We develop a novel measurement framework based on Gaussian process coregionalization model to address a long-lasting debate in psychometrics: whether psychological features like personality share a common structure across the population or vary uniquely for individuals. We propose idiographic personality Gaussian process (IPGP), an intermediate model that accommodates both shared trait structure across individuals and "idiographic" deviations. IPGP leverages the Gaussian process coregionalization model to conceptualize responses of grouped survey batteries but adjusted to non-Gaussian ordinal data, and exploits stochastic variational inference for latent factor estimation. Using both synthetic data and a novel survey, we show that IPGP improves both prediction of actual responses and estimation of intrapersonal response patterns compared to existing benchmarks. In the survey study, IPGP also identifies unique clusters of personality taxonomies, displaying great potential in advancing individualized approaches to psychological diagnosis.