The Health and Retirement Study International Partner Surveys (HRS IPS) have rich longitudinal data, but the brevity of cognitive batteries is a limitation. We used data from a substudy of the English Longitudinal Study of Ageing (ELSA) administering detailed cognitive assessments with the Harmonized Cognitive Assessment Protocol (ELSA-HCAP) (N=1273) to inform approaches for estimating cognition in ELSA (N=11,213). We compared two novel approaches: confirmatory factor analysis (CFA)- and regression-based prediction. Compared to estimates from the full HCAP battery, estimated cognitive functioning derived using regression models or CFA had high correlations (regression: r=0.85 [95% confidence interval [CI]: 0.83 to 0.87]; CFA: r=0.83 [95% CI: 0.81 to 0.85]) and reasonable mean squared error (regression: 0.25 [0.22 to 0.27]; CFA: 0.29 [0.26 to 0.32]) in held-out data. The use of additional items from waves 7 to 9 improved performance. Both approaches are recommended for future research; the similarity in approaches may be due to the brevity of available cognitive assessments in ELSA. Estimates of cognitive functioning informed by English Longitudinal Study of Ageing-Harmonized Cognitive Assessment Protocol (ELSA-HCAP) data had an adequate performance. Standard errors were smaller for associations with example risks when using measures informed by ELSA-HCAP. Performance was better when including additional cognitive measures available in waves 7 to 9. Conceptual advantages to the confirmatory factor analysis (CFA) approach were not important in practice due to the brevity of the ELSA cognitive battery.