# stan_nlmer: Bayesian nonlinear models with group-specific terms via Stan In rstanarm: Bayesian Applied Regression Modeling via Stan

## Description Bayesian inference for NLMMs with group-specific coefficients that have unknown covariance matrices with flexible priors.

## Usage

 ```1 2 3 4 5``` ```stan_nlmer(formula, data = NULL, subset, weights, na.action, offset, contrasts = NULL, ..., prior = normal(), prior_aux = exponential(), prior_covariance = decov(), prior_PD = FALSE, algorithm = c("sampling", "meanfield", "fullrank"), adapt_delta = NULL, QR = FALSE, sparse = FALSE) ```

## Arguments

`formula, data`

Same as for `nlmer`. We strongly advise against omitting the `data` argument. Unless `data` is specified (and is a data frame) many post-estimation functions (including `update`, `loo`, `kfold`) are not guaranteed to work properly.

`subset, weights, offset`

Same as `glm`.

`na.action, contrasts`

Same as `glm`, but rarely specified.

`...`

Further arguments passed to the function in the rstan package (`sampling`, `vb`, or `optimizing`), corresponding to the estimation method named by `algorithm`. For example, if `algorithm` is `"sampling"` it is possibly to specify `iter`, `chains`, `cores`, `refresh`, etc.

`prior`

The prior distribution for the regression coefficients. `prior` should be a call to one of the various functions provided by rstanarm for specifying priors. The subset of these functions that can be used for the prior on the coefficients can be grouped into several "families":

 Family Functions Student t family `normal`, `student_t`, `cauchy` Hierarchical shrinkage family `hs`, `hs_plus` Laplace family `laplace`, `lasso` Product normal family `product_normal`

See the priors help page for details on the families and how to specify the arguments for all of the functions in the table above. To omit a prior —i.e., to use a flat (improper) uniform prior— `prior` can be set to `NULL`, although this is rarely a good idea.

Note: Unless `QR=TRUE`, if `prior` is from the Student t family or Laplace family, and if the `autoscale` argument to the function used to specify the prior (e.g. `normal`) is left at its default and recommended value of `TRUE`, then the default or user-specified prior scale(s) may be adjusted internally based on the scales of the predictors. See the priors help page and the Prior Distributions vignette for details on the rescaling and the `prior_summary` function for a summary of the priors used for a particular model.

`prior_aux`

The prior distribution for the "auxiliary" parameter (if applicable). The "auxiliary" parameter refers to a different parameter depending on the `family`. For Gaussian models `prior_aux` controls `"sigma"`, the error standard deviation. For negative binomial models `prior_aux` controls `"reciprocal_dispersion"`, which is similar to the `"size"` parameter of `rnbinom`: smaller values of `"reciprocal_dispersion"` correspond to greater dispersion. For gamma models `prior_aux` sets the prior on to the `"shape"` parameter (see e.g., `rgamma`), and for inverse-Gaussian models it is the so-called `"lambda"` parameter (which is essentially the reciprocal of a scale parameter). Binomial and Poisson models do not have auxiliary parameters.

`prior_aux` can be a call to `exponential` to use an exponential distribution, or `normal`, `student_t` or `cauchy`, which results in a half-normal, half-t, or half-Cauchy prior. See `priors` for details on these functions. To omit a prior —i.e., to use a flat (improper) uniform prior— set `prior_aux` to `NULL`.

`prior_covariance`

Cannot be `NULL`; see `decov` for more information about the default arguments.

`prior_PD`

A logical scalar (defaulting to `FALSE`) indicating whether to draw from the prior predictive distribution instead of conditioning on the outcome.

`algorithm`

A string (possibly abbreviated) indicating the estimation approach to use. Can be `"sampling"` for MCMC (the default), `"optimizing"` for optimization, `"meanfield"` for variational inference with independent normal distributions, or `"fullrank"` for variational inference with a multivariate normal distribution. See `rstanarm-package` for more details on the estimation algorithms. NOTE: not all fitting functions support all four algorithms.

`adapt_delta`

Only relevant if `algorithm="sampling"`. See the adapt_delta help page for details.

`QR`

A logical scalar defaulting to `FALSE`, but if `TRUE` applies a scaled `qr` decomposition to the design matrix. The transformation does not change the likelihood of the data but is recommended for computational reasons when there are multiple predictors. See the QR-argument documentation page for details on how rstanarm does the transformation and important information about how to interpret the prior distributions of the model parameters when using `QR=TRUE`.

`sparse`

A logical scalar (defaulting to `FALSE`) indicating whether to use a sparse representation of the design (X) matrix. If `TRUE`, the the design matrix is not centered (since that would destroy the sparsity) and likewise it is not possible to specify both `QR = TRUE` and `sparse = TRUE`. Depending on how many zeros there are in the design matrix, setting `sparse = TRUE` may make the code run faster and can consume much less RAM.

## Details

The `stan_nlmer` function is similar in syntax to `nlmer` but rather than performing (approximate) maximum marginal likelihood estimation, Bayesian estimation is by default performed via MCMC. The Bayesian model adds independent priors on the "coefficients" — which are really intercepts — in the same way as `stan_nlmer` and priors on the terms of a decomposition of the covariance matrices of the group-specific parameters. See `priors` for more information about the priors.

The supported transformation functions are limited to the named "self-starting" functions in the stats library: `SSasymp`, `SSasympOff`, `SSasympOrig`, `SSbiexp`, `SSfol`, `SSfpl`, `SSgompertz`, `SSlogis`, `SSmicmen`, and `SSweibull`.

## Value

A stanreg object is returned for `stan_nlmer`.

`stanreg-methods` and `nlmer`.
The vignette for `stan_glmer`, which also discusses `stan_nlmer` models. http://mc-stan.org/rstanarm/articles/
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```data("Orange", package = "datasets") Orange\$circumference <- Orange\$circumference / 100 Orange\$age <- Orange\$age / 100 fit <- stan_nlmer( circumference ~ SSlogis(age, Asym, xmid, scal) ~ Asym|Tree, data = Orange, # for speed only chains = 1, iter = 1000 ) print(fit) posterior_interval(fit) plot(fit, regex_pars = "b\\[") ```