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Mixed effect autoregressive model (order 1)

Source: R/model_doc.R
MixedAR1.Rd

Mixed effect autoregressive model (order 1)

Arguments

max_score

Maximum value that the score can take. Note that even if discrete=FALSE, max_score must be an integer.

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).

  • Unlike the AR1 model, the discretisation of predictions is not implemented

  • For more details see the vignette.

Parameters

Population parameters:

  • sigma: Standard deviation of the autoregression

  • mu_logit_slope: Population mean of the logit of slope

  • sigma_logit_slope: Population standard deviation of the logit of slope

  • mu_inf: Population mean of y_inf

  • sigma_inf: Population standard deviation of y_inf

Patient-dependent parameters:

  • slope: Autocorrelation parameter

  • y_inf: Autoregression mean

  • intercept: Intercept

Other parameters:

  • y_mis: Missing values

See list_parameters(model = "MixedAR1") for more details.

Priors

The priors are passed as a named list with elements sigma, mu_logit_slope, sigma_logit_slope, mu_inf, sigma_inf 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).

  • mu_logit_slope ~ normal(x1, x2).

  • sigma_logit_slope ~ normal+(x1, x2).

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

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

NB: For sigma, sigma_logit_slope and sigma_inf, usually x1=0 to define a half-normal distribution since the parameter is constrained to 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 priors for mu_logit_slope and sigma_logit_slope have "reasonable" ranges and translate to a prior on slope that is approximately uniform.

  • The default prior for mu_inf spans the entire range of the score.

  • The default prior for sigma_inf translates to a range in the distribution of y_inf to be at most max_score.

Examples

EczemaModel("MixedAR1", max_score = 100)
#> MixedAR1 model (continuous)
#> max_score = 100 
#> Prior: 
#> - sigma / max_score ~ normal+(0,0.1)
#> - mu_logit_slope ~ normal(0,1)
#> - sigma_logit_slope ~ normal+(0,1.5)
#> - mu_inf / max_score ~ normal(0.5,0.25)
#> - sigma_inf / max_score ~ normal+(0.5,0.25)