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 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>,
Cheng-Te
Chen<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
--
Cengiz Zopluoglu
-------------- next part --------------
"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
"4.1" 4 "1" 1 1 0 0 0 0
"4.2" 4 "2" 1 0 1 0 0 0
"4.3" 4 "3" 1 0 0 1 0 0
"4.4" 4 "4" 1 0 0 0 1 0
"4.5" 4 "5" 1 0 0 0 0 1
"5.1" 5 "1" 1 1 0 0 0 0
"5.2" 5 "2" 0 0 1 0 0 0
"5.3" 5 "3" 1 0 0 1 0 0
"5.4" 5 "4" 1 0 0 0 1 0
"5.5" 5 "5" 1 0 0 0 0 1
"6.1" 6 "1" 0 1 0 0 0 0
"6.2" 6 "2" 1 0 1 0 0 0
"6.3" 6 "3" 1 0 0 1 0 0
"6.4" 6 "4" 1 0 0 0 1 0
"6.5" 6 "5" 0 0 0 0 0 1
"7.1" 7 "1" 1 1 0 0 0 0
"7.2" 7 "2" 0 0 1 0 0 0
"7.3" 7 "3" 0 0 0 1 0 0
"7.4" 7 "4" 1 0 0 0 1 0
"7.5" 7 "5" 1 0 0 0 0 1
"8.1" 8 "1" 1 1 0 0 0 0
"8.2" 8 "2" 0 0 1 0 0 0
"8.3" 8 "3" 1 0 0 1 0 0
"8.4" 8 "4" 1 0 0 0 1 0
"8.5" 8 "5" 1 0 0 0 0 1
"9.1" 9 "1" 1 1 0 0 0 0
"9.2" 9 "2" 0 0 1 0 0 0
"9.3" 9 "3" 1 0 0 1 0 0
"9.4" 9 "4" 1 0 0 0 1 0
"9.5" 9 "5" 1 0 0 0 0 1
"10.1" 10 "1" 0 1 0 0 0 0
"10.2" 10 "2" 0 0 1 0 0 0
"10.3" 10 "3" 1 0 0 1 0 0
"10.4" 10 "4" 1 0 0 0 1 0
"10.5" 10 "5" 1 0 0 0 0 1
"11.1" 11 "1" 0 1 0 0 0 0
"11.2" 11 "2" 0 0 1 0 0 0
"11.3" 11 "3" 1 0 0 1 0 0
"11.4" 11 "4" 1 0 0 0 1 0
"11.5" 11 "5" 1 0 0 0 0 1
"12.1" 12 "1" 1 1 0 0 0 0
"12.2" 12 "2" 0 0 1 0 0 0
"12.3" 12 "3" 1 0 0 1 0 0
"12.4" 12 "4" 1 0 0 0 1 0
"12.5" 12 "5" 0 0 0 0 0 1
"13.1" 13 "1" 0 1 0 0 0 0
"13.2" 13 "2" 0 0 1 0 0 0
"13.3" 13 "3" 0 0 0 1 0 0
"13.4" 13 "4" 1 0 0 0 1 0
"13.5" 13 "5" 0 0 0 0 0 1
"14.1" 14 "1" 0 1 0 0 0 0
"14.2" 14 "2" 0 0 1 0 0 0
"14.3" 14 "3" 0 0 0 1 0 0
"14.4" 14 "4" 1 0 0 0 1 0
"14.5" 14 "5" 0 0 0 0 0 1
"15.1" 15 "1" 1 1 0 0 0 0
"15.2" 15 "2" 0 0 1 0 0 0
"15.3" 15 "3" 0 0 0 1 0 0
"15.4" 15 "4" 1 0 0 0 1 0
"15.5" 15 "5" 1 0 0 0 0 1
"16.1" 16 "1" 1 1 0 0 0 0
"16.2" 16 "2" 0 0 1 0 0 0
"16.3" 16 "3" 0 0 0 1 0 0
"16.4" 16 "4" 1 0 0 0 1 0
"16.5" 16 "5" 0 0 0 0 0 1
"17.1" 17 "1" 1 1 0 0 0 0
"17.2" 17 "2" 0 0 1 0 0 0
"17.3" 17 "3" 0 0 0 1 0 0
"17.4" 17 "4" 1 0 0 0 1 0
"17.5" 17 "5" 0 0 0 0 0 1
"18.1" 18 "1" 1 1 0 0 0 0
"18.2" 18 "2" 0 0 1 0 0 0
"18.3" 18 "3" 1 0 0 1 0 0
"18.4" 18 "4" 1 0 0 0 1 0
"18.5" 18 "5" 0 0 0 0 0 1
"19.1" 19 "1" 1 1 0 0 0 0
"19.2" 19 "2" 0 0 1 0 0 0
