content of "Applied Linear Statistical Models" by Neter, Kutner, et al. What is the best book(s) on the subject?

Regards,
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Nik Tuzov
PhD
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Lots of choices, but Molenberghs is good; Brown and Prescot is good and  more readable,  Fitzmaurice and Laird is also quite readable and more comprehensive than Brown and Prescot.
If you are using SAS, the SAS manual on Mixed Models is a good starting point.  Virtually all the books are based on SAS coding.  There are good books on Stata coding (Rabe-Hesketh),
I'm less familiar with R books in this area.
SPSS you will have to see if anyone else on the listserve knows of any; SPSS has been rather slow at developing advanced statistical methods.  Probably because it is "owner of the day" of the SPSS software.

Ray

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Raymond Hoffmann, PhD
Professor of Biostatistics
Medical College of Wisconsin
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There are several. Start with
Linear Mixed Models for Longitudinal Data (09) by Verbeke, Geert - Molenberghs,

and

Mixed-Effects Models in S and S-PLUS (Statistics and Computing)

José Pinheiro (Author), Douglas Bates

Pinheiro has mixed model software in R as well


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Chris Barker, Ph.D.
www,barkerstats.com

---
"In composition you have all the time you want to decide what to say in 15 seconds, in improvisation you have 15 seconds."
-Steve Lacy
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I noticed that you have been getting some wonderful suggestions. But, I just wanted to throw one more into the mix:

Linear Mixed Models: A Practical Guide Using Statistical Software.
West, Welch, and Galecki

As the title indicates, the topics are covered through examples. And, at the end of each chapter the book provides syntax for SAS, SPSS, R (I might be missing some software from the list).

This will be a great book if you have not decided on the software that you will be using, or if you are familiar with one software but need to use a different one.

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David Reyes-Gastelum
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I second the recommendation for West et al's book. It takes some specific data set examples of different common models, and shows them in 5 packages: R, SAS, SPSS, Stata and HLM.

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Michael Kruger
Information Resources Inc
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Original Message:
Sent: 05-30-2013 10:28
From: David Reyes-Gastelum
Subject: A question about Random and Mixed Effects models

I noticed that you have been getting some wonderful suggestions. But, I just wanted to throw one more into the mix:

Linear Mixed Models: A Practical Guide Using Statistical Software.
West, Welch, and Galecki

As the title indicates, the topics are covered through examples. And, at the end of each chapter the book provides syntax for SAS, SPSS, R (I might be missing some software from the list).

This will be a great book if you have not decided on the software that you will be using, or if you are familiar with one software but need to use a different one.

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David Reyes-Gastelum
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Hi all who are interested in Random and Mixed Model effects:
The book by Thomas Lorenzen and Virgil Anderson "Design of Experiments: A No-Name Approach" leads implicitly to an interesting research question:  What is the correct model?  Should we use a restricted model or an unrestricted model?  I have generally used the unrestricted model but sometimes the restricted model gives a more reasonable set of variance components.  The "No-Name Approach" book generally uses a restricted model with Sum effects = 0 for some sets of effects (even for cases where I SEE NO SCIENTIFIC REASON FOR THE EFFECTS TO SUM TO ZERO.  Why does the data act as if such restrictions are present?  
I have seldom seen this problem discussed in the literature.  It deserves more study and comments.  Has anyone in the eGroup seen good references on this?
A background comment:  Is the restriction Sum effects = 0 a restriction on the model  or just a restriction on the set of equations because the ANOVA model is over-parameterized.  Depending on how you answer this question you will get different sets of variance components.
Jim Lucas



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James Lucas
J M Lucas & Associates
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Original Message:
Sent: 05-31-2013 00:54
From: Michael Kruger
Subject: A question about Random and Mixed Effects models

I second the recommendation for West et al's book. It takes some specific data set examples of different common models, and shows them in 5 packages: R, SAS, SPSS, Stata and HLM.

