LEM Textbook Examples
Applied Latent Class Analysis
Chapter 11 Latent Markov Chains by Rolf Langeheine and Frank van de Pol


Table 1 on page 310

  man 5
  dim 2 2 2 2 2
  lab A B C D E
  mod A 
     B|A  
     C|B eq1 B|A
     D|C eq1 C|B
     E|D eq1 D|C
  
  dat [891 176 119 106 111 60 52  92 120 64 51  67 54  50  49  176
       237 107  68 107  80 75 51 200 136 95 64 187 99 165 172 1066]


*** STATISTICS ***

  Number of iterations = 2
  Converge criterion   = 0.0000000000

  X-squared            = 1287.1450 (0.0000)
  L-squared            = 1266.0235 (0.0000)
  Cressie-Read         = 1264.6861 (0.0000)
  Dissimilarity index  = 0.2188
  Degrees of freedom   = 28
  Log-likelihood       = -15893.52403
  Number of parameters = 3 (+1)
  Sample size          = 5147.0
  BIC(L-squared)       = 1026.7307
  AIC(L-squared)       = 1210.0235
  BIC(log-likelihood)  = 31812.6866
  AIC(log-likelihood)  = 31793.0481

  Eigenvalues information matrix
   17374.2297 16434.5436  5059.7212


*** FREQUENCIES ***

  A B C D E     observed  estimated  std. res.
  1 1 1 1 1     891.000    553.838     14.327
  1 1 1 1 2     176.000    231.401     -3.642
  1 1 1 2 1     119.000     92.849      2.714
  1 1 1 2 2     106.000    235.235     -8.426
  1 1 2 1 1     111.000     92.849      1.884
  1 1 2 1 2      60.000     38.794      3.405
  1 1 2 2 1      52.000     94.388     -4.363
  1 1 2 2 2      92.000    239.132     -9.515
  1 2 1 1 1     120.000     92.849      2.818
  1 2 1 1 2      64.000     38.794      4.047
  1 2 1 2 1      51.000     15.566      8.981
  1 2 1 2 2      67.000     39.436      4.389
  1 2 2 1 1      54.000     94.388     -4.157
  1 2 2 1 2      50.000     39.436      1.682
  1 2 2 2 1      49.000     95.951     -4.793
  1 2 2 2 2     176.000    243.093     -4.303
  2 1 1 1 1     237.000    288.855     -3.051
  2 1 1 1 2     107.000    120.688     -1.246
  2 1 1 2 1      68.000     48.426      2.813
  2 1 1 2 2     107.000    122.687     -1.416
  2 1 2 1 1      80.000     48.426      4.537
  2 1 2 1 2      75.000     20.233     12.176
  2 1 2 2 1      51.000     49.228      0.253
  2 1 2 2 2     200.000    124.719      6.741
  2 2 1 1 1     136.000    293.640     -9.199
  2 2 1 1 2      95.000    122.687     -2.500
  2 2 1 2 1      64.000     49.228      2.105
  2 2 1 2 2     187.000    124.719      5.577
  2 2 2 1 1      99.000    298.504    -11.547
  2 2 2 1 2     165.000    124.719      3.607
  2 2 2 2 1     172.000    303.449     -7.546
  2 2 2 2 2    1066.000    768.792     10.719

Table 2 on page 311

 man 5
  dim 2 2 2 2 2
  lab A B C D E
  mod A 
     B|A  
     C|B 
     D|C 
     E|D 
  
  dat [891 176 119 106 111 60 52  92 120 64 51  67 54  50  49  176
       237 107  68 107  80 75 51 200 136 95 64 187 99 165 172 1066]
* P(A) *

  1              0.4348  (0.0069)
  2              0.5652  (0.0069)

* P(B|A) *

  1 | 1          0.7181  (0.0095)
  2 | 1          0.2819  (0.0095)
  1 | 2          0.3180  (0.0086)
  2 | 2          0.6820  (0.0086)

* P(C|B) *

  1 | 1          0.7152  (0.0090)
  2 | 1          0.2848  (0.0090)
  1 | 2          0.2998  (0.0090)
  2 | 2          0.7002  (0.0090)

* P(D|C) *

  1 | 1          0.7037  (0.0090)
  2 | 1          0.2963  (0.0090)
  1 | 2          0.2719  (0.0088)
  2 | 2          0.7281  (0.0088)

* P(E|D) *

  1 | 1          0.6857  (0.0092)
  2 | 1          0.3143  (0.0092)
  1 | 2          0.2383  (0.0083)
  2 | 2          0.7617  (0.0083)

Table 3 on page 315

Model 1(M) - A: simple Markov with time homogeneous transitions

  man 5
  dim 2 2 2 2 2
  lab A B C D E
  mod A 
     B|A  
     C|B eq1 B|A
     D|C eq1 C|B
     E|D eq1 D|C
  
  dat [891 176 119 106 111 60 52  92 120 64 51  67 54  50  49  176
       237 107  68 107  80 75 51 200 136 95 64 187 99 165 172 1066]

*** STATISTICS ***

  Number of iterations = 2
  Converge criterion   = 0.0000000000

  X-squared            = 1287.1450 (0.0000)
  L-squared            = 1266.0235 (0.0000)
  Cressie-Read         = 1264.6861 (0.0000)
  Dissimilarity index  = 0.2188
  Degrees of freedom   = 28
  Log-likelihood       = -15893.52403
  Number of parameters = 3 (+1)
  Sample size          = 5147.0
  BIC(L-squared)       = 1026.7307
  AIC(L-squared)       = 1210.0235
  BIC(log-likelihood)  = 31812.6866
  AIC(log-likelihood)  = 31793.0481

Model 1 (M) - Part B: simple Markov with time heterogeneous transitions

  man 5
  dim 2 2 2 2 2
  lab A B C D E
  mod A 
     B|A  
     C|B 
     D|C 
     E|D 
  
  dat [891 176 119 106 111 60 52  92 120 64 51  67 54  50  49  176
       237 107  68 107  80 75 51 200 136 95 64 187 99 165 172 1066]

*** STATISTICS ***

  Number of iterations = 2
  Converge criterion   = 0.0000000000

  X-squared            = 1239.4728 (0.0000)
  L-squared            = 1209.3446 (0.0000)
  Cressie-Read         = 1215.0281 (0.0000)
  Dissimilarity index  = 0.2188
  Degrees of freedom   = 22
  Log-likelihood       = -15865.18459
  Number of parameters = 9 (+1)
  Sample size          = 5147.0
  BIC(L-squared)       = 1021.3288
  AIC(L-squared)       = 1165.3446
  BIC(log-likelihood)  = 31807.2847
  AIC(log-likelihood)  = 31748.3692

