The direction of parameter 'd' in 2PLM is same with Item trace lines?

[Seongho Bae]

Dear all,

Is the direction of parameter 'd' in 2PLM same with Item trace lines?

I know the 'd' is item difficulty parameter; so if items are easy, I can expect get negative difficulty values.

But, I can't get negative difficulty values in coef() function when using 2PLM; even I tried with Graded response model with polytomous items.

Like this;

$Non_EQ_1
       a1     d g u
par 1.321 1.663 0 1

$Non_EQ_2
       a1     d g u
par 2.184 2.172 0 1

$Non_EQ_3
      a1    d g u
par 1.05 1.67 0 1

$Non_EQ_4
       a1     d g u
par 1.152 1.578 0 1

$Non_EQ_5
       a1   d g u
par 2.248 2.4 0 1

$Non_EQ_6
       a1     d g u
par 3.147 0.876 0 1

$Non_EQ_7
       a1     d g u
par 2.787 0.615 0 1

$Non_EQ_8
       a1    d g u
par 1.038 1.15 0 1

$EQ_9
       a1     d g u
par 6.334 7.933 0 1

$EQ_10
        a1      d g u
par 55.251 75.871 0 1

$EQ_11
       a1     d g u
par 1.794 2.096 0 1

$EQ_12
      a1     d g u
par 1.57 2.124 0 1

$EQ_13
       a1     d g u
par 1.088 1.415 0 1

$EQ_14
       a1     d g u
par 0.823 1.864 0 1

$EQ_15
       a1     d g u
par 1.913 1.838 0 1

$EQ_16
       a1     d g u
par 0.727 1.162 0 1

$GroupPars
    MEAN_1 COV_11
par      0      1

What is parameter 'd' means in coef()? And why I can not get negative difficulty values in if items were easy?

--

Seongho

[Phil Chalmers]

The d parameter is an *easiness* parameter, not difficulty; higher values indicate the that item has a large positive response rate. Use itemplot(shiny=TRUE) and try it out.

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[Mark Taper]

As Dr. Chalmers says the parameter labeled "d" is actually an easiness parameter.  To turn it into the question difficulty parameter that you might expect, divide d by minus a.  This gives you a question difficulty parameter that increases as the questions get harder.  the value of this Qdif is the ability value at the inflection point of the logistic curve.

Recast.m2v=function(mirtmod,dosort=T){#Extracts item parameters of interest to a dataframe 

  #Requires packages mirt and reshape2

  #Arguments mirtmod= a one dimensional mirt model object, and dosort a boolean indicator whether to sort in asscending question difficulty order (default=T)

  #Value dataframe of     item        a1          d    g       Qdif p.S_X2

  tmp=mod2values(mirtmod)

  tmp=tmp[,c("item","name","value")]  #keeping just vars of interest

  tmp=tmp[1:(dim(tmp)[1]-2),] #stripping out group mean and cov

  tmp=tmp[tmp$name!="u",]  #all upperbounds of interest are 1 so this can be stripped too

  out=dcast(tmp,item~...)

  out$Qdif=-out$d/out$a1 # Turning the easiness parameter d into a question difficulty parameter

  out=merge(out,itemfit(mirtmod)[,c("item","p.S_X2")]) #adding in item fit stat

  if(dosort) {out=out[order(out$Qdif),]} #sorting in ascending Qdif 

  return(out)

}

Best MLT

[Aiden loe]

Hihi, 

Could I clarify the d parameter.

Using this approach (divide d by minus a) as proposed below to convert easiness to item difficulty, can it be extended out for polytomous response options? 

i.e., how would I calculate the item difficulty for the item below? 

$q20

            a1    d1        d2       d3

par 1.365  1.985  -0.086  -1.831

SE  0.091  0.115   0.089   0.111

I am trying to use the d parameters for a CAT. 

Kind regards,

Aiden

[Seongho Bae]

Hi, Aiden.

If you have just one dimension in your model, just do coef(mod1, IRTpars = T)

Seongho

Sent from Nylas N1, the extensible, open source mail client.

[Aiden]

Thank you!

Kind regards,

Aiden

[Jeanne Sinclair]

I'm picking up on this older post about converting 'd' (easiness parameter) to the traditional IRT difficulty parameter. 

For multidimensional IRT, does one divide 'd' by -(a1) for the difficulty parameter of the first factor, and divide 'd' by -(a2) for the difficulty parameter of the 2nd factor?

Thank you,

Jeanne

[Phil Chalmers]

https://groups.google.com/forum/#!searchin/mirt-package/multidimensional$20difficulty%7Csort:relevance/mirt-package/F0eycFHdgS8/-vz1PXh9DwAJ

Phil

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[Jeanne Sinclair]

Thanks! That makes sense.

On Tuesday, October 3, 2017 at 1:53:49 PM UTC-4, Phil Chalmers wrote:

https://groups.google.com/forum/#!searchin/mirt-package/multidimensional$20difficulty%7Csort:relevance/mirt-package/F0eycFHdgS8/-vz1PXh9DwAJ

Phil

On Tue, Oct 3, 2017 at 1:47 PM, Jeanne Sinclair <jeanneh...@gmail.com> wrote:

I'm picking up on this older post about converting 'd' (easiness parameter) to the traditional IRT difficulty parameter. 

For multidimensional IRT, does one divide 'd' by -(a1) for the difficulty parameter of the first factor, and divide 'd' by -(a2) for the difficulty parameter of the 2nd factor?

Thank you,

Jeanne

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