"19.3" 19 "3" 0 0 0 1 0 0
"19.4" 19 "4" 1 0 0 0 1 0
"19.5" 19 "5" 1 0 0 0 0 1
"20.1" 20 "1" 1 1 0 0 0 0
"20.2" 20 "2" 0 0 1 0 0 0
"20.3" 20 "3" 0 0 0 1 0 0
"20.4" 20 "4" 1 0 0 0 1 0
"20.5" 20 "5" 0 0 0 0 0 1
"21.1" 21 "1" 1 1 0 0 0 0
"21.2" 21 "2" 0 0 1 0 0 0
"21.3" 21 "3" 0 0 0 1 0 0
"21.4" 21 "4" 1 0 0 0 1 0
"21.5" 21 "5" 0 0 0 0 0 1
"22.1" 22 "1" 1 1 0 0 0 0
"22.2" 22 "2" 1 0 1 0 0 0
"22.3" 22 "3" 0 0 0 1 0 0
"22.4" 22 "4" 1 0 0 0 1 0
"22.5" 22 "5" 0 0 0 0 0 1
"23.1" 23 "1" 1 1 0 0 0 0
"23.2" 23 "2" 0 0 1 0 0 0
"23.3" 23 "3" 0 0 0 1 0 0
"23.4" 23 "4" 1 0 0 0 1 0
"23.5" 23 "5" 0 0 0 0 0 1
"24.1" 24 "1" 1 1 0 0 0 0
"24.2" 24 "2" 0 0 1 0 0 0
"24.3" 24 "3" 0 0 0 1 0 0
"24.4" 24 "4" 1 0 0 0 1 0
"24.5" 24 "5" 1 0 0 0 0 1
"25.1" 25 "1" 1 1 0 0 0 0
"25.2" 25 "2" 0 0 1 0 0 0
"25.3" 25 "3" 0 0 0 1 0 0
"25.4" 25 "4" 1 0 0 0 1 0
"25.5" 25 "5" 0 0 0 0 0 1
"26.1" 26 "1" 0 1 0 0 0 0
"26.2" 26 "2" 0 0 1 0 0 0
"26.3" 26 "3" 1 0 0 1 0 0
"26.4" 26 "4" 1 0 0 0 1 0
"26.5" 26 "5" 0 0 0 0 0 1
"27.1" 27 "1" 1 1 0 0 0 0
"27.2" 27 "2" 0 0 1 0 0 0
"27.3" 27 "3" 1 0 0 1 0 0
"27.4" 27 "4" 1 0 0 0 1 0
"27.5" 27 "5" 0 0 0 0 0 1
"28.1" 28 "1" 1 1 0 0 0 0
"28.2" 28 "2" 1 0 1 0 0 0
"28.3" 28 "3" 1 0 0 1 0 0
"28.4" 28 "4" 1 0 0 0 1 0
"28.5" 28 "5" 1 0 0 0 0 1
"29.1" 29 "1" 0 1 0 0 0 0
"29.2" 29 "2" 0 0 1 0 0 0
"29.3" 29 "3" 1 0 0 1 0 0
"29.4" 29 "4" 1 0 0 0 1 0
"29.5" 29 "5" 1 0 0 0 0 1
"30.1" 30 "1" 1 1 0 0 0 0
"30.2" 30 "2" 0 0 1 0 0 0
"30.3" 30 "3" 0 0 0 1 0 0
"30.4" 30 "4" 1 0 0 0 1 0
"30.5" 30 "5" 0 0 0 0 0 1
"31.1" 31 "1" 1 1 0 0 0 0
"31.2" 31 "2" 0 0 1 0 0 0
"31.3" 31 "3" 0 0 0 1 0 0
"31.4" 31 "4" 0 0 0 0 1 0
"31.5" 31 "5" 0 0 0 0 0 1
"32.1" 32 "1" 0 1 0 0 0 0
"32.2" 32 "2" 0 0 1 0 0 0
"32.3" 32 "3" 1 0 0 1 0 0
"32.4" 32 "4" 0 0 0 0 1 0
"32.5" 32 "5" 0 0 0 0 0 1
"33.1" 33 "1" 1 1 0 0 0 0
"33.2" 33 "2" 0 0 1 0 0 0
"33.3" 33 "3" 1 0 0 1 0 0
"33.4" 33 "4" 1 0 0 0 1 0
"33.5" 33 "5" 0 0 0 0 0 1
"34.1" 34 "1" 1 1 0 0 0 0
"34.2" 34 "2" 0 0 1 0 0 0
"34.3" 34 "3" 0 0 0 1 0 0
"34.4" 34 "4" 1 0 0 0 1 0
"34.5" 34 "5" 0 0 0 0 0 1
"35.1" 35 "1" 1 1 0 0 0 0
"35.2" 35 "2" 0 0 1 0 0 0
"35.3" 35 "3" 0 0 0 1 0 0
"35.4" 35 "4" 1 0 0 0 1 0
"35.5" 35 "5" 0 0 0 0 0 1
"36.1" 36 "1" 1 1 0 0 0 0
"36.2" 36 "2" 1 0 1 0 0 0
"36.3" 36 "3" 1 0 0 1 0 0
"36.4" 36 "4" 1 0 0 0 1 0