Model 2 (MS) - Part A: Mover-Stayer with time homogeneous transitions

 lat 1
  man 5
  dim 2 2 2 2 2 2
  mod X 
      A|X
      B|XA eq2
      C|XB eq1 B|XA
      D|XC eq1 B|XA
      E|XD eq1 B|XA
  
    
    dat [891 176 119 106 111 60 52  92 120 64 51  67 54  50  49  176
         237 107  68 107  80 75 51 200 136 95 64 187 99 165 172 1066]
  
  des [1 0 2 0 -1 0 -1 0]
  sta B|XA [.3 .7 .7 .3 1 0 0 1]
  
  see 12345

*** STATISTICS ***

  Number of iterations = 20
  Converge criterion   = 0.0000007555
  Seed random values   = 12345

  X-squared            = 322.8656 (0.0000)
  L-squared            = 323.5790 (0.0000)
  Cressie-Read         = 322.0601 (0.0000)
  Dissimilarity index  = 0.0874
  Degrees of freedom   = 26
  Log-likelihood       = -15422.30179
  Number of parameters = 5 (+1)
  Sample size          = 5147.0
  BIC(L-squared)       = 101.3786
  AIC(L-squared)       = 271.5790
  BIC(log-likelihood)  = 30887.3344
  AIC(log-likelihood)  = 30854.6036

Model 2 (MS) - Part B: Mover-Stayer with time heterogeneous transitions

  lat 1
  man 5
  dim 2 2 2 2 2 2
  mod X 
      A|X
      B|XA eq2
      C|XB eq2
      D|XC eq2
      E|XD eq2
    
    dat [891 176 119 106 111 60 52  92 120 64 51  67 54  50  49  176
         237 107  68 107  80 75 51 200 136 95 64 187 99 165 172 1066]
  
  des [1 0 2 0 -1 0 -1 0
       3 0 4 0 -1 0 -1 0
       5 0 6 0 -1 0 -1 0
       7 0 8 0 -1 0 -1 0]
  sta B|XA [.3 .7 .7 .3 1 0 0 1]
  sta C|XB [.3 .7 .7 .3 1 0 0 1]
  sta D|XC [.3 .7 .7 .3 1 0 0 1]
  sta E|XD [.3 .7 .7 .3 1 0 0 1]  
  
  see 12345

*** STATISTICS ***

  Number of iterations = 20
  Converge criterion   = 0.0000008469
  Seed random values   = 12345

  X-squared            = 272.3254 (0.0000)
  L-squared            = 270.8196 (0.0000)
  Cressie-Read         = 271.2376 (0.0000)
  Dissimilarity index  = 0.0844
  Degrees of freedom   = 20
  Log-likelihood       = -15395.92208
  Number of parameters = 11 (+1)
  Sample size          = 5147.0
  BIC(L-squared)       = 99.8962
  AIC(L-squared)       = 230.8196
  BIC(log-likelihood)  = 30885.8520
  AIC(log-likelihood)  = 30813.8442

Model 3 (MM) - Part A: two-chain mixed Markov with time homogeneous transitions

 lat 1
  man 5
  dim 2 2 2 2 2 2
  mod X 
      A|X
      B|AX
      C|BX eq1 B|AX
      D|CX eq1 B|AX
      E|DX eq1 B|AX
  
    dat [891 176 119 106 111 60 52  92 120 64 51  67 54  50  49  176
         237 107  68 107  80 75 51 200 136 95 64 187 99 165 172 1066]
  
  see 12345

*** STATISTICS ***

  Number of iterations = 145
  Converge criterion   = 0.0000009866
  Seed random values   = 12345

  X-squared            = 148.9007 (0.0000)
  L-squared            = 146.1760 (0.0000)
  Cressie-Read         = 147.7271 (0.0000)
  Dissimilarity index  = 0.0668
  Degrees of freedom   = 24
  Log-likelihood       = -15333.60030
  Number of parameters = 7 (+1)
  Sample size          = 5147.0
  BIC(L-squared)       = -58.9321
  AIC(L-squared)       = 98.1760
  BIC(log-likelihood)  = 30727.0238
  AIC(log-likelihood)  = 30681.2006

Model 3 (MM) - Part B: two-chain mixed Markov with time heterogeneous transitions

 lat 1
  man 5
  dim 2 2 2 2 2 2
  mod X 
      A|X
      B|AX
      C|BX 
      D|CX 
      E|DX 
  
    dat [891 176 119 106 111 60 52  92 120 64 51  67 54  50  49  176
         237 107  68 107  80 75 51 200 136 95 64 187 99 165 172 1066]

*** STATISTICS ***

  Number of iterations = 113
  Converge criterion   = 0.0000009701
  Seed random values   = 5759

  X-squared            = 97.4952 (0.0000)
  L-squared            = 94.8786 (0.0000)
  Cressie-Read         = 96.4983 (0.0000)
  Dissimilarity index  = 0.0556
  Degrees of freedom   = 12
  Log-likelihood       = -15307.95159
  Number of parameters = 19 (+1)
  Sample size          = 5147.0
  BIC(L-squared)       = -7.6755
  AIC(L-squared)       = 70.8786
  BIC(log-likelihood)  = 30778.2804
  AIC(log-likelihood)  = 30653.9032

Model 4 (MMS) -Part A: 2 Markov and 1 Stayer chains with time homogeneous transitions

   lat 1
   man 5
   dim 3 2 2 2 2 2
   mod X 
       A|X
       B|XA eq2
       C|XB eq1 B|XA
       D|XC eq1 B|XA
       E|XD eq1 B|XA
    
    dat [891 176 119 106 111 60 52  92 120 64 51  67 54  50  49  176
         237 107  68 107  80 75 51 200 136 95 64 187 99 165 172 1066]
  
    des [1 0 2 0 3 0 4 0 -1 0 -1 0]
  
    sta B|AX [.3 .7 .3 .7  .3 .7 .3 .7 1 0 0 1]

*** STATISTICS ***

  Number of iterations = 668
  Converge criterion   = 0.0000009869
  Seed random values   = 4192

  X-squared            = 61.8818 (0.0000)
  L-squared            = 62.3440 (0.0000)
  Cressie-Read         = 61.9801 (0.0000)
  Dissimilarity index  = 0.0354
  Degrees of freedom   = 22
  Log-likelihood       = -15291.68430
  Number of parameters = 9 (+1)
  Sample size          = 5147.0
  BIC(L-squared)       = -125.6717
  AIC(L-squared)       = 18.3440
  BIC(log-likelihood)  = 30660.2841
  AIC(log-likelihood)  = 30601.3686

