IRT analysis #

The Item response theory tab (inside the Reliability analysis module) fits unidimensional IRT and multidimensional IRT (MIRT) models to questionnaire, test, or survey items. Unlike classical reliability metrics, which summarize the scale as a whole, IRT models each item individually — estimating how difficult it is, how well it discriminates between respondents, and where each person falls on the latent trait.

CTT vs. IRT in one sentence: Classical Test Theory asks “how reliable is the total score?”; Item Response Theory asks “how does each item behave across the full range of ability?”

What is θ? θ (theta) is the estimated latent trait — ability, attitude, symptom severity, whatever the scale measures. It’s on a standardised scale centred at 0 with SD ≈ 1 (positive values above average, negative below). Unlike raw scores, θ is on an interval scale: the distance between θ = 0.5 and 1.0 is the same as between 1.0 and 1.5.

How to use #

1. Select your items — at least two numeric variables
2. Pick a dimensionality mode (unidimensional, exploratory, or confirmatory)
3. Click Diagnostics & Mokken to check data suitability before fitting a model
4. Choose a model type, estimation method, and scoring method
5. Optionally select a grouping variable for DIF
6. Adjust advanced tuning only if you know why you need to
7. Toggle output options and plots
8. Click Run IRT analysis

Requirements #

• At least two numeric variables must be selected.
• Items must be dichotomous (two unique values) or polytomous (ordinal, or continuous with 3–10 integer categories). Variables with more than 10 unique values or non-integer values are excluded unless their type is explicitly set to ordinal in the data view.
• For confirmatory MIRT, each item must be assigned to at least one factor.
• At least one output option must be enabled.

Automatic item classification: DataSuite inspects each variable before analysis. Binary variables are always treated as dichotomous. Ordinal variables are polytomous. Continuous variables with 3–10 unique integer values are inferred as polytomous — but you’ll see a note when this happens. For best results, set variable types explicitly in the data view.

Preliminary analysis #

Click Diagnostics & Mokken to run a set of quick diagnostics without fitting an IRT model. This is a low-cost way to catch problems before committing to a full analysis.

Item classification summary #

Lists how each selected variable was classified (dichotomous, polytomous, or excluded) and why. Excluded variables show a reason — e.g. too many unique values or non-integer data.

Sample size adequacy #

Warns when the sample is too small for the selected model:

These are rough guidelines — smaller samples can work but produce less stable parameter estimates. Multidimensional models generally need larger samples too; the more factors and parameters, the more respondents you need.

Item summary table #

A per-item table showing the variable type, number of response categories, and missing data count and percentage.

Unidimensionality check #

Uses the eigenvalue ratio of the inter-item correlation matrix (polychoric when available, Pearson as a fallback). The first eigenvalue divided by the second indicates how dominant the first factor is:

Why unidimensionality matters: unidimensional IRT models assume all items measure a single latent trait. If the data is substantially multidimensional, item parameter estimates become distorted and person scores lose meaning. When the ratio is below 2, either explore the structure with factor analysis or switch to exploratory or confirmatory MIRT.

Subject quality screening #

Six flags identify respondents whose data may be unreliable:

What are these flags? Longstring detects straight-lining — people who click the same answer repeatedly. Low IRV catches near-zero variability across items. Person-total correlation compares each person’s response pattern to the rest of the sample, and RIR does the same using random subsamples for stability. Mahalanobis distance identifies multivariate outliers whose overall response pattern is unusually far from the sample center.

A button below the results lets you insert quality flags into the dataset — two new columns are added: IRT_QC_nFlags (count of flags per person) and IRT_QC_Flags (the flag letters, e.g. “LV”).

Mokken scale analysis #

A nonparametric IRT approach that doesn’t assume a specific functional form for item response curves. Several analyses are reported — read them together to decide whether parametric IRT is worth attempting.

When to use Mokken vs. parametric IRT: Mokken has weaker assumptions — it doesn’t require items to follow a logistic function, only that item responses increase monotonically with the trait. Use it as a preliminary screen. If Mokken scalability is poor, parametric IRT is unlikely to fare better.