"36.5" 36 "5" 0 0 0 0 0 1
"37.1" 37 "1" 1 1 0 0 0 0
"37.2" 37 "2" 0 0 1 0 0 0
"37.3" 37 "3" 1 0 0 1 0 0
"37.4" 37 "4" 1 0 0 0 1 0
"37.5" 37 "5" 0 0 0 0 0 1
"38.1" 38 "1" 1 1 0 0 0 0
"38.2" 38 "2" 0 0 1 0 0 0
"38.3" 38 "3" 0 0 0 1 0 0
"38.4" 38 "4" 1 0 0 0 1 0
"38.5" 38 "5" 0 0 0 0 0 1
"39.1" 39 "1" 1 1 0 0 0 0
"39.2" 39 "2" 1 0 1 0 0 0
"39.3" 39 "3" 0 0 0 1 0 0
"39.4" 39 "4" 1 0 0 0 1 0
"39.5" 39 "5" 0 0 0 0 0 1
"40.1" 40 "1" 1 1 0 0 0 0
"40.2" 40 "2" 0 0 1 0 0 0
"40.3" 40 "3" 1 0 0 1 0 0
"40.4" 40 "4" 1 0 0 0 1 0
"40.5" 40 "5" 0 0 0 0 0 1
"41.1" 41 "1" 0 1 0 0 0 0
"41.2" 41 "2" 0 0 1 0 0 0
"41.3" 41 "3" 0 0 0 1 0 0
"41.4" 41 "4" 1 0 0 0 1 0
"41.5" 41 "5" 0 0 0 0 0 1
"42.1" 42 "1" 0 1 0 0 0 0
"42.2" 42 "2" 0 0 1 0 0 0
"42.3" 42 "3" 0 0 0 1 0 0
"42.4" 42 "4" 1 0 0 0 1 0
"42.5" 42 "5" 0 0 0 0 0 1
"43.1" 43 "1" 1 1 0 0 0 0
"43.2" 43 "2" 0 0 1 0 0 0
"43.3" 43 "3" 1 0 0 1 0 0
"43.4" 43 "4" 1 0 0 0 1 0
"43.5" 43 "5" 1 0 0 0 0 1
"44.1" 44 "1" 1 1 0 0 0 0
"44.2" 44 "2" 0 0 1 0 0 0
"44.3" 44 "3" 0 0 0 1 0 0
"44.4" 44 "4" 1 0 0 0 1 0
"44.5" 44 "5" 0 0 0 0 0 1
"45.1" 45 "1" 1 1 0 0 0 0
"45.2" 45 "2" 0 0 1 0 0 0
"45.3" 45 "3" 1 0 0 1 0 0
"45.4" 45 "4" 1 0 0 0 1 0
"45.5" 45 "5" 1 0 0 0 0 1
"46.1" 46 "1" 0 1 0 0 0 0
"46.2" 46 "2" 0 0 1 0 0 0
"46.3" 46 "3" 0 0 0 1 0 0
"46.4" 46 "4" 1 0 0 0 1 0
"46.5" 46 "5" 0 0 0 0 0 1
"47.1" 47 "1" 0 1 0 0 0 0
"47.2" 47 "2" 1 0 1 0 0 0
"47.3" 47 "3" 0 0 0 1 0 0
"47.4" 47 "4" 1 0 0 0 1 0
"47.5" 47 "5" 0 0 0 0 0 1
"48.1" 48 "1" 1 1 0 0 0 0
"48.2" 48 "2" 0 0 1 0 0 0
"48.3" 48 "3" 0 0 0 1 0 0
"48.4" 48 "4" 1 0 0 0 1 0
"48.5" 48 "5" 1 0 0 0 0 1
"49.1" 49 "1" 1 1 0 0 0 0
"49.2" 49 "2" 0 0 1 0 0 0
"49.3" 49 "3" 0 0 0 1 0 0
"49.4" 49 "4" 1 0 0 0 1 0
"49.5" 49 "5" 0 0 0 0 0 1
"50.1" 50 "1" 1 1 0 0 0 0
"50.2" 50 "2" 0 0 1 0 0 0
"50.3" 50 "3" 1 0 0 1 0 0
"50.4" 50 "4" 1 0 0 0 1 0
"50.5" 50 "5" 0 0 0 0 0 1
"51.1" 51 "1" 1 1 0 0 0 0
"51.2" 51 "2" 1 0 1 0 0 0
"51.3" 51 "3" 0 0 0 1 0 0
"51.4" 51 "4" 0 0 0 0 1 0
"51.5" 51 "5" 1 0 0 0 0 1
"52.1" 52 "1" 1 1 0 0 0 0
"52.2" 52 "2" 0 0 1 0 0 0
"52.3" 52 "3" 0 0 0 1 0 0
"52.4" 52 "4" 1 0 0 0 1 0
"52.5" 52 "5" 1 0 0 0 0 1
"53.1" 53 "1" 1 1 0 0 0 0
"53.2" 53 "2" 0 0 1 0 0 0
"53.3" 53 "3" 0 0 0 1 0 0
"53.4" 53 "4" 1 0 0 0 1 0
"53.5" 53 "5" 1 0 0 0 0 1
