Thanks for your suggestion, Dimitris.

I know (and use) all of these R packages for IRT (I am actually writer of
one of them, EstCRM). I also use specialized commercial software such as
BILOG and MULTILOG.

My goal is to be able to estimate IRT model parameters in a nonlinear mixed
effects regression framework. Recently, there has been some efforts to do
that as I give one reference in m previous e-mail. There are two advantages
of using non-linear mixed effects regression for IRT estimation. One of
them is that it gives a kind of unified approach, because it is very
flexible. You can change the nonlinear model however you like, and try to
estimate very different models. Then, see which one fits your data better.
So, you don't have to force yourself to fit regular and well know IRT
models if you have reasons to fit another model. Second, it allows you to
model higher clusters. Most of the time, we collect data from clusters, and
the subjects within a cluster are not independent from each other. It's a
well known concept in HLM framework, and measured by intra-class
correlation coefficient. I have never seen in IRT literature about this
issue, and we really don't know how cluster dependencies might affect IRT
parameter estimation. So, nonlinear mixed effects regression approach might
allow you to model a third (or may be a fourth) cluster above the students,
and take the cluster dependencies into account while estimating IRT
parameters. It also provides flexibilities for other IRT applications (
such as detecting DIF items).

Anyway, my goal is not basically estimating IRT parameters. I can do it in
so many different ways by using other softwares. My goal is to do it in a
nonlinear mixed effects regression framework, and see how well it does
comparing to the traditional estimation methods. I think ICC component is
very important and its possible impacts were never adressed in IRT
literature for parameter estimation. This is open to investigation. But, I
need to figure out this nlme() thing first. I can use SAS, because people
already provided all SAS syntax to estimate IRT parameters for all
well-known models in nonlinear mized effect approach. But, I want to see it
if nlme() can replicate what they did since I am an R fan.







