[R-sig-ME] A three-level GLMM with binomial link in R

Ben Bolker bbo|ker @end|ng |rom gm@||@com
Fri Mar 12 20:45:10 CET 2021 


On 3/12/21 12:13 PM, Hedyeh Ahmadi wrote:
> Here are my comments/questions:
> 
>  1. I have tried changing the site, family, and id to factor and I get
>     the same results.
>  2. Unfortunately, I can't share my data due to privacy issues but if
>     you tell me what other information you need, I can provide it.

   We know you can't share the data.  Part of the art of getting 
software help is figuring out how you can create a shareable version of 
your data set, *or* a shareable version of something that will generate 
the same errors you're experiencing.  We need to do a bisection search 
between the private data you have, which causes problems with factor 
expansion in the grouping variables and is surprisingly memory-hungry, 
and the reproducible examples that I have constructed that mimic some 
aspects of your data set but don't show either problem.  Since we can't 
look at your data, the burden falls on you to create a 
reproducible/shareable example we can work with.

    Assuming that

lmer(y ~ 1  +(1|site/family/id) , data =dd)

does show problems with your actual data set, can you anonymize the 
levels of site, family, and id, something like

   anon_fac <- function(x, prefix="S") {
       factor(x, levels=levels(x), labels=paste0(prefix, 
seq(length(levels(x))))
   }

   anon_dd <- transform(dd, select=c(family, site, id))
   anon_dd <- transform(anon_dd,
           site=anon_fac(site,"S"),
           family=anon_fac(family,"F"),
           id=anon_fac(id,"I")
   )

This should provide a data set that contains *no* information other than 
the pattern of co-occurrence of grouping levels. I don't know who's in 
charge of data privacy for your group, but it's hard to imagine how 
sharing this would present a risk of personal identification ...

https://stackoverflow.com/questions/10454973/how-to-create-example-data-set-from-private-data-replacing-variable-names-and-l

https://stackoverflow.com/questions/5963269/how-to-make-a-great-r-reproducible-example/6699112#6699112


>  3. Note that when I run the three-way interaction code in my PC it
>     again runs out of memory and the error says the following. When I
>     tried to run it on interactive HPC, it kicks me out as it takes too
>     much memory/time so I will have to submit a batch script.
>     "Error: cannot allocate vector of size 18.1 Gb
>     In addition: Warning message:
>     In ans * length(l) :
>     Error: cannot allocate vector of size 18.1 Gb"
>  4. When I take out all the fixed effects, the problem still exists.


   That's good in one sense, as it simplifies the problem.

>  5. *Question:* Also note that my data has 22945 rows, and some
>     individuals have only baseline measurement only, some individuals
>     have baseline and 1 year measurement. A variable called eventname is
>     the indicator of that. I am now confused as my "id" variable does
>     not have this information (i.e. the order of measurement). How would
>     the model recognize that which repeated measure is measurment1 (i.e.
>     baseline) and which one is measurment2(i.e. 1 year)?  Or maybe
>     because I don't have a random slope, I don't need to define the
>     repeated measure structure and adding eventname as a fixed effect is
>     sufficient?

    Let's deal with this after we have the basic problems sorted.  If 
you want to account for the possible effects of ordering, then you'd 
need to add this variable ...

