createItem() for creating custom graded and gpcm items

[Phil Chalmers]

This is just pointing to a chat that Felix and I had about how to construct your own IRT models from scratch using the createItem() function. Might be useful to someone in the future looking to construct their own IRT model that isn't common. https://github.com/philchalmers/mirt/issues/32#issuecomment-42317346

[Phil Chalmers]

This should work out of the box. Are you passing an arbitrary response
vector or matrix instead of estimating the scores from the data? I
haven't tested the former yet, so that might be the issue.

Phil

On Wed, May 21, 2014 at 6:58 AM, Dr. Hans Hansen <bea...@gmx.de> wrote:
> hi phil,
>
> when using fscores on a model with items created from scratch i get the
> following error:
>
> Error in LoadPars(itemtype = itemtype, itemloc = itemloc, lambdas = lambdas,
> :
> Unknown itemtype gpcm2 gpcm2 gpcm2 gpcm2 gpcm2 gpcm2 gpcm2 gpcm2
>
> Is that resolvable?
>
> best, felix
>
>
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[Dr. Hans Hansen]

Hi Phil, you are right, this happens when i pass a response.pattern to fscores(). Thanks, felix

[Phil Chalmers]

Thanks Felix; it looks to work on the latest dev version now. See below.

Phil 

> require(mirt)
Loading required package: mirt
Loading required package: stats4
Loading required package: lattice
> 
> name <- 'old2PL'
> par <- c(a = .5, b = -2)
> est <- c(TRUE, TRUE)
> P.old2PL <- function(par,Theta, ncat){
+     a <- par[1]
+     b <- par[2]
+     P1 <- 1 / (1 + exp(-1*a*(Theta - b)))
+     cbind(1-P1, P1)
+ }
> x <- createItem(name, par=par, est=est, P=P.old2PL)
> 
> dat <- expand.table(LSAT7)
> mod <- mirt(dat, 1, c(rep('2PL',4), 'old2PL'), customItems=list(old2PL=x))
Iteration: 24, Log-Lik: -2658.805, Max-Change: 0.00005
> fscores(mod, response.pattern=c(0,0,1,1,0))
     Item.1 Item.2 Item.3 Item.4 Item.5 Freq         F1     SE_F1
[1,]      0      0      1      1      0    1 -0.7549973 0.6728278
> fscores(mod, response.pattern=matrix(c(0,0,1,1,0, 1,1,0,0,1), 2, byrow=TRUE))
     Item.1 Item.2 Item.3 Item.4 Item.5 Freq         F1     SE_F1
[1,]      0      0      1      1      0    1 -0.7549973 0.6728278
[2,]      1      1      0      0      1    1 -0.5995563 0.6803557
> 
> sessionInfo()
R version 3.1.0 (2014-04-10)
Platform: x86_64-pc-linux-gnu (64-bit)

locale:
 [1] LC_CTYPE=en_CA.UTF-8       LC_NUMERIC=C               LC_TIME=en_CA.UTF-8       
 [4] LC_COLLATE=en_CA.UTF-8     LC_MONETARY=en_CA.UTF-8    LC_MESSAGES=en_CA.UTF-8   
 [7] LC_PAPER=en_CA.UTF-8       LC_NAME=C                  LC_ADDRESS=C              
[10] LC_TELEPHONE=C             LC_MEASUREMENT=en_CA.UTF-8 LC_IDENTIFICATION=C       

attached base packages:
[1] stats4    stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] mirt_1.3.6      lattice_0.20-29 testthat_0.8.1  devtools_1.5   

loaded via a namespace (and not attached):
 [1] digest_0.6.4         evaluate_0.5.5       GPArotation_2012.3-1 grid_3.1.0          
 [5] httr_0.3             memoise_0.2.1        numDeriv_2012.9-1    parallel_3.1.0      
 [9] Rcpp_0.11.1          RCurl_1.95-4.1       stringr_0.6.2        tools_3.1.0         
[13] whisker_0.3-2 

On Mon, May 26, 2014 at 4:14 PM, Dr. Hans Hansen <bea...@gmx.de> wrote:

Hi Phil, you are right, this happens when i pass a response.pattern to fscores(). Thanks, felix

--

[Dr. Hans Hansen]

great, thanks a lot!

[Dr. Hans Hansen]

Hi Phil,

i found another problem regarding this issue: i cannot fix the item parameters and calculate mean/cov:

library(mirt)
set.seed(1223)
name <- 'gpcm2'
par <- c(a = 1.5, b1 = -1, b2 = .3, b3 = 1)
est <- c(TRUE, TRUE, TRUE, TRUE)

summation = function(upto, Theta = seq(-4,4,.1), a, b){
    x = rep(0,length(Theta))
    if (upto > 0) x = apply(sapply(1:upto, function(x) (a*(Theta - b[x]))),1,sum)
    return(exp(x))
}

P.gpcm2 <- function(par,Theta, ncat){
    a <- par[1]
    b <- par[2:length(par)]
    nominator = sapply(0:(ncat-1), summation, Theta = Theta, a = a, b = b)
    denominator = apply(nominator,1,sum)
    ret <- nominator/denominator
    ret <- ifelse(ret > (1-1e-10), (1-1e-10), ret)
    ret <- ifelse(ret < 1e-10, 1e-10, ret)
    return(ret)
}

x <- createItem(name, par=par, est=est, P=P.gpcm2)

dat <- Science
mod <- mirt( dat, 1, "gpcm2", customItems=list(gpcm2=x))

pars = mod2values(mod)
pars$est = pars$est==FALSE
mod <- mirt( dat, 1, "gpcm2", customItems=list(gpcm2=x), pars=pars)

would be great if you could look into this!

thanks a lot, felix

[Phil Chalmers]

What is the line 'pars$est = pars$est==FALSE' supposed to be doing; do you mean pars$est <- FALSE?

Phil

--

[Dr. Hans Hansen]

No, it should set the item parameters to FALSE, but the GROUP parameters to TRUE. (It doesnt make too much sense here, but i use item parameters from other models).

[Phil Chalmers]

So, something like this?

pars = mod2values(mod)
pars$est <- FALSE

pars$est[17:18] <- TRUE

mod <- mirt( dat, 1, "gpcm2", customItems=list(gpcm2=x), pars=pars)

This seems to work fine on the latest dev (converges in 2 iterations, 9 if you set TOL = 1e-7). 

> coef(mod, digits = 10)
$Comfort
            a        b1        b2       b3
par 0.8652818 -3.268075 -2.881734 1.532433

$Work
            a        b1        b2       b3
par 0.8403551 -2.035006 -1.032612 2.058211

$Future
           a        b1         b2        b3
par 2.215178 -2.087085 -0.9778947 0.8335761

$Benefit
            a        b1        b2       b3
par 0.7233524 -2.899758 -1.105971 1.627087

$GroupPars
         MEAN_1    COV_11
par 5.48909e-05 0.9997952

On Wed, Jun 11, 2014 at 11:31 AM, Dr. Hans Hansen <bea...@gmx.de> wrote:

No, it should set the item parameters to FALSE, but the GROUP parameters to TRUE.

--