A three-level GLMM with binomial link in R
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:
* X1: num [1:22945] 9.25 NA 9.22 NA 9.22 NA 9.42 NA 9.25 NA ...
* X2: int [1:22945] 117 140 128 125 113 138 126 130 120 121 ...
* X3: chr [1:22945] "Female" "Male" "Male" "Male" "Male"
* site: chr [1:22945] "site15" "site15" "site15" "site15" "site15" ... (I have 21 sites)
* family: int [1:22945] 0 1 1 1 1 3 3 4 4 5 ...
* 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.
* 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.
* 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?
2. At this point I don't think this is a memory issue as m2 did not run on a supercomputer 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?
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
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 at gmail.com>
Sent: Tuesday, March 9, 2021 4:12 PM
To: Hedyeh Ahmadi <hedyehah at usc.edu>; r-sig-mixed-models at r-project.org <r-sig-mixed-models at r-project.org>
Subject: Re: [R-sig-ME] A three-level GLMM with binomial link in R
Sent: Tuesday, March 9, 2021 4:12 PM
To: Hedyeh Ahmadi <hedyehah at usc.edu>; r-sig-mixed-models at r-project.org <r-sig-mixed-models at 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$ >
>
>
>
>
> ------------------------------------------------------------------------
> *From:* R-sig-mixed-models <r-sig-mixed-models-bounces at r-project.org> on
> behalf of Ben Bolker <bbolker at gmail.com>
> *Sent:* Friday, March 5, 2021 5:44 PM
> *To:* r-sig-mixed-models at r-project.org <r-sig-mixed-models at 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$Y <- simulate(form[-2], newdata=dd, family=gaussian,
>
> newparams=list(beta=rep(1,4),theta=rep(1,3),sigma=1))[[1]]
> library(peakRAM)
> mem <- peakRAM(
> m <- lmer(form, data=dd, REML=FALSE)
> )
>
> mem
> Function_Call Elapsed_Time_sec Total_RAM_Used_MiB
> 1 m<-lmer(form,data=dd,REML=FALSE) 1.754 10.3
> Peak_RAM_Used_MiB
> 1 120.7
>
>
> On 3/5/21 4:52 PM, Robert Long wrote:
>> Perhaps because of the different ways they store objects internally while
>> fitting the models.
>>
>> On Fri, 5 Mar 2021, 21:47 Hedyeh Ahmadi, <hedyehah at usc.edu> wrote:
>>
>>> Thank you for the reply Robert - If I am running out of memory in lmer(),
>>> do you know why lme() runs just fine?
>>>
>>> Best,
>>>
>>> Hedyeh Ahmadi, Ph.D.
>>> Statistician
>>> Keck School of Medicine
>>> Department of Preventive Medicine
>>> University of Southern California
>>>
>>> Postdoctoral Scholar
>>> Institute for Interdisciplinary Salivary Bioscience Research (IISBR)
>>> University of California, Irvine
>>>
>>> LinkedIn
>>> https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k70OXW4fU$
> <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$
> >
>>>
>>>
>>>
>>>
>>> ------------------------------
>>> *From:* Robert Long <longrob604 at gmail.com>
>>> *Sent:* Friday, March 5, 2021 1:43 PM
>>> *To:* Hedyeh Ahmadi <hedyehah at usc.edu>
>>> *Cc:* Dexter Locke <dexter.locke at gmail.com>; R-mixed models mailing list <
>>> r-sig-mixed-models at r-project.org>; Megan M. Herting <herting at usc.edu>;
>>> Elisabeth Burnor <burnor at 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 at 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$>
>
>>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!5uCe7IsPHtgAoEp8Qsbn8bXOUBLGi7pVfXIjHwMUHVDbmnOSRCu7OHKGGuIvhag$
> <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$>>
>>>>
>>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k70OXW4fU$
>
>>> <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$>>
>>>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k70OXW4fU$
>
>>> <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$>>
>>>>
>>>
>>>
>>>
>>>
>>> ________________________________
>>> From: Dexter Locke <dexter.locke at gmail.com>
>>> Sent: Friday, March 5, 2021 1:01 PM
>>> To: Hedyeh Ahmadi <hedyehah at usc.edu>
>>> Cc: r-sig-mixed-models at r-project.org <r-sig-mixed-models at r-project.org>;
>>> Megan M. Herting <herting at usc.edu>; Elisabeth Burnor <burnor at usc.edu>
>>> Subject: Re: [R-sig-ME] A three-level GLMM with binomial link in R
>>>
>>> Hi Hedyeh,
>>>
>>> What is the problem you are having? Specifically, what is the estimation
>>> issue with lmer and lme?
>>>
>>> Can you provide a reproducible example? Can you provide the complete
>>> errors you are seeing?
>>>
>>> The current questions are vague, so it will be challenging for list
>>> members to provide much guidance.
>>>
>>> -Dexter
>>>
>>>
>>> On Fri, Mar 5, 2021 at 3:27 PM Hedyeh Ahmadi <hedyehah at usc.edu<mailto:
>>> hedyehah at usc.edu>> wrote:
>>> Hi All,
>>> I was wondering what would be a powerful package in R to run GLMM with
>>> logit link that can handle a data set with N=22945 and 3 nested random
>>> intercepts. So far, I have tried glmer() from lme4 and it's giving me a lot
>>> of estimation issues. Any other package I should try?
>>>
>>> I am asking for another package as I am having the same issue with lmer()
>>> for similar LMM with continuous outcome, while lme() from nlme package runs
>>> the models with no problem.
>>>
>>> Thank you in advance.
>>>
>>> Best,
>>>
>>> Hedyeh Ahmadi, Ph.D.
>>> Statistician
>>> Keck School of Medicine
>>> Department of Preventive Medicine
>>> University of Southern California
>>>
>>> Postdoctoral Scholar
>>> Institute for Interdisciplinary Salivary Bioscience Research (IISBR)
>>> University of California, Irvine
>>>
>>> LinkedIn
>>> https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k70OXW4fU$
> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k70OXW4fU$>
>
>>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!5uCe7IsPHtgAoEp8Qsbn8bXOUBLGi7pVfXIjHwMUHVDbmnOSRCu7OHKGGuIvhag$
> <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$>
>>>> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!7bcqr_mYJEwUBwSQ-hoyGUZPrR-Wz2RGDxVbFlFtbA0oveGsE7tg-2k70OXW4fU$
>
>>> <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$>>
>>> <
>>> https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!8UfGozITdR3cNo929aSVEsbVNgbIul9f91q4hA3PAf0ywits0jIKVDAQdYkAXFg$
> <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$>>
>>> <
>>> https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!8UfGozITdR3cNo929aSVEsbVNgbIul9f91q4hA3PAf0ywits0jIKVDAQdYkAXFg$
> <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$>>
>>> <
>>> https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!8UfGozITdR3cNo929aSVEsbVNgbIul9f91q4hA3PAf0ywits0jIKVDAQdYkAXFg$
> <https://urldefense.com/v3/__http://www.linkedin.com/in/hedyeh-ahmadi__;!!LIr3w8kk_Xxm!8UfGozITdR3cNo929aSVEsbVNgbIul9f91q4hA3PAf0ywits0jIKVDAQdYkAXFg$>
>>>>>
>>>
>>>
>>>
>>>
>>>
>>> [[alternative HTML version deleted]]
>>>
>>> _______________________________________________
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