> 
> Thanks again for all your help on this.
> 
> Best,
> 
> Hedyeh Ahmadi, Ph.D.
> Statistician
> Keck School of Medicine
> Department of Preventive Medicine
> University of Southern California
> 
> Postdoctoral Scholar
> Institute for Interdisciplinary Salivary Bioscience Research (IISBR)
> University of California, Irvine
> 
> LinkedIn
> www.linkedin.com/in/hedyeh-ahmadi <http://www.linkedin.com/in/hedyeh-ahmadi>
> <http://www.linkedin.com/in/hedyeh-ahmadi><http://www.linkedin.com/in/hedyeh-ahmadi>
> 
> 
> 
> 
> ------------------------------------------------------------------------
> *From:* Ben Bolker <bbolker using gmail.com>
> *Sent:* Thursday, March 11, 2021 3:55 PM
> *To:* Hedyeh Ahmadi <hedyehah using usc.edu>; r-sig-mixed-models using r-project.org 
> <r-sig-mixed-models using r-project.org>; Megan M. Herting <herting using usc.edu>; 
> Elisabeth Burnor <burnor using usc.edu>
> *Subject:* Re: [R-sig-ME] A three-level GLMM with binomial link in R
> 
> 
> On 3/11/21 1:11 PM, Hedyeh Ahmadi wrote:
>> Hi Ben,
>> Thank you for all the help and informative replies. Here is some info 
>> about my data and my answers:
>> 
>>   * Yes, I am running the exact model however this is just my toy model
>>     to get the code to work.
>>   * Reminder, I am trying to get lmer with a continuous outcome (but
>>     same data structure, with 3 random intercept) work before moving to
>>     glmer() with a logit link with a categorical 0/1 outcome.
>>   * Here are some information about my data:
>>       o X1: num [1:22945] 9.25 NA 9.22 NA 9.22 NA 9.42 NA 9.25 NA ...
>>       o X2: int [1:22945] 117 140 128 125 113 138 126 130 120 121 ...
>>       o X3: chr [1:22945] "Female" "Male" "Male" "Male" "Male"
>>       o site: chr [1:22945] "site15" "site15" "site15" "site15" "site15"
>>         ... (I have 21 sites)
>>       o family: int [1:22945] 0 1 1 1 1 3 3 4 4 5 ...
>>       o id: chr [1:22945] "id1" "id2" "id2" "id3" "id3"...
>>   * The following model gives me the error that "Error: couldn't
>>     evaluate grouping factor id:(family:site) within model frame: try
>>     adding grouping factor to data frame explicitly if possible" - I ran
>>     this same model on a supercomputer and it *gave me the same error*,
>>     so this is not a memory limit issue.
> 
> So far I can't replicate this.  It seemed fishy to me that family was an
> integer (I would try explicitly converting it to a factor), but doesn't
> actually cause any problems in my example.
> 
>    (This differs from your example but not in ways I would expect to be
> important: in particular, the types of the grouping variables are the
> same [chr, int, chr]
> 
> n <- 10000
> set.seed(101)
> dd <- data.frame(y=rnorm(n),
>                    x1=rnorm(n),
>                    x2=rnorm(n),
>                    x3=rnorm(n),
>                    site=sample(paste0("s",1:15),size=n,replace=TRUE),
>                    family=sample(1:100,size=n,replace=TRUE),
>                    id=sample(paste0("id",1:20),size=n,replace=TRUE))
> library(lme4)
> lmer(y~1 + x1 + x2 + x3 + (1|site/family/id), data=dd)
> 
> ###
> 
> What is meant by "adding grouping factor to data frame explicitly" would
> be in this case expanding out the nested terms:
> 
>    dd <- within(dd,
> {
>       site_family <- interaction(site,family)
>       site_family_id <- interaction(site,family,id)
> })
> 
> lmer(y~1 + x1 + x2 + x3 + (1|site) + (1|site_family) +
> (1|site_family_id), data =dd)
> 
> 
> 
>>       o m2 <- lmer(cbcl_scr_syn_internal_r ~ 1 + X1 + X2 + X3 +
>>         (1|site/family/id), data=dd, REML = FALSE)
>>   * The following *model ran on a supercomputer*.  This is the model
>>     that previously would give me the error "Error: cannot allocate
>>     vector of size 2.3 Gb". Here I am*reducing the number of sites to
>>     see if it runs, and it did* run on a supercomputer.
>>       o m11 <- lmer(cbcl_scr_syn_internal_r ~ 1 + X1 +X2 + X3
>>         +(1|site/family/id) ,
>>              data=dd[-which(dd$abcd_site %in% c("site01","site02",
>>         "site04", "site05", "site06", "site07", "site08","site09")),],
>>         na.action=na.exclude, REML=FALSE)
>> 
>> Questions:
>> 
>>  1. What I don't understand is that in m2, why lmer() does not
>>     recognizes the grouping factor that it does recognize in m11?
> 
>    I'm not sure either.
> 
>>  2. At this point I don't think this is a memory issue as *m2 did not
>>     run on a supercompute*r and it's giving me *the same error as my
>>     personal computer*. However, in m11, the same grouping structure is
>>     being recognized when I reduce the number of sites from 21 to 13 -
>>     could this be because of severe imbalance in my family/id nesting,
>>     meaning most families have only one kid but some have 2 and a few
>>     have 3 kids?
