how to explain what the difficulty parameter d really represents?

[Oce]

In one-dimensional IRT, the difficulty parameter b can be visualized in the item trace line and could be explained by word easily (the threshold trait value which the subject more likely to endorsed the items than the other one). While I understand b = -d/a, I found it difficult to describe what d really mean... (I understand why d is preferred -- its format resembles the logic of regression, and I can understand it is an "intercept".... just found it hard to explain what it really is....)


Also, is it possible to represent b in terms of d in the bifactor/mirt model?

Thanks!

[Phil Chalmers]

On Sun, Aug 7, 2016 at 11:55 PM, Oce <oce....@gmail.com> wrote:

In one-dimensional IRT, the difficulty parameter b can be visualized in the item trace line and could be explained by word easily (the threshold trait value which the subject more likely to endorsed the items than the other one).

That doesn't sounds right. It's the theta value required to have a probability of .5 for adjacent categories. 

 

While I understand b = -d/a, I found it difficult to describe what d really mean... (I understand what d is preferred as its formally resembles the logic of regression, and I can understand it is an "intercept".... just found it hard to explain what it really is....) Thanks!

If you know it's an intercept then it should be clear what the value is. It's the logit value which a person with theta=0 has of answering the item. So if d = 1, then plogis(1) = .73, while if d = -1, then plogis(-1) = .26. This has the same interpretation for multidimensional models as well. 

 

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[Oce]

That doesn't sounds right. It's the theta value required to have a probability of .5 for adjacent categories. 

Phil, thanks for the clarification! Is .5 only for dichotomous items or applies for polytomous items too?  I have been thinking it was the theta value for a person switch to endorse the next category...

 

If you know it's an intercept then it should be clear what the value is. It's the logit value which a person with theta=0 has of answering the item. So if d = 1, then plogis(1) = .73, while if d = -1, then plogis(-1) = .26. This has the same interpretation for multidimensional models as well. 

Sorry this may sounds silly,  I would like see if I understand correctly -- say if i have run bifactor analysis for polytomous items --- does it mean if d1 = 5, d2 = 1, d3 = -1, a person with theta1 = 0 and theta2 = 0 will answer the item: plogis(5)+plogis(1) + plogis(-1) = 1.993307. And as the data is categorical, so I would expect a person with mean ability in both trait factor most likely answer 2?

Thanks so much.

 

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[Phil Chalmers]

On Aug 8, 2016 1:56 PM, "Oce" <oce....@gmail.com> wrote:
>>
>>
>>
>> That doesn't sounds right. It's the theta value required to have a probability of .5 for adjacent categories. 
>
>
> Phil, thanks for the clarification! Is .5 only for dichotomous items or applies for polytomous items too?  I have been thinking it was the theta value for a person switch to endorse the next category...

Polytomous as well.

>>
>>  
>> If you know it's an intercept then it should be clear what the value is. It's the logit value which a person with theta=0 has of answering the item. So if d = 1, then plogis(1) = .73, while if d = -1, then plogis(-1) = .26. This has the same interpretation for multidimensional models as well. 
>
>
> Sorry this may sounds silly,  I would like see if I understand correctly -- say if i have run bifactor analysis for polytomous items --- does it mean if d1 = 5, d2 = 1, d3 = -1, a person with theta1 = 0 and theta2 = 0 will answer the item: plogis(5)+plogis(1) + plogis(-1) = 1.993307. And as the data is categorical, so I would expect a person with mean ability in both trait factor most likely answer 2?

No you don't add them, they are for distinct categories (it looks like you have fit a graded model). It's the probability that a respondent with 0 thetas selects the next category. Hence, why they are always ordered highest to lowest.

[Oce]

No you don't add them, they are for distinct categories (it looks like you have fit a graded model). It's the probability that a respondent with 0 thetas selects the next category. Hence, why they are always ordered highest to lowest.

I see, I finally seem to understand -- can I say, if d1=5, d2=1, d3=-1, the probability a respondent with 0 thetas will have 1-plogis(5) = .0067 probability of choosing the first category, plogis(5) - plogis(1) = .262 probability of choosing the second category, plogis(1)-plogis(-1) and plogis(-1) for the third and last categories? (Yes I have a graded model).

Thanks!

[Phil Chalmers]

Yes that seems correct.

Phil

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[Oce]

Thank you so much for your clear explanation!