Description Usage Arguments Details Value See Also Examples

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.

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`...` |
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 |

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. Any finite sample
realized from this stochastic process is jointly multivariate
normal, with a covariance matrix defined by the covariance
kernel *k_p(x)*, where *p* is the vector of parameters
of the GP:

*f(x) ~ MVN(0, k_p(x))*

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.

An object of class `'gp_term'`

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

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 | ```
## 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)
``` |

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