> 
>     It seems surprising.
>     Is there any way we can get a reproducible example?  For example,
> suppose you randomize your X1, X2, X3 and anonymize all of your grouping
> variables: would you then be able to share the data set?
> 
>     Does the problem (let's say just the first problem) still occur if
> you leave out the fixed effects? (I would expect so, and that would
> simplify things somewhat - we're trying to get to the *simplest* example
> that still demonstrates the problem.)
> 
> 
>> 
>> Sorry about the long email and thank you for your help in advance.
>> 
>> Best,
>> 
>> Hedyeh Ahmadi, Ph.D.
>> Statistician
>> Keck School of Medicine
>> Department of Preventive Medicine
>> University of Southern California
>> 
>> Postdoctoral Scholar
>> Institute for Interdisciplinary Salivary Bioscience Research (IISBR)
>> University of California, Irvine
>> 
>> LinkedIn
>> https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!51-zg2ISp-lS-4HEW0ZNNEVE1ZD8ujdJZYx90xVOnZ-x6A7l6eu2KhSgMhYCJq4$ 
> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!51-zg2ISp-lS-4HEW0ZNNEVE1ZD8ujdJZYx90xVOnZ-x6A7l6eu2KhSgMhYCJq4$>  
> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!51-zg2ISp-lS-4HEW0ZNNEVE1ZD8ujdJZYx90xVOnZ-x6A7l6eu2KhSgMhYCJq4$ 
>  >
>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!51-zg2ISp-lS-4HEW0ZNNEVE1ZD8ujdJZYx90xVOnZ-x6A7l6eu2KhSgMhYCJq4$ 
>  ><https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!51-zg2ISp-lS-4HEW0ZNNEVE1ZD8ujdJZYx90xVOnZ-x6A7l6eu2KhSgMhYCJq4$ >
>> 
>> 
>> 
>> 
>> ------------------------------------------------------------------------
>> *From:* Ben Bolker <bbolker using gmail.com>
>> *Sent:* Tuesday, March 9, 2021 4:12 PM
>> *To:* Hedyeh Ahmadi <hedyehah using usc.edu>; r-sig-mixed-models using r-project.org 
>> <r-sig-mixed-models using r-project.org>
>> *Subject:* Re: [R-sig-ME] A three-level GLMM with binomial link in R
>>     OK, then it would be very helpful to have more details about your
>> data set. Are one or more of X1, X2, X3 categorical predictors with many
>> levels ... ?  Any chance we can see str() or summary() ?  Are you using
>> exactly the formula you told us about, or something slightly different?
>> 
>>     The computational burden of a large number of fixed effect parameters
>> will be much worse for glmer than for lmer, unless you use nAGQ=0.
>> glmmTMB would be able to help in two ways: (1) it doesn't scale as badly
>> for large numbers of fixed effects; (2) it allows sparse fixed-effect
>> model matrices (something we keep meaning to (re)implement in lme4) ...
>> 
>>    Making X1 into a 1000-level factor brings the required memory up by
>> about a factor of 10 and increases the run time from seconds to minutes.
>> 
>> 
>> Base model:
>> 
>>                        Function_Call Elapsed_Time_sec Total_RAM_Used_MiB
>> 1 m<-lmer(form,data=dd,REML=FALSE)            1.903               10.4
>>     Peak_RAM_Used_MiB
>> 1             107.7
>> 
>> With X=1000-level factor (no derivative calculations):
>> 
>>    Function_Call
>> 1
>> m2<-lmer(form,data=dd2,REML=FALSE,control=lmerControl(calc.derivs=FALSE),verbose=10)
>>     Elapsed_Time_sec Total_RAM_Used_MiB Peak_RAM_Used_MiB
>> 1          559.735              608.8             984.5
>> 
>> 
>> With derivative calculation at the end:
>> 
>>                                    Function_Call Elapsed_Time_sec
>> 1 m3<-lmer(form,data=dd2,REML=FALSE,verbose=10)          677.975
>>     Total_RAM_Used_MiB Peak_RAM_Used_MiB
>> 1              608.7            1148.7
>>   >
>>   >
>> 
>> ---
>> ibrary(lme4)
>> set.seed(101)
>> N <- 22945
>> ns <- 100
>> nf <- 100
>> nid <- 100
>> dd <- data.frame(X1=rnorm(N),
>>                    X2=rnorm(N),
>>                    X3=rnorm(N),
>>                    site=sample(ns, replace=TRUE, size=N),
>>                    family=sample(nf, replace=TRUE, size=N),
>>                    id=sample(nid, replace=TRUE, size=N))
>> form <- Y ~ 1 + X1 + X2 + X3 + (1|site/family/id)
>> dd$Y <- simulate(form[-2], newdata=dd, family=gaussian,
>>                    
>> newparams=list(beta=rep(1,4),theta=rep(1,3),sigma=1))[[1]]
>> library(peakRAM)
>> system.time(mem <- peakRAM(
>>       m <- lmer(form, data=dd, REML=FALSE)
>>       ))
>> print(mem)
>> 
>> dd2 <- transform(dd,
>>           X1=factor(sample(1000,size=N,replace=TRUE)))
>> 
>> system.time(mem2 <- peakRAM(
>>       m2 <- lmer(form, data=dd2, REML=FALSE,
>> control=lmerControl(calc.derivs=FALSE), verbose=10)
>> ))
>> print(mem2)
>> 
>> system.time(mem3 <- peakRAM(
>>       m3 <- lmer(form, data=dd2, REML=FALSE, verbose=10)
>> ))
>> print(mem3)
>> 
>> 
>> On 3/8/21 11:29 AM, Hedyeh Ahmadi wrote:
>>> Thank you for the toy example. This same example in my PC gives the 
>>> following memory use output:
>>> 
>>> 
>>>  > mem
