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Autoregressive model (order 1)

Source: R/model_doc.R
AR1.Rd

Autoregressive model (order 1)

Arguments

max_score

Maximum value that the score can take

discrete

Whether to use a discrete normal distribution. This will be used to check whether the data is discrete or not, and for rounding predictions (cf. testing).

prior

Named list of the model's priors. If NULL, uses the default prior for the model (see default_prior()).

Details

  • Details of the model are available in the paper.

  • The model takes as input a continuous score defined between 0 and max_score.

  • The model is naive as the likelihood is non-truncated and not discretised (when discrete = TRUE). As a result, sampling from the prior predictive distribution can be challenging if the score is near the bounds and the variance is sufficiently large.

  • For more details see the vignette.

  • The model is naive as it is trained with a non-truncated distribution

  • For more details see the vignette.

Parameters

  • sigma: Standard deviation of the autoregression

  • slope: Autocorrelation parameter

  • intercept: Intercept

  • y_inf: Autoregression mean

  • y_mis: Missing values

See list_parameters(model = "AR1") for more details.

Priors

The priors are passed as a named list with elements sigma, y_inf and slope specifying priors for the corresponding parameters. Each element of the list should be a vector of length 2, containing values for x1 and x2, x2 > 0, such as:

  • sigma / max_score ~ normal+(x1, x2).

  • y_inf / max_score ~ normal(x1, x2).

  • slope ~ beta(x1, x2).

NB: For sigma, usually x1=0 to define a half-normal distribution since the parameter is constrained to be positive. NB: For slope, both x1 and x2 must be positive.

Default priors

  • The default prior for sigma translates to a width of the predictive distribution to be at most max_score.

  • The default prior for y_inf covers the full range of the score.

  • The default prior for slope is uniform in 0-1.

Examples

EczemaModel("AR1", max_score = 100)
#> AR1 model (continuous)
#> max_score = 100 
#> Prior: 
#> - sigma / max_score ~ normal+(0,0.1)
#> - slope ~ beta(1,1)
#> - y_inf / max_score ~ normal(0.5,0.25)