Model 4 (MMS) - Part B: 2 Markov and 1 Stayer chains with time heterogeneous transitions. Notice that the results below do not match with the results in the book. In particular, the BIC and the dissimilarity index don't match.

    lat 1
    man 5
    dim 3 2 2 2 2 2
    mod X 
        A|X
        B|XA eq2
        C|XB eq2
        D|XC eq2
        E|XD eq2
    
      dat [891 176 119 106 111 60 52  92 120 64 51  67 54  50  49  176
           237 107  68 107  80 75 51 200 136 95 64 187 99 165 172 1066]
  
    des [1 0  2 0  3 0  4 0 -1 0 -1 0
         5 0  6 0  7 0  8 0 -1 0 -1 0
         9 0 10 0 11 0 12 0 -1 0 -1 0
        13 0 14 0 15 0 16 0 -1 0 -1 0]
  
  sta B|XA [.3 .7 .3 .7  .3 .7 .3 .7 1 0 0 1]
  sta C|XB [.3 .7 .3 .7  .3 .7 .3 .7 1 0 0 1]
  sta D|XC [.3 .7 .3 .7  .3 .7 .3 .7 1 0 0 1]
  sta E|XD [.3 .7 .3 .7  .3 .7 .3 .7 1 0 0 1]
  
  see 123457

*** STATISTICS ***

  Number of iterations = 652
  Converge criterion   = 0.0000009941
  Seed random values   = 123457

  X-squared            = 6.5738 (0.7650)
  L-squared            = 6.5553 (0.7667)
  Cressie-Read         = 6.5660 (0.7657)
  Dissimilarity index  = 0.0092
  Degrees of freedom   = 10
  Log-likelihood       = -15263.78996
  Number of parameters = 21 (+1)
  Sample size          = 5147.0
  BIC(L-squared)       = -78.9064
  AIC(L-squared)       = -13.4447
  BIC(log-likelihood)  = 30707.0495
  AIC(log-likelihood)  = 30569.5799

Model 5 (IPIPS) - part A: 2 independence and 1 Stayer segments with time homogeneous transitions

  lat 1
  man 5
  dim 3 2 2 2 2 2
  mod X 
      A|X 
      B|AX eq2
      C|BX eq2
      D|CX eq2
      E|DX eq2
    
  dat [891 176 119 106 111 60 52  92 120 64 51  67 54  50  49  176
       237 107  68 107  80 75 51 200 136 95 64 187 99 165 172 1066]
  
  des [1 0 1 0 2 0 2 0 -1 0 0 -1 
       1 0 1 0 2 0 2 0 -1 0 0 -1
       1 0 1 0 2 0 2 0 -1 0 0 -1 
       1 0 1 0 2 0 2 0 -1 0 0 -1]
  
  sta B|AX [.3 .7 .3 .7 .3 .7 .3 .7 1 0 0 1]
  sta C|BX [.3 .7 .3 .7 .3 .7 .3 .7 1 0 0 1]
  sta D|CX [.3 .7 .3 .7 .3 .7 .3 .7 1 0 0 1]
  sta E|DX [.3 .7 .3 .7 .3 .7 .3 .7 1 0 0 1]

  see 123457

*** STATISTICS ***

  Number of iterations = 328
  Converge criterion   = 0.0000009864
  Seed random values   = 123457

  X-squared            = 135.7883 (0.0000)
  L-squared            = 130.8476 (0.0000)
  Cressie-Read         = 133.8057 (0.0000)
  Dissimilarity index  = 0.0482
  Degrees of freedom   = 24
  Log-likelihood       = -15325.93610
  Number of parameters = 7 (+1)
  Sample size          = 5147.0
  BIC(L-squared)       = -74.2605
  AIC(L-squared)       = 82.8476
  BIC(log-likelihood)  = 30711.6954
  AIC(log-likelihood)  = 30665.8722

Model 5 (IPIPS) - part B: 2 independence and 1 Stayer segments with time heterogeneous transitions

    lat 1
    man 5
    dim 3 2 2 2 2 2
    mod X 
        A|X 
        B|AX eq2
        C|BX eq2
        D|CX eq2
        E|DX eq2
    
      dat [891 176 119 106 111 60 52  92 120 64 51  67 54  50  49  176
           237 107  68 107  80 75 51 200 136 95 64 187 99 165 172 1066]
  
    des [1 0 1 0 2 0 2 0 -1 0 0 -1 
         3 0 3 0 4 0 4 0 -1 0 0 -1
         5 0 5 0 6 0 6 0 -1 0 0 -1 
         7 0 7 0 8 0 8 0 -1 0 0 -1]
  
  sta B|AX [.3 .7 .3 .7 .3 .7 .3 .7 1 0 0 1]
  sta C|BX [.3 .7 .3 .7 .3 .7 .3 .7 1 0 0 1]
  sta D|CX [.3 .7 .3 .7 .3 .7 .3 .7 1 0 0 1]
  sta E|DX [.3 .7 .3 .7 .3 .7 .3 .7 1 0 0 1]
  
  see 123457

*** STATISTICS ***

  Number of iterations = 314
  Converge criterion   = 0.0000009748
  Seed random values   = 123457

  X-squared            = 80.3806 (0.0000)
  L-squared            = 77.2374 (0.0000)
  Cressie-Read         = 79.1875 (0.0000)
  Dissimilarity index  = 0.0331
  Degrees of freedom   = 18
  Log-likelihood       = -15299.13098
  Number of parameters = 13 (+1)
  Sample size          = 5147.0
  BIC(L-squared)       = -76.5937
  AIC(L-squared)       = 41.2374
  BIC(log-likelihood)  = 30709.3622
  AIC(log-likelihood)  = 30624.2620

Model 6 (MMM) - Part A: three-chain mixed Markov with time homogeneous transitions

 lat 1
  man 5
  dim 3 2 2 2 2 2
  mod X 
      A|X
      B|AX 
      C|BX eq1 B|AX
      D|CX eq1 B|AX
      E|DX eq1 B|AX
  
    dat [891 176 119 106 111 60 52  92 120 64 51  67 54  50  49  176
         237 107  68 107  80 75 51 200 136 95 64 187 99 165 172 1066]

*** STATISTICS ***

  Number of iterations = 1666
  Converge criterion   = 0.0000009985
  Seed random values   = 4173

