model_fitting.md
In RprobitB: Bayesian Probit Choice Modeling

setting prior parameter works

Code
  prior
Output
  $eta
  [1] 0

  $Psi
       [,1]
  [1,]    1

  $delta
  [1] 1

  $xi
  [1] 0 0

  $D
       [,1] [,2]
  [1,]    1    0
  [2,]    0    1

  $nu
  [1] 4

  $Theta
       [,1] [,2]
  [1,]    1    0
  [2,]    0    1

  $kappa
  [1] 4

  $E
       [,1] [,2]
  [1,]    1    0
  [2,]    0    1

  $zeta
  [1] NA

  $Z
  [1] NA

  attr(,"class")
  [1] "RprobitB_prior" "list"

setting of initial Gibbs values works

Code
  init
Output
  $alpha0
  [1] 0

  $z0
  [1] 1 1

  $m0
  [1] 1 1

  $b0
       [,1] [,2]
  [1,]    0    0
  [2,]    0    0

  $Omega0
       [,1] [,2]
  [1,]    1    1
  [2,]    0    0
  [3,]    0    0
  [4,]    1    1

  $beta0
       [,1] [,2]
  [1,]    0    0
  [2,]    0    0

  $U0
       [,1] [,2] [,3] [,4] [,5] [,6]
  [1,]    0    0    0    0    0    0
  [2,]    0    0    0    0    0    0

  $Sigma0
       [,1] [,2]
  [1,]    1    0
  [2,]    0    1

  $d0
  [1] NA

RprobitB_latent_class setting works

Code
  RprobitB_latent_classes(list(C = 2))
Output
  Latent classes
  C = 2

Code
  (out <- RprobitB_latent_classes(list(weight_update = TRUE, dp_update = TRUE)))
Output
  Latent classes
  DP-based update: TRUE 
  Weight-based update: TRUE 
  Initial classes: 1 
  Maximum classes: 10 
  Updating buffer: 100 
  Minimum class weight: 0.01 
  Maximum class weight: 0.99 
  Mimumum class distance: 0.1

Code
  str(out)
Output
  List of 9
   $ weight_update: logi TRUE
   $ dp_update    : logi TRUE
   $ C            : num 1
   $ Cmax         : num 10
   $ buffer       : num 100
   $ epsmin       : num 0.01
   $ epsmax       : num 0.99
   $ distmin      : num 0.1
   $ class_update : logi TRUE
   - attr(*, "class")= chr "RprobitB_latent_classes"

building of RprobitB_normalization works

Code
  RprobitB_normalization(level = "B", scale = "price := -1", form = form, re = re,
    alternatives = alternatives, base = "B")
Output
  Level: Utility differences with respect to alternative 'B'.
  Scale: Coefficient of effect 'price' (alpha_1) fixed to -1.

Gibbs sampling works

Code
  print(model)
Output
  Probit model 'choice ~ a | b | c'.

Code
  summary(model)
Output
  Probit model
  Formula: choice ~ a | b | c 
  R: 2000, B: 1000, Q: 1
  Level: Utility differences with respect to alternative 'B'.
  Scale: Coefficient of the 1. error term variance fixed to 1.

  Gibbs sample statistics
            true    mean      sd      R^
   alpha

       1   -0.49   -0.50    0.04    1.00
       2   -0.28   -0.31    0.04    1.00
       3    0.14    0.15    0.04    1.00
       4    0.85    0.88    0.06    1.00
       5   -0.64   -0.52    0.05    1.01

   Sigma

     1,1    1.00    1.00    0.00    1.00

Code
  print(coef(model))
Output
           Estimate   (sd)
  1     a     -0.50 (0.04)
  2   b_A     -0.31 (0.04)
  3 ASC_A      0.15 (0.04)
  4   c_A      0.88 (0.06)
  5   c_B     -0.52 (0.05)

Ordered probit model estimation works

Code
  print(model)
Output
  Probit model 'opinion_on_sth ~ age + gender'.

Code
  summary(model)
Output
  Probit model
  Formula: opinion_on_sth ~ age + gender 
  R: 1000, B: 500, Q: 1
  Level: Fixed first utility threshold to 0.
  Scale: Error term variance fixed to 1.