>>>                       Function_Call                            
>>> Elapsed_Time_sec         Total_RAM_Used_MiB    Peak_RAM_Used_MiB
>>>    m<-lmer(form,data=dd,REML=FALSE)             2.64                     
>>>                  10.3                                       130.1
>>> 
>>> When I run peakRAM() for my actual data, it take one hour plus then my 
>>> PC slows down, then I have to stop R to be able to use my PC.
>>> 
>>> Best,
>>> 
>>> Hedyeh Ahmadi, Ph.D.
>>> Statistician
>>> Keck School of Medicine
>>> Department of Preventive Medicine
>>> University of Southern California
>>> 
>>> Postdoctoral Scholar
>>> Institute for Interdisciplinary Salivary Bioscience Research (IISBR)
>>> University of California, Irvine
>>> 
>>> LinkedIn
>>> https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!5O8KlsAUILt44__IHSzbCUgVs7dWxAB8FS9wiKC3j5P6hGrnuJSGckmCIR91AZs$ 
> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!5O8KlsAUILt44__IHSzbCUgVs7dWxAB8FS9wiKC3j5P6hGrnuJSGckmCIR91AZs$> 
> 
>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!5O8KlsAUILt44__IHSzbCUgVs7dWxAB8FS9wiKC3j5P6hGrnuJSGckmCIR91AZs$ 
> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!5O8KlsAUILt44__IHSzbCUgVs7dWxAB8FS9wiKC3j5P6hGrnuJSGckmCIR91AZs$>> 
> 
>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!5O8KlsAUILt44__IHSzbCUgVs7dWxAB8FS9wiKC3j5P6hGrnuJSGckmCIR91AZs$ 
> 
>>  >
>>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!5O8KlsAUILt44__IHSzbCUgVs7dWxAB8FS9wiKC3j5P6hGrnuJSGckmCIR91AZs$ 
> 
>>  ><https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!5O8KlsAUILt44__IHSzbCUgVs7dWxAB8FS9wiKC3j5P6hGrnuJSGckmCIR91AZs$ 
>  >
>>> 
>>> 
>>> 
>>> 
>>> ------------------------------------------------------------------------
>>> *From:* R-sig-mixed-models <r-sig-mixed-models-bounces using r-project.org> on 
>>> behalf of Ben Bolker <bbolker using gmail.com>
>>> *Sent:* Friday, March 5, 2021 5:44 PM
>>> *To:* r-sig-mixed-models using r-project.org <r-sig-mixed-models using r-project.org>
>>> *Subject:* Re: [R-sig-ME] A three-level GLMM with binomial link in R
>>>     Here's an example that conforms approximately to the structure of
>>> your data: on my machine the peak RAM usage is 121 Mb, far short of your
>>> 2.3 Gb ...  so I still suspect there is something going on that we don't
>>> know about/haven't guessed yet.
>>> 
>>> set.seed(101)
>>> N <- 22945
>>> ns <- 100
>>> nf <- 100
>>> nid <- 100
>>> dd <- data.frame(X1=rnorm(N),
>>>                    X2=rnorm(N),
>>>                    X3=rnorm(N),
>>>                    site=sample(ns, replace=TRUE, size=N),
>>>                    family=sample(nf, replace=TRUE, size=N),
>>>                    id=sample(nid, replace=TRUE, size=N))
>>> form <- Y ~ 1 + X1 + X2 + X3 + (1|site/family/id)
>>> dd$Y <- simulate(form[-2], newdata=dd, family=gaussian,
>>>                    
>>> newparams=list(beta=rep(1,4),theta=rep(1,3),sigma=1))[[1]]
>>> library(peakRAM)
>>> mem <- peakRAM(
>>>       m <- lmer(form, data=dd, REML=FALSE)
>>> )
>>> 
>>> mem
>>>                        Function_Call Elapsed_Time_sec Total_RAM_Used_MiB
>>> 1 m<-lmer(form,data=dd,REML=FALSE)            1.754               10.3
>>>     Peak_RAM_Used_MiB
>>> 1             120.7
>>> 
>>> 
>>> On 3/5/21 4:52 PM, Robert Long wrote:
>>>> Perhaps because of the different ways they store objects internally while
>>>> fitting the models.
>>>> 
>>>> On Fri, 5 Mar 2021, 21:47 Hedyeh Ahmadi, <hedyehah using usc.edu> wrote:
>>>> 
>>>>> Thank you for the reply Robert - If I am running out of memory in lmer(),
>>>>> do you know why lme() runs just fine?
>>>>>
>>>>> Best,
>>>>>
>>>>> Hedyeh Ahmadi, Ph.D.
>>>>> Statistician
>>>>> Keck School of Medicine
>>>>> Department of Preventive Medicine
>>>>> University of Southern California
>>>>>
>>>>> Postdoctoral Scholar
>>>>> Institute for Interdisciplinary Salivary Bioscience Research (IISBR)
>>>>> University of California, Irvine
>>>>>
>>>>> LinkedIn
>>>>> https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k70OXW4fU$ 
> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k70OXW4fU$> 
> 
>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k70OXW4fU$ 
> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k70OXW4fU$>> 
> 
>> 
>>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k70OXW4fU$ 
> 
>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k70OXW4fU$ 
> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k70OXW4fU$>>> 
> 
>> 
>>> 
>>>>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k70OXW4fU$ 
> 
>> 
>>>  >
>>>>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k70OXW4fU$ 
> 
>> 
>>>  >
>>>>>
>>>>>
>>>>>
>>>>>
>>>>> ------------------------------
>>>>> *From:* Robert Long <longrob604 using gmail.com>
>>>>> *Sent:* Friday, March 5, 2021 1:43 PM
