Estimation of survival and capture probabilities in open population capture–recapture models when covariates are subject to measurement error

Predictor variables (or covariates) are frequently used in a capture–recapture analysis when estimating demographic quantities such as population size or survival probabilities. If these predictor variables are measured with error and subsequently used in the analysis, then estimates of the model parameters may be biased. Several approaches have been proposed to account for error-in-variables in capture–recapture models, however these methods generally assume the population is closed; hence quantities of interest for open populations such as the survival probabilities do not appear in the likelihood. To account for measurement error in environmental time-varying covariates for open population capture–recapture data, the well-known Cormack–Jolly–Seber model and two statistical methods are considered: (1) simulation–extrapolation; and (2) regression calibration, as well as a new method which accounts for correlation (arising from measurement error) between the survival and capture probabilities. Several simulation studies are conducted to examine the method performances, and a case study is presented which uses capture–recapture data on the Little Penguin Eudyptula minor and sea-surface temperature data as an environmental covariate to model their survival and capture probabilities.