[R-sig-ME] A three-level GLMM with binomial link in R
Ben Bolker
bbo|ker @end|ng |rom gm@||@com
Wed Mar 17 19:31:01 CET 2021
On 3/16/21 12:44 PM, Hedyeh Ahmadi wrote:
> Hello all,
> I am just forwarding my previous email again just in case and taking out
> some parts that I already figured out - thank you for all your help:
>
> I'll think more about how to share a data set that would create the same
> error. Sorry, I am not very simulation savvy, but I'll try harder next time.
>
> On the bright side, I was able to run the following model by implicitly
> defining the group structure (slightly different from what was suggested
> in the previous email) and it does give me the same estimation as lme()
> with *random = ~1|site/family/id***random structure - so the memory
> issue resolved for this model! Thank you for the suggestion.
>
> dd$site_family <- interaction(dd$site, dd$family)
> m2.1 <- lmer(cbcl_scr_syn_internal_r ~ 1 + X1 + X2 + X3+ (1|site)
> +(1|site_family/id), data=dd, REML = FALSE)
I'm glad you solved the problem, although I'm still bothered by the
fact that I don't understand it.
>
> *But now getting to my last question: *My data has 22945 rows, and some
> individuals have only baseline measurement, 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? *
It makes the most sense (to me) to add eventname as a fixed effect.
>
> OR do I need to run a model with additional random intercept of
> eventname (i.e. (1|site/family/id/eventname))but in doing so lme() gives
> me the number of observation equal to number of grouping for *eventname
> %in% id %in% family %in% site *as follows.**Would that be okay?
>
> Number of Observations: 13388
> Number of Groups:
> site family %in% site
> 21 9393
> id %in% family %in% site eventname %in% id %in% family %in% abcd_site
> 11111 13388
>
>
> Again, thank you so much for your time.
>
>
> 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:* Hedyeh Ahmadi <hedyehah using usc.edu>
> *Sent:* Friday, March 12, 2021 12:54 PM
> *To:* r-sig-mixed-models using r-project.org
> <r-sig-mixed-models using r-project.org>; Ben Bolker <bbolker using gmail.com>
> *Subject:* Re: [R-sig-ME] A three-level GLMM with binomial link in R
> I'll think more about how to share a data set that would create the same
> error. Sorry, I am not very simulation savvy but I'll try harder next time.
>
> On the bright side, I was able to run the following model by implicitly
> defining the group structure (slightly different from what was suggested
> in the previous email) and it does give me the same estimation as lme()
> with *random = ~1|site/family/id**random* structure - so the memory
> issue resolved for this model! Thank you for the suggestion.
>
> dd$site_family <- interaction(dd$site, dd$family)
> m2.1 <- lmer(cbcl_scr_syn_internal_r ~ 1 + X1 + X2 + X3+ (1|site)
> +(1|site_family/id), data=dd, REML = FALSE)
>
> *But now getting to my last question: *My data has 22945 rows, and some
> individuals have only baseline measurement, 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? *
>
> OR do I need to run a model with additional random intercept of
> eventname but in doing so lme() gives me the number of observation equal
> to umber of grouping for *eventname %in% id %in% family %in% site *as
> follows.**Would that be okay?
>
> Number of Observations: 13388
> Number of Groups:
> site family %in% site
> 21 9393
> id %in% family %in% site eventname %in% id %in% family %in% abcd_site
> 11111 13388
>
> The model formula with eventname as random slope in lme() would be as
> follows but I have not been able to reproduce this in lmer() similar to
> implicit formatting of m2.1 shown above - any help would be appreciated
> here. Keep in mind created an implicit three-way and four-way
> interaction takes too much memory on my personal PC so I am trying to
> find a way around it as I did in m2.1.
>
> m3 <- lme(cbcl_scr_syn_internal_r ~ 1 +X1+ X2 + X3, random =
> ~1|site/family/id//eventname,
> data=dd, na.action=na.exclude,method="ML")
>
> Again, thank you so much for your time.
>
> 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:* Friday, March 12, 2021 11:45 AM
> *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
>
>
> 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://urldefense.com/v3/__https://stackoverflow.com/questions/10454973/how-to-create-example-data-set-from-private-data-replacing-variable-names-and-l__;!!LIr3w8kk_Xxm!86i5mS45OmW-JeD4GGs4ZQyanE9ePtf5QzjgYVkL_Rg284MkmW9z-lQGP70cEP4$
> <https://urldefense.com/v3/__https://stackoverflow.com/questions/10454973/how-to-create-example-data-set-from-private-data-replacing-variable-names-and-l__;!!LIr3w8kk_Xxm!86i5mS45OmW-JeD4GGs4ZQyanE9ePtf5QzjgYVkL_Rg284MkmW9z-lQGP70cEP4$>
>
>
> https://urldefense.com/v3/__https://stackoverflow.com/questions/5963269/how-to-make-a-great-r-reproducible-example/6699112*6699112__;Iw!!LIr3w8kk_Xxm!86i5mS45OmW-JeD4GGs4ZQyanE9ePtf5QzjgYVkL_Rg284MkmW9z-lQGfDnxgGI$
> <https://urldefense.com/v3/__https://stackoverflow.com/questions/5963269/how-to-make-a-great-r-reproducible-example/6699112*6699112__;Iw!!LIr3w8kk_Xxm!86i5mS45OmW-JeD4GGs4ZQyanE9ePtf5QzjgYVkL_Rg284MkmW9z-lQGfDnxgGI$>
>
>
>
>> 3. Note that when I run the three-way interaction code in my PC it
>> again runs out of memory and the error says the following. When I
>> tried to run it on interactive HPC, it kicks me out as it takes too
>> much memory/time so I will have to submit a batch script.
