This paper presents a general framework for estimating smoothing parameters in statistical models with regular likelihoods constructed using unknown smooth functions of covariates. The method is numerically stable and convergent, enabling quantification of smoothing parameter uncertainty. This addresses a known issue with AIC for such models, improving model selection tools. Smooth functions are represented using reduced rank spline-like smoothers with quadratic penalties. Model estimation is done via penalized likelihood maximization, with smoothing parameters estimated using Laplace approximate marginal likelihood. The framework covers generalized additive models for non-exponential family responses, generalized additive models for location scale and shape, Cox proportional hazards models, and multivariate additive models. The method reduces implementation of new model classes to coding standard derivatives of the log likelihood. The paper discusses the general framework, smoothness selection methods, and provides examples of model implementations. It also covers the use of Laplace approximate marginal likelihood for smoothing parameter estimation and the correction of conditional AIC for smoothing parameter uncertainty. The methods are applied to various models, including GAMLSS models and extended generalized additive models. The paper concludes with simulation results and examples, and provides further details in supplementary appendices.This paper presents a general framework for estimating smoothing parameters in statistical models with regular likelihoods constructed using unknown smooth functions of covariates. The method is numerically stable and convergent, enabling quantification of smoothing parameter uncertainty. This addresses a known issue with AIC for such models, improving model selection tools. Smooth functions are represented using reduced rank spline-like smoothers with quadratic penalties. Model estimation is done via penalized likelihood maximization, with smoothing parameters estimated using Laplace approximate marginal likelihood. The framework covers generalized additive models for non-exponential family responses, generalized additive models for location scale and shape, Cox proportional hazards models, and multivariate additive models. The method reduces implementation of new model classes to coding standard derivatives of the log likelihood. The paper discusses the general framework, smoothness selection methods, and provides examples of model implementations. It also covers the use of Laplace approximate marginal likelihood for smoothing parameter estimation and the correction of conditional AIC for smoothing parameter uncertainty. The methods are applied to various models, including GAMLSS models and extended generalized additive models. The paper concludes with simulation results and examples, and provides further details in supplementary appendices.