Re: [R] Estimating IRT models by using nlme() function
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
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/ Volume
37, Number 2http://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
Sheuhttps://mail.google.com/mail/u/0/html/compose/static_files/goog_851944013,
Cheng-Te
Chenhttps://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
1.1 110 1 0 0 0 0
1.2 120 0 1 0 0 0
1.3 130 0 0 1 0 0
1.4 141 0 0 0 1 0
1.5 150 0 0 0 0 1
2.1 211 1 0 0 0 0
2.2 220 0 1 0 0 0
2.3 230 0 0 1 0 0
2.4 241 0 0 0 1 0
2.5 250 0 0 0 0 1
3.1 310 1 0 0 0 0
3.2 320 0 1 0 0 0
3.3 331 0 0 1 0 0
3.4 341 0 0 0 1 0
3.5 350 0 0 0 0 1
..
..
1000.1 100011 1 0 0 0 0
1000.2 100020 0 1 0 0 0
1000.3 100031 0 0 1 0 0
1000.4 100041 0 0 0 1 0
1000.5 100050 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
Re: [R] Estimating IRT models by using nlme() function
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.rizopou...@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.htmlhttp://cran.r-project.org/web/views/Psychometrics.html I hope it helps. Best, Dimitris On 11/11/2011 9:38 PM, Cengiz ZopluoÄlu 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 2http://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 Sheuhttps://mail.google.com/**mail/u/0/html/compose/static_** files/goog_851944013https://mail.google.com/mail/u/0/html/compose/static_files/goog_851944013 , Cheng-Te Chenhttps://mail.google.com/**mail/u/0/html/compose/static_** files/goog_851944013https://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 1.1 110 1 0 0 0 0 1.2 120 0 1 0 0 0 1.3 130 0 0 1 0 0 1.4 141 0 0 0 1 0 1.5 150 0 0 0 0 1 2.1 211 1 0 0 0 0 2.2 220 0 1 0 0 0 2.3 230 0 0 1 0 0 2.4 241 0 0 0 1 0 2.5 250 0 0 0 0 1 3.1 310 1 0 0 0 0 3.2 320 0 1 0 0 0 3.3 331 0 0 1 0 0 3.4 341 0 0 0 1 0 3.5 350 0 0 0 0 1 .. .. 1000.1 100011 1 0 0 0 0
