SummaryWe conducted confirmatory factor analysis (CFA) of responses (N=803) to a self‐reported measure of optimism, using full‐information estimation via adaptive quadrature (AQ), an alternative estimation method for ordinal data. We evaluated AQ results in terms of the number of iterations required to achieve convergence, model fit, parameter estimates, standard errors (SE), and statistical significance, across four link‐functions (logit, probit, log‐log, complimentary log‐log) using 3–10 and 20 quadrature points. We compared AQ results with those obtained using maximum likelihood, robust maximum likelihood, and robust diagonally weighted least‐squares estimation. Compared to the other two link‐functions, logit and probit not only produced fit statistics, parameters estimates, SEs, and levels of significance that varied less across numbers of quadrature points, but also fitted the data better and provided larger completely standardised loadings than did maximum likelihood and diagonally weighted least‐squares. Our findings demonstrate the viability of using full‐information AQ to estimate CFA models with real‐world ordinal data.