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Binomial random walk model

Source: R/model_doc.R
BinRW.Rd

This is a state-space model defined by a Binomial measurement error and a latent random walk. For more details see the vignette.

Arguments

max_score

Maximum value that the score can take

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.

Parameters

Population parameters:

  • sigma: Standard deviation of the random walk (in logit scale)

  • mu_logit_y0: Population mean of the initial condition (in logit scale)

  • sigma_logit_y0: Population standard deviation of the initial condition (logit scale)

Patient-dependent parameters:

  • logit_y0: Logit of the initial condition

Observation-dependent (patient- and time-dependent) parameters:

  • y_lat: Latent score (probability)

  • logit_lat: logit of y_lat

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

Priors

The priors are passed as a named list with elements sigma, mu_logit_y0 and sigma_logit_y0 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 ~ normal+(x1, x2).

  • mu_logit_y0 ~ normal(x1, x2)

  • sigma_logit_y0 ~ normal+(x1, x2)

NB: For sigma and sigma_logit_y0, usually x1=0 to define a half-normal distribution since the parameters are constrained to be positive.

Default priors

  • The default priors do not depend on max_score, and are printed in the examples section.

  • The default prior for sigma translates to an odd ratio increment of at most 5 (~ 2 * upper bound of prior).

  • The default priors for mu_logit_y0 and sigma_logit_y0 translates to an approximately uniform prior on y0.

Examples

EczemaModel("BinRW", max_score = 100)
#> BinRW model (discrete)
#> max_score = 100 
#> Prior: 
#> - sigma ~ normal+(0,0.4)
#> - mu_logit_y0 ~ normal(0,1)
#> - sigma_logit_y0 ~ normal(0,1.5)