Total score from two-dimensional model

[Conal Monaghan]

Hi,

     I was wondering if it were possible to calculate an overall fscore based on a two-dimensional model? For example, if participants complete 16 items from a two-dimensional scale, can I give them a singular total score. e.g., If I use the dataset "Data" and imagine mirt() is loaded:

# Specify the model

model <- '

F1 = 1-8

F2 = 9-16

COV = F1*F2

              ' 

# Run the two-dimensional model in Mirt

IRTModel <- mirt(data[,c(13:15, 18:22, 2,3, 5:10)], model = model, type = "graded")

# Find the fscore for a specific response pattern (produces the two factor scores, one for each factor, and associated errors). I will create a response pattern using seq()

fScore <- fscores(IRTModel, method = "MAP", response.pattern = c(seq(1,16)))

# Extract total fscore ? 

This is where I am lost

Kind Regards and thanks for your help in advance,

  Conal Monaghan

[Phil Chalmers]

Hi Conal,

I don't think what you are asking for is immediately feasible. You'd either need to create a higher-order model (which in this case, wouldn't be identified anyway), which could be done by simply creating a linear composite based on the two factor scores for trait (that's an ad-hoc and old way to achieve this), or perhaps re-frame the estimation in terms of a bifactor model, where the common variance will be encapsulated within the general factor instead. I would vote for the latter, and I find it the easiest to interpret. HTH.

Phil

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[Conal Monaghan]

Hi Phil, 

       thank you for your reply and approaches for going forth. For the study at hand, I think the simple linear composite would be OK, although not as accurate as other approaches. The three-dimensional plot produced by mirt() to represent the two-dimensional model shows the linear composite towards the higher order factor on the y-axis. To that end, what would be the best way using mirt() to extract that score for a specific response pattern?

      Kind Regards, and thanks again,

                 Conal 

Phil

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[Phil Chalmers]

On Mon, Feb 20, 2017 at 7:38 PM, Conal Monaghan <conal.m...@gmail.com> wrote:

Hi Phil, 

       thank you for your reply and approaches for going forth. For the study at hand, I think the simple linear composite would be OK, although not as accurate as other approaches. The three-dimensional plot produced by mirt() to represent the two-dimensional model shows the linear composite towards the higher order factor on the y-axis. To that end, what would be the best way using mirt() to extract that score for a specific response pattern?

The fscores() function is what you want to do this. To help avoid some systematic bias created by using points estimates you could also look into the plausible-value imputation option, which generally makes secondary inferences more justifiable. Cheers.

Phil

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