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Michael Kruger
Information Resources Inc
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James:  You bring up  a long discussed problem.  Ron Hocking has a paper in AM Stat about 30 or so years ago.  If you start with the unrestricted model and impose the restrictions on the random effects (a thing that was used so one could carry out computations and evaluate expected mean squares by hand using summation notation) you also change the definition of the associated variance components.  This change in definition of the variance component is ignored by those who use the restricted model, but if you use the expected mean squares from the new definition of the variance components in the restricted model and look at the expected mean squares for the unrestricted model you get the same estimates of the variance components.  There is a relationship between unstricted variance components and the new definiton of the restricted variance components.  I think you can see it easily by working through a 2 way mixed model.  Anyway, the restrictions on the random effects random variables do not make any sense unless you redefine the variance component parameters.  I use the "Unrestricted Model" as does most mixed models software.  There are some "old" programs that used the summation notation for estimating the variance components and used the "restricted model", but did not redefine the variance components accordingly.  Those results are wrong.

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George Milliken
-------------------------------------------







Original Message:
Sent: 06-03-2013 10:47
From: James Lucas
Subject: A question about Random and Mixed Effects models

Hi all who are interested in Random and Mixed Model effects:
The book by Thomas Lorenzen and Virgil Anderson "Design of Experiments: A No-Name Approach" leads implicitly to an interesting research question:  What is the correct model?  Should we use a restricted model or an unrestricted model?  I have generally used the unrestricted model but sometimes the restricted model gives a more reasonable set of variance components.  The "No-Name Approach" book generally uses a restricted model with Sum effects = 0 for some sets of effects (even for cases where I SEE NO SCIENTIFIC REASON FOR THE EFFECTS TO SUM TO ZERO.  Why does the data act as if such restrictions are present?  
I have seldom seen this problem discussed in the literature.  It deserves more study and comments.  Has anyone in the eGroup seen good references on this?
A background comment:  Is the restriction Sum effects = 0 a restriction on the model  or just a restriction on the set of equations because the ANOVA model is over-parameterized.  Depending on how you answer this question you will get different sets of variance components.
Jim Lucas



-------------------------------------------
James Lucas
J M Lucas & Associates
-------------------------------------------







Original Message:
Sent: 05-31-2013 00:54
From: Michael Kruger
Subject: A question about Random and Mixed Effects models

I second the recommendation for West et al's book. It takes some specific data set examples of different common models, and shows them in 5 packages: R, SAS, SPSS, Stata and HLM.

-------------------------------------------
Michael Kruger
Information Resources Inc
-------------------------------------------

Hi George,
I am familiar with some of your comments because I was a student at Texas A&M at the time this question originally came up and read those articles many years ago.
I disagree with some of your comments because in some cases there are true model restrictions.  Sometimes the restricted model is the correct model.  For example there can be a "splitter" in an industrial flow so when one flow increases the other flows decrease.  I have seen cases (many proprietary) where a restricted model is appropriate (and I believe I remember some from the "No-Name Approach").  If the wrong model is used then wrong inferences can be made.  If you use the unrestricted model and there are truly restrictions then you are using the wrong model. This is the problem that has not been discussed in the literature (as far as I know).
Jim

-------------------------------------------
James Lucas
J M Lucas & Associates
-------------------------------------------







Original Message:
Sent: 06-03-2013 12:00
From: George Milliken
Subject: A question about Random and Mixed Effects models

James:  You bring up  a long discussed problem.  Ron Hocking has a paper in AM Stat about 30 or so years ago.  If you start with the unrestricted model and impose the restrictions on the random effects (a thing that was used so one could carry out computations and evaluate expected mean squares by hand using summation notation) you also change the definition of the associated variance components.  This change in definition of the variance component is ignored by those who use the restricted model, but if you use the expected mean squares from the new definition of the variance components in the restricted model and look at the expected mean squares for the unrestricted model you get the same estimates of the variance components.  There is a relationship between unstricted variance components and the new definiton of the restricted variance components.  I think you can see it easily by working through a 2 way mixed model.  Anyway, the restrictions on the random effects random variables do not make any sense unless you redefine the variance component parameters.  I use the "Unrestricted Model" as does most mixed models software.  There are some "old" programs that used the summation notation for estimating the variance components and used the "restricted model", but did not redefine the variance components accordingly.  Those results are wrong.