  X-squared            = 46.5833 (0.0007)
  L-squared            = 47.0824 (0.0006)
  Cressie-Read         = 46.7078 (0.0006)
  Dissimilarity index  = 0.0300
  Degrees of freedom   = 20
  Log-likelihood       = -15284.05348
  Number of parameters = 11 (+1)
  Sample size          = 5147.0
  BIC(L-squared)       = -123.8410
  AIC(L-squared)       = 7.0824
  BIC(log-likelihood)  = 30662.1148
  AIC(log-likelihood)  = 30590.1070

Model 6 (MMM) - Part B: three-chain mixed Markov with time heterogeneous transitions

  lat 1
  man 5
  dim 3 2 2 2 2 2
  mod X 
      A|X
      B|AX 
      C|BX 
      D|CX 
      E|DX 
  
    dat [891 176 119 106 111 60 52  92 120 64 51  67 54  50  49  176
         237 107  68 107  80 75 51 200 136 95 64 187 99 165 172 1066]

*** STATISTICS ***

  Number of iterations = 2877
  Converge criterion   = 0.0000009998
  Seed random values   = 3113

  X-squared            = 1.7243 (0.4223)
  L-squared            = 1.7080 (0.4257)
  Cressie-Read         = 1.7187 (0.4234)
  Dissimilarity index  = 0.0042
  Degrees of freedom   = 2
  Log-likelihood       = -15261.36632
  Number of parameters = 29 (+1)
  Sample size          = 5147.0
  BIC(L-squared)       = -15.3843
  AIC(L-squared)       = -2.2920
  BIC(log-likelihood)  = 30770.5716
  AIC(log-likelihood)  = 30580.7326

Model 7 (LM) - part A: latent Markov with time homogeneous transitions

 lat 5
  man 5
  dim 2 2 2 2 2 2 2 2 2 2
  lab V W X Y Z A B C D E
  mod V 
      W|V 
      X|W eq1 W|V
      Y|X eq1 W|V
      Z|Y eq1 W|V  
      A|V 
      B|W eq1 A|V
      C|X eq1 A|V
      D|Y eq1 A|V
      E|Z eq1 A|V 
    
    dat [891 176 119 106 111 60 52  92 120 64 51  67 54  50  49  176
         237 107  68 107  80 75 51 200 136 95 64 187 99 165 172 1066]

*** STATISTICS ***

  Number of iterations = 225
  Converge criterion   = 0.0000009939
  Seed random values   = 1634

  X-squared            = 243.8422 (0.0000)
  L-squared            = 235.9275 (0.0000)
  Cressie-Read         = 240.4108 (0.0000)
  Dissimilarity index  = 0.0824
  Degrees of freedom   = 26
  Log-likelihood       = -15378.47608
  Number of parameters = 5 (+1)
  Sample size          = 5147.0
  BIC(L-squared)       = 13.7271
  AIC(L-squared)       = 183.9275
  BIC(log-likelihood)  = 30799.6830
  AIC(log-likelihood)  = 30766.9522

Model 7 (LM) - part B: latent Markov with time heterogeneous transitions

 lat 5
  man 5
  dim 2 2 2 2 2 2 2 2 2 2
  lab V W X Y Z A B C D E
  mod V 
      W|V 
      X|W 
      Y|X 
      Z|Y  
      A|V
      B|W eq1 A|V
      C|X eq1 A|V
      D|Y eq1 A|V
      E|Z eq1 A|V 
    
    dat [891 176 119 106 111 60 52  92 120 64 51  67 54  50  49  176
         237 107  68 107  80 75 51 200 136 95 64 187 99 165 172 1066]

*** STATISTICS ***

  Number of iterations = 738
  Converge criterion   = 0.0000009934
  Seed random values   = 2970

  X-squared            = 131.0249 (0.0000)
  L-squared            = 130.2462 (0.0000)
  Cressie-Read         = 130.6406 (0.0000)
  Dissimilarity index  = 0.0700
  Degrees of freedom   = 20
  Log-likelihood       = -15325.63541
  Number of parameters = 11 (+1)
  Sample size          = 5147.0
  BIC(L-squared)       = -40.6772
  AIC(L-squared)       = 90.2462
  BIC(log-likelihood)  = 30745.2787
  AIC(log-likelihood)  = 30673.2708

Model 8 (LC) - Latent class model:

 lat 1
  man 5
  dim 2 2 2 2 2 2
  mod X
      A|X 
      B|X  eq1 A|X
      C|X  eq1 A|X
      D|X  eq1 A|X
      E|X  eq1 A|X
    
    dat [891 176 119 106 111 60 52  92 120 64 51  67 54  50  49  176
         237 107  68 107  80 75 51 200 136 95 64 187 99 165 172 1066]

*** STATISTICS ***

  Number of iterations = 38
  Converge criterion   = 0.0000008156
  Seed random values   = 4627

  X-squared            = 426.6019 (0.0000
  L-squared            = 414.0631 (0.0000)
  Cressie-Read         = 420.4050 (0.0000)
  Dissimilarity index  = 0.1160
  Degrees of freedom   = 28
  Log-likelihood       = -15467.54385
  Number of parameters = 3 (+1)
  Sample size          = 5147.0
  BIC(L-squared)       = 174.7704
  AIC(L-squared)       = 358.0631
  BIC(log-likelihood)  = 30960.7262
  AIC(log-likelihood)  = 30941.0877

Model 9 (LMRr) - latent Markov plus random response with time homogeneous transitions

  lat 5
  man 5
  dim 3 3 3 3 3 2 2 2 2 2
  lab V W X Y Z A B C D E
  mod V 
      W|V 
      X|W eq1 W|V
      Y|X eq1 W|V
      Z|Y eq1 W|V  
  
      A|V eq2
      B|W eq1 A|V
      C|X eq1 A|V
      D|Y eq1 A|V
      E|Z eq1 A|V 
  
    
    dat [891 176 119 106 111 60 52  92 120 64 51  67 54  50  49  176
         237 107  68 107  80 75 51 200 136 95 64 187 99 165 172 1066]
  
  des [1 0 2 0 -1 -1]
  sta A|V [.3 .7 .3 .7 .5 .5]
  
  see 123457
  ite 10000
  mit 10

*** STATISTICS ***

  Number of iterations = 7941
  Converge criterion   = 0.0000009991
  Seed random values   = 123457

  X-squared            = 116.9087 (0.0000)
  L-squared            = 112.7703 (0.0000)
  Cressie-Read         = 115.2835 (0.0000)
  Dissimilarity index  = 0.0486
  Degrees of freedom   = 21
  Log-likelihood       = -15316.89745
  Number of parameters = 10 (+1)
  Sample size          = 5147.0
  BIC(L-squared)       = -66.6993
  AIC(L-squared)       = 70.7703
  BIC(log-likelihood)  = 30719.2566
  AIC(log-likelihood)  = 30653.7949

