Nonlinear regression

[Richard Bailey]

A quick question for the group because I'm struggling to find a definitive answer: Can R-inla (or INLA methodology in general) be used to fit ad hoc nonlinear or generalized nonlinear fixed-effect or mixed-effect regression models? If it's possible, could you point me to a good place to start learning how to do this?

Many thanks and best wishes to all,

Richard.

[Richard Bailey]

To clarify further, I'm referring to a nonlinear fixed-effect model, which may also include random and residual effects on the nonlinear parameters.

[Finn Lindgren]

Hi Richard,

it's not entirely clear what you're asking. Do you mean "nonlinear effects of covariates", as in generalised additive models? Then yes, this is what inla does best.

Can you explain/define mathematically what you mean by "random and residual effects on the nonlinear parameters"?

If you mean more fundamental types of nonlinearity with respect to the latent gaussian variables, then inlabru might help. It depends on precisely what mathematical structure you need in your model.

Finn

Finn

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Finn Lindgren
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[Richard Bailey]

Hi Finn,

Many thanks for responding, I'll try and clarify the question and why I'm asking (I'm not always very precise with terminology due to not being a trained statistician, so apologies for that). I'm developing a software and interested to know if I can incorporate R-inla, but not really sure where to start.

I'm expecting the relationship between a predictor and response to follow a parametric nonlinear curve, such as a logistic curve or a normal or lognormal distribution, as in the type of model that might be fit with nlme or nlmer. e.g. for a logistic curve the objective would be to estimate the parameters 'm' (location) and 's' (scale) with respect to the predictor 'x'. I may then want to include predictors (not necessarily as fixed effects) of variation in either or both of m and s. So the first question is whether the parameters of a parametric nonlinear function of y with respect to x could be estimated in a fixed effects model?

I'm also interested in whether parametric nonlinear functions can be fitted elsewhere in the model? For example, could I use a parametric nonlinear function for change in y with respect to x to predict the autocorrelation among data points and fit this as a residual model, estimating the nonlinear parameters as part of the model fit? I'm thinking of a 1D model as a starting point, but I'm interested in more complex spatial models too.

Best wishes,

Richard.