### Author Topic: Parameterization of the partial credit model  (Read 149 times)

#### sccdle

• Newbie
• • Posts: 1 ##### Parameterization of the partial credit model
« on: March 09, 2019, 12:06:23 AM »
Hi, there,

I am running a simulation study using item parameters estimated from the partial credit model (model item + item*step), and hoping to get some clarification on the exact parameterization used in ConQuest.

1. What are the parameters that I should use to compute the probability that person i receives a score k on item j? My current output produces estimates for item, item*step, and thresholds.

2. What's the right formula (i.e., exact parameterization) to compute such a probability?

I am also curious about the interpretation of the ConQuest parameters. For example, what does each of the three (item, item*step, threshold) mean? How the ConQuest parameters can be mapped (or transformed) into the usual PCM parameterization with step difficulty? One thing I sort of figured out from the manual is that the threshold is the theta level at which a person has 50% chance scoring at this category or higher. Is this correct? Does it mean that the threshold is sort of like the graded response model parameterization?

Many thanks!
Ying

#### dan_c

• Jr. Member
•     • Posts: 71 ##### Re: Parameterization of the partial credit model
« Reply #1 on: March 11, 2019, 11:18:10 AM »
The item response model fitted by ACER ConQuest is the multidimensional random coefficients multinomial logit model (MRCMLM). The parametrisation is presented in:

Adams, R.J., Wilson, M.R., and Wang, W.C. 1997. The multidimensional random coefficients multinomial logit. Applied Psychological Measurement, 21, 1–24.

See, the section describing he response probability model.

If you are using integer scoring, you can see both the item deltas and thresholds by using the command `itanal`.