[R] Estimating IRT models by using nlme() function
Joshua Wiley
jwiley.psych at gmail.com
Fri Nov 11 22:00:59 CET 2011
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 Zopluoğlu <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" 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
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"1000.5" 1000 "5" 0 0 0 0 0 1
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