-------------------------------------------
George Milliken
-------------------------------------------







Original Message:
Sent: 06-03-2013 10:47
From: James Lucas
Subject: A question about Random and Mixed Effects models

Hi all who are interested in Random and Mixed Model effects:
The book by Thomas Lorenzen and Virgil Anderson "Design of Experiments: A No-Name Approach" leads implicitly to an interesting research question:  What is the correct model?  Should we use a restricted model or an unrestricted model?  I have generally used the unrestricted model but sometimes the restricted model gives a more reasonable set of variance components.  The "No-Name Approach" book generally uses a restricted model with Sum effects = 0 for some sets of effects (even for cases where I SEE NO SCIENTIFIC REASON FOR THE EFFECTS TO SUM TO ZERO.  Why does the data act as if such restrictions are present?  
I have seldom seen this problem discussed in the literature.  It deserves more study and comments.  Has anyone in the eGroup seen good references on this?
A background comment:  Is the restriction Sum effects = 0 a restriction on the model  or just a restriction on the set of equations because the ANOVA model is over-parameterized.  Depending on how you answer this question you will get different sets of variance components.
Jim Lucas



-------------------------------------------
James Lucas
J M Lucas & Associates
-------------------------------------------

Hi George,
I am familiar with some of your comments because I was a student at Texas A&M at the time this question originally came up and read those articles many years ago.
I disagree with some of your comments because in some cases there are true model restrictions.  Sometimes the restricted model is the correct model.  For example there can be a "splitter" in an industrial flow so when one flow increases the other flows decrease.  I have seen cases (many proprietary) where a restricted model is appropriate (and I believe I remember some from the "No-Name Approach").  If the wrong model is used then wrong inferences can be made.  If you use the unrestricted model and there are truly restrictions then you are using the wrong model. This is the problem that has not been discussed in the literature (as far as I know).
Jim

-------------------------------------------
James Lucas
J M Lucas & Associates
-------------------------------------------







Original Message:
Sent: 06-03-2013 12:00
From: George Milliken
Subject: A question about Random and Mixed Effects models

James:  You bring up  a long discussed problem.  Ron Hocking has a paper in AM Stat about 30 or so years ago.  If you start with the unrestricted model and impose the restrictions on the random effects (a thing that was used so one could carry out computations and evaluate expected mean squares by hand using summation notation) you also change the definition of the associated variance components.  This change in definition of the variance component is ignored by those who use the restricted model, but if you use the expected mean squares from the new definition of the variance components in the restricted model and look at the expected mean squares for the unrestricted model you get the same estimates of the variance components.  There is a relationship between unstricted variance components and the new definiton of the restricted variance components.  I think you can see it easily by working through a 2 way mixed model.  Anyway, the restrictions on the random effects random variables do not make any sense unless you redefine the variance component parameters.  I use the "Unrestricted Model" as does most mixed models software.  There are some "old" programs that used the summation notation for estimating the variance components and used the "restricted model", but did not redefine the variance components accordingly.  Those results are wrong.

-------------------------------------------
George Milliken
-------------------------------------------







Original Message:
Sent: 06-03-2013 10:47
From: James Lucas
Subject: A question about Random and Mixed Effects models

Hi all who are interested in Random and Mixed Model effects:
The book by Thomas Lorenzen and Virgil Anderson "Design of Experiments: A No-Name Approach" leads implicitly to an interesting research question:  What is the correct model?  Should we use a restricted model or an unrestricted model?  I have generally used the unrestricted model but sometimes the restricted model gives a more reasonable set of variance components.  The "No-Name Approach" book generally uses a restricted model with Sum effects = 0 for some sets of effects (even for cases where I SEE NO SCIENTIFIC REASON FOR THE EFFECTS TO SUM TO ZERO.  Why does the data act as if such restrictions are present?  
I have seldom seen this problem discussed in the literature.  It deserves more study and comments.  Has anyone in the eGroup seen good references on this?
A background comment:  Is the restriction Sum effects = 0 a restriction on the model  or just a restriction on the set of equations because the ANOVA model is over-parameterized.  Depending on how you answer this question you will get different sets of variance components.
Jim Lucas



