Polytomous Item Analysis

Both handle ordered polytomous items but model different transition probabilities. The GRM (Samejima, 1969) models cumulative boundary response functions — the probability of scoring at or above each category — and allows item-specific discrimination. The PCM (Masters, 1982) models adjacent-category transitions — the probability of choosing category k over k-1 — and constrains discrimination to be equal across items (Rasch-family). Choose GRM when items vary in discriminating power and when a cumulative model fits the construct; choose PCM when equal discrimination is defensible and Rasch-family measurement properties are desired.

Disordered thresholds occur when a higher category boundary has a lower difficulty estimate than a lower boundary — meaning respondents are, in effect, more likely to skip a middle category. Examine the threshold estimates and the Category Response Functions: if CRF peaks are absent or very low for a middle category, it is rarely used. The remedy is to collapse the underused category with an adjacent one and re-run the analysis, checking that the revised scale has ordered thresholds.

Yes. Classical test theory approaches — corrected item-total (polyserial) correlations, item means, item standard deviations, and coefficient alpha-if-deleted — are simpler diagnostics that do not require IRT software and are robust with smaller samples. They do not, however, provide threshold estimates, information functions, or formal model-fit statistics. A combined CTT-and-IRT approach is common in applied scale development.

A minimum of about 200 respondents is generally recommended for the simpler Rasch-family polytomous models (PCM, RSM), and 300–500 for the GRM with multiple response categories and many items. Smaller samples produce unstable discrimination and threshold estimates. When sample size is limited, use CTT-based diagnostics and treat IRT results as exploratory.

Not necessarily. IRT provides richer diagnostics — information functions, invariant parameters, model-data fit — but requires larger samples and more technical expertise. For routine scale development with 200+ respondents and standard Likert formats, an IRT analysis adds substantial value. For small studies or preliminary item screening, CTT indices (item-total correlations, alpha-if-deleted) are efficient and sufficient as a first pass.