GRM summary error finding item parameters + multiple difficulty parameters? about idealstan HOT 3 OPEN

After some additional thought and internet searching on the second issue, I realized that the cutpoints are the response category-specific difficulty parameters. Is this true for the graded response models?

If so, then that raises an additional question for you. Why do you use reg_diff in the following line of code to calculate the non-missing inflated midpoints (lines of indifference)?

reg_mid <- (reg_diff+cuts[[c]])/reg_discrim

In fact, I'm struggling to understand the role of the reg_diff parameter generally in the context of the graded response model. Any clarification on this additional point would be much appreciated.

from idealstan.

hi @PatrickJEdwards - thanks for all these Qs, and I'll do my best to help you understand the package. the GRM does add some complexity as there are varying intercepts/cutpoints for each item (difficulties). When I wrote the package, this was not easy to code because Stan did not have varying-length arrays. It does now, and I could refactor, but that's a project for the future.

In any case, this model does work and it should have all the info you need. What would help me though is if you could share some subset of your data so I can see what you are doing and run it myself. Or perhaps you can generate/replace with fake data if you can't share it.

In response to your second Q, the GRM is parameterized by having C cutpoints for J items, so there is an array/matrix of dimension C x J. Each item also has an intercept, which is essentially the difficulty mentioned above. The actual difficulty is the result of intercept - cutpoint c for level c, which the code above is inverting to get the midpoint. (of course if you find a bug in the code, am happy to fix, but it looks correct).

from idealstan.

Hi @saudiwin, thank you for the prompt reply! Thank you for answering my questions and clearing things up for me.

Attached is an anonymized subset of my data: idealstan_GithubExampleData_subset.csv

I believe the following code would reproduce the error:

#Create Danish GAL-TAN `idealstan` object:
idealstan_object <- id_make(
  score_data = Nat_DAN_IRT_Data_long_GALTAN,
  person_id = "person_id",
  item_id = "item_id",
  time_id = "time_id",
  group_id = "group_id",
  model_id = "model_id",
  unbounded = FALSE,
  outcome_disc = "outcome_disc",
  ordered_id = "ordered_id"
)

#Specify `idealstan` model with random-walk prior and PRE-FIXED CONSTANTS:
idealstan_output_PREFIX <- id_estimate(
  idealdata = idealstan_object,
  model_type = 5,
  vary_ideal_pts = "random_walk",
  fixtype = "prefix",
  const_type = "items",
  restrict_ind_high = "61",
  restrict_ind_low = "34",
  ncores = parallel::detectCores(),
  grainsize = 1,
  nchains = 4,
  id_refresh = 10,
  time_var = 1, #Default=10. Lower values = LESS conservative prior.
  restrict_var = F
)

#Estimate item parameters:
items_summary <- summary(idealstan_output_PREFIX, pars = "items")

#Should produce error: 
#`Error: Can't find the following variable(s) in the output: steps_votes`

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