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I agree with Preston Botter that this is an advanced application of IRT and support the advice that you might want to look for consultation.

However, I am aware of a possible realisation. The R package TAM provides a (not officially supported/documented) solution for this issue using the so-called Q-matrix (quite possible that the following idea works for other software packages as well).

First note that in case of the 2 parameter logistic model the loading structure of the factor loadings (discrimination parameter in IRT) is estimated in order to best fit the data. More importantly, the discrimination parameter (B-matrix in TAM) is the relative weight of the respective items in the total score.

Next, the Q-matrix is typically used as a binary matrix for asigning the loading of items to different latent dimensions. However, in TAM it is possible to assign values other than zero or one to the Q-matrix. The values of Q are multiplied to the faktor loadings (discrimination parameter in IRT; 1 in case of the Rasch model). Thus, we can force a loading other than 1 to items in the Rasch model (or multidimensional versions thereof).

I agree with @Preston Botter that this is an advanced application of IRT and support the advice that you might want to look for consultation.

However, I am aware of a possible realization. The R package TAM provides a (not officially supported/documented) solution for this issue using the so-called Q-matrix (quite possible that the following idea works for other software packages as well).

First, note that in case of the 2 parameter logistic model the loading structure of the factor loadings (discrimination parameter in IRT) is estimated in order to best fit the data. More importantly, the discrimination parameter (B-matrix in TAM) is the relative weight of the respective items in the total score.

Next, the Q-matrix is typically used as a binary matrix for assigning the loading of items to different latent dimensions. However, in TAM it is possible to assign values other than zero or one to the Q-matrix. The values of Q are multiplied to the factor loadings (discrimination parameter in IRT; 1 in case of the Rasch model). Thus, we can force a loading other than 1 to items in the Rasch model (or multidimensional versions thereof).

Next, the Q-matrix is typically used as a binary matrix for asigning the loading of items to different latent dimensions. However, in TAM it is possible to assign values other than one to the Q-matrix. The values of Q are multiplied to the faktor loadings (discrimination parameter in IRT; 1 in case of the Rasch model). Thus, we can force a different loading other than 1 to items in the Rasch model (or multidimensional versions thereof).

Next, the Q-matrix is typically used as a binary matrix for asigning the loading of items to different latent dimensions. However, in TAM it is possible to assign values other than zero or one to the Q-matrix. The values of Q are multiplied to the faktor loadings (discrimination parameter in IRT; 1 in case of the Rasch model). Thus, we can force a loading other than 1 to items in the Rasch model (or multidimensional versions thereof).

I agree with Preston Botter that this is an advanced application of IRT.

First note that in case of the 2 parameter logistic model the loading structure of the factor (discrimination parameter in IRT) is estimated in order to best fit the data. More importantly, in other words the discrimination parameter (B-matrix in TAM) is the relative weight of the respective item in the total score.

Next, the Q-matrix is typically used as a binary matrix for asigning the loading of items to different latent dimensions. However, in TAM it is possible to assign values other than one to the Q-matrix. The values of Q are multiplied to the faktor loadings (discrimination parameter in IRT; 1 in case of the Rasch model).

A word of caution: I'm not sure of what will happen if both relativ loading structure via Q-matrix are given and discrimination parameter are estimated.

I agree with Preston Botter that this is an advanced application of IRT and support the advice that you might want to look for consultation.

First note that in case of the 2 parameter logistic model the loading structure of the factor loadings (discrimination parameter in IRT) is estimated in order to best fit the data. More importantly, the discrimination parameter (B-matrix in TAM) is the relative weight of the respective items in the total score.

Next, the Q-matrix is typically used as a binary matrix for asigning the loading of items to different latent dimensions. However, in TAM it is possible to assign values other than one to the Q-matrix. The values of Q are multiplied to the faktor loadings (discrimination parameter in IRT; 1 in case of the Rasch model). Thus, we can force a different loading other than 1 to items in the Rasch model (or multidimensional versions thereof).

A word of caution: I'm not sure of what will happen if both, relativ loading structure via Q-matrix are given and discrimination parameter are estimated.