Model 10 (LMM) - latent mixed Markov model:

lat 6
  man 5
  dim 2 2 2 2 2 2 2 2 2 2 2
  lab P V W X Y Z A B C D E
  mod P
      V|P 
      W|VP 
      X|WP eq1 W|VP
      Y|XP eq1 W|VP
      Z|YP eq1 W|VP 
      
      A|VP 
      B|WP eq1 A|VP
      C|XP eq1 A|VP
      D|YP eq1 A|VP
      E|ZP eq1 A|VP 
    
    dat [891 176 119 106 111 60 52  92 120 64 51  67 54  50  49  176
         237 107  68 107  80 75 51 200 136 95 64 187 99 165 172 1066]
  
  see 123457
  ite 10000

*** STATISTICS ***

  Number of iterations = 8041
  Converge criterion   = 0.0000009997
  Seed random values   = 123457

  X-squared            = 45.3736 (0.0010)
  L-squared            = 46.0087 (0.0008)
  Cressie-Read         = 45.5416 (0.0009)
  Dissimilarity index  = 0.0311
  Degrees of freedom   = 20
  Log-likelihood       = -15283.51666
  Number of parameters = 11 (+1)
  Sample size          = 5147.0
  BIC(L-squared)       = -124.9147
  AIC(L-squared)       = 6.0087
  BIC(log-likelihood)  = 30661.0412
  AIC(log-likelihood)  = 30589.0333

Model 11(LMS) - latent Mover-Stayer with time homogeneous transitions

  lat 6
  man 5
  dim 2 2 2 2 2 2 2 2 2 2 2
  lab P V W X Y Z A B C D E
  mod P
      V|P 
      W|VP eq2
      X|WP eq1 W|VP
      Y|XP eq1 W|VP
      Z|YP eq1 W|VP 
      
      A|VP 
      B|WP eq1 A|VP
      C|XP eq1 A|VP
      D|YP eq1 A|VP
      E|ZP eq1 A|VP 
    
    dat [891 176 119 106 111 60 52  92 120 64 51  67 54  50  49  176
         237 107  68 107  80 75 51 200 136 95 64 187 99 165 172 1066]
  
  des [1 0 2 0 -1 0 -1 0]
  sta W|VP [.3 .7 .3 .7 1 0 0 1]
   
  see 123457
  ite 10000
  
*** STATISTICS ***

  Number of iterations = 9495
  Converge criterion   = 0.0000010000
  Seed random values   = 123457

  X-squared            = 67.6133 (0.0000)
  L-squared            = 68.6580 (0.0000)
  Cressie-Read         = 67.8937 (0.0000)
  Dissimilarity index  = 0.0382
  Degrees of freedom   = 22
  Log-likelihood       = -15294.84133
  Number of parameters = 9 (+1)
  Sample size          = 5147.0
  BIC(L-squared)       = -119.3577
  AIC(L-squared)       = 24.6580
  BIC(log-likelihood)  = 30666.5982
  AIC(log-likelihood)  = 30607.6827

Model 12 (pLMS) - Part A: partially latent Mover-Stayer with time homogeneous transitions

 lat 6
  man 5
  dim 2 2 2 2 2 2 2 2 2 2 2
  lab P V W X Y Z A B C D E
  mod P
      V|P 
      W|VP eq2
      X|WP eq1 W|VP
      Y|XP eq1 W|VP
      Z|YP eq1 W|VP 
      
      A|VP eq2
      B|WP eq1 A|VP
      C|XP eq1 A|VP
      D|YP eq1 A|VP
      E|ZP eq1 A|VP 
    
    dat [891 176 119 106 111 60 52  92 120 64 51  67 54  50  49  176
         237 107  68 107  80 75 51 200 136 95 64 187 99 165 172 1066]
  
   
  des [1 0 2 0 -1 0 -1 0
       3 0 4 0 -1 0 -1 0]
  sta W|VP [.3 .7 .3 .7 1 0 0 1]
  sta A|VP [.3 .7 .3 .7 1 0 0 1]
  
  see 123457
  ite 10000

*** STATISTICS ***

  Number of iterations = 797
  Converge criterion   = 0.0000009762
  Seed random values   = 123457

  X-squared            = 122.3660 (0.0000)
  L-squared            = 119.2194 (0.0000)
  Cressie-Read         = 121.1190 (0.0000)
  Dissimilarity index  = 0.0507
  Degrees of freedom   = 24
  Log-likelihood       = -15320.12203
  Number of parameters = 7 (+1)
  Sample size          = 5147.0
  BIC(L-squared)       = -85.8886
  AIC(L-squared)       = 71.2194
  BIC(log-likelihood)  = 30700.0672
  AIC(log-likelihood)  = 30654.2441

Model 12 (pLMS) - Part B: partially latent Mover-Stayer with time heterogeneous transitions

 lat 6
  man 5
  dim 2 2 2 2 2 2 2 2 2 2 2
  lab P V W X Y Z A B C D E
  mod P
      V|P 
      W|VP eq2
      X|WP eq2
      Y|XP eq2
      Z|YP eq2
      
      A|VP eq2
      B|WP eq1 A|VP
      C|XP eq1 A|VP
      D|YP eq1 A|VP
      E|ZP eq1 A|VP
    
    dat [891 176 119 106 111 60 52  92 120 64 51  67 54  50  49  176
         237 107  68 107  80 75 51 200 136 95 64 187 99 165 172 1066]
  
   
  des [1 0 2 0 -1 0 -1 0
       3 0 4 0 -1 0 -1 0
       5 0 6 0 -1 0 -1 0
       7 0 8 0 -1 0 -1 0
       9 0 10 0 -1 0 -1 0]
     
  sta W|VP [.3 .7 .3 .7 1 0 0 1]
  sta X|WP [.3 .7 .3 .7 1 0 0 1]
  sta Y|XP [.3 .7 .3 .7 1 0 0 1]
  sta Z|YP [.3 .7 .3 .7 1 0 0 1]
  
  sta A|VP [.3 .7 .3 .7 1 0 0 1]
  
  see 123457
  ite 10000
  
*** STATISTICS ***

  Number of iterations = 1027
  Converge criterion   = 0.0000009968
  Seed random values   = 123457

