Algorithm 1 Recipe to compute the in‐plus‐out‐of‐questionnaire log likelihood for a particular included itemset $S_{\text{in}}$ and a corresponding excluded itemset $S_{\text{out}}$.

Fit abilities, thresholds, and discrimination parameters through penalized maximum likelihood estimation on the included itemset $S_{\text{in}}$ as in (5). Compute the in‐questionnaire log likelihood of the parameters obtained in step 1 on the included itemset $S_{\text{in}}$ as in (6). Fit thresholds and discrimination parameters with the abilities fixed to those obtained in step 1 through (weakly) penalized maximum likelihood estimation on the excluded items $S_{\text{out}}$ as in (7). Compute the out‐of‐questionnaire log likelihood of the thresholds and discrimination parameters obtained in step 3 and the abilities obtained in step 1 on the excluded itemset $S_{\text{out}}$ as in (8). Add the out‐of‐questionnaire log likelihood from step 4 to the in‐questionnaire log likelihood from step 2.