Repeated directional responses may vary between individuals in both overall orientation and sensitivity to explanatory cues. We study homogeneous angular regression with correlated Gaussian cue coefficients and a circular random intercept, separating observation concentration from resultant length. Constructive identification conditions recover the joint coefficient law, intercept concentration and observation-error parameters, including unknown uniform contamination. The argument combines repeated contrasts, an arc-support restriction and joint Fourier deconvolution, and extends to exogenous continuous designs. Integration in coefficient coordinates yields smooth population scores even when resultant cancellation prevents a regular latent mode. A fixed-proposal adaptive importance algorithm evaluates the marginal likelihood and its derivatives. In 8,000 independent simulated datasets, 7,998 fits pass numerical checks, and 12,799 of 12,800 local profile intervals are available. Correlation profile-set coverage nevertheless ranges from 91.9% to 94.8% at the nominal 95% level. Greater precision and numerical availability therefore do not ensure calibrated inference. An exploratory extension to 150 Canadian weather stations is evaluated on 259,807 three-hour forecasts from a new 2026 period after fitting on 2023-2025 data. With circular station rotations in all matched models, independent station slopes give modest predictive gains over slopes shared within regions, in all five regions. Estimating their correlations adds no useful predictive gain; this does not assess parameter uncertainty, and predictive calibration remains imperfect. The application uses a noncancelling mean and Laplace integration, so it illustrates the model class rather than testing the proposed algorithm.

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