gp {brms} | R Documentation |

## Set up Gaussian process terms in brms

### Description

Set up a Gaussian process (GP) term in brms. The function does not evaluate its arguments – it exists purely to help set up a model with GP terms.

### Usage

```
gp(
...,
by = NA,
k = NA,
cov = "exp_quad",
iso = TRUE,
gr = TRUE,
cmc = TRUE,
scale = TRUE,
c = 5/4
)
```

### Arguments

`...` |
One or more predictors for the GP. |

`by` |
A numeric or factor variable of the same length as each predictor. In the numeric vector case, the elements multiply the values returned by the GP. In the factor variable case, a separate GP is fitted for each factor level. |

`k` |
Optional number of basis functions for computing approximate
GPs. If |

`cov` |
Name of the covariance kernel. By default,
the exponentiated-quadratic kernel |

`iso` |
A flag to indicate whether an isotropic ( |

`gr` |
Logical; Indicates if auto-grouping should be used (defaults
to |

`cmc` |
Logical; Only relevant if |

`scale` |
Logical; If |

`c` |
Numeric value only used in approximate GPs. Defines the
multiplicative constant of the predictors' range over which
predictions should be computed. A good default could be |

### Details

A GP is a stochastic process, which
describes the relation between one or more predictors
`x = (x_1, ..., x_d)`

and a response `f(x)`

, where
`d`

is the number of predictors. A GP is the
generalization of the multivariate normal distribution
to an infinite number of dimensions. Thus, it can be
interpreted as a prior over functions. The values of `f( )`

at any finite set of locations are jointly multivariate
normal, with a covariance matrix defined by the covariance
kernel `k_p(x_i, x_j)`

, where `p`

is the vector of parameters
of the GP:

`(f(x_1), \ldots f(x_n) \sim MVN(0, (k_p(x_i, x_j))_{i,j=1}^n) .`

The smoothness and general behavior of the function `f`

depends only on the choice of covariance kernel.
For a more detailed introduction to Gaussian processes,
see https://en.wikipedia.org/wiki/Gaussian_process.

Below, we describe the currently supported covariance kernels:

"exp_quad": The exponentiated quadratic kernel is defined as

`k(x_i, x_j) = sdgp^2 \exp(- || x_i - x_j ||^2 / (2 lscale^2))`

, where`|| . ||`

is the Euclidean norm,`sdgp`

is a standard deviation parameter, and`lscale`

is characteristic length-scale parameter. The latter practically measures how close two points`x_i`

and`x_j`

have to be to influence each other substantially.

In the current implementation, `"exp_quad"`

is the only supported
covariance kernel. More options will follow in the future.

### Value

An object of class `'gp_term'`

, which is a list
of arguments to be interpreted by the formula
parsing functions of brms.

### See Also

### Examples

```
## Not run:
# simulate data using the mgcv package
dat <- mgcv::gamSim(1, n = 30, scale = 2)
# fit a simple GP model
fit1 <- brm(y ~ gp(x2), dat, chains = 2)
summary(fit1)
me1 <- conditional_effects(fit1, ndraws = 200, spaghetti = TRUE)
plot(me1, ask = FALSE, points = TRUE)
# fit a more complicated GP model
fit2 <- brm(y ~ gp(x0) + x1 + gp(x2) + x3, dat, chains = 2)
summary(fit2)
me2 <- conditional_effects(fit2, ndraws = 200, spaghetti = TRUE)
plot(me2, ask = FALSE, points = TRUE)
# fit a multivariate GP model
fit3 <- brm(y ~ gp(x1, x2), dat, chains = 2)
summary(fit3)
me3 <- conditional_effects(fit3, ndraws = 200, spaghetti = TRUE)
plot(me3, ask = FALSE, points = TRUE)
# compare model fit
loo(fit1, fit2, fit3)
# simulate data with a factor covariate
dat2 <- mgcv::gamSim(4, n = 90, scale = 2)
# fit separate gaussian processes for different levels of 'fac'
fit4 <- brm(y ~ gp(x2, by = fac), dat2, chains = 2)
summary(fit4)
plot(conditional_effects(fit4), points = TRUE)
## End(Not run)
```

*brms*version 2.21.0 Index]