fitting data to gpcm(ltm or mirt?)

R에서 응답자료를 gpcm 모형으로 분석하고자 할 때 ltm 또는 gpcm 패키지를 쓸 수 있다.

You can use the package <gpcm> or <ltm> to fit your data to gpcm.

두 패키지의 가장 큰 차이점은 모수를 다른 방식으로 사용한다는 점이다.

The difference between two functions, gpcm and ltm is that they use different parameterization.

이제 두 함수 ltm::gpcm과 mirt::mirt를 통해 주어진 자료를 gpcm에 적합시키자.

Now, let's see how we can fit the data to gpcm via <ltm::gpcm> and <mirt::mirt>.

library("mirt")

library("ltm")

apply(R.gpcm, 2, unique)

n.item = ncol(R.gpcm); n.subj = nrow(R.gpcm);

fit.gpcm.mirt <- mirt(data=R.gpcm, 1, itemtype="gpcm")

cf.mirt <- coef(fit.gpcm.mirt, IRTpars=T)

# coef(fit.gpcm)

cf.mirt.mat <- matrix(NA, nrow=n.item, ncol=ncat)

for (i in 1:n.item) {

  cf.mirt.mat[i,1:length(cf.mirt[[i]])] = cf.mirt[[i]]

}

cf.ltm <- coef(fit.gpcm.ltm <- gpcm(R.gpcm, 

                                    constraint="gpcm", 

                                    control=list(GHk=62, optimizer="optim",

                                                 optimMethod="BFGS", verbose=T)), IRT.param=T)

cf.ltm.mat <- matrix(NA, nrow=n.item, ncol=ncat  verbose=T)

for (i in 1:n.item) {

  cf.ltm.mat[i,1] = cf.ltm[[i]][length(cf.ltm[[i]])]

  cf.ltm.mat[i,2:length(cf.ltm[[i]])] = cf.ltm[[i]][-length(cf.ltm[[i]])]

}

cf.mirt.mat

cf.ltm.mat

cf.mirt.mat - cf.ltm.mat

fit.gpcm.mirt@logLik

fit.gpcm.ltm$log.Lik

두 함수에 의해 추정된 모수와 logLikelihood를 비교해보자. 조금 차이가 있다.

If you look at the estimated parameters and the log likelihood from the two functions,

you could notice the slight difference!

실습용 데이터

R.gpcm <-

  structure(c(2, 3, 2, 4, 4, 1, 2, 2, 2, 2, 1, 1, 2, 1, 1, 4, 1, 

              1, 2, 2, 1, 3, 1, 1, 2, 4, 4, 1, 4, 2, 2, 1, 1, 3, 3, 4, 1, 1, 

              4, 1, 1, 4, 4, 3, 1, 1, 3, 2, 0, 1, 1, 3, 1, 1, 4, 2, 3, 1, 2, 

              1, 4, 4, 1, 1, 2, 2, 2, 1, 1, 4, 1, 2, 2, 2, 2, 4, 1, 2, 4, 1, 

              1, 0, 2, 2, 2, 4, 4, 2, 1, 4, 3, 4, 2, 1, 2, 3, 1, 4, 1, 1, 1, 

              2, 4, 1, 4, 4, 4, 4, 2, 4, 0, 4, 4, 2, 2, 4, 1, 2, 2, 4, 3, 2, 

              0, 1, 4, 0, 2, 2, 2, 0, 4, 0, 4, 1, 3, 3, 0, 2, 1, 4, 2, 2, 3, 

              4, 1, 2, 3, 2, 0, 2, 0, 0, 1, 0, 3, 2, 3, 2, 3, 1, 4, 2, 2, 1, 

              4, 2, 2, 2, 1, 4, 2, 4, 2, 4, 4, 1, 0, 2, 1, 2, 2, 3, 1, 3, 4, 

              3, 4, 1, 3, 4, 2, 2, 1, 1, 2, 4, 2, 4, 2, 1, 1, 1, 1, 1, 3, 2, 

              1, 2, 1, 1, 1, 1, 1, 1, 1, 3, 0, 0, 1, 1, 0, 2, 1, 1, 1, 1, 4, 

              2, 1, 1, 2, 1, 3, 1, 2, 3, 0, 1, 2, 1, 1, 1, 2, 2, 0, 1, 1, 1, 

              1, 0, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 3, 1, 1, 2, 

              2, 1, 2, 1, 2, 2, 3, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 3, 1, 2, 1, 