  X-squared            = 10.9133 (0.8980)
  L-squared            = 10.9762 (0.8954)
  Cressie-Read         = 10.9320 (0.8972)
  Dissimilarity index  = 0.0132
  Degrees of freedom   = 18
  Log-likelihood       = -15266.00040
  Number of parameters = 13 (+1)
  Sample size          = 5147.0
  BIC(L-squared)       = -142.8549
  AIC(L-squared)       = -25.0238
  BIC(log-likelihood)  = 30643.1010
  AIC(log-likelihood)  = 30558.0008

Table 4 on page 319

Model 1: Mover-Stayer model with stationary transition probabilities

 lat 1
  man 5
  dim 2 2 2 2 2 2
  mod X 
      A|X
      B|XA eq2
      C|XB eq1 B|XA
      D|XC eq1 B|XA
      E|XD eq1 B|XA
  
    
    dat [891 176 119 106 111 60 52  92 120 64 51  67 54  50  49  176
         237 107  68 107  80 75 51 200 136 95 64 187 99 165 172 1066]
  
  des [1 0 2 0 -1 0 -1 0]
  sta B|XA [.3 .7 .7 .3 1 0 0 1]
  
  see 12345
*** (CONDITIONAL) PROBABILITIES ***

* P(X) *

  1              0.7068
  2              0.2932

* P(A|X) *

  1 | 1          0.4199
  2 | 1          0.5801
  1 | 2          0.4707
  2 | 2          0.5293

* P(B|XA) *

  1 | 1 1        0.5864
  2 | 1 1        0.4136
  1 | 1 2        0.4034
  2 | 1 2        0.5966
  1 | 2 1        1.0000 *
  2 | 2 1        0.0000 *
  1 | 2 2        0.0000 *
  2 | 2 2        1.0000 *

* P(C|XB) *

  1 | 1 1        0.5864
  2 | 1 1        0.4136
  1 | 1 2        0.4034
  2 | 1 2        0.5966
  1 | 2 1        1.0000 *
  2 | 2 1        0.0000 *
  1 | 2 2        0.0000 *
  2 | 2 2        1.0000 *

* P(D|XC) *

  1 | 1 1        0.5864
  2 | 1 1        0.4136
  1 | 1 2        0.4034
  2 | 1 2        0.5966
  1 | 2 1        1.0000 *
  2 | 2 1        0.0000 *
  1 | 2 2        0.0000 *
  2 | 2 2        1.0000 *

* P(E|XD) *

  1 | 1 1        0.5864
  2 | 1 1        0.4136
  1 | 1 2        0.4034
  2 | 1 2        0.5966
  1 | 2 1        1.0000 *
  2 | 2 1        0.0000 *
  1 | 2 2        0.0000 *
  2 | 2 2        1.0000 *

Model 2: two-chain mixed Markov model with stationary transition probabilities

  lat 1
  man 5
  dim 2 2 2 2 2 2
  mod X 
      A|X
      B|AX
      C|BX eq1 B|AX
      D|CX eq1 B|AX
      E|DX eq1 B|AX
  
    dat [891 176 119 106 111 60 52  92 120 64 51  67 54  50  49  176
         237 107  68 107  80 75 51 200 136 95 64 187 99 165 172 1066]
*** (CONDITIONAL) PROBABILITIES ***

* P(X) *

  1              0.5364  (0.0176)
  2              0.4636  (0.0176)

* P(A|X) *

  1 | 1          0.1840  (0.0116)
  2 | 1          0.8160  (0.0116)
  1 | 2          0.7250  (0.0146)
  2 | 2          0.2750  (0.0146)

* P(B|XA) *

  1 | 1 1        0.3123  (0.0234)
  2 | 1 1        0.6877  (0.0234)
  1 | 1 2        0.1838  (0.0070)
  2 | 1 2        0.8162  (0.0070)
  1 | 2 1        0.8274  (0.0075)
  2 | 2 1        0.1726  (0.0075)
  1 | 2 2        0.7139  (0.0245)
  2 | 2 2        0.2861  (0.0245)

* P(C|XB) *

  1 | 1 1        0.3123  (0.0234)
  2 | 1 1        0.6877  (0.0234)
  1 | 1 2        0.1838  (0.0070)
  2 | 1 2        0.8162  (0.0070)
  1 | 2 1        0.8274  (0.0075)
  2 | 2 1        0.1726  (0.0075)
  1 | 2 2        0.7139  (0.0245)
  2 | 2 2        0.2861  (0.0245)

* P(D|XC) *

  1 | 1 1        0.3123  (0.0234)
  2 | 1 1        0.6877  (0.0234)
  1 | 1 2        0.1838  (0.0070)
  2 | 1 2        0.8162  (0.0070)
  1 | 2 1        0.8274  (0.0075)
  2 | 2 1        0.1726  (0.0075)
  1 | 2 2        0.7139  (0.0245)
  2 | 2 2        0.2861  (0.0245)

* P(E|XD) *

  1 | 1 1        0.3123  (0.0234)
  2 | 1 1        0.6877  (0.0234)
  1 | 1 2        0.1838  (0.0070)
  2 | 1 2        0.8162  (0.0070)
  1 | 2 1        0.8274  (0.0075)
  2 | 2 1        0.1726  (0.0075)
  1 | 2 2        0.7139  (0.0245)
  2 | 2 2        0.2861  (0.0245)

Table 5 on page 321 based on the Mover-Mover-Stayer model with stationary transition probabilities

  
    lat 1
    man 5
    dim 3 2 2 2 2 2
    mod X 
        A|X
        B|XA eq2
        C|XB eq1 B|XA
        D|XC eq1 B|XA
        E|XD eq1 B|XA
    
    dat [891 176 119 106 111 60 52  92 120 64 51  67 54  50  49  176
         237 107  68 107  80 75 51 200 136 95 64 187 99 165 172 1066]
  
    des [1 0 2 0 3 0 4 0 -1 0 -1 0]
  
    sta B|AX [.3 .7 .3 .7  .3 .7 .3 .7 1 0 0 1]
*** (CONDITIONAL) PROBABILITIES ***

* P(X) *

  1              0.4239
  2              0.4215
  3              0.1545

* P(A|X) *

  1 | 1          0.1965
  2 | 1          0.8035
  1 | 2          0.6074
  2 | 2          0.3926
  1 | 3          0.6177
  2 | 3          0.3823

* P(B|XA) *

  1 | 1 1        0.2809
  2 | 1 1        0.7191
  1 | 1 2        0.1914
  2 | 1 2        0.8086
  1 | 2 1        0.7409
  2 | 2 1        0.2591
  1 | 2 2        0.6528
  2 | 2 2        0.3472
  1 | 3 1        1.0000 *
  2 | 3 1        0.0000 *
  1 | 3 2        0.0000 *
  2 | 3 2        1.0000 *