-------------------------------------------
James Lucas
J M Lucas & Associates
-------------------------------------------

Jim,

My opinion is that the sum to zero constraints are an unwanted hangover from certain fixed effects models.  That constraint introduces a negative covariance among random effects.  Yes, you get different estimates of the variance components, but that's because Var alpha "means" different things in the two models.  Hocking 1985, The Analysis of Linear Models, section 10.4 has an especially clear discussion of the two models.  A summary of that is in my notes for our 2nd semester methods class.  Go to  http://www.public.iastate.edu/~pdixon/stat511/notes/part%203.pdf and look at slides 110 - 1106

Philip
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Philip Dixon
Iowa State Univ
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Hi Philip,
Thank you for the comment.
I believe that my answer to George Millikan's comment also answers yours.
However, I believe that both your comments show the need to answer my question more fully in the literature.
While I agree, that in most cases, he unrestricted model is appropriate; there are other cases when the restricted model is appropriate.
The difference between these cases and discussions of potential errors when the wrong model is used has not been discussed in the literature and this question should be discussed.
Jim

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James Lucas
J M Lucas & Associates
-------------------------------------------







Original Message:
Sent: 06-03-2013 12:35
From: Philip Dixon
Subject: A question about Random and Mixed Effects models

Jim,

My opinion is that the sum to zero constraints are an unwanted hangover from certain fixed effects models.  That constraint introduces a negative covariance among random effects.  Yes, you get different estimates of the variance components, but that's because Var alpha "means" different things in the two models.  Hocking 1985, The Analysis of Linear Models, section 10.4 has an especially clear discussion of the two models.  A summary of that is in my notes for our 2nd semester methods class.  Go to  http://www.public.iastate.edu/~pdixon/stat511/notes/part%203.pdf and look at slides 110 - 1106

Philip
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Philip Dixon
Iowa State Univ
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Dear James The sum to zero constraint can also be expressed as a BLUP defined on the unconstrained model. We addressed this in McLean, Sanders & Stroup 1991 American Statistician. I'm on vacation & unable to access details Till I get back to Lincoln. Alternatively George is right that sum to zero model xan be viwed as a particular kind of covariance structure Big problem with sum to zero constraint is that it gets messy with unbalaced data &I REALLY messy with complex design &part unbalaced data. Nelder's take on this issue was instructive: "This way madness lies." Walt ------------------------------------------- Walter Stroup Univ Of Nebraska -------------------------------------------
Original Message: Sent: 06-03-2013 13:29 From: James Lucas Subject: A question about Random and Mixed Effects models Hi Philip, Thank you for the comment. I believe that my answer to George Millikan's comment also answers yours. However, I believe that both your comments show the need to answer my question more fully in the literature. While I agree, that in most cases, he unrestricted model is appropriate; there are other cases when the restricted model is appropriate. The difference between these cases and discussions of potential errors when the wrong model is used has not been discussed in the literature and this question should be discussed. Jim ------------------------------------------- James Lucas J M Lucas & Associates -------------------------------------------
Original Message: Sent: 06-03-2013 12:35 From: Philip Dixon Subject: A question about Random and Mixed Effects models Jim, My opinion is that the sum to zero constraints are an unwanted hangover from certain fixed effects models. That constraint introduces a negative covariance among random effects. Yes, you get different estimates of the variance components, but that's because Var alpha "means" different things in the two models. Hocking 1985, The Analysis of Linear Models, section 10.4 has an especially clear discussion of the two models. A summary of that is in my notes for our 2nd semester methods class. Go to http://www.public.iastate.edu/~pdixon/stat511/notes/part%203.pdf <http://www.public.iastate.edu/~pdixon/stat511/notes/part%203.pdf> and look at slides 110 - 1106 Philip ------------------------------------------- Philip Dixon Iowa State Univ -------------------------------------------