Package: kits 0.25.2

kits: Psychometric Tools for the Kids in Taiwan Developmental Scale

Tools for the developmental scale of KIT (Kids in Taiwan: National Longitudinal Study of Child Development and Care). Each model is written once and 'RTMB' gives every derivative (the conditional maximum likelihood, the person scores, the threshold standard errors, the norms); the closed-form steps use base R, and the data are handled with 'dplyr', 'tidyr' and 'purrr'. Items are calibrated with the partial credit model (Masters, 1982) <doi:10.1007/BF02296272> by conditional maximum likelihood, written as the elementary symmetric functions of the step parameters. Cohorts are linked by mean/sigma (Marco, 1977) <doi:10.1111/j.1745-3984.1977.tb00033.x> on the Thurstonian thresholds, and anchor items link to the D score of the Global Scales for Early Development (Weber et al., 2019) <doi:10.1136/bmjgh-2019-001724>. Person scores are weighted likelihood estimates (Warm, 1989) <doi:10.1007/BF02294627>; for the partial credit model they equal the Jeffreys modal estimates (Firth, 1993) <doi:10.1093/biomet/80.1.27> (Magis, 2015) <doi:10.1007/s11336-013-9378-5>, which are computed by the Newton method of 'RTMB', one per item set and raw score. Norms are continuous sinh-arcsinh norms (Jones and Pewsey, 2009) <doi:10.1093/biomet/asp053> fitted by maximum likelihood with the polynomial model and bounds of 'cNORM' (Lenhard and Lenhard, 2021) <doi:10.1177/0013164420928457>, minimised by nlminb with the gradient and Hessian of 'RTMB'. Differential item functioning combines the likelihood-ratio test of Andersen (1973) <doi:10.1007/BF02291180> with the item-pair test of Bechger and Maris (2015) <doi:10.1007/s11336-014-9408-y>, computed by CML in each group. The linking error at each score and through a chain of links, the statistics of the waves as a vertical scale, the precision of each form across the scale, and IRT true-score and observed-score equating of raw scores follow Kolen and Brennan (2014) <doi:10.1007/978-1-4939-0317-7>. The plots are drawn with 'plotly'. The algorithms are also exported as plain functions (the 'algo_' layer) that chain with the pipe, and kits_algorithm() names the steps, formulas and references behind a result; teaching scripts in 'inst/scripts' recompute the estimates with 'RTMB' on the demo data. The companion package 'kitsPreview' computes the same results with 'dexter' and 'cNORM' for validation.

Authors:Jie-Wen Tsai [aut, cre]