In conjunction with appropriately designed test, cognitive diagnosis models (CDMs) can be used to identify students’ mastery or nonmastery of skills in a domain. The diagnostic and finer-grained information from CDMs can lead to tailored instruction and remediation. In this chapter, we introduce the generalized deterministic input, noisy “and” gate (G-DINA) model as a general CDM framework. In addition to various CDM formulations, the G-DINA model framework subsumes parameter
estimation, model fit evaluation, Q-matrix validation, differential item functioning analysis, and classification accuracy estimation. Using empirically based simulated data, we illustrate how CDM analysis can be performed using the GDINA R package.

The present study compared the consistency of the results of three nonparametric differential item functioning (DIF) techniques – the Cumulative Common Log-Odds Ratio (CCLOR), Standardized Mean Difference (SMD), and the Mantel Test (Mantel) in detecting gender DIF in the Emotional Quotient Scale – College Version. The sample comprised 1,229 college students (male = 657; women= 572) from a state university in the Philippines. The agreement of the DIF methods was determined using classification consistency and matching percentages. Results show that CCLOR and Mantel agreed perfectly in detecting gender DIF items. SMD, on the other hand, had a moderate to high agreement with the two other DIF techniques. The agreement among the DIF methods was lower when DIF effect size was considered.

Logistic regression is often confronted with separation of likelihood problem, especially with unbalanced success–failure distribution. We propose to address this issue by drawing a ranked set sample (RSS). Simulation studies illustrated the advantages of logistic regression models fitted with RSS samples with small sample size regardless of the distribution of the binary response. As sample size increases, RSS eventually becomes comparable to SRS, but still has the advantage over SRS in mitigating the problem of separation of likelihood. Even in the presence of ranking errors, models from RSS samples yield higher predictive ability than its SRS counterpart.

We introduce panel models and identify its link to spatial-temporal models. Both models are characterized and differentiated through the variance-covariance matrix of the disturbance term. The resulting estimates or tests are as complicated as the nature of the said variance-covariance matrix. Some iterative methods typically used in computational statistics are also presented. These methods are used in conducting statistical inference for spatial-temporal models.