Scalability coefficients (Loevinger’s H) #

Per-item Hi and the total scale H indicate how well items form a Guttman-like scale:

Item-pair H matrix (H_ij) #

A symmetric matrix of pairwise scalability coefficients. Useful for spotting item pairs that cluster together (high H_ij) versus pairs that barely scale together (low or negative H_ij). Negative values flag items that may need reverse scoring or exclusion.

Monotonicity check #

Tests whether the probability of endorsing each item increases (or at least doesn’t decrease) with the latent trait. Items with significant violations may not conform to a monotone homogeneity model. Only items with violations are listed.

Invariant item ordering (IIO) #

Tests whether items maintain the same order of difficulty across respondents. The coefficient H_T summarises IIO across the scale:

• H_T ≥ 0.3 — items order consistently; a single difficulty ranking applies to everyone
• H_T < 0.3 — item ordering depends on who’s responding

Why IIO matters: when IIO holds you can say “item A is harder than item B” without qualification. When it fails, that statement is only true on average — some respondents find A easier than B. Required for nonparametric person ordering.

Local independence (rest-score method) #

A nonparametric counterpart to the Q3 / LD-X² checks done in the main analysis. Item pairs whose conditional association exceeds chance (after controlling for rest-score) are flagged. Redundant pairs inflate reliability and should be reviewed.

Nonparametric reliability #

Three model-free reliability estimates, reported side by side:

• Molenaar–Sijtsma (ρ) — the preferred nonparametric reliability for Mokken scales
• α — Cronbach’s alpha, shown for reference
• λ₂ — Guttman’s lambda₂, typically a slightly higher lower bound than α

Automated item selection (AISP) #

Assigns items to scales at the user-specified H lowerbound (default 0.3 — set via the AISP lowerbound input in the output panel). If all items land in a single scale, that supports unidimensionality. Items assigned to scale 0 were not selected — they may not fit any scale.

Dimensionality #

The Dimensionality selector at the top of the model settings controls the overall structure of the IRT model. The rest of the UI adapts to the choice.

Unidimensional #

All items measure a single latent trait. This is the standard IRT setting — suitable for well-targeted questionnaires and tests with a single intended construct.

Exploratory #

Fits an exploratory multidimensional IRT (MIRT) model. You pick:

• Number of dimensions — how many latent factors to extract
• Rotation method — how the factor solution is oriented (see below)

Exploratory MIRT is analogous to exploratory factor analysis but preserves the IRT likelihood. Use it when you suspect multiple traits but don’t yet have a specific hypothesis about which item loads on which factor.

Rotation methods:

• Orthogonal rotations (Varimax, Quartimax, Equamax, Varimin, Geomin T, Bentler T, Bifactor) produce uncorrelated factors. Simpler to interpret; factor correlations are fixed at 0.
• Oblique rotations (Oblimin, Promax, Quartimin, Simplimax, Cluster, Geomin Q, Bentler Q, Biquartimin) allow factors to correlate. More realistic for most psychological constructs — related traits usually are correlated. Oblimin is a sensible default.
• None (unrotated) shows the raw solution, dominated by a general factor; rarely directly interpretable.

Confirmatory #

Fits a confirmatory MIRT model using a factor structure that you specify. Two ways to define the structure:

• Factor assignment widget — a matrix of items (rows) × factors (columns). Click a cell to toggle whether an item loads on a factor. This is the same widget used in CFA.
• mirt syntax — a text editor in the accordion. Syntax is FactorName = item1, item2, ... (one line per factor; items can be 1-based indices or variable names). Edit freely and click Apply to update the widget.

The Correlated factors checkbox controls whether factors are allowed to covary (oblique) or constrained to be orthogonal.

