## 2 Materials and Methods
### Analytical Plan  
Here we report only on the analyses and results for the subtests in Battery 1: approximate number system, equivalence, attention shifting, card-sorting classification, card-sorting hypothesis testing, card-sorting inference making, and narrative memory. We scored these subtests in different ways depending on whether the subtest was adaptive or not. Approximate number system, equivalence, card sorting-inference making, and narrative memory, had all been administered using a planned missing approach, in which different age groups received age-appropriate items according to their estimated ability, with overlap of items between age groups when possible. Items were calibrated by conducting IRT analysis. IRT is built upon the assumption that the probability of a respondent passing an item is a function of the respondent's position on the latent trait continuum and the item properties [54]. In the current study, we employed the 2 PL model which includes two item parameters--slope and difficulty. The slope parameter represents the degree to which an item distinguishes individuals of different estimated ability. The difficulty parameter reflects the trait level where the probability of an individual passing that item is 0.50. We computed IRT-based person scores using the expected a posteriori estimator (EAP). The 2 PL IRT models and personal score estimates were conducted using the'mirt' package [55] embedded in the R environment [56]. The attention-shifting test generated three types of measures including number of targets (the shape that should be touched) touched, number of commission errors, and number of omission errors. Errors of commission occur when the test-taker touches a shape that is not the target. Errors of omission occur when the test-taker fails to touch the target. These counts constitute the scores. Regarding card sorting-classification, when the test-taker moves a card (sorts it) to the correct pile, one point is earned. The sum of the correct responses for the 24 items constitutes the classification score. In the card sorting-hypothesis testing task, two types of scores are reported: the total number of incorrect sorts and the number of perseverative errors. Perseverative errors occur when the test-taker continues to sort according to the same rule (for example, by color) even after a rule change has been indicated. Descriptive statistics, including the sample mean, standard deviation, minimum, maximum, skewness, and kurtosis, were derived using the base program embedded in R [56]. We also plotted score distribution for each measure in Battery 1. Pearson correlation coefficients were generated to examine the associations between age and the 10 measures. We use the equivalence subtest to demonstrate how to prepare a subtest for adaptive administration through a simulation study. Simulation research for CAT allows researchers to evaluate the efficiency of the CAT approach as compared to the traditional linear test. The elements of CAT include an item bank with pre-calibrated items, the algorithm for selecting items, the process of estimating ability after each item is administered, the stopping rule, and the final estimation of ability. As described above, the equivalence subtest was calibrated with the 2 PL IRT model. We then conducted the simulation using the catR package [57] embedded in the R environment [56]. We first generated the true abilities for 1500 cases according to the population parameters (M = 0, SD = 1). The first item was selected optimally at the ability level of 0 that is driven by Maximum Fisher information (MFI). The algorithm for selecting the next item given the current ability estimate and a set of previously administered items was MFI. We used EAP to estimate the ability after each item was administered. We manipulated the stopping criteria in different ways. In the first set of designs, the CAT process stopped when 10, 15, 20, 25, and 30 items were administered.