"54.1" 54 "1" 1 1 0 0 0 0
"54.2" 54 "2" 0 0 1 0 0 0
"54.3" 54 "3" 1 0 0 1 0 0
"54.4" 54 "4" 1 0 0 0 1 0
"54.5" 54 "5" 1 0 0 0 0 1
"55.1" 55 "1" 1 1 0 0 0 0
"55.2" 55 "2" 0 0 1 0 0 0
"55.3" 55 "3" 1 0 0 1 0 0
"55.4" 55 "4" 1 0 0 0 1 0
"55.5" 55 "5" 0 0 0 0 0 1
"56.1" 56 "1" 1 1 0 0 0 0
"56.2" 56 "2" 0 0 1 0 0 0
"56.3" 56 "3" 0 0 0 1 0 0
"56.4" 56 "4" 1 0 0 0 1 0
"56.5" 56 "5" 0 0 0 0 0 1
"57.1" 57 "1" 0 1 0 0 0 0
"57.2" 57 "2" 0 0 1 0 0 0
"57.3" 57 "3" 1 0 0 1 0 0
"57.4" 57 "4" 1 0 0 0 1 0
"57.5" 57 "5" 0 0 0 0 0 1
"58.1" 58 "1" 1 1 0 0 0 0
"58.2" 58 "2" 0 0 1 0 0 0
"58.3" 58 "3" 0 0 0 1 0 0
"58.4" 58 "4" 1 0 0 0 1 0
"58.5" 58 "5" 0 0 0 0 0 1
"59.1" 59 "1" 1 1 0 0 0 0
"59.2" 59 "2" 0 0 1 0 0 0
"59.3" 59 "3" 0 0 0 1 0 0
"59.4" 59 "4" 1 0 0 0 1 0
"59.5" 59 "5" 0 0 0 0 0 1
"60.1" 60 "1" 1 1 0 0 0 0
"60.2" 60 "2" 0 0 1 0 0 0
"60.3" 60 "3" 1 0 0 1 0 0
"60.4" 60 "4" 1 0 0 0 1 0
"60.5" 60 "5" 0 0 0 0 0 1
"61.1" 61 "1" 1 1 0 0 0 0
"61.2" 61 "2" 0 0 1 0 0 0
"61.3" 61 "3" 0 0 0 1 0 0
"61.4" 61 "4" 1 0 0 0 1 0
"61.5" 61 "5" 0 0 0 0 0 1
"62.1" 62 "1" 1 1 0 0 0 0
"62.2" 62 "2" 0 0 1 0 0 0
"62.3" 62 "3" 0 0 0 1 0 0
"62.4" 62 "4" 0 0 0 0 1 0
"62.5" 62 "5" 0 0 0 0 0 1
"63.1" 63 "1" 1 1 0 0 0 0
"63.2" 63 "2" 0 0 1 0 0 0
"63.3" 63 "3" 0 0 0 1 0 0
"63.4" 63 "4" 1 0 0 0 1 0
"63.5" 63 "5" 1 0 0 0 0 1
"64.1" 64 "1" 1 1 0 0 0 0
"64.2" 64 "2" 0 0 1 0 0 0
"64.3" 64 "3" 0 0 0 1 0 0
"64.4" 64 "4" 1 0 0 0 1 0
"64.5" 64 "5" 1 0 0 0 0 1
"65.1" 65 "1" 0 1 0 0 0 0
"65.2" 65 "2" 0 0 1 0 0 0
"65.3" 65 "3" 0 0 0 1 0 0
"65.4" 65 "4" 1 0 0 0 1 0
"65.5" 65 "5" 0 0 0 0 0 1
"66.1" 66 "1" 1 1 0 0 0 0
"66.2" 66 "2" 1 0 1 0 0 0
"66.3" 66 "3" 1 0 0 1 0 0
"66.4" 66 "4" 1 0 0 0 1 0
"66.5" 66 "5" 1 0 0 0 0 1
"67.1" 67 "1" 0 1 0 0 0 0
"67.2" 67 "2" 0 0 1 0 0 0
"67.3" 67 "3" 0 0 0 1 0 0
"67.4" 67 "4" 0 0 0 0 1 0
"67.5" 67 "5" 0 0 0 0 0 1
"68.1" 68 "1" 0 1 0 0 0 0
"68.2" 68 "2" 0 0 1 0 0 0
"68.3" 68 "3" 1 0 0 1 0 0
"68.4" 68 "4" 1 0 0 0 1 0
"68.5" 68 "5" 0 0 0 0 0 1
"69.1" 69 "1" 1 1 0 0 0 0
"69.2" 69 "2" 0 0 1 0 0 0
"69.3" 69 "3" 0 0 0 1 0 0
"69.4" 69 "4" 1 0 0 0 1 0
"69.5" 69 "5" 1 0 0 0 0 1
"70.1" 70 "1" 1 1 0 0 0 0
"70.2" 70 "2" 0 0 1 0 0 0
"70.3" 70 "3" 1 0 0 1 0 0
"70.4" 70 "4" 1 0 0 0 1 0
"70.5" 70 "5" 0 0 0 0 0 1
"71.1" 71 "1" 1 1 0 0 0 0
"71.2" 71 "2" 0 0 1 0 0 0