When to use confirmatory vs. exploratory MIRT: confirmatory mode is appropriate when you have a theoretical model of which items tap which trait — e.g. an emotion questionnaire with a predefined positive/negative affect structure. Exploratory mode is appropriate when the structure is unknown or tentative.

Model types #

Select a model from the Model type dropdown. Auto detects the best fit based on item types: 2PL for dichotomous items, Graded Response Model for polytomous items. The dropdown disables options that don’t match the current dimensionality mode (e.g. Rasch is only available in unidimensional; PC2PL/PC3PL only in MD).

Dichotomous items #

Polytomous items #

Nonparametric items #

These don’t assume a parametric curve shape — they fit the item response function flexibly. Use when standard parametric models misfit but Mokken scalability is acceptable. Both are UD-only.

Partially compensatory (MD only) #

In standard MIRT, a high value on one dimension can “compensate” for a low value on another. Partially compensatory models restrict that trade-off — every dimension must contribute.

Rasch vs. 2PL: the Rasch model constrains all items to have equal discrimination — only difficulty varies. This has a practical advantage: raw total scores become sufficient statistics for the latent trait, meaning everyone with the same total score gets the same ability estimate. The 2PL model relaxes this, letting each item discriminate differently, which typically improves fit but means raw scores are no longer sufficient.

What is the guessing parameter? In the 3PL model, the lower asymptote (c) represents the probability of answering correctly by chance. For a 4-option multiple-choice item, you’d expect c ≈ 0.25. This parameter is notoriously hard to estimate and requires large samples (N > 500). If your test isn’t multiple-choice, use 2PL instead.

What is unfolding? In standard (cumulative) IRT the probability of endorsing an item increases monotonically with θ. In unfolding (ideal-point) models it’s single-peaked — respondents agree with items closest to their position and reject items too extreme or too moderate relative to their own view. Political attitude items often behave this way.

Estimation method #

The UI offers all of mirt’s estimators. For most unidimensional models, the default EM is both fast and reliable. Multidimensional models typically need MHRM once you go beyond two dimensions.

Standard errors in MIRT: EM and QMCEM do not compute the information matrix for multidimensional models — you’ll see a note when SEs are missing. Use MHRM if you need standard errors on item parameters.

Scoring method #

Controls how person ability (θ) is estimated after the model is fit:

Which scoring method? EAP is the safest default — it always produces a finite estimate and handles extreme response patterns gracefully. WLE is a good alternative if you want no Bayesian shrinkage but still want finite estimates. MLE is theoretically “purer” (no prior influence) but fails for people who answer everything correctly or incorrectly.

Differential item functioning (DIF) #

DIF tests whether items function differently across groups (e.g. gender, language). Select a categorical or binary grouping variable to enable DIF analysis. DataSuite uses Woods’s (2009) constrained-baseline approach: a multiple-group model is fit with every item constrained equal across groups, then each non-anchor item’s constraint is released one at a time and the resulting likelihood ratio is tested.

Anchor items #

When a DIF grouping variable is selected, an anchor items panel appears. Anchor items are assumed to be DIF-free and serve as the reference for testing other items. By default, all items are anchors (free baseline approach). Deselect items you want to test for DIF — only non-anchor items will be tested.

What is DIF? An item shows DIF when people from different groups with the same ability level have different probabilities of endorsing it. For example, if men and women of equal math ability have different chances of answering a particular math item correctly, that item has DIF. DIF doesn’t necessarily mean bias — the item might legitimately measure something that differs between groups — but it warrants investigation.

For Rasch and GRSM models (constrained discrimination), only difficulty parameters are tested. For other unidimensional models, discrimination and difficulty are tested jointly. For multidimensional models, all per-dimension discriminations plus the intercept are tested together.

Advanced tuning #

These options live in the Advanced tuning accordion. Leave defaults unless you know why you’re changing them.

Output options #

Tables #

Plot options #

Reading results #

Model fit #

Two tables appear when model fit is enabled:

Information criteria — AIC, BIC, and log-likelihood. Lower AIC/BIC values indicate better fit-complexity trade-offs. These are most useful when comparing models or dimensionalities.