>>>>> *To:* Hedyeh Ahmadi <hedyehah using usc.edu>
>>>>> *Cc:* Dexter Locke <dexter.locke using gmail.com>; R-mixed models mailing list <
>>>>> r-sig-mixed-models using r-project.org>; Megan M. Herting <herting using usc.edu>;
>>>>> Elisabeth Burnor <burnor using usc.edu>
>>>>> *Subject:* Re: [R-sig-ME] A three-level GLMM with binomial link in R
>>>>>
>>>>> You've run out of memory. Try running it on a machine with much larger RAM.
>>>>>
>>>>> On Fri, 5 Mar 2021, 21:18 Hedyeh Ahmadi, <hedyehah using usc.edu> wrote:
>>>>>
>>>>> Hi - Thank you for the informative replies.
>>>>>
>>>>> I will try those other packages. If MASS::glmmPQL uses lme() then this
>>>>> should work for me.
>>>>>
>>>>> My data structure is complex so it's hard to give reproducible example but
>>>>> for example for two of my models I get the following errors in lmer() while
>>>>> lme() runs smoothly.
>>>>>
>>>>> 1- Error: cannot allocate vector of size 2.3 Gb.
>>>>>
>>>>> 2- Error: couldn't evaluate grouping factor id:(family:site) within model
>>>>> frame: try adding grouping factor to data frame explicitly if possible.
>>>>> (note that the id variable works for simpler lmer() models so the variable
>>>>> itself is not an issue)
>>>>>
>>>>> My model looks like the following nested structure:
>>>>> lmer(Y ~ 1 + X1 + X2 + X3 + (1|site/family/id), data=dd, REML = FALSE)
>>>>>
>>>>> Best,
>>>>>
>>>>> Hedyeh Ahmadi, Ph.D.
>>>>> Statistician
>>>>> Keck School of Medicine
>>>>> Department of Preventive Medicine
>>>>> University of Southern California
>>>>>
>>>>> Postdoctoral Scholar
>>>>> Institute for Interdisciplinary Salivary Bioscience Research (IISBR)
>>>>> University of California, Irvine
>>>>>
>>>>> LinkedIn
>>>>> https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k70OXW4fU$ 
> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k70OXW4fU$> 
> 
>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k70OXW4fU$ 
> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k70OXW4fU$>> 
> 
>> 
>>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k70OXW4fU$ 
> 
>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k70OXW4fU$ 
> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k70OXW4fU$>>> 
> 
>> 
>>> 
>>>>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!5uCe7IsPHtgAoEp8Qsbn8bXOUBLGi7pVfXIjHwMUHVDbmnOSRCu7OHKGGuIvhag$ 
> 
>> 
>>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!5uCe7IsPHtgAoEp8Qsbn8bXOUBLGi7pVfXIjHwMUHVDbmnOSRCu7OHKGGuIvhag$ 
> 
>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!5uCe7IsPHtgAoEp8Qsbn8bXOUBLGi7pVfXIjHwMUHVDbmnOSRCu7OHKGGuIvhag$ 
> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!5uCe7IsPHtgAoEp8Qsbn8bXOUBLGi7pVfXIjHwMUHVDbmnOSRCu7OHKGGuIvhag$>>>>
>>>>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k70OXW4fU$ 
> 
>> 
>>> 
>>>>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!5uCe7IsPHtgAoEp8Qsbn8bXOUBLGi7pVfXIjHwMUHVDbmnOSRCu7OHKGGuIvhag$ 
> 
>> 
>>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!5uCe7IsPHtgAoEp8Qsbn8bXOUBLGi7pVfXIjHwMUHVDbmnOSRCu7OHKGGuIvhag$ 
> 
>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!5uCe7IsPHtgAoEp8Qsbn8bXOUBLGi7pVfXIjHwMUHVDbmnOSRCu7OHKGGuIvhag$ 
> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!5uCe7IsPHtgAoEp8Qsbn8bXOUBLGi7pVfXIjHwMUHVDbmnOSRCu7OHKGGuIvhag$>>>>
>>>>>>
>>>>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k70OXW4fU$ 
> 
>> 
>>> 
>>>>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!5uCe7IsPHtgAoEp8Qsbn8bXOUBLGi7pVfXIjHwMUHVDbmnOSRCu7OHKGGuIvhag$ 
> 
>> 
>>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!5uCe7IsPHtgAoEp8Qsbn8bXOUBLGi7pVfXIjHwMUHVDbmnOSRCu7OHKGGuIvhag$ 
> 
>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!5uCe7IsPHtgAoEp8Qsbn8bXOUBLGi7pVfXIjHwMUHVDbmnOSRCu7OHKGGuIvhag$ 
> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!5uCe7IsPHtgAoEp8Qsbn8bXOUBLGi7pVfXIjHwMUHVDbmnOSRCu7OHKGGuIvhag$>>>>
>>>>>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k70OXW4fU$ 
> 
>> 
>>> 
>>>>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!5uCe7IsPHtgAoEp8Qsbn8bXOUBLGi7pVfXIjHwMUHVDbmnOSRCu7OHKGGuIvhag$ 
> 
>> 
>>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!5uCe7IsPHtgAoEp8Qsbn8bXOUBLGi7pVfXIjHwMUHVDbmnOSRCu7OHKGGuIvhag$ 
> 
>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!5uCe7IsPHtgAoEp8Qsbn8bXOUBLGi7pVfXIjHwMUHVDbmnOSRCu7OHKGGuIvhag$ 
> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!5uCe7IsPHtgAoEp8Qsbn8bXOUBLGi7pVfXIjHwMUHVDbmnOSRCu7OHKGGuIvhag$>>>>
>>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>> ________________________________
>>>>> From: Dexter Locke <dexter.locke using gmail.com>
>>>>> Sent: Friday, March 5, 2021 1:01 PM
>>>>> To: Hedyeh Ahmadi <hedyehah using usc.edu>
>>>>> Cc: r-sig-mixed-models using r-project.org <r-sig-mixed-models using r-project.org>;