              1, 1, 1, 2, 2, 2, 1, 2, 1, 4, 3, 2, 2, 0, 3, 3, 2, 3, 3, 2, 0, 

              4, 3, 3, 0, 4, 2, 2, 3, 3, 2, 4, 3, 3, 3, 3, 4, 2, 3, 2, 4, 2, 

              3, 3, 4, 3, 0, 3, 3, 2, 2, 3, 4, 3, 2, 3, 3, 3, 0, 2, 2, 3, 4, 

              3, 3, 3, 3, 2, 2, 0, 3, 3, 3, 3, 0, 4, 3, 2, 3, 4, 3, 4, 2, 2, 

              3, 4, 0, 2, 3, 2, 0, 2, 2, 2, 2, 4, 3, 3, 3, 3, 2, 2, 3, 2, 2, 

              4, 2, 3, 0, 4, 0, 2, 2, 1, 4, 0, 2, 2, 3, 0, 2, 1, 3, 3, 1, 3, 

              1, 2, 3, 2, 1, 3, 1, 4, 4, 1, 1, 1, 4, 2, 1, 1, 4, 2, 4, 2, 0, 

              2, 1, 3, 3, 3, 2, 2, 1, 1, 2, 1, 1, 3, 1, 1, 1, 2, 2, 0, 3, 2, 

              1, 0, 1, 2, 1, 1, 1, 0, 2, 1, 2, 1, 1, 4, 1, 3, 2, 2, 1, 2, 1, 

              1, 1, 2, 3, 2, 2, 3, 2, 0, 2, 2, 3, 4, 3, 1, 3, 4, 0, 3, 0, 3, 

              2, 2, 2, 1, 2, 3, 2, 2, 2, 1, 0, 2, 2, 0, 0, 4, 0, 0, 2, 2, 1, 

              1, 0, 2, 1, 0, 3, 0, 2, 3, 2, 0, 2, 1, 2, 3, 0, 1, 2, 1, 1, 1, 

              4, 1, 0, 0, 4, 0, 0, 2, 1, 1, 1, 1, 3, 0, 3, 1, 1, 0, 2, 1, 2, 

              0, 0, 0, 4, 0, 1, 2, 0, 3, 1, 1, 1, 4, 0, 1, 2, 0, 0, 2, 0, 2, 

              2, 2, 1, 1, 3, 3, 3, 2, 2, 0, 1, 3, 1, 3, 0, 4, 0, 3, 3, 0, 3, 

              3, 0, 4, 3, 3, 1, 3, 1, 3, 1, 4, 1, 1, 3, 3, 2, 3, 2, 0, 3, 1, 

              3, 2, 3, 3, 3, 1, 3, 1, 3, 4, 0, 3, 3, 0, 0, 3, 3, 2, 0, 1, 4, 

              1, 0, 1, 0, 0, 1, 1, 3, 3, 1, 3, 1, 0, 4, 1, 1, 1, 0, 3, 1, 1, 

              2, 3, 1, 4, 2, 3, 3, 4, 0, 3, 1, 0, 1, 1, 1, 1, 1, 3, 3, 1, 1, 

              3, 3, 3, 0, 1, 1, 4, 0, 2, 0, 2, 3, 1, 1, 1, 0, 1, 1, 1, 3, 1, 

              1, 1, 0, 3, 1, 4, 1, 1, 1, 3, 4, 1, 1, 1, 2, 3, 1, 1, 3, 1, 3, 

              1, 4, 3, 1, 1, 0, 4, 1, 4, 3, 3, 4, 4, 1, 2, 4, 3, 1, 0, 1, 2, 

              1, 1, 3, 3, 1, 0, 1, 0, 3, 1, 3, 2, 0, 3, 4, 4, 3, 4, 1, 4, 2, 

              3, 1, 2, 0, 2, 4, 1, 1, 1, 4, 1, 1, 4, 3, 3, 4, 1, 2, 2, 4, 3, 

              2, 3, 1, 2, 0, 4, 1, 1, 3, 1, 4, 2, 1, 2, 2, 1, 0, 4, 1, 1, 1, 

              2, 1, 2, 0, 2, 2, 2, 2, 0, 1, 3, 4, 1, 2, 1, 2, 1, 1, 3, 4, 2, 

              2, 2, 3, 0, 2, 3, 4, 1, 1, 3, 1, 0, 2, 1, 0, 2, 1, 1, 3, 3, 1, 

              2, 3, 0, 1, 0, 1, 2, 1, 3, 4, 1, 4, 2, 3, 4, 2, 2, 3, 4, 1, 1, 

              1, 1, 1, 2, 2, 4, 2, 2, 4, 1, 2, 1, 2, 1, 2, 2, 1, 4, 3, 3, 3, 

              1, 1, 3, 1, 1, 4, 3, 3, 4, 3, 1, 0, 2, 1, 2, 1, 4, 1, 1, 1, 3, 

              0, 1, 1, 1, 2, 1, 4, 1, 4, 2, 2, 0, 3, 1, 4, 2, 0, 1, 4, 1, 1, 

              3, 4, 3, 0, 2, 3, 2, 0, 1, 1, 1, 0, 2, 4, 1, 3, 2, 1, 0, 2, 1, 

              1, 1, 1, 2, 3, 2, 3, 4, 0, 3, 1, 1, 3, 4, 2, 3, 1, 1, 1, 1, 0, 

              3, 3, 3, 3, 0, 3, 2, 3, 3, 0, 1, 4, 4, 1, 4, 0, 4), 

            .Dim = c(100L, 10L), 

            .Dimnames = list(NULL, c("Item_1", "Item_2", "Item_3", "Item_4", "Item_5", 

                                     "Item_6", "Item_7", "Item_8", "Item_9", "Item_10")))