problems

Author: ben-domingue

about.qmd

@@ -51,3 +51,6 @@ If you use data, we encourage you to note that you used the IRW and to cite the
   + Luis Anunciação
   + Ayaan Gupta
   + Nishka Jain
+  + Nomin-Erdene Bayarsaikhan
+  + Frances Raphael
+  + Aanya Tashfeen  

problems.qmd

@@ -24,6 +24,10 @@ We are going to start thinking about IRT models next week and I wanted to begin
 - Pick two items, one that is easy (most people get it right) and one that is hard (most do not). Can you estimate a logistic regression wherein you’re regressing the response for a single item on the sum score. How do the intercepts from these regressions look vis-a-vis your intuition about the difficulty of the items? 
 - Reconsider the above analysis with the `andrich_mudfold` table. What qualitatively different pattern do you notice between the relationship between item responses and sum scores here? 
 
+### A comparison of the 1-3PL approaches.
+
+The 1PL, 2PL, and 3PL are all commonly used with dichotomous responses. We can examine the differences in the estimated response funtions for each of these models when applied to data from the Brazilian ENEM assessment, see [here](https://github.com/ben-domingue/252/blob/main/c4/enem1.R). What do you think of the differences between the approaches? 
+
 ### Predictions
 
 One of the most powerful ideas (in my view) related to thinking about the performance of your models is to look at predictions ([This paper](https://pubmed.ncbi.nlm.nih.gov/28841086/) is really powerful on this point). We’re going to look at some predictive comparisons in an IRT context. Code [here](https://github.com/ben-domingue/252/blob/main/ps4/prediction.R).
@@ -91,6 +95,9 @@ We’re going to build on ideas from [Josh Gilbert](https://onlinelibrary.wiley.
 - Consider the raw coefficients on `treat` from `m0` and `m1a`. What scale are they each on? How are these scales similar? How are they different? 
 - If we look at `m2` and `m3a`, we might think this suggests that there is treatment effect heterogeneity such that the treatment is more effective for those who are higher-ability at baseline. What would you say about this inference? How might the story be in fact more complicated? What evidence do we have on this point?
 
+### A first analysis of polytomous response data
+We can use data from a [PROM](https://commonfund.nih.gov/promis) related to chronic pain. In [this code](https://github.com/ben-domingue/252/blob/main/c9/polyexample.R) we will consider the graded response model, the generalized partial credit model, and the sequential ratio model applied to this data. How would you describe the differences between the category response function and the expected response function for the three models across this data? *Note:* An alternative view of how these models have very different implications can be found [here](https://link.springer.com/article/10.1007/s41237-025-00262-9).
+
 ### Rating Scale Framework
 
 The rating scale framework