2011/11/12 Dimitris Rizopoulos <d.rizopoulos@erasmusmc.nl>

> Note that there are several IRT dedicated packages in R, such as the ltm
> and eRm packages. For more info you may check the Psychometrics Task View
> at: http://cran.r-project.org/web/**views/Psychometrics.html<http://cran.r-project.org/web/views/Psychometrics.html>
>
>
> I hope it helps.
>
> Best,
> Dimitris
>
>
>
>
> On 11/11/2011 9:38 PM, Cengiz Zopluoğlu wrote:
>
>> Hi,
>>
>> I have a question about estimating IRT models by using nlme, not just
>> rasch
>> model, but also other models.
>>
>> Behavior Research Methods
>> <http://www.springerlink.com/**content/1554-351x/<http://www.springerlink.com/content/1554-351x/>>
>>  Volume
>> 37, Number 2<http://www.springerlink.com/**content/1554-351x/37/2/<http://www.springerlink.com/content/1554-351x/37/2/>>,
>> 202-218,
>>
>> DOI: 10.3758/BF03192688
>> Using SAS PROC NLMIXED to fit item response theory models (2005).
>> Ching-Fan
>> Sheu<https://mail.google.com/**mail/u/0/html/compose/static_**
>> files/goog_851944013<https://mail.google.com/mail/u/0/html/compose/static_files/goog_851944013>
>> >,
>> Cheng-Te Chen<https://mail.google.com/**mail/u/0/html/compose/static_**
>> files/goog_851944013<https://mail.google.com/mail/u/0/html/compose/static_files/goog_851944013>
>> >,
>> Ya-Hui Su and Wen-Chung Wang
>>
>> An example of this is provided in the paper above. They use SAS PROC
>> NLMIXED, and estimate all possible binary and Polytomous IRT models. I
>> want
>> to replicate what they did using R and nlme package. I am able to fit
>> rasch
>> model, but have some error messages for 2PL IRT model. So, I could not go
>> beyond that.
>>
>> This is really important for me, because any nonlinear model can be fitted
>> by using this approach. I would like to see how well nlme() package
>> recovers true parameters, not just regular IRT models but also some other
>> less used IRT models.
>>
>> Here is the example. Let's say I have the following dataset. 1000 people
>> responds five items.
>>
>>
>>            ID  Item Response d1 d2 d3 d4 d5
>>
>>      1.1  1    1        0  1  0  0  0  0
>>
>>      1.2  1    2        0  0  1  0  0  0
>>
>>      1.3  1    3        0  0  0  1  0  0
>>
>>      1.4  1    4        1  0  0  0  1  0
>>
>>      1.5  1    5        0  0  0  0  0  1
>>
>>      2.1  2    1        1  1  0  0  0  0
>>
>>      2.2  2    2        0  0  1  0  0  0
>>
>>      2.3  2    3        0  0  0  1  0  0
>>
>>      2.4  2    4        1  0  0  0  1  0
>>
>>      2.5  2    5        0  0  0  0  0  1
>>
>>      3.1  3    1        0  1  0  0  0  0
>>
>>      3.2  3    2        0  0  1  0  0  0
>>
>>      3.3  3    3        1  0  0  1  0  0
>>
>>      3.4  3    4        1  0  0  0  1  0
>>
>>      3.5  3    5        0  0  0  0  0  1
>>
>>      ..............................
>>
>>      ..............................
>>
>> 1000.1 1000    1        1  1  0  0  0  0
>>
>> 1000.2 1000    2        0  0  1  0  0  0
>>
>> 1000.3 1000    3        1  0  0  1  0  0
>>
>> 1000.4 1000    4        1  0  0  0  1  0
>>
>> 1000.5 1000    5        0  0  0  0  0  1
>>
>> The items are nested within students. Response is the actual dependent
>> variable. d1, d2, d3, d4, and d5 are the corresponding dummy codes for
>> each
>> item. We treat persons as random effects, and item parameters as fixed
>> effects. To fit Rasch model, I run the following code:
>>
>>
>>   d<- read.table("data.txt", header=TRUE)
>> d1<- d$d1
>> d2<- d$d2
>> d3<- d$d3
>> d4<- d$d4
>> d5<- d$d5
>>  ##############################**#############################
>> onePL<- function(b1,b2,b3,b4,b5,theta) { #nonlinear model to fit
>>     b= b1*d1+b2*d2+b3*d3+b4*d4+b5*d5
>>     exp((theta-b))/(1+exp((theta-**b)))
>> }
>> ##############################**##############################**#########
>> nlme(model=Response ~ onePL(b1,b2,b3,b4,b5,theta),
>> data = d,
>> fixed = b1+b2+b3+b4+b5 ~ 1,
>> random = theta ~ 1 | ID,
>> start=c(b1=0,b2=0,b3=0,b4=0,**b5=0),
>> )
>>
>>   *OUTPUT *
>>
>>
>>  Nonlinear mixed-effects model fit by maximum likelihood
>>   Model: Response ~ onePL(b1, b2, b3, b4, b5, theta)
>>   Data: d
>>   Log-likelihood: -2597.344
>>   Fixed: b1 + b2 + b3 + b4 + b5 ~ 1
>>         b1         b2         b3         b4         b5
>>  -1.1240371  1.5931634  0.2574785 -2.0993236  0.8881437
>>  Random effects:
>>  Formula: theta ~ 1 | ID
>>             theta  Residual
>>  StdDev: 0.9765999 0.3780802
>>  Number of Observations: 5000
>>  Number of Groups: 1000
>>
>>
>> This make sense to me. Actually, the data was simulated data, and the b
>> parameters were close to true values used to generate data. Also the
>> standard deviation of random effects (theta or latent ability level in
>> this
>> case) was close to 1 that was used to generate IRT person ability
>> parameters.
>>
>> Then, I run the following code to estimate 2 PL IRT model. It was all
>> same,
>> just add an additional "a" parameter for each item.
>>
>>
>>   twoPL<- function(a1,a2,a3,a4,a5,b1,b2,**b3,b4,b5,theta) {
>>     a= a1*d1+a2*d2+a3*d3+a4*d4+a5*d5
>>     b= b1*d1+b2*d2+b3*d3+b4*d4+b5*d5
>>     exp(a*(theta-b))/(1+exp(a*(**theta-b)))
>> }
>>  nlme(model=Response ~ twoPL(a1,a2,a3,a4,a5,b1,b2,b3,**b4,b5,theta),
>> data = d,
>> fixed = a1+a2+a3+a4+a5+b1+b2+b3+b4+b5 ~ 1,
>> random = theta ~ 1 | ID,
>> start=c(a1=1,a2=1,a3=1,a4=1,**a5=1,b1=0,b2=0,b3=0,b4=0,b5=0)**,
>> )
>>
>>
>> It gives the following error:
>>
>> *Error in MEEM(object, conLin, control$niterEM) :
>>   Singularity in backsolve at level 0, block 1*
>>
>>
>> Is there anyone who have an idea what I am doing wrong? Is there any error
>> in the syntax? I never used nlme package before, so I might be missing
>> some
>> components in the code. Or, is this just estimation problem and nlme() can
>> not fit this model for some reason?
>>
>> I would appreciate any help.
>>
>> Thanks
>>
>>
>>
>> ______________________________**________________
>> R-help@r-project.org mailing list
>> https://stat.ethz.ch/mailman/**listinfo/r-help<https://stat.ethz.ch/mailman/listinfo/r-help>
>> PLEASE do read the posting guide http://www.R-project.org/**
>> posting-guide.html <http://www.R-project.org/posting-guide.html>
>> and provide commented, minimal, self-contained, reproducible code.
>>
>
> --
> Dimitris Rizopoulos
> Assistant Professor
> Department of Biostatistics
> Erasmus University Medical Center
>
> Address: PO Box 2040, 3000 CA Rotterdam, the Netherlands
> Tel: +31/(0)10/7043478
> Fax: +31/(0)10/7043014
> Web: http://www.erasmusmc.nl/**biostatistiek/<http://www.erasmusmc.nl/biostatistiek/>
>



-- 

Cengiz Zopluoglu

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