# A - Notation

The notation in this chapter follows .

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