Slope parameters and model simulation

[B Morgan]

Hi Phil 

I hope you are doing well. I have two questions, one theoretical and one mirt related:

1. With respect to the slope parameters in a unidimensional graded response model, what type of values would be expected. I have read the literature and most people talk about slope parameters for the 2PL. In some graded models I have slope parameters > 5 (the factor loadings are also really large, almost all close to 1 [lets say about .70 and above], and the polyserial-total correlation coefficients are close to 1 [this is theoretically expected]). Would this be considered normal (the standard errors are usually not that large and the sample sizes are usually 500 +). 

2. With respect to the simulation function in mirt, I just want to check my understanding. If for the model command we put in our estimated model, does the simulation function automatically take all the necessary parameters when simulating the data?

Many thanks

Brandon

[Phil Chalmers]

Hi Brandon,

On Sat, Sep 26, 2020 at 6:00 AM B Morgan <bmorgan....@gmail.com> wrote:

Hi Phil 

I hope you are doing well. I have two questions, one theoretical and one mirt related:

1. With respect to the slope parameters in a unidimensional graded response model, what type of values would be expected. I have read the literature and most people talk about slope parameters for the 2PL. In some graded models I have slope parameters > 5 (the factor loadings are also really large, almost all close to 1 [lets say about .70 and above], and the polyserial-total correlation coefficients are close to 1 [this is theoretically expected]). Would this be considered normal (the standard errors are usually not that large and the sample sizes are usually 500 +). 

I wouldn't say it's unheard of, many tests have extremely discriminating items that are around 4 or more and end up being quite informative when estimating the latent trait terms. The downside comes from a numerical perspective in that larger slopes could experience numerical roundoff problems if they are also combined with extreme intercept locations (relates to how logits components are managed in the exponentiated portions), but with larger sample sizes this issue would eventually go away --- and in your case, if you're seeing smaller SEs or CIs I wouldn't worry much as there's enough information in the data to avoid most numerical issues.  

 

2. With respect to the simulation function in mirt, I just want to check my understanding. If for the model command we put in our estimated model, does the simulation function automatically take all the necessary parameters when simulating the data?

Yes, that's correct. I originally constructed this argument as a way for users to generate plausible datasets that could replicate common errors and such for the purpose of keeping response vectors entirely absent (and therefore anonymous), but of course you could use it for other purposes, such as parametric bootstrapping to evaluate some aspect of model fit, for instance. HTH.

Phil

 

Many thanks

Brandon

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[B Morgan]

Hi Phil

Great, thank you, that clears it up for me. Thank you very much, I really appreciate it.

Kind regards

Brandon