Absolute fit (M2 statistic):

What is the M2 statistic? A limited-information goodness-of-fit test designed for IRT models. Unlike χ² tests that compare all possible response patterns, M2 uses first- and second-order margins, making it practical for tests with many items. A significant p-value suggests misfit, but with large samples even trivial misfit becomes significant — focus on RMSEA and CFI instead.

Model comparison #

Available for unidimensional models when enabled. DataSuite fits an alternative model and reports AIC, BIC, and (for nested models) a likelihood ratio test:

• Dichotomous items: Rasch vs. 2PL — tests whether allowing discrimination to vary improves fit
• Polytomous items: GRM vs. GPCM — compares the two common polytomous models
• Mixed data: 2PL + graded vs. 2PL + GPCM — the polytomous parametrisation is swapped; 2PL is kept for binary items in both fits

Reading the comparison: if AIC and BIC both favour the simpler model, there’s no reason to add complexity. If the likelihood ratio test is significant and AIC/BIC prefer the more complex model, the additional parameters are justified. When AIC and BIC disagree, BIC penalises complexity more heavily — lean toward the simpler model unless you have theoretical reasons for the complex one.

Dimensionality comparison #

(Exploratory mode.) Fits models at neighbouring dimensionalities and reports AIC, BIC, log-likelihood, and a likelihood ratio test between adjacent solutions. Answers the question “is the extra dimension worth it?”

Confirmatory vs exploratory fit #

(Confirmatory mode.) Compares your confirmatory solution against an unconstrained exploratory fit at the same dimensionality. A non-significant p-value indicates the constraints are tenable; a significant p-value suggests the data prefer a more flexible structure.

Factor loadings #

(MD only.) A table of rotated factor loadings — items in rows, factors in columns. Values > 0.3 are generally considered meaningful.

Factor correlations #

(MD, oblique only.) A correlation matrix showing how strongly the factors covary. High factor correlations (> 0.8) may indicate the factors are not well separated.

Item statistics #

A combined table with one row per item. Columns depend on which output options are enabled and on dimensionality.

Unidimensional parameter columns:

• Discrimination (a) — how sharply the item distinguishes between ability levels. Colour-coded: red for low (< 0.65), amber for moderate (0.65–1.0), no colour for high (> 1.0)
• Difficulty (b) — the θ level at which a person has a 50% probability of endorsing the item (dichotomous) or the expected response is at the midpoint (polytomous). Higher = harder
• Threshold (b1, b2, …) — for polytomous items, the θ values where adjacent category probabilities cross
• Guessing (c) — lower asymptote (3PL, 4PL)
• Upper asymptote (u) — upper bound on endorsement probability (3PLu, 4PL)
• SE columns — standard error for each parameter

Multidimensional parameter columns:

• a1, a2, … — discrimination on each dimension (slope vector)
• d or d1, d2, … — intercept (or per-category intercepts for polytomous items); replaces the unidimensional b
• MDISC — multidimensional discrimination; vector length of the a parameters across dimensions
• MDIFF — multidimensional difficulty; −intercept / MDISC. Reported as “Mean location” and noted as approximate for polytomous items

Fit columns:

• S-X² — Orlando and Thissen’s item-level fit statistic with degrees of freedom and p-value. A significant p-value suggests misfit
• Infit MNSQ and Outfit MNSQ — Rasch-family mean-square fit statistics

Infit vs. outfit: infit is information-weighted — it emphasises responses from people whose ability is near the item’s difficulty level (where the item is most informative). Outfit is unweighted and sensitive to unexpected responses far from the item’s difficulty. Values between 0.5 and 1.5 are considered productive for measurement. Values above 2.0 suggest the item is degrading rather than contributing to measurement. For non-Rasch models, the 0.5–1.5 band is shown for reference; with varying slopes these statistics have different distributional properties.