* P(C|XB) *

  1 | 1 1        0.2809
  2 | 1 1        0.7191
  1 | 1 2        0.1914
  2 | 1 2        0.8086
  1 | 2 1        0.7409
  2 | 2 1        0.2591
  1 | 2 2        0.6528
  2 | 2 2        0.3472
  1 | 3 1        1.0000 *
  2 | 3 1        0.0000 *
  1 | 3 2        0.0000 *
  2 | 3 2        1.0000 *

* P(D|XC) *

  1 | 1 1        0.2809
  2 | 1 1        0.7191
  1 | 1 2        0.1914
  2 | 1 2        0.8086
  1 | 2 1        0.7409
  2 | 2 1        0.2591
  1 | 2 2        0.6528
  2 | 2 2        0.3472
  1 | 3 1        1.0000 *
  2 | 3 1        0.0000 *
  1 | 3 2        0.0000 *
  2 | 3 2        1.0000 *

* P(E|XD) *

  1 | 1 1        0.2809
  2 | 1 1        0.7191
  1 | 1 2        0.1914
  2 | 1 2        0.8086
  1 | 2 1        0.7409
  2 | 2 1        0.2591
  1 | 2 2        0.6528
  2 | 2 2        0.3472
  1 | 3 1        1.0000 *
  2 | 3 1        0.0000 *
  1 | 3 2        0.0000 *
  2 | 3 2        1.0000 *

Table 6 on page 326

Model 1: simple Markov model

  man 5
  dim 2 2 2 2 2
  lab A B C D E
  mod A 
     B|A  
     C|B eq1 B|A
     D|C eq1 C|B
     E|D eq1 D|C
  
  dat [891 176 119 106 111 60 52  92 120 64 51  67 54  50  49  176
       237 107  68 107  80 75 51 200 136 95 64 187 99 165 172 1066]

*** (CONDITIONAL) PROBABILITIES ***

* P(A) *

  1              0.4348  (0.0069)
  2              0.5652  (0.0069)

* P(B|A) *

  1 | 1          0.7053  (0.0046)
  2 | 1          0.2947  (0.0046)
  1 | 2          0.2830  (0.0044)
  2 | 2          0.7170  (0.0044)

* P(C|B) *

  1 | 1          0.7053  (0.0046)
  2 | 1          0.2947  (0.0046)
  1 | 2          0.2830  (0.0044)
  2 | 2          0.7170  (0.0044)

* P(D|C) *

  1 | 1          0.7053  (0.0046)
  2 | 1          0.2947  (0.0046)
  1 | 2          0.2830  (0.0044)
  2 | 2          0.7170  (0.0044)

* P(E|D) *

  1 | 1          0.7053  (0.0046)
  2 | 1          0.2947  (0.0046)
  1 | 2          0.2830  (0.0044)
  2 | 2          0.7170  (0.0044)

Model 2: latent Markov model

  lat 5
  man 5
  dim 2 2 2 2 2 2 2 2 2 2
  lab V W X Y Z A B C D E
  mod V 
      W|V 
      X|W eq1 W|V
      Y|X eq1 W|V
      Z|Y eq1 W|V  
      A|V 
      B|W eq1 A|V
      C|X eq1 A|V
      D|Y eq1 A|V
      E|Z eq1 A|V 
    
    dat [891 176 119 106 111 60 52  92 120 64 51  67 54  50  49  176
         237 107  68 107  80 75 51 200 136 95 64 187 99 165 172 1066]
* P(V) *

  1              0.4453  (0.0116)
  2              0.5547  (0.0116)

* P(W|V) *

  1 | 1          0.9441  (0.0061)
  2 | 1          0.0559  (0.0061)
  1 | 2          0.0645  (0.0056)
  2 | 2          0.9355  (0.0056)

* P(X|W) *

  1 | 1          0.9441  (0.0061)
  2 | 1          0.0559  (0.0061)
  1 | 2          0.0645  (0.0056)
  2 | 2          0.9355  (0.0056)

* P(Y|X) *

  1 | 1          0.9441  (0.0061)
  2 | 1          0.0559  (0.0061)
  1 | 2          0.0645  (0.0056)
  2 | 2          0.9355  (0.0056)

* P(Z|Y) *

  1 | 1          0.9441  (0.0061)
  2 | 1          0.0559  (0.0061)
  1 | 2          0.0645  (0.0056)
  2 | 2          0.9355  (0.0056)

* P(A|V) *

  1 | 1          0.8411  (0.0073)
  2 | 1          0.1589  (0.0073)
  1 | 2          0.1526  (0.0063)
  2 | 2          0.8474  (0.0063)

* P(B|W) *

  1 | 1          0.8411  (0.0073)
  2 | 1          0.1589  (0.0073)
  1 | 2          0.1526  (0.0063)
  2 | 2          0.8474  (0.0063)

* P(C|X) *

  1 | 1          0.8411  (0.0073)
  2 | 1          0.1589  (0.0073)
  1 | 2          0.1526  (0.0063)
  2 | 2          0.8474  (0.0063)

* P(D|Y) *

  1 | 1          0.8411  (0.0073)
  2 | 1          0.1589  (0.0073)
  1 | 2          0.1526  (0.0063)
  2 | 2          0.8474  (0.0063)

* P(E|Z) *

  1 | 1          0.8411  (0.0073)
  2 | 1          0.1589  (0.0073)
  1 | 2          0.1526  (0.0063)
  2 | 2          0.8474  (0.0063)

Table 7 on page 328 based on the latent Markov model with random response

  lat 5
  man 5
  dim 3 3 3 3 3 2 2 2 2 2
  lab V W X Y Z A B C D E
  mod V 
      W|V 
      X|W eq1 W|V
      Y|X eq1 W|V
      Z|Y eq1 W|V  
  
      A|V eq2
      B|W eq1 A|V
      C|X eq1 A|V
      D|Y eq1 A|V
      E|Z eq1 A|V 
  
    
    dat [891 176 119 106 111 60 52  92 120 64 51  67 54  50  49  176
         237 107  68 107  80 75 51 200 136 95 64 187 99 165 172 1066]
  
  des [1 0 2 0 -1 -1]
  sta A|V [.3 .7 .3 .7 .5 .5]
  
  see 123457
  ite 10000
  mit 10
*** (CONDITIONAL) PROBABILITIES ***

* P(V) *

  1              0.3536
  2              0.2412
  3              0.4051

* P(W|V) *

  1 | 1          0.9583
  2 | 1          0.0125
  3 | 1          0.0292
  1 | 2          0.0207
  2 | 2          0.9267
  3 | 2          0.0526
  1 | 3          0.0441
  2 | 3          0.0881
  3 | 3          0.8678

