[R] mirt-simdata question.

Thu Jul 11 15:34:11 CEST 2019

Hi. Again.

I still cannot understand that why the simulated categories have opposite of normal distribution. Theta is set as normal function. Then, more obs. should have more proportion of middle categories. But, all items of simulated data have the most probabilities at the least ability category �0� or the highest �4� .
Isn�t it strange?

Please check and run the code from my previous mail.

Thank you.

Soonhwa(Suna) Paek
University of Wisconsin- Milwaukee
Educational Psychology- Statistics and Measurements
262-441-3019. paek using uwm.edu

________________________________
From: Suna Paek
Sent: Thursday, July 11, 2019 8:03:58 AM
To: Doran, Harold; R-help using R-project.org
Subject: Re: mirt-simdata question.

Thank you for answering.
I know mirt is not related the distribution of categories.
My study is factor analysis results difference of limited information methods and full information methods. I need a simulation data to compare those. And limited information factor analysis need an assumption of normality.

I do not know whether other ways of simulating code for multi- dimensions and categorical items than Mirt.
If you have some idea, please let me know.

Thank you for quick answering.
I always think R is the best program. I appreciate all team of R-program.

Best,

Soonhwa(Suna) Paek
University of Wisconsin- Milwaukee
Educational Psychology- Statistics and Measurements
262-441-3019. paek using uwm.edu

________________________________
From: Doran, Harold <HDoran using air.org>
Sent: Thursday, July 11, 2019 7:42:56 AM
To: Suna Paek; R-help using R-project.org
Subject: RE: mirt-simdata question.

You're asking a question unrelated to R programming and so you won't get a useful response here. However, your question also suggests a misunderstanding of IRT. Generating multi-dimensional data involves generating ability estimates with additional nuisance dimensions and that has no relationship with the distributional properties of the categorical values.

Probably better to start a thread on another email list that can help you first understand MIRT.

-----Original Message-----
From: R-help <r-help-bounces using r-project.org> On Behalf Of Suna Paek
Sent: Wednesday, July 10, 2019 8:49 PM
To: R-help using R-project.org
Subject: Re: [R] mirt-simdata question.

Hi. again.

Still the same problem, but I made a new code to see better of my question.
Like the first email, I still want each item's categories to have a normal distribution. it doesn't have to statistically fit. I made 2 different code. And, I found if the histogram is the opposite, they will be normal distributions.
In detail, most items have the highest frequencies(probabilities) in the first category and the last category. The middle categories are fewer frequencies.

Is there any way to opposite the frequency, so that each item has normal category distribution?

I have to figure out this problem. Please help me!

###two dimensional 10 items 5 categorical data simulation Theta <- rmvnorm((1000*2), sigma = sigma)

set.seed(12)
#slope matrix of 10=items, item1-5:factor1, item6-10: factor2 aa <- matrix(c(rlnorm(5,.2,.2),rep(0,10),rlnorm(5,.2,.2)),10) #rlnorm-log normal distribution dd<-matrix(rnorm((10*5),0,.3), 10) dd <- t(apply(dd, 1, sort, decreasing=TRUE)) #sort since intercepts are ordered
polytomous5 <- simdata(aa, dd, 1000, Theta=Theta, itemtype = 'gpcm')
summary(polytomous5)
hist(polytomous5[,1])
hist(polytomous5[,2])
hist(polytomous5[,3])
hist(polytomous5[,4])
hist(polytomous5[,5])
hist(polytomous5[,6])
hist(polytomous5[,7])
hist(polytomous5[,8])
hist(polytomous5[,9])
hist(polytomous5[,10])

Theta <- rmvnorm((1000*2), sigma =sigma)
set.seed(12)
#set a parameters
a <- matrix(c(2.5,NA,2.0,NA,1.5,NA,1.0,NA,0.5,NA,NA,0.5,NA,1.0,NA,1.5,NA,2.0,NA,2.5),ncol=2,byrow=TRUE)
d<-matrix(rnorm((10*5),0,.3), 10)
d <- t(apply(d, 1, sort, decreasing=TRUE)) #sort since intercepts are ordered
polytomous51 <- simdata(a, d, 1000, Theta=Theta, itemtype = 'gpcm')
summary(polytomous51)
hist(polytomous51[,1])
hist(polytomous51[,2])
hist(polytomous51[,3])
hist(polytomous51[,4])
hist(polytomous51[,5])
hist(polytomous51[,6])
hist(polytomous51[,7])
hist(polytomous51[,8])
hist(polytomous51[,9])
hist(polytomous51[,10])

Soonhwa(Suna) Paek
Educational Psychology-Statistics and Measurements University of Wisconsin-Milwaukee paek using uwm.edu 262-441-3019

________________________________
From: Suna Paek
Sent: Wednesday, July 10, 2019 5:58 PM
To: R-help using R-project.org
Subject: Re: mirt-simdata question.

Hi. I always thank you all of the R program worker and researchers.

I am using R for my thesis, and I have a question.

I am simulating multi-dimensional and categorical items (polytomous) with mirt-simdata.
However, I wish each items' categories are normal distribution. I checked a lot of information from the internet. Unfortunately, I couldn't find a good one.
It looks like before version, there is a 'simdata_normal' function, but not anymore.
Is there another way to simulate the normal distribution of the multi-dimensional item polytomous-responses?

Here is my code, I was working on.

#two dimensional categorical data simulation Theta <- rmvnorm(10000, sigma = matrix(c(1, .5, .5, 1), 2)) #correlation of .5
summary(Theta)

set.seed(12345)
#slope matrix of 20 rows=items, a1=10 factor 1, a2=10 factor 2 aa <- matrix(c(rlnorm(20,.2,.3),rep(0,40),rlnorm(20,.2,.3)),40) #rlnorm-log normal distribution dd<-matrix(rnorm((40*4),0,2.0), 40) dd <- t(apply(dd, 1, sort, decreasing=TRUE)) #sort since intercepts are ordered
polytomous4 <- simdata(aa, dd, 10000, Theta=Theta, itemtype = 'gpcm')
summary(polytomous4)

Can anyone please check and help me?
I desperately have to figure out this problem as soon as possible.

Thank you very much for reading my question.
Have a good day.
God bless you!

Best,

Soonhwa(Suna) Paek
Educational Psychology-Statistics and Measurements University of Wisconsin-Milwaukee paek using uwm.edu 262-441-3019

Soonhwa(Suna) Paek
Educational Psychology-Statistics and Measurements University of Wisconsin-Milwaukee paek using uwm.edu 262-441-3019

________________________________
From: Suna Paek
Sent: Wednesday, July 10, 2019 3:46 PM
To: R-windows using R-project.org
Subject: mirt-simdata question.