>>>>> Megan M. Herting <herting using usc.edu>; Elisabeth Burnor <burnor using usc.edu>
>>>>> Subject: Re: [R-sig-ME] A three-level GLMM with binomial link in R
>>>>>
>>>>> Hi Hedyeh,
>>>>>
>>>>> What is the problem you are having? Specifically, what is the estimation
>>>>> issue with lmer and lme?
>>>>>
>>>>> Can you provide a reproducible example? Can you provide the complete
>>>>> errors you are seeing?
>>>>>
>>>>> The current questions are vague, so it will be challenging for list
>>>>> members to provide much guidance.
>>>>>
>>>>> -Dexter
>>>>>
>>>>>
>>>>> On Fri, Mar 5, 2021 at 3:27 PM Hedyeh Ahmadi <hedyehah using usc.edu<mailto:
>>>>> hedyehah using usc.edu>> wrote:
>>>>> Hi All,
>>>>> I was wondering what would be a powerful package in R to run GLMM with
>>>>> logit link that can handle a data set with N=22945 and 3 nested random
>>>>> intercepts. So far, I have tried glmer() from lme4 and it's giving me a lot
>>>>> of estimation issues. Any other package I should try?
>>>>>
>>>>> I am asking for another package as I am having the same issue with lmer()
>>>>> for similar LMM with continuous outcome, while lme() from nlme package runs
>>>>> the models with no problem.
>>>>>
>>>>> Thank you in advance.
>>>>>
>>>>> Best,
>>>>>
>>>>> Hedyeh Ahmadi, Ph.D.
>>>>> Statistician
>>>>> Keck School of Medicine
>>>>> Department of Preventive Medicine
>>>>> University of Southern California
>>>>>
>>>>> Postdoctoral Scholar
>>>>> Institute for Interdisciplinary Salivary Bioscience Research (IISBR)
>>>>> University of California, Irvine
>>>>>
>>>>> LinkedIn
>>>>> https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k70OXW4fU$ 
> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k70OXW4fU$> 
> 
>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k70OXW4fU$ 
> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k70OXW4fU$>> 
> 
>> 
>>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k70OXW4fU$ 
> 
>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k70OXW4fU$ 
> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k70OXW4fU$>>> 
> 
>> 
>>> 
>>>>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!5uCe7IsPHtgAoEp8Qsbn8bXOUBLGi7pVfXIjHwMUHVDbmnOSRCu7OHKGGuIvhag$ 
> 
>> 
>>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!5uCe7IsPHtgAoEp8Qsbn8bXOUBLGi7pVfXIjHwMUHVDbmnOSRCu7OHKGGuIvhag$ 
> 
>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!5uCe7IsPHtgAoEp8Qsbn8bXOUBLGi7pVfXIjHwMUHVDbmnOSRCu7OHKGGuIvhag$ 
> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!5uCe7IsPHtgAoEp8Qsbn8bXOUBLGi7pVfXIjHwMUHVDbmnOSRCu7OHKGGuIvhag$>>>>
>>>>> <
>>>>> https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!8UfGozITdR3cNo929aSVEsbVNgbIul9f91q4hA3PAf0ywits0jIKVDAQdYkAXFg$ 
> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!8UfGozITdR3cNo929aSVEsbVNgbIul9f91q4hA3PAf0ywits0jIKVDAQdYkAXFg$> 
> 
>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!8UfGozITdR3cNo929aSVEsbVNgbIul9f91q4hA3PAf0ywits0jIKVDAQdYkAXFg$ 
> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!8UfGozITdR3cNo929aSVEsbVNgbIul9f91q4hA3PAf0ywits0jIKVDAQdYkAXFg$>> 
> 
>> 
>>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!8UfGozITdR3cNo929aSVEsbVNgbIul9f91q4hA3PAf0ywits0jIKVDAQdYkAXFg$ 
> 
>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!8UfGozITdR3cNo929aSVEsbVNgbIul9f91q4hA3PAf0ywits0jIKVDAQdYkAXFg$ 
> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!8UfGozITdR3cNo929aSVEsbVNgbIul9f91q4hA3PAf0ywits0jIKVDAQdYkAXFg$>>>
>>>>>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k70OXW4fU$ 
> 
>> 
>>> 
>>>>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!5uCe7IsPHtgAoEp8Qsbn8bXOUBLGi7pVfXIjHwMUHVDbmnOSRCu7OHKGGuIvhag$ 
> 
>> 
>>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!5uCe7IsPHtgAoEp8Qsbn8bXOUBLGi7pVfXIjHwMUHVDbmnOSRCu7OHKGGuIvhag$ 
> 
>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!5uCe7IsPHtgAoEp8Qsbn8bXOUBLGi7pVfXIjHwMUHVDbmnOSRCu7OHKGGuIvhag$ 
> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!5uCe7IsPHtgAoEp8Qsbn8bXOUBLGi7pVfXIjHwMUHVDbmnOSRCu7OHKGGuIvhag$>>>>
>>>>> <
>>>>> https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!8UfGozITdR3cNo929aSVEsbVNgbIul9f91q4hA3PAf0ywits0jIKVDAQdYkAXFg$ 
> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!8UfGozITdR3cNo929aSVEsbVNgbIul9f91q4hA3PAf0ywits0jIKVDAQdYkAXFg$> 
> 
>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!8UfGozITdR3cNo929aSVEsbVNgbIul9f91q4hA3PAf0ywits0jIKVDAQdYkAXFg$ 
> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!8UfGozITdR3cNo929aSVEsbVNgbIul9f91q4hA3PAf0ywits0jIKVDAQdYkAXFg$>> 
> 
>> 
>>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!8UfGozITdR3cNo929aSVEsbVNgbIul9f91q4hA3PAf0ywits0jIKVDAQdYkAXFg$ 
> 
>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!8UfGozITdR3cNo929aSVEsbVNgbIul9f91q4hA3PAf0ywits0jIKVDAQdYkAXFg$ 
> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!8UfGozITdR3cNo929aSVEsbVNgbIul9f91q4hA3PAf0ywits0jIKVDAQdYkAXFg$>>>
>>>>>>>
>>>>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k70OXW4fU$ 
> 
>> 
>>> 
>>>>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!5uCe7IsPHtgAoEp8Qsbn8bXOUBLGi7pVfXIjHwMUHVDbmnOSRCu7OHKGGuIvhag$ 
> 
>> 
>>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!5uCe7IsPHtgAoEp8Qsbn8bXOUBLGi7pVfXIjHwMUHVDbmnOSRCu7OHKGGuIvhag$ 
> 
>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!5uCe7IsPHtgAoEp8Qsbn8bXOUBLGi7pVfXIjHwMUHVDbmnOSRCu7OHKGGuIvhag$ 
> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!5uCe7IsPHtgAoEp8Qsbn8bXOUBLGi7pVfXIjHwMUHVDbmnOSRCu7OHKGGuIvhag$>>>>
>>>>> <
>>>>> https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!8UfGozITdR3cNo929aSVEsbVNgbIul9f91q4hA3PAf0ywits0jIKVDAQdYkAXFg$ 
> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!8UfGozITdR3cNo929aSVEsbVNgbIul9f91q4hA3PAf0ywits0jIKVDAQdYkAXFg$> 
> 
>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!8UfGozITdR3cNo929aSVEsbVNgbIul9f91q4hA3PAf0ywits0jIKVDAQdYkAXFg$ 
> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!8UfGozITdR3cNo929aSVEsbVNgbIul9f91q4hA3PAf0ywits0jIKVDAQdYkAXFg$>> 
> 
>> 
>>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!8UfGozITdR3cNo929aSVEsbVNgbIul9f91q4hA3PAf0ywits0jIKVDAQdYkAXFg$ 
> 
>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!8UfGozITdR3cNo929aSVEsbVNgbIul9f91q4hA3PAf0ywits0jIKVDAQdYkAXFg$ 
> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!8UfGozITdR3cNo929aSVEsbVNgbIul9f91q4hA3PAf0ywits0jIKVDAQdYkAXFg$>>>
>>>>>>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k70OXW4fU$ 
> 
>> 
>>> 
>>>>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!5uCe7IsPHtgAoEp8Qsbn8bXOUBLGi7pVfXIjHwMUHVDbmnOSRCu7OHKGGuIvhag$ 
> 
>> 
>>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!5uCe7IsPHtgAoEp8Qsbn8bXOUBLGi7pVfXIjHwMUHVDbmnOSRCu7OHKGGuIvhag$ 
> 
>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!5uCe7IsPHtgAoEp8Qsbn8bXOUBLGi7pVfXIjHwMUHVDbmnOSRCu7OHKGGuIvhag$ 
> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!5uCe7IsPHtgAoEp8Qsbn8bXOUBLGi7pVfXIjHwMUHVDbmnOSRCu7OHKGGuIvhag$>>>>
>>>>> <
>>>>> https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!8UfGozITdR3cNo929aSVEsbVNgbIul9f91q4hA3PAf0ywits0jIKVDAQdYkAXFg$ 
> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!8UfGozITdR3cNo929aSVEsbVNgbIul9f91q4hA3PAf0ywits0jIKVDAQdYkAXFg$> 
> 
>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!8UfGozITdR3cNo929aSVEsbVNgbIul9f91q4hA3PAf0ywits0jIKVDAQdYkAXFg$ 
> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!8UfGozITdR3cNo929aSVEsbVNgbIul9f91q4hA3PAf0ywits0jIKVDAQdYkAXFg$>> 
> 
>> 
>>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!8UfGozITdR3cNo929aSVEsbVNgbIul9f91q4hA3PAf0ywits0jIKVDAQdYkAXFg$ 
> 
>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!8UfGozITdR3cNo929aSVEsbVNgbIul9f91q4hA3PAf0ywits0jIKVDAQdYkAXFg$ 
> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!8UfGozITdR3cNo929aSVEsbVNgbIul9f91q4hA3PAf0ywits0jIKVDAQdYkAXFg$>>>
>>>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>          [[alternative HTML version deleted]]
>>>>>
>>>>> _______________________________________________
>>>>> R-sig-mixed-models using r-project.org<mailto:R-sig-mixed-models using r-project.org>
>>>>> mailing list
>>>>> https://urldefense.com/v3/__https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k7pcSE0ic$ 
> <https://urldefense.com/v3/__https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k7pcSE0ic$> 
> 
>> <https://urldefense.com/v3/__https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k7pcSE0ic$ 
> <https://urldefense.com/v3/__https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k7pcSE0ic$>> 
> 
>> 
>>> <https://urldefense.com/v3/__https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k7pcSE0ic$ 
> 
>> <https://urldefense.com/v3/__https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k7pcSE0ic$ 
> <https://urldefense.com/v3/__https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k7pcSE0ic$>>> 
> 
>> 
>>> 
>>>>> <https://urldefense.com/v3/__https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models__;!!LIr3w8kk_Xxm!5uCe7IsPHtgAoEp8Qsbn8bXOUBLGi7pVfXIjHwMUHVDbmnOSRCu7OHKG8rJcsmY$ 
> 
>> 
>>> <https://urldefense.com/v3/__https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models__;!!LIr3w8kk_Xxm!5uCe7IsPHtgAoEp8Qsbn8bXOUBLGi7pVfXIjHwMUHVDbmnOSRCu7OHKG8rJcsmY$ 
> 
>> <https://urldefense.com/v3/__https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models__;!!LIr3w8kk_Xxm!5uCe7IsPHtgAoEp8Qsbn8bXOUBLGi7pVfXIjHwMUHVDbmnOSRCu7OHKG8rJcsmY$ 
> <https://urldefense.com/v3/__https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models__;!!LIr3w8kk_Xxm!5uCe7IsPHtgAoEp8Qsbn8bXOUBLGi7pVfXIjHwMUHVDbmnOSRCu7OHKG8rJcsmY$>>>>
