Update latent classes

Low-level sampler kernels for class weights, allocations, sizes, the weight-based class update, and Dirichlet-process class updates.

Usage

sample_allocation(prob)

update_s(delta, m)

update_z(s, beta, b, Omega)

update_m(C, z, non_zero = FALSE)

update_classes_wb(
  s,
  b,
  Omega,
  epsmin = 0.01,
  epsmax = 0.7,
  deltamin = 0.1,
  deltashift = 0.5,
  identify_classes = FALSE,
  Cmax = 10L
)

update_classes_dp(
  beta,
  z,
  b,
  Omega,
  delta,
  mu_b_0,
  Sigma_b_0,
  n_Omega_0,
  V_Omega_0,
  identify_classes = FALSE,
  Cmax = 10L
)

Arguments

prob

[numeric(C)]
Class probabilities.

delta

[numeric(1)]
Dirichlet concentration parameter.

m

[numeric(C)]
Class sizes.

s

[numeric(C)]
Class weights.

beta

[matrix(P, N)]
Individual coefficient draws in columns.

b

[matrix(P, C)]
Class means in columns.

Omega

[matrix(P * P, C)]
Vectorized class covariance matrices in columns.

C

[integer(1)]
Number of classes.

z

[numeric(N)]
Class allocations numbered from one to C.

non_zero

[logical(1)]
Replace empty class sizes by one?

epsmin

[numeric(1)]
Remove the smallest class when its weight is below this threshold.

epsmax

[numeric(1)]
Split the largest class when its weight exceeds this threshold.

deltamin

[numeric(1)]
Merge the two closest classes when the Euclidean distance between their means is below this threshold.

deltashift

[numeric(1)]
Scale of the mean displacement along the leading covariance eigenvector after splitting a class.

identify_classes

[logical(1)]
Order the current active classes by size?

Cmax

[integer(1)]
Maximum number of classes.

mu_b_0

[numeric(P)]
Prior mean for class means.

Sigma_b_0

[matrix(P, P)]
Prior covariance for class means.

n_Omega_0

[integer(1)]
Prior degrees of freedom for class covariances.

V_Omega_0

[matrix(P, P)]
Prior scale matrix for class covariances.

Value

The functions return one sampler update:

• sample_allocation(): an integer class label.

• update_s(): a C by 1 numeric matrix of class weights.

• update_z(): an N by 1 numeric matrix of allocations.

• update_m(): a C by 1 numeric matrix of class sizes.

• update_classes_wb(): a list with s, b, Omega, and update_type, where the latter is zero for no update, one for removal, two for splitting, and three for merging.

• update_classes_dp(): a list with z, b, Omega, and C.

References

Neal RM (2000). “Markov Chain Sampling Methods for Dirichlet Process Mixture Models.” Journal of Computational and Graphical Statistics, 9(2), 249–265. doi:10.1080/10618600.2000.10474879 .

Oelschläger L, Bauer D (2021). “Bayes Estimation of Latent Class Mixed Multinomial Probit Models.” In Proceedings of the 100th Annual Meeting of the Transportation Research Board. https://trid.trb.org/view/1759753.

Examples

### a latent class state of six deciders with one random coefficient
set.seed(1)
beta <- matrix(c(-1, -1.2, -0.8, 1, 1.3, 0.9), nrow = 1)
b <- matrix(c(-1, 1), nrow = 1)
Omega <- matrix(c(0.2, 0.2), nrow = 1)

### the weights, the allocations, and the class sizes are drawn in turn
s <- update_s(delta = 1, m = c(3, 3))
z <- update_z(s, beta, b, Omega)
m <- update_m(C = 2, z = z)
sample_allocation(c(0.5, 0.3, 0.2))
#> [1] 1

### the weight-based update splits a class that grew too large
update_classes_wb(s = c(0.9, 0.1), b = b, Omega = Omega)
#> $s
#> [1] 0.45 0.45 0.10
#> 
#> $b
#>            [,1]      [,2] [,3]
#> [1,] -0.7763932 -1.223607    1
#> 
#> $Omega
#>      [,1] [,2] [,3]
#> [1,]  0.2  0.2  0.2
#> 
#> $update_type
#> [1] 2
#> 

### the Dirichlet process update draws the class count from the data
update_classes_dp(
  beta = beta, z = z, b = b, Omega = Omega, delta = 1,
  mu_b_0 = 0, Sigma_b_0 = diag(1), n_Omega_0 = 4, V_Omega_0 = diag(1)
)
#> $z
#>      [,1]
#> [1,]    1
#> [2,]    1
#> [3,]    1
#> [4,]    2
#> [5,]    2
#> [6,]    2
#> 
#> $b
#>            [,1]      [,2]
#> [1,] -0.8195659 0.7048773
#> 
#> $Omega
#>            [,1]      [,2]
#> [1,] 0.09673685 0.6384678
#> 
#> $C
#> [1] 2
#>