# mcmc: Perform Markov chain Monte Carlo simulation for fitting a... In RprobitB: Bayes Estimation of Latent Class Mixed Multinomial Probit Models

## Description

This function performs Markov chain Monte Carlo simulation for fitting a (latent class) (mixed) (multinomial) probit model to discrete choice data.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```mcmc( data, scale = list(parameter = "s", index = 1, value = 1), R = 10000, B = R/2, Q = 1, print_progress = TRUE, prior = NULL, latent_classes = NULL, seed = NULL ) ```

## Arguments

 `data` An object of class `RprobitB_data`. `scale` A named list of three elements, determining the parameter normalization with respect to the utility scale: `parameter`: Either `"a"` (for a linear coefficient of `"alpha"`) or `"s"` (for a variance of the error-term covariance matrix `"Sigma"`). `index`: The index of the parameter that gets fixed. `value`: The value for the fixed parameter. `R` The number of iterations of the Gibbs sampler. `B` The length of the burn-in period, i.e. a non-negative number of samples to be discarded. `Q` The thinning factor for the Gibbs samples, i.e. only every `Q`th sample is kept. `print_progress` A boolean, determining whether to print the Gibbs sampler progress and the estimated remaining computation time. `prior` A named list of parameters for the prior distributions of the normalized parameters: `eta`: The mean vector of length `P_f` of the normal prior for `alpha`. `Psi`: The covariance matrix of dimension `P_f` x `P_f` of the normal prior for `alpha`. `delta`: The concentration parameter of length 1 of the Dirichlet prior for `s`. `xi`: The mean vector of length `P_r` of the normal prior for each `b_c`. `D`: The covariance matrix of dimension `P_r` x `P_r` of the normal prior for each `b_c`. `nu`: The degrees of freedom (a natural number greater than `P_r`) of the Inverse Wishart prior for each `Omega_c`. `Theta`: The scale matrix of dimension `P_r` x `P_r` of the Inverse Wishart prior for each `Omega_c`. `kappa`: The degrees of freedom (a natural number greater than `J-1`) of the Inverse Wishart prior for `Sigma`. `E`: The scale matrix of dimension `J-1` x `J-1` of the Inverse Wishart prior for `Sigma`. `latent_classes` Either `NULL` or a list of parameters specifying the number and the latent classes: `C`: The number (greater or equal 1) of latent classes, which is set to 1 per default and is ignored if `P_r = 0`. If `update = TRUE`, `C` equals the initial number of classes. `update`: A boolean, determining whether to update `C`. Ignored if `P_r = 0`. If `update = FALSE`, all of the following elements are ignored. `Cmax`: The maximum number of latent classes. `buffer`: The updating buffer (number of iterations to wait before the next update). `epsmin`: The threshold weight for removing latent classes (between 0 and 1). `epsmax`: The threshold weight for splitting latent classes (between 0 and 1). `distmin`: The threshold difference in means for joining latent classes (non-negative). `seed` Set a seed for the Gibbs sampling.

## Details

See the vignette "Model fitting" for more details: `vignette("model_fitting", package = "RprobitB")`.

## Value

An object of class `RprobitB_model`.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23``` ```## Not run: ### probit model p = simulate(form = choice ~ var | 0, N = 100, T = 10, J = 2, seed = 1) m1 = mcmc(data = p, seed = 1) ### multinomial probit model mnp = simulate(form = choice ~ var | 0, N = 100, T = 10, J = 3, seed = 1) m2 = mcmc(data = mnp, seed = 1) ### mixed multinomial probit model mmnp = simulate(form = choice ~ 0 | var, N = 100, T = 10, J = 3, re = "var", seed = 1) m3 = mcmc(data = mmnp, seed = 1) ### mixed multinomial probit model with 2 latent classes lcmmnp = simulate(form = choice ~ 0 | var, N = 100, T = 10, J = 3, re = "var", seed = 1, C = 2) m4 = mcmc(data = lcmmnp, latent_classes = list("C" = 2), seed = 1) ### update of latent classes m5 = mcmc(data = lcmmnp, latent_classes = list("update" = TRUE), seed = 1) ## End(Not run) ```

RprobitB documentation built on Nov. 12, 2021, 5:08 p.m.