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