>>>>> <
>>>>> https://urldefense.com/v3/__https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models__;!!LIr3w8kk_Xxm!8UfGozITdR3cNo929aSVEsbVNgbIul9f91q4hA3PAf0ywits0jIKVDAQM6wKtNs$ 
> <https://urldefense.com/v3/__https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models__;!!LIr3w8kk_Xxm!8UfGozITdR3cNo929aSVEsbVNgbIul9f91q4hA3PAf0ywits0jIKVDAQM6wKtNs$> 
> 
>> <https://urldefense.com/v3/__https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models__;!!LIr3w8kk_Xxm!8UfGozITdR3cNo929aSVEsbVNgbIul9f91q4hA3PAf0ywits0jIKVDAQM6wKtNs$ 
> <https://urldefense.com/v3/__https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models__;!!LIr3w8kk_Xxm!8UfGozITdR3cNo929aSVEsbVNgbIul9f91q4hA3PAf0ywits0jIKVDAQM6wKtNs$>> 
> 
>> 
>>> <https://urldefense.com/v3/__https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models__;!!LIr3w8kk_Xxm!8UfGozITdR3cNo929aSVEsbVNgbIul9f91q4hA3PAf0ywits0jIKVDAQM6wKtNs$ 
> 
>> <https://urldefense.com/v3/__https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models__;!!LIr3w8kk_Xxm!8UfGozITdR3cNo929aSVEsbVNgbIul9f91q4hA3PAf0ywits0jIKVDAQM6wKtNs$ 
> <https://urldefense.com/v3/__https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models__;!!LIr3w8kk_Xxm!8UfGozITdR3cNo929aSVEsbVNgbIul9f91q4hA3PAf0ywits0jIKVDAQM6wKtNs$>>>
>>>>>>
>>>>>
>>>>>          [[alternative HTML version deleted]]
>>>>>
>>>>> _______________________________________________
>>>>> R-sig-mixed-models using r-project.org mailing list
>>>>> https://urldefense.com/v3/__https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k7pcSE0ic$ 
> <https://urldefense.com/v3/__https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k7pcSE0ic$> 
> 
>> <https://urldefense.com/v3/__https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k7pcSE0ic$ 
> <https://urldefense.com/v3/__https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k7pcSE0ic$>> 
> 
>> 
>>> <https://urldefense.com/v3/__https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k7pcSE0ic$ 
> 
>> <https://urldefense.com/v3/__https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k7pcSE0ic$ 
> <https://urldefense.com/v3/__https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k7pcSE0ic$>>> 
> 
>> 
>>> 
>>>>> <https://urldefense.com/v3/__https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models__;!!LIr3w8kk_Xxm!5uCe7IsPHtgAoEp8Qsbn8bXOUBLGi7pVfXIjHwMUHVDbmnOSRCu7OHKG8rJcsmY$ 
> 
>> 
>>> <https://urldefense.com/v3/__https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models__;!!LIr3w8kk_Xxm!5uCe7IsPHtgAoEp8Qsbn8bXOUBLGi7pVfXIjHwMUHVDbmnOSRCu7OHKG8rJcsmY$ 
> 
>> <https://urldefense.com/v3/__https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models__;!!LIr3w8kk_Xxm!5uCe7IsPHtgAoEp8Qsbn8bXOUBLGi7pVfXIjHwMUHVDbmnOSRCu7OHKG8rJcsmY$ 
> <https://urldefense.com/v3/__https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models__;!!LIr3w8kk_Xxm!5uCe7IsPHtgAoEp8Qsbn8bXOUBLGi7pVfXIjHwMUHVDbmnOSRCu7OHKG8rJcsmY$>>>>
>>>>>
>>>>>
>>>> 
>>>>        [[alternative HTML version deleted]]
>>>> 
>>>> _______________________________________________
>>>> R-sig-mixed-models using r-project.org mailing list
>>>> https://urldefense.com/v3/__https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k7pcSE0ic$ 
> <https://urldefense.com/v3/__https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k7pcSE0ic$> 
> 
>> <https://urldefense.com/v3/__https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k7pcSE0ic$ 
> <https://urldefense.com/v3/__https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k7pcSE0ic$>> 
> 
>> 
>>> <https://urldefense.com/v3/__https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k7pcSE0ic$ 
> 
>> <https://urldefense.com/v3/__https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k7pcSE0ic$ 
> <https://urldefense.com/v3/__https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k7pcSE0ic$>>> 
> 
>> 
>>> 
>>>>
>>> 
>>> _______________________________________________
>>> R-sig-mixed-models using r-project.org mailing list
>>> https://urldefense.com/v3/__https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k7pcSE0ic$ 
> <https://urldefense.com/v3/__https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k7pcSE0ic$> 
> 
>> <https://urldefense.com/v3/__https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k7pcSE0ic$ 
> <https://urldefense.com/v3/__https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k7pcSE0ic$>> 
> 
>> 
>>> <https://urldefense.com/v3/__https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k7pcSE0ic$ 
> 
>> <https://urldefense.com/v3/__https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k7pcSE0ic$ 
> <https://urldefense.com/v3/__https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k7pcSE0ic$>>> 
> 
>> 
>>>

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