Interpreting discrimination:

• > 1.0 — high discrimination; the item differentiates well between ability levels
• 0.65–1.0 — moderate; adequate but less sharp
• < 0.65 — low; the item provides little information about the trait
• Negative — the item is inversely related to the trait; check whether it needs reverse scoring

MDISC and MDIFF: in a MIRT model an item has a vector of discriminations, one per dimension. MDISC collapses this vector into a single length, and MDIFF gives a corresponding overall difficulty. Think of them as “where does this item sit overall” summaries — useful for quick ranking, but you still need the per-dimension loadings to understand what the item actually measures.

Local dependence #

Flagged item pairs and their statistics:

• Q3 — Yen’s Q3, the correlation between item residuals after controlling for the latent trait. |Q3| > 0.2 is flagged
• Q3* — mean-corrected Q3 (Marais 2013); the average off-diagonal Q3 is subtracted, making the threshold interpretable even when global residuals are slightly biased
• LD-X² — a chi-squared test of local dependence. p < .05 is flagged

If no pairs are flagged by either method, the local independence assumption is supported.

What causes local dependence? Two items may share variance beyond what the latent trait explains — for example, items with overlapping content (“I feel anxious” and “I feel nervous”), items sharing a common stimulus (a reading passage), or items that form a testlet. Local dependence inflates item parameter estimates and biases reliability upward. Consider combining dependent items into a testlet or removing one from each flagged pair.

Person ability estimates #

A summary table of the θ distribution:

• Mean θ — average ability in the sample (centred near 0 for well-targeted tests)
• SD θ — spread of ability estimates
• Min / Max θ — range of estimated abilities
• Mean SE — average standard error across all persons; smaller is more precise

In multidimensional mode, a row is shown per dimension (F1, F2, …).

A button below the table inserts θ and SE into the dataset. If person fit is also enabled, the Zh statistic is inserted as well. Column names reflect the scoring method — e.g. IRT_Theta_EAP, IRT_SE_EAP, IRT_Zh (unidimensional) or IRT_Theta1_EAP, IRT_SE1_EAP, IRT_Theta2_EAP, … (multidimensional).

If extreme response patterns were filtered (all-minimum or all-maximum responses under MLE), a note reports how many persons were excluded from person-level statistics.

Person fit #

Reports the count of misfitting persons using two criteria:

• |Zh| > 2 — standardized person fit residual; aberrant response patterns
• Outfit > 1.5 — unexpected responses on items far from the person’s ability level (Rasch convention)

What does person misfit mean? A person whose responses don’t match the model’s expectations might be guessing randomly, responding carelessly, or have knowledge that doesn’t align with the trait dimension (e.g. a specialist who aces hard items but misses easy ones). A small percentage of misfit (< 5%) is normal. Systematic patterns (e.g. all high-ability persons misfit) warrant investigation. For non-Rasch models, Zh is the more reliable person-fit indicator — the outfit > 1.5 threshold is a Rasch convention.

Reliability and separation #

In MIRT, reliability, separation, and targeting are reported per dimension. Item reliability and item separation are Rasch-style indices; they appear with a “(Rasch-style)” label when the fitted model isn’t Rasch.

Interpretation thresholds for reliability:

Person separation interpretation:

Test targeting interpretation:

If respondents were dropped because θ or SE was non-finite (typically MLE on extreme patterns), a note reports the count.

What is person separation? If person separation is 3, the test can distinguish about 4 distinct ability groups (strata ≈ (4 × separation + 1) / 3). A test that can only separate people into “high” and “low” (separation < 2) isn’t very useful for individual-level decisions.

Test targeting: when person mean and item mean are close (difference near 0), the test is well matched to the sample. A large positive difference means the test is too easy — most people are above the item difficulty range. A large negative difference means it’s too hard.

Score conversion table #

(Unidimensional only.) Maps every possible raw (sum) score to a θ estimate and its standard error, using the test’s expected score function (equating). When an EAPsum conversion is available, it appears in additional columns alongside the equating result.