>> "Error: cannot allocate vector of size 18.1 Gb
>> In addition: Warning message:
>> In ans * length(l) :
>> Error: cannot allocate vector of size 18.1 Gb"
>> 4. When I take out all the fixed effects, the problem still exists.
>
>
> That's good in one sense, as it simplifies the problem.
>
>> 5. *Question:* Also note that my data has 22945 rows, and some
>> individuals have only baseline measurement only, some individuals
>> have baseline and 1 year measurement. A variable called eventname is
>> the indicator of that. I am now confused as my "id" variable does
>> not have this information (i.e. the order of measurement). How would
>> the model recognize that which repeated measure is measurment1 (i.e.
>> baseline) and which one is measurment2(i.e. 1 year)? Or maybe
>> because I don't have a random slope, I don't need to define the
>> repeated measure structure and adding eventname as a fixed effect is
>> sufficient?
>
> Let's deal with this after we have the basic problems sorted. If
> you want to account for the possible effects of ordering, then you'd
> need to add this variable ...
>
>>
>> Thanks again for all your help on this.
>>
>> Best,
>>
>> Hedyeh Ahmadi, Ph.D.
>> Statistician
>> Keck School of Medicine
>> Department of Preventive Medicine
>> University of Southern California
>>
>> Postdoctoral Scholar
>> Institute for Interdisciplinary Salivary Bioscience Research (IISBR)
>> University of California, Irvine
>>
>> LinkedIn
>> https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!86i5mS45OmW-JeD4GGs4ZQyanE9ePtf5QzjgYVkL_Rg284MkmW9z-lQGJrML1Sk$
> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!86i5mS45OmW-JeD4GGs4ZQyanE9ePtf5QzjgYVkL_Rg284MkmW9z-lQGJrML1Sk$>
> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!86i5mS45OmW-JeD4GGs4ZQyanE9ePtf5QzjgYVkL_Rg284MkmW9z-lQGJrML1Sk$
> >
>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!86i5mS45OmW-JeD4GGs4ZQyanE9ePtf5QzjgYVkL_Rg284MkmW9z-lQGJrML1Sk$
> ><https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!86i5mS45OmW-JeD4GGs4ZQyanE9ePtf5QzjgYVkL_Rg284MkmW9z-lQGJrML1Sk$ >
>>
>>
>>
>>
>> ------------------------------------------------------------------------
>> *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$>>
>
>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!51-zg2ISp-lS-4HEW0ZNNEVE1ZD8ujdJZYx90xVOnZ-x6A7l6eu2KhSgMhYCJq4$
>
>> >
>>> <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$>>>
>
>>
>>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!5O8KlsAUILt44__IHSzbCUgVs7dWxAB8FS9wiKC3j5P6hGrnuJSGckmCIR91AZs$
>
>>
>>> >
>>>> <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$
>
>> <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$>>>
>
>>
>>>
>>>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k70OXW4fU$
>
>>
>>> <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!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!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!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!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$>>>
>
>>
>>>
>>>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k70OXW4fU$
>
>>
>>> <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!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$>>>
>
>>
>>>
>>>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!8UfGozITdR3cNo929aSVEsbVNgbIul9f91q4hA3PAf0ywits0jIKVDAQdYkAXFg$
>
>>
>>> <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!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$>>>
>
>>
>>>
>>>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!8UfGozITdR3cNo929aSVEsbVNgbIul9f91q4hA3PAf0ywits0jIKVDAQdYkAXFg$
>
>>
>>> <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!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$>>>
>
>>
>>>
>>>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!8UfGozITdR3cNo929aSVEsbVNgbIul9f91q4hA3PAf0ywits0jIKVDAQdYkAXFg$
>
>>
>>> <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!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$>>>
>
>>
>>>
>>>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!8UfGozITdR3cNo929aSVEsbVNgbIul9f91q4hA3PAf0ywits0jIKVDAQdYkAXFg$
>
>>
>>> <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$>>>
>
>>
>>>
>>>> <https://urldefense.com/v3/__https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k7pcSE0ic$
>
>>
>>> <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!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$>>>
>
>>
>>>
>>>> <https://urldefense.com/v3/__https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models__;!!LIr3w8kk_Xxm!8UfGozITdR3cNo929aSVEsbVNgbIul9f91q4hA3PAf0ywits0jIKVDAQM6wKtNs$
>
>>
>>> <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$>>>
>
>>
>>>
>>>> <https://urldefense.com/v3/__https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k7pcSE0ic$
>
>>
>>> <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!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$>>>
>
>>
>>>
>>>> <https://urldefense.com/v3/__https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k7pcSE0ic$
>
>>
>>> <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$>>>
>
>>
>>>
>>>> <https://urldefense.com/v3/__https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k7pcSE0ic$
>
>>
>>> <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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