"71.3" 71 "3" 0 0 0 1 0 0
"71.4" 71 "4" 1 0 0 0 1 0
"71.5" 71 "5" 0 0 0 0 0 1
"72.1" 72 "1" 1 1 0 0 0 0
"72.2" 72 "2" 0 0 1 0 0 0
"72.3" 72 "3" 1 0 0 1 0 0
"72.4" 72 "4" 1 0 0 0 1 0
"72.5" 72 "5" 0 0 0 0 0 1
"73.1" 73 "1" 1 1 0 0 0 0
"73.2" 73 "2" 0 0 1 0 0 0
"73.3" 73 "3" 0 0 0 1 0 0
"73.4" 73 "4" 1 0 0 0 1 0
"73.5" 73 "5" 0 0 0 0 0 1
"74.1" 74 "1" 1 1 0 0 0 0
"74.2" 74 "2" 1 0 1 0 0 0
"74.3" 74 "3" 0 0 0 1 0 0
"74.4" 74 "4" 1 0 0 0 1 0
"74.5" 74 "5" 1 0 0 0 0 1
"75.1" 75 "1" 1 1 0 0 0 0
"75.2" 75 "2" 0 0 1 0 0 0
"75.3" 75 "3" 0 0 0 1 0 0
"75.4" 75 "4" 1 0 0 0 1 0
"75.5" 75 "5" 0 0 0 0 0 1
"76.1" 76 "1" 1 1 0 0 0 0
"76.2" 76 "2" 0 0 1 0 0 0
"76.3" 76 "3" 0 0 0 1 0 0
"76.4" 76 "4" 1 0 0 0 1 0
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Hi Cengiz, This message is more likely to be answered on the R Sig mixed models list. I took the liberty of copying that list and including the original data for them. Cheers, Josh 2011/11/11 Cengiz Zopluo?lu <cen.zop at gmail.com>:> 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 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>, > Cheng-Te Chen<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 > -- > > Cengiz Zopluoglu > > ______________________________________________ > R-help at r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. > >-- Joshua Wiley Ph.D. Student, Health Psychology Programmer Analyst II, ATS Statistical Consulting Group University of California, Los Angeles https://joshuawiley.com/ -------------- next part -------------- "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 "4.1" 4 "1" 1 1 0 0 0 0 "4.2" 4 "2" 1 0 1 0 0 0 "4.3" 4 "3" 1 0 0 1 0 0 "4.4" 4 "4" 1 0 0 0 1 0 "4.5" 4 "5" 1 0 0 0 0 1 "5.1" 5 "1" 1 1 0 0 0 0 "5.2" 5 "2" 0 0 1 0 0 0 "5.3" 5 "3" 1 0 0 1 0 0 "5.4" 5 "4" 1 0 0 0 1 0 "5.5" 5 "5" 1 0 0 0 0 1 "6.1" 6 "1" 0 1 0 0 0 0 "6.2" 6 "2" 1 0 1 0 0 0 "6.3" 6 "3" 1 0 0 1 0 0 "6.4" 6 "4" 1 0 0 0 1 0 "6.5" 6 "5" 0 0 0 0 0 1 "7.1" 7 "1" 1 1 0 0 0 0 "7.2" 7 "2" 0 0 1 0 0 0 "7.3" 7 "3" 0 0 0 1 0 0 "7.4" 7 "4" 1 0 0 0 1 0 "7.5" 7 "5" 1 0 0 0 0 1 "8.1" 8 "1" 1 1 0 0 0 0 "8.2" 8 "2" 0 0 1 0 0 0 "8.3" 8 "3" 1 0 0 1 0 0 "8.4" 8 "4" 1 0 0 0 1 0 "8.5" 8 "5" 1 0 0 0 0 1 "9.1" 9 "1" 1 1 0 0 0 0 "9.2" 9 "2" 0 0 1 0 0 0 "9.3" 9 "3" 1 0 0 1 0 0 "9.4" 9 "4" 1 0 0 0 1 0 "9.5" 9 "5" 1 0 0 0 0 1 "10.1" 10 "1" 0 1 0 0 0 0 "10.2" 10 "2" 0 0 1 0 0 0 "10.3" 10 "3" 1 0 0 1 0 0 "10.4" 10 "4" 1 0 0 0 1 0 "10.5" 10 "5" 1 0 0 0 0 1 "11.1" 11 "1" 0 1 0 0 0 0 "11.2" 11 "2" 0 0 1 0 0 0 "11.3" 11 "3" 1 0 0 1 0 0 "11.4" 11 "4" 1 0 0 0 1 0 "11.5" 11 "5" 1 0 0 0 0 1 "12.1" 12 "1" 1 1 0 0 0 0 "12.2" 12 "2" 0 0 1 0 0 0 "12.3" 12 "3" 1 0 0 1 0 0 "12.4" 12 "4" 1 0 0 0 1 0 "12.5" 12 "5" 0 0 0 0 0 1 "13.1" 13 "1" 0 1 0 0 0 0 "13.2" 13 "2" 0 0 1 0 0 0 "13.3" 13 "3" 0 0 0 1 0 0 "13.4" 13 "4" 1 0 0 0 1 0 "13.5" 13 "5" 0 0 0 0 0 1 "14.1" 14 "1" 0 1 0 0 0 0 "14.2" 14 "2" 0 0 1 0 0 0 "14.3" 14 "3" 0 0 0 1 0 0 "14.4" 14 "4" 1 0 0 0 1 0 "14.5" 14 "5" 0 0 0 0 0 1 "15.1" 15 "1" 1 1 0 0 0 0 "15.2" 15 "2" 0 0 1 0 0 0 "15.3" 15 "3" 0 0 0 1 0 0 "15.4" 15 "4" 1 0 0 0 1 0 "15.5" 15 "5" 1 0 0 0 0 1 "16.1" 16 "1" 1 1 0 0 0 0 "16.2" 16 "2" 0 0 1 0 0 0 "16.3" 16 "3" 0 0 0 1 0 0 "16.4" 16 "4" 1 0 0 0 1 0 "16.5" 16 "5" 0 0 0 0 0 1 "17.1" 17 "1" 1 1 0 0 0 0 "17.2" 17 "2" 0 0 1 0 0 0 "17.3" 17 "3" 0 0 0 1 0 0 "17.4" 17 "4" 1 0 0 0 1 0 "17.5" 17 "5" 0 0 0 0 0 1 "18.1" 18 "1" 1 1 0 0 0 0 "18.2" 18 "2" 0 0 1 0 0 0 "18.3" 18 "3" 1 0 0 1 0 0 "18.4" 18 "4" 1 0 0 0 1 0 "18.5" 18 "5" 0 0 0 0 0 1 "19.1" 19 "1" 1 1 0 0 0 0 "19.2" 19 "2" 0 0 1 0 0 0 "19.3" 19 "3" 0 0 0 1 0 0 "19.4" 19 "4" 1 0 0 0 1 0 "19.5" 19 "5" 1 0 0 0 0 1 "20.1" 20 "1" 1 1 0 0 0 0 "20.2" 20 "2" 0 0 1 0 0 0 "20.3" 20 "3" 0 0 0 1 0 0 "20.4" 20 "4" 1 0 0 0 1 0 "20.5" 20 "5" 0 0 0 0 0 1 "21.1" 21 "1" 1 1 0 0 0 0 "21.2" 21 "2" 0 0 1 0 0 0 "21.3" 21 "3" 0 0 0 1 0 0 "21.4" 21 "4" 1 0 0 0 1 0 "21.5" 21 "5" 0 0 0 0 0 1 "22.1" 22 "1" 1 1 0 0 0 0 "22.2" 22 "2" 1 0 1 0 0 0 "22.3" 22 "3" 0 0 0 1 0 0 "22.4" 22 "4" 1 0 0 0 1 0 "22.5" 22 "5" 0 0 0 0 0 1 "23.1" 23 "1" 1 1 0 0 0 0 "23.2" 23 "2" 0 0 1 0 0 0 "23.3" 23 "3" 0 0 0 1 0 0 "23.4" 23 "4" 1 0 0 0 1 0 "23.5" 23 "5" 0 0 0 0 0 1 "24.1" 24 "1" 1 1 0 0 0 0 "24.2" 24 "2" 0 0 1 0 0 0 "24.3" 24 "3" 0 0 0 1 0 0 "24.4" 24 "4" 1 0 0 0 1 0 "24.5" 24 "5" 1 0 0 0 0 1 "25.1" 25 "1" 1 1 0 0 0 0 "25.2" 25 "2" 0 0 1 0 0 0 "25.3" 25 "3" 0 0 0 1 0 0 "25.4" 25 "4" 1 0 0 0 1 0 "25.5" 25 "5" 0 0 0 0 0 1 "26.1" 26 "1" 0 1 0 0 0 0 "26.2" 26 "2" 0 0 1 0 0 0 "26.3" 26 "3" 1 0 0 1 0 0 "26.4" 26 "4" 1 0 0 0 1 0 "26.5" 26 "5" 0 0 0 0 0 1 "27.1" 27 "1" 1 1 0 0 0 0 "27.2" 27 "2" 0 0 1 0 0 0 "27.3" 27 "3" 1 0 0 1 0 0 "27.4" 27 "4" 1 0 0 0 1 0 "27.5" 27 "5" 0 0 0 0 0 1 "28.1" 28 "1" 1 1 0 0 0 0 "28.2" 28 "2" 1 0 1 0 0 0 "28.3" 28 "3" 1 0 0 1 0 0 "28.4" 28 "4" 1 0 0 0 1 0 "28.5" 28 "5" 1 0 0 0 0 1 "29.1" 29 "1" 0 1 0 0 0 0 "29.2" 29 "2" 0 0 1 0 0 0 "29.3" 29 "3" 1 0 0 1 0 0 "29.4" 29 "4" 1 0 0 0 1 0 "29.5" 29 "5" 1 0 0 0 0 1 "30.1" 30 "1" 1 1 0 0 0 0 "30.2" 30 "2" 0 0 1 0 0 0 "30.3" 30 "3" 0 0 0 1 0 0 "30.4" 30 "4" 1 0 0 0 1 0 "30.5" 30 "5" 0 0 0 0 0 1 "31.1" 31 "1" 1 1 0 0 0 0 "31.2" 31 "2" 0 0 1 0 0 0 "31.3" 31 "3" 0 0 0 1 0 0 "31.4" 31 "4" 0 0 0 0 1 0 "31.5" 31 "5" 0 0 0 0 0 1 "32.1" 32 "1" 0 1 0 0 0 0 "32.2" 32 "2" 0 0 1 0 0 0 "32.3" 32 "3" 1 0 0 1 0 0 "32.4" 32 "4" 0 0 0 0 1 0 "32.5" 32 "5" 0 0 0 0 0 1 "33.1" 33 "1" 1 1 0 0 0 0 "33.2" 33 "2" 0 0 1 0 0 0 "33.3" 33 "3" 1 0 0 1 0 0 "33.4" 33 "4" 1 0 0 0 1 0 "33.5" 33 "5" 0 0 0 0 0 1 "34.1" 34 "1" 1 1 0 0 0 0 "34.2" 34 "2" 0 0 1 0 0 0 "34.3" 34 "3" 0 0 0 1 0 0 "34.4" 34 "4" 1 0 0 0 1 0 "34.5" 34 "5" 0 0 0 0 0 1 "35.1" 35 "1" 1 1 0 0 0 0 "35.2" 35 "2" 0 0 1 0 0 0 "35.3" 35 "3" 0 0 0 1 0 0 "35.4" 35 "4" 1 0 0 0 1 0 "35.5" 35 "5" 0 0 0 0 0 1 "36.1" 36 "1" 1 1 0 0 0 0 "36.2" 36 "2" 1 0 1 0 0 0 "36.3" 36 "3" 1 0 0 1 0 0 "36.4" 36 "4" 1 0 0 0 1 0 "36.5" 36 "5" 0 0 0 0 0 1 "37.1" 37 "1" 1 1 0 0 0 0 "37.2" 37 "2" 0 0 1 0 0 0 "37.3" 37 "3" 1 0 0 1 0 0 "37.4" 37 "4" 1 0 0 0 1 0 "37.5" 37 "5" 0 0 0 0 0 1 "38.1" 38 "1" 1 1 0 0 0 0 "38.2" 38 "2" 0 0 1 0 0 0 "38.3" 38 "3" 0 0 0 1 0 0 "38.4" 38 "4" 1 0 0 0 1 0 "38.5" 38 "5" 0 0 0 0 0 1 "39.1" 39 "1" 1 1 0 0 0 0 "39.2" 39 "2" 1 0 1 0 0 0 "39.3" 39 "3" 0 0 0 1 0 0 "39.4" 39 "4" 1 0 0 0 1 0 "39.5" 39 "5" 0 0 0 0 0 1 "40.1" 40 "1" 1 1 0 0 0 0 "40.2" 40 "2" 0 0 1 0 0 0 "40.3" 40 "3" 1 0 0 1 0 0 "40.4" 40 "4" 1 0 0 0 1 0 "40.5" 40 "5" 0 0 0 0 0 1 "41.1" 41 "1" 0 1 0 0 0 0 "41.2" 41 "2" 0 0 1 0 0 0 "41.3" 41 "3" 0 0 0 1 0 0 "41.4" 41 "4" 1 0 0 0 1 0 "41.5" 41 "5" 0 0 0 0 0 1 "42.1" 42 "1" 0 1 0 0 0 0 "42.2" 42 "2" 0 0 1 0 0 0 "42.3" 42 "3" 0 0 0 1 0 0 "42.4" 42 "4" 1 0 0 0 1 0 "42.5" 42 "5" 0 0 0 0 0 1 "43.1" 43 "1" 1 1 0 0 0 0 "43.2" 43 "2" 0 0 1 0 0 0 "43.3" 43 "3" 1 0 0 1 0 0 "43.4" 43 "4" 1 0 0 0 1 0 "43.5" 43 "5" 1 0 0 0 0 1 "44.1" 44 "1" 1 1 0 0 0 0 "44.2" 44 "2" 0 0 1 0 0 0 "44.3" 44 "3" 0 0 0 1 0 0 "44.4" 44 "4" 1 0 0 0 1 0 "44.5" 44 "5" 0 0 0 0 0 1 "45.1" 45 "1" 1 1 0 0 0 0 "45.2" 45 "2" 0 0 1 0 0 0 "45.3" 45 "3" 1 0 0 1 0 0 "45.4" 45 "4" 1 0 0 0 1 0 "45.5" 45 "5" 1 0 0 0 0 1 "46.1" 46 "1" 0 1 0 0 0 0 "46.2" 46 "2" 0 0 1 0 0 0 "46.3" 46 "3" 0 0 0 1 0 0 "46.4" 46 "4" 1 0 0 0 1 0 "46.5" 46 "5" 0 0 0 0 0 1 "47.1" 47 "1" 0 1 0 0 0 0 "47.2" 47 "2" 1 0 1 0 0 0 "47.3" 47 "3" 0 0 0 1 0 0 "47.4" 47 "4" 1 0 0 0 1 0 "47.5" 47 "5" 0 0 0 0 0 1 "48.1" 48 "1" 1 1 0 0 0 0 "48.2" 48 "2" 0 0 1 0 0 0 "48.3" 48 "3" 0 0 0 1 0 0 "48.4" 48 "4" 1 0 0 0 1 0 "48.5" 48 "5" 1 0 0 0 0 1 "49.1" 49 "1" 1 1 0 0 0 0 "49.2" 49 "2" 0 0 1 0 0 0 "49.3" 49 "3" 0 0 0 1 0 0 "49.4" 49 "4" 1 0 0 0 1 0 "49.5" 49 "5" 0 0 0 0 0 1 "50.1" 50 "1" 1 1 0 0 0 0 "50.2" 50 "2" 0 0 1 0 0 0 "50.3" 50 "3" 1 0 0 1 0 0 "50.4" 50 "4" 1 0 0 0 1 0 "50.5" 50 "5" 0 0 0 0 0 1 "51.1" 51 "1" 1 1 0 0 0 0 "51.2" 51 "2" 1 0 1 0 0 0 "51.3" 51 "3" 0 0 0 1 0 0 "51.4" 51 "4" 0 0 0 0 1 0 "51.5" 51 "5" 1 0 0 0 0 1 "52.1" 52 "1" 1 1 0 0 0 0 "52.2" 52 "2" 0 0 1 0 0 0 "52.3" 52 "3" 0 0 0 1 0 0 "52.4" 52 "4" 1 0 0 0 1 0 "52.5" 52 "5" 1 0 0 0 0 1 "53.1" 53 "1" 1 1 0 0 0 0 "53.2" 53 "2" 0 0 1 0 0 0 "53.3" 53 "3" 0 0 0 1 0 0 "53.4" 53 "4" 1 0 0 0 1 0 "53.5" 53 "5" 1 0 0 0 0 1 "54.1" 54 "1" 1 1 0 0 0 0 "54.2" 54 "2" 0 0 1 0 0 0 "54.3" 54 "3" 1 0 0 1 0 0 "54.4" 54 "4" 1 0 0 0 1 0 "54.5" 54 "5" 1 0 0 0 0 1 "55.1" 55 "1" 1 1 0 0 0 0 "55.2" 55 "2" 0 0 1 0 0 0 "55.3" 55 "3" 1 0 0 1 0 0 "55.4" 55 "4" 1 0 0 0 1 0 "55.5" 55 "5" 0 0 0 0 0 1 "56.1" 56 "1" 1 1 0 0 0 0 "56.2" 56 "2" 0 0 1 0 0 0 "56.3" 56 "3" 0 0 0 1 0 0 "56.4" 56 "4" 1 0 0 0 1 0 "56.5" 56 "5" 0 0 0 0 0 1 "57.1" 57 "1" 0 1 0 0 0 0 "57.2" 57 "2" 0 0 1 0 0 0 "57.3" 57 "3" 1 0 0 1 0 0 "57.4" 57 "4" 1 0 0 0 1 0 "57.5" 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Dimitris Rizopoulos
2011-Nov-12 08:15 UTC
[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 Zopluo?lu 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 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>, > Cheng-Te Chen<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 at r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide 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/