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Abstract Online calibration estimates new item parameters alongside previously calibrated items, supporting efficient item replenishment. However, most existing online calibration procedures for Cognitive Diagnostic Computerized Adaptive Testing (CD‐CAT) lack mechanisms to ensure content balance during live testing. This limitation can lead to uneven content coverage, potentially undermining the alignment with instructional goals. This research extends the current calibration framework by integrating a two‐phase test design with a content‐balancing item selection method into the online calibration procedure. Simulation studies evaluated item parameter recovery and attribute profile estimation accuracy under the proposed procedure. Results indicated that the developed procedure yielded more accurate new item parameter estimates. The procedure also maintained content representativeness under both balanced and unbalanced constraints. Attribute profile estimation was sensitive to item parameter values. Accuracy declined when items had larger parameter values. Calibration improved with larger sample sizes and smaller parameter values. Longer test lengths contributed more to profile estimation than to new item calibration. These findings highlight design trade‐offs in adaptive item replenishment and suggest new directions for hybrid calibration methods. 

The distance between homes and childcare providers serves as a crucial factor in evaluating accessibility and equity in early childhood education. Spatial mismatch between childcare demand and supply is suggested when families opt for facilities further than the nearest available options, a situation scarcely scrutinized in existing literature, especially among under-six children from economically disadvantaged backgrounds. To fill this research gap, this study leverages the excess commuting analysis to delve into the extent of extended travel undertaken by subsidized families to access childcare services. Utilizing real enrollment data from the Florida’s School Readiness program, it quantifies the disparity between actual and shortest possible commuting distances, investigating the tendencies of low-income families to forgo nearby providers for their young children. Furthermore, the research probes into age-related disparities in excess commuting, examining to what degree childcare facilities are more conveniently located for certain age groups compared to others. The analysis unveils substantial spatial mismatch in subsidized childcare, with a significant portion of low-income families choosing more distant providers, resulting in a 51.3% surplus in commuting distance. It also highlights a noticeable age- dependent trend in this mismatch: parents of infants face a dual disadvantage with longer commutes, compared to families with five-year-olds who have closer access to providers. The findings advocate for policy reforms that address these disparities, enhancing the efficiency and equity of childcare resource allocation.