  Gibbs sample statistics
            true    mean      sd      R^
   alpha

       1   -0.95   -1.07    0.05    1.00
       2   -0.55   -0.88    0.08    1.00

   Sigma

     1,1    1.00    1.00    0.00     NaN

   d

       1    0.91    0.45    0.03    1.87
       2    0.20   -0.40    0.07    1.33
       3    0.90    0.46    0.07    1.12

Code
  print(coef(model))
Output
            Estimate   (sd)
  1    age     -1.07 (0.05)
  2 gender     -0.88 (0.08)

Ranked probit model estimation works

Code
  print(model)
Output
  Probit model 'product ~ price'.

Code
  summary(model)
Output
  Probit model
  Formula: product ~ price 
  R: 1000, B: 500, Q: 1
  Level: Utility differences with respect to alternative 'C'.
  Scale: Coefficient of the 1. error term variance fixed to 1.

  Gibbs sample statistics
            true    mean      sd      R^
   alpha

       1   -0.53   -0.48    0.03    1.02
       2   -0.30   -0.28    0.04    1.05
       3    0.15    0.16    0.03    1.00

   Sigma

     1,1    1.00    1.00    0.00    1.00
     1,2   -0.24   -0.26    0.04    1.06
     2,2    0.58    0.48    0.08    1.07

Code
  print(coef(model))
Output
           Estimate   (sd)
  1 price     -0.48 (0.03)
  2 ASC_A     -0.28 (0.04)
  3 ASC_B      0.16 (0.03)

computation of sufficient statistics works

Code
  ss
Output
  $N
  [1] 2

  $T
  [1] 1 2

  $J
  [1] 3

  $P_f
  [1] 3

  $P_r
  [1] 2

  $Tvec
  [1] 1 2

  $csTvec
  [1] 0 1

  $W
  $W[[1]]
              v1 ASC_A ASC_B
  [1,] -1.113883     1     0
  [2,]  1.107852     0     1

  $W[[2]]
               v1 ASC_A ASC_B
  [1,] -0.5546814     1     0
  [2,] -0.4088169     0     1

  $W[[3]]
             v1 ASC_A ASC_B
  [1,] -1.41141     1     0
  [2,] -1.39625     0     1


  $X
  $X[[1]]
             v2_A       v2_B
  [1,] -0.3053884  0.0000000
  [2,]  0.0000000 -0.3053884

  $X[[2]]
           v2_A     v2_B
  [1,] 1.511781 0.000000
  [2,] 0.000000 1.511781

  $X[[3]]
            v2_A      v2_B
  [1,] 0.3898432 0.0000000
  [2,] 0.0000000 0.3898432


  $y
       [,1] [,2]
  [1,]    1   NA
  [2,]    1    1

  $WkW
             [,1]       [,2]       [,3]       [,4]
   [1,]  3.540485  0.9634269  0.9634269  3.3439801
   [2,] -3.079974  0.0000000 -0.6972149  0.0000000
   [3,]  0.000000 -3.0799742  0.0000000 -0.6972149
   [4,] -3.079974 -0.6972149  0.0000000  0.0000000
   [5,]  3.000000  0.0000000  0.0000000  0.0000000
   [6,]  0.000000  3.0000000  0.0000000  0.0000000
   [7,]  0.000000  0.0000000 -3.0799742 -0.6972149
   [8,]  0.000000  0.0000000  3.0000000  0.0000000
   [9,]  0.000000  0.0000000  0.0000000  3.0000000

  $XkX
  $XkX[[1]]
             [,1]       [,2]       [,3]       [,4]
  [1,] 0.09326207 0.00000000 0.00000000 0.00000000
  [2,] 0.00000000 0.09326207 0.00000000 0.00000000
  [3,] 0.00000000 0.00000000 0.09326207 0.00000000
  [4,] 0.00000000 0.00000000 0.00000000 0.09326207

  $XkX[[2]]
          [,1]    [,2]    [,3]    [,4]
  [1,] 2.43746 0.00000 0.00000 0.00000
  [2,] 0.00000 2.43746 0.00000 0.00000
  [3,] 0.00000 0.00000 2.43746 0.00000
  [4,] 0.00000 0.00000 0.00000 2.43746


  $rdiff
  [1] NA