Why convert raw to θ? Raw scores are ordinal — the difference between 10 and 15 isn’t necessarily the same as between 25 and 30. IRT θ scores are on an interval scale, meaning equal differences in θ represent equal differences in ability. The conversion table lets you translate familiar raw scores into this measurement-quality scale.

Expected scores by dimension #

(MD only.) Shows the expected total score as a function of each dimension while holding the other dimensions at θ = 0. Useful for understanding how each dimension contributes to observed scores.

DIF results #

A table with one row per tested item showing the χ² statistic, degrees of freedom, and p-value. The grouping variable name is displayed above the table.

Plots #

Item Characteristic Curves (ICCs) #

Dichotomous items: a single overlay chart showing the probability of correct response (y-axis) across the ability range (x-axis) for all items. Each curve is a logistic function shaped by the item’s parameters. Steeper curves indicate higher discrimination; curves shifted right indicate harder items.

Polytomous items: two chart types are drawn:

• Category Response Curves — one chart per item, showing the probability of each response category as a function of θ. The curves cross at the threshold parameters
• Expected Score Curves — one overlay chart showing the expected item score as a function of θ for all items. Useful for comparing item difficulty and discrimination at a glance

Information curves #

Several panels are drawn:

1. Item information curves — each item’s contribution to measurement precision across the θ range. Peaked curves show where each item is most informative
2. Test information curve — the sum of all item information functions. Shows where the test as a whole measures most precisely
3. Standard error curve — the inverse square root of test information. Lower SE = more precise measurement
4. Test Characteristic Curve — expected total score as a function of θ. Shows the nonlinear relationship between ability and raw scores
5. Conditional reliability curve — reliability as a function of θ, computed as 1 − SE(θ)² / σ²θ. A dashed reference line marks 0.70

Reading the information curve: the peak of the test information curve tells you where the test is most precise. A test designed for clinical screening (distinguishing disordered from non-disordered) should peak near the clinical cutoff. A test designed for general ability measurement should have a broad, flat information curve. Narrow peaks mean the test is precise for a small ability range but imprecise elsewhere.

Wright map #

A two-panel display with a shared θ axis:

• Left panel — a horizontal histogram of person ability estimates
• Right panel — item difficulty markers with labels (de-clumped to avoid overlap)

For multidimensional models, separate person histograms and item locations are drawn for each dimension.

Reading the Wright map: items and persons are plotted on the same scale. Items at the same height as a cluster of persons are optimally targeted for those people — they provide maximum information. Items far above the person distribution are too hard (almost everyone gets them wrong); items far below are too easy (almost everyone gets them right). A well-targeted test has items spread across the person distribution.

Factor loadings heatmap #

(MD only.) Items on one axis, factors on the other, cell colour encoding loading magnitude. A quick visual summary of which items load on which factors — especially useful for exploratory MIRT after rotation.

Assumptions #

• Unidimensionality (UD mode) — all items measure a single latent trait. Use the preliminary analysis to check this before fitting a UD model. In MD mode this is replaced by the weaker assumption that items measure the specified number of traits.
• Local independence — after controlling for the latent trait(s), item responses are independent. Violated when items share content, share a stimulus, or form testlets. Check with the local dependence output.
• Monotonicity — the probability of endorsing higher categories increases with ability. Checked via Mokken analysis in the preliminary analysis.
• Correct model specification — the chosen model (Rasch, 2PL, etc.) adequately describes the data. Check model fit and consider model comparison.
• Sufficient sample size — IRT parameters are estimated less precisely with small samples. See sample size guidelines.
• Items should be scored in the same direction. Negatively worded items need reverse scoring before IRT analysis — use the questionnaire scoring guide or the internal consistency tab’s reverse scoring feature.

Missing data #

Missing values are handled by the global missing data setting. With listwise deletion, any case missing a value on any item is excluded. The number of complete cases is reported in the output.