* P(X|W) *

  1 | 1          0.9583
  2 | 1          0.0125
  3 | 1          0.0292
  1 | 2          0.0207
  2 | 2          0.9267
  3 | 2          0.0526
  1 | 3          0.0441
  2 | 3          0.0881
  3 | 3          0.8678

* P(Y|X) *

  1 | 1          0.9583
  2 | 1          0.0125
  3 | 1          0.0292
  1 | 2          0.0207
  2 | 2          0.9267
  3 | 2          0.0526
  1 | 3          0.0441
  2 | 3          0.0881
  3 | 3          0.8678

* P(Z|Y) *

  1 | 1          0.9583
  2 | 1          0.0125
  3 | 1          0.0292
  1 | 2          0.0207
  2 | 2          0.9267
  3 | 2          0.0526
  1 | 3          0.0441
  2 | 3          0.0881
  3 | 3          0.8678

* P(A|V) *

  1 | 1          0.0926
  2 | 1          0.9074
  1 | 2          0.9422
  2 | 2          0.0578
  1 | 3          0.5000
  2 | 3          0.5000

* P(B|W) *

  1 | 1          0.0926
  2 | 1          0.9074
  1 | 2          0.9422
  2 | 2          0.0578
  1 | 3          0.5000
  2 | 3          0.5000

* P(C|X) *

  1 | 1          0.0926
  2 | 1          0.9074
  1 | 2          0.9422
  2 | 2          0.0578
  1 | 3          0.5000
  2 | 3          0.5000

* P(D|Y) *

  1 | 1          0.0926
  2 | 1          0.9074
  1 | 2          0.9422
  2 | 2          0.0578
  1 | 3          0.5000
  2 | 3          0.5000

* P(E|Z) *

  1 | 1          0.0926
  2 | 1          0.9074
  1 | 2          0.9422
  2 | 2          0.0578
  1 | 3          0.5000
  2 | 3          0.5000

Table 8 on page 331 based on the partially latent Mover-Stayer model with nonstationary transition probabilities

  
  lat 6
  man 5
  dim 2 2 2 2 2 2 2 2 2 2 2
  lab P V W X Y Z A B C D E
  mod P
      V|P 
      W|VP eq2
      X|WP eq2
      Y|XP eq2
      Z|YP eq2
      
      A|VP eq2
      B|WP eq1 A|VP
      C|XP eq1 A|VP
      D|YP eq1 A|VP
      E|ZP eq1 A|VP
    
    dat [891 176 119 106 111 60 52  92 120 64 51  67 54  50  49  176
         237 107  68 107  80 75 51 200 136 95 64 187 99 165 172 1066]
  
   
  des [1 0 2 0 -1 0 -1 0
       3 0 4 0 -1 0 -1 0
       5 0 6 0 -1 0 -1 0
       7 0 8 0 -1 0 -1 0
       9 0 10 0 -1 0 -1 0]
     
  sta W|VP [.3 .7 .3 .7 1 0 0 1]
  sta X|WP [.3 .7 .3 .7 1 0 0 1]
  sta Y|XP [.3 .7 .3 .7 1 0 0 1]
  sta Z|YP [.3 .7 .3 .7 1 0 0 1]
  
  sta A|VP [.3 .7 .3 .7 1 0 0 1]
  
  see 123457
  ite 10000
*** (CONDITIONAL) PROBABILITIES ***

* P(P) *

  1              0.8336
  2              0.1664

* P(V|P) *

  1 | 1          0.6248
  2 | 1          0.3752
  1 | 2          0.6038
  2 | 2          0.3962

* P(W|PV) *

  1 | 1 1        0.8111
  2 | 1 1        0.1889
  1 | 1 2        0.0167
  2 | 1 2        0.9833
  1 | 2 1        1.0000 *
  2 | 2 1        0.0000 *
  1 | 2 2        0.0000 *
  2 | 2 2        1.0000 *

* P(X|PW) *

  1 | 1 1        0.8922
  2 | 1 1        0.1078
  1 | 1 2        0.0618
  2 | 1 2        0.9382
  1 | 2 1        1.0000 *
  2 | 2 1        0.0000 *
  1 | 2 2        0.0000 *
  2 | 2 2        1.0000 *

* P(Y|PX) *

  1 | 1 1        0.9478
  2 | 1 1        0.0522
  1 | 1 2        0.1037
  2 | 1 2        0.8963
  1 | 2 1        1.0000 *
  2 | 2 1        0.0000 *
  1 | 2 2        0.0000 *
  2 | 2 2        1.0000 *

* P(Z|PY) *

  1 | 1 1        1.0000
  2 | 1 1        0.0000
  1 | 1 2        0.1299
  2 | 1 2        0.8701
  1 | 2 1        1.0000 *
  2 | 2 1        0.0000 *
  1 | 2 2        0.0000 *
  2 | 2 2        1.0000 *

* P(A|PV) *

  1 | 1 1        0.1743
  2 | 1 1        0.8257
  1 | 1 2        0.7787
  2 | 1 2        0.2213
  1 | 2 1        1.0000 *
  2 | 2 1        0.0000 *
  1 | 2 2        0.0000 *
  2 | 2 2        1.0000 *

* P(B|PW) *

  1 | 1 1        0.1743
  2 | 1 1        0.8257
  1 | 1 2        0.7787
  2 | 1 2        0.2213
  1 | 2 1        1.0000 *
  2 | 2 1        0.0000 *
  1 | 2 2        0.0000 *
  2 | 2 2        1.0000 *

* P(C|PX) *

  1 | 1 1        0.1743
  2 | 1 1        0.8257
  1 | 1 2        0.7787
  2 | 1 2        0.2213
  1 | 2 1        1.0000 *
  2 | 2 1        0.0000 *
  1 | 2 2        0.0000 *
  2 | 2 2        1.0000 *

* P(D|PY) *

  1 | 1 1        0.1743
  2 | 1 1        0.8257
  1 | 1 2        0.7787
  2 | 1 2        0.2213
  1 | 2 1        1.0000 *
  2 | 2 1        0.0000 *
  1 | 2 2        0.0000 *
  2 | 2 2        1.0000 *

* P(E|PZ) *

  1 | 1 1        0.1743
  2 | 1 1        0.8257
  1 | 1 2        0.7787
  2 | 1 2        0.2213
  1 | 2 1        1.0000 *
  2 | 2 1        0.0000 *
  1 | 2 2        0.0000 *
  2 | 2 2        1.0000 *

Table 9 on page 334 for multiple group analysis

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