Re: [R] problem with the ltm package - 3PL model

From: Dimitris Rizopoulos <dimitris.rizopoulos_at_med.kuleuven.be>
Date: Thu, 28 Feb 2008 10:03:29 +0100

Hi Xavier,

the reason you observe this feature is that in the 'constraint' argument you should specify the values under the additive parameterization, i.e., when in the second column of the matrix supplied in 'constraint' you specify 2, then you need to provide the easiness parameters (not the difficulty parameters) in the third column. Check the Details section of ?tpm() and the following for an illustration:

library(ltm)

fit <- tpm(LSAT)
cf <- coef(fit)

constr <- rbind(

    cbind(1:3, c(1,1,1), cf[1:3, 1]),
    cbind(1:3, c(3,3,3), cf[1:3, 3]),
    cbind(1:3, c(2,2,2), - cf[1:3, 2] * cf[1:3, 3])
)

fit2 <- tpm(LSAT, constraint = constr)

coef(fit)[1:3, ]
coef(fit2)[1:3, ]

I hope it's more clear now.

Best,
Dimitris

ps, you may find more info regarding ltm as well as sample analyses files at the R wiki page:
http://wiki.r-project.org/rwiki/doku.php?id=packages:cran:ltm



Dimitris Rizopoulos
Biostatistical Centre
School of Public Health
Catholic University of Leuven

Address: Kapucijnenvoer 35, Leuven, Belgium

Tel: +32/(0)16/336899
Fax: +32/(0)16/337015
Web: http://med.kuleuven.be/biostat/
     http://www.student.kuleuven.be/~m0390867/dimitris.htm

Dear Dimitris:

I am working with ltm package. I have been analyzing a data with 3PL model and I need to do two estimation.
In the first, the 40 items parameters are free, and the second the estimation of the 1-10 items are fixed, those correspond to the last 10 items
parameters of the first simulation. The remaining items parameters (11-40) are free.

I have a problem, when I try to fix the ten items parameters in the second
simulation,the difficult parameters are not fixed. Why?.

I will like to know if you know the problem.

Thank you for your response,

Xavier G. Ordoņez

An example the process:

> para.est.I <- tpm(Apli.sample.I,IRT.param = TRUE)
> par.est.I <- coef(para.est.I)

    Gussng Dffclt Dscrmn

V32  0.009 -2.453  0.747
V33  0.310  0.444  0.694
V34  0.327  0.873  1.036
V35  0.031 -3.067  0.343
V36  0.054 -0.934  1.130
V37  0.001 -1.991  0.582
V38  0.004 -1.686  0.571
V39  0.003 -2.470  0.910
V40  0.207  0.421  1.307
V41  0.114 -0.843  1.024

> fix.c <-
> cbind(rep(1:10),rep(1,10),matrix(as.vector(t(par.est.I[31:40,])[1,])))
> fix.b <-
> cbind(rep(1:10),rep(2,10),matrix(as.vector(t(par.est.I[31:40,])[2,])))
> fix.a <-
> cbind(rep(1:10),rep(3,10),matrix(as.vector(t(par.est.I[31:40,])[3,])))
> fixx <- rbind(fix.c,fix.b,fix.a)

> para.est.II <- tpm(Apli.sample.I,constraint = fixx,IRT.param = TRUE)

    Gussng Dffclt Dscrmn

V2   0.009  3.284  0.747
V3   0.310 -0.640  0.694
V4   0.327 -0.843  1.036
V5   0.031  8.942  0.343
V6   0.054  0.827  1.130
V7   0.001  3.421  0.582
V8   0.004  2.953  0.571
V9   0.003  2.714  0.910
V10  0.207 -0.322  1.307
V11  0.114  0.823  1.024

> coef(para.est.II)[1:10,]==coef(para.est.I)[31:40,]

    Gussng Dffclt Dscrmn
V2 TRUE FALSE TRUE
V3 TRUE FALSE TRUE
V4 TRUE FALSE TRUE
V5 TRUE FALSE TRUE
V6 TRUE FALSE TRUE
V7 TRUE FALSE TRUE
V8 TRUE FALSE TRUE
V9 TRUE FALSE TRUE
V10 TRUE FALSE TRUE
V11 TRUE FALSE TRUE Disclaimer: http://www.kuleuven.be/cwis/email_disclaimer.htm



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