Missing data and IRT: IRT handles missing data more gracefully than classical methods — person ability can still be estimated from the items a person did answer. However, DataSuite’s current implementation uses listwise deletion for model fitting. If you’re losing many cases, consider whether imputation is appropriate, but be aware that imputing item responses can distort IRT parameter estimates more than it would affect classical reliability.

Reporting checklist #

Method:

• Dimensionality (unidimensional, exploratory MIRT with k dimensions and rotation, or confirmatory MIRT with specified factor structure)
• IRT model used (e.g. “A graded response model was fit using the mirt R package”)
• Estimation method (EM, QMCEM, MHRM, …)
• Scoring method for person ability (EAP, MAP, MLE, WLE)
• Number of items and sample size (total and complete cases)
• Item types (dichotomous, polytomous, or mixed)
• How missing data were handled
• Any advanced tuning choices that deviate from defaults
• Software and R packages used

Results:

• Model fit indices (at minimum RMSEA, CFI; include AIC/BIC when comparing models or dimensionalities)
• Item parameter estimates with standard errors (per dimension for MD, plus MDISC/MDIFF)
• Item fit statistics (S-X², infit/outfit where applicable)
• Person ability distribution (mean, SD, range), per dimension for MD
• Marginal reliability and person separation, per dimension for MD
• Factor loadings (and correlations for oblique solutions) for MIRT
• Any problematic items (poor discrimination, misfit, local dependence)
• DIF results if applicable, including grouping variable and anchor strategy
• Wright map or other visualisations as figures

R reproducibility #

Every analysis prints the underlying R code to the R console. IRT analysis uses the mirt R package for model fitting, rotations, item and person parameters, fit statistics, DIF, and score conversion. Preliminary analysis additionally uses mokken for scalability, monotonicity, IIO, rest-score local independence, and nonparametric reliability. Citations for R packages appear automatically at the top of the output.

Common pitfalls #

Running IRT without checking data first. The preliminary analysis is there for a reason — it catches unidimensionality violations, careless responders, and items that don’t fit a monotone model. Fitting an IRT model to unsuitable data produces parameters that look precise but mean nothing. Always run Diagnostics & Mokken first.

Choosing 3PL by default. The guessing parameter is appealing (“my test has multiple-choice items!”) but extremely difficult to estimate. With fewer than 500 respondents, guessing parameters are often poorly identified and can destabilise the entire model. Start with 2PL; only add the guessing parameter if you have a large sample and the 2PL shows systematic misfit at low ability levels.

Using EM at high dimensionality. EM scales badly beyond two dimensions — it may be very slow or fail to converge. Switch to MHRM for 3+ dimensions; it’s much faster and also gives you standard errors for item parameters.

Reading MIRT loadings without rotation. An unrotated MIRT solution is dominated by a general factor and isn’t directly interpretable. Pick an oblique rotation (Oblimin is a sensible default) unless you have a specific reason to prefer orthogonal or unrotated output.

Ignoring item fit. A well-fitting model overall (good RMSEA) can still have individual items that misfit badly. Always check item-level S-X² and infit/outfit statistics. A single misfitting item can distort person scores for everyone near that item’s difficulty level.

Over-interpreting DIF. A statistically significant DIF result doesn’t automatically mean the item is biased. Small DIF effects become significant with large samples. Look at the magnitude of parameter differences between groups, not just the p-value. Items with DIF may legitimately measure a real group difference rather than a testing artifact.

Treating IRT scores as “better” raw scores. θ estimates have standard errors — they’re not exact. Two people with θ = 0.5 and θ = 0.7 may not be meaningfully different if both have SE = 0.3. Always consider the SE when interpreting individual scores, and use the conditional reliability curve to understand where the test measures precisely and where it doesn’t.

Forcing a parametric model when Mokken fails. If items don’t form a scalable Mokken scale (H < 0.3), they’re unlikely to fit a parametric IRT model either. Poor Mokken scalability usually indicates the items aren’t measuring a single construct — consider factor analysis or switch to multidimensional IRT before attempting a single unidimensional parametric fit.