A - Notation
The notation in this chapter follows Wright and Masters (1982).
| Section | Symbol | Term | Description |
|---|---|---|---|
| 4.6 | \(\beta_n\) | Ability | True (but unknown) developmental score of child \(n\) |
| 4.6 | \(\delta_i\) | Difficulty | True (but unknown) difficulty of item \(i\) |
| 4.6 | \(\pi_{ni}\) | Probability | True (but unknown) probability that child \(n\) passes item \(i\) |
| 6.1 | \(\hat\beta_n\) | Ability | Estimated developmental score (D-score) of child \(n\) |
| 6.1 | \(\hat\delta_i\) | Difficulty | Estimated difficulty of item \(i\) |
| 6.1 | \(P_{ni}\) | Probability | Estimated probability that child \(n\) passes item \(i\) |
| 6.1 | \(x_{ni}\) | Data | Observed response of child \(n\) on item \(i\), 0 or 1 |
| 6.1 | \(W_{ni}\) | Variance | Variance of \(x_{ni}\) |
| 6.1 | \(z_{ni}\) | Residual | Standardized residual between \(x_{ni}\) and \(P_{ni}\) |
| 6.1 | \(N\) | Count | Number of measurements (children) |
| 6.1 | \(L\) | Count | Number of items (milestones) |
| 6.4 | \(P(\hat\delta_i)\) | Probability | Conditional probability of passing item \(i\) |
| 6.4 | \(I(\hat\delta_i)\) | Information | Item information function of item \(i\) |
| 6.5 | \(R\) | Reliability | True test reliability |
| 6.5 | \(\hat R\) | Reliability | Estimated test reliability |
| 6.5 | \(\sigma_e^2\) | Variance | True error variance |
| 6.5 | \(\hat\sigma_{\hat e}^2\) | Variance | Estimated error variance |
| 6.5 | \(\hat\sigma_{\hat e}\) | Variance | Standard error of measurement (sem) |
| 9.2 | \(f\) | Factor | Age-adjustment factor |