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Table 2 and Table 3 using roll conflict data.
lat 1
man 4
dim 2 2 2 2 2
mod X
A|X
B|X
C|X
D|X
dat [20 2
6 1
9 2
4 1
38 7
25 6
24 6
23 42]
*** STATISTICS ***
Number of iterations = 77
Converge criterion = 0.0000009342
Seed random values = 2131
X-squared = 2.7200 (0.8431)
L-squared = 2.7199 (0.8431)
Cressie-Read = 2.7174 (0.8434)
Dissimilarity index = 0.0386
Degrees of freedom = 6
Log-likelihood = -504.46767
Number of parameters = 9 (+1)
Sample size = 216.0
BIC(L-squared) = -29.5317
AIC(L-squared) = -9.2801
BIC(log-likelihood) = 1057.3129
AIC(log-likelihood) = 1026.9353
*** LOG-LINEAR PARAMETERS ***
* TABLE X [or P(X)] *
effect beta std err z-value exp(beta) Wald df prob
X
1 -0.4737 0.1443 -3.283 0.6227
2 0.4737 1.6060 10.78 1 0.001
* TABLE XA [or P(A|X)] *
effect beta std err z-value exp(beta) Wald df prob
A
1 -1.4724 0.9301 -1.583 0.2294
2 1.4724 4.3599 2.51 1 0.113
XA
1 1 -1.0161 0.9337 -1.088 0.3620
1 2 1.0161 2.7624
2 1 1.0161 2.7624
2 2 -1.0161 0.3620 1.18 1 0.276
* TABLE XB [or P(B|X)] *
effect beta std err z-value exp(beta) Wald df prob
B
1 -0.4828 0.2502 -1.930 0.6171
2 0.4828 1.6206 3.72 1 0.054
XB
1 1 -0.7837 0.2428 -3.228 0.4567
1 2 0.7837 2.1895
2 1 0.7837 2.1895
2 2 -0.7837 0.4567 10.42 1 0.001
* TABLE XC [or P(C|X)] *
effect beta std err z-value exp(beta) Wald df prob
C
1 -0.5087 0.3002 -1.694 0.6013
2 0.5087 1.6632 2.87 1 0.090
XC
1 1 -0.8638 0.2920 -2.958 0.4215
1 2 0.8638 2.3723
2 1 0.8638 2.3723
2 2 -0.8638 0.4215 8.75 1 0.003
* TABLE XD [or P(D|X)] *
effect beta std err z-value exp(beta) Wald df prob
D
1 0.1695 0.1641 1.033 1.1848
2 -0.1695 0.8440 1.07 1 0.302
XD
1 1 -0.7708 0.1512 -5.098 0.4626
1 2 0.7708 2.1615
2 1 0.7708 2.1615
2 2 -0.7708 0.4626 25.99 1 0.000
*** (CONDITIONAL) PROBABILITIES ***
* P(X) *
1 0.2794 (0.0581)
2 0.7206 (0.0581)
* P(A|X) *
1 | 1 0.0068 (0.0253)
2 | 1 0.9932 (0.0253)
1 | 2 0.2865 (0.0404)
2 | 2 0.7135 (0.0404)
* P(B|X) *
1 | 1 0.0736 (0.0656)
2 | 1 0.9264 (0.0656)
1 | 2 0.6461 (0.0486)
2 | 2 0.3539 (0.0486)
* P(C|X) *
1 | 1 0.0604 (0.0660)
2 | 1 0.9396 (0.0660)
1 | 2 0.6705 (0.0497)
2 | 2 0.3295 (0.0497)
* P(D|X) *
1 | 1 0.2310 (0.0952)
2 | 1 0.7690 (0.0952)
1 | 2 0.8677 (0.0383)
2 | 2 0.1323 (0.0383)
Table 4 on page 69
Independence Model:
lat 1
man 4
dim 1 2 2 2 2
lab X A B C D
mod
X
A|X
B|X
C|X
D|X
dat [20 2
6 1
9 2
4 1
38 7
25 6
24 6
23 42]
*** STATISTICS ***
Number of iterations = 2 Converge criterion = 0.0000000000 Seed random values = 1595
X-squared = 104.1071 (0.0000) L-squared = 81.0842 (0.0000) Cressie-Read = 94.3049 (0.0000) Dissimilarity index = 0.2369 Degrees of freedom = 11 Log-likelihood = -543.64982 Number of parameters = 4 (+1) Sample size = 216.0 BIC(L-squared) = 21.9562 AIC(L-squared) = 59.0842 BIC(log-likelihood) = 1108.8008 AIC(log-likelihood) = 1095.2996
Two-class LCM: See the output in the previous example
Table 5 on page 71.
Model H1: two-class LCM. See previous example.
Model H2: H1 + B & C parallel indicators
lat 1
man 4
dim 2 2 2 2 2
lab X A B C D
mod
X
A|X
B|X
C|X eq1 B|X
D|X
dat [20 2
6 1
9 2
4 1
38 7
25 6
24 6
23 42]
*** STATISTICS ***
Number of iterations = 74 Converge criterion = 0.0000008459 Seed random values = 2955
X-squared = 2.8379 (0.9441) L-squared = 2.8857 (0.9413) Cressie-Read = 2.8500 (0.9434) Dissimilarity index = 0.0401 Degrees of freedom = 8 Log-likelihood = -504.55057 Number of parameters = 7 (+1) Sample size = 216.0 BIC(L-squared) = -40.1165 AIC(L-squared) = -13.1143 BIC(log-likelihood) = 1046.7281 AIC(log-likelihood) = 1023.1011
Model H3: H2 + D equal error rate
lat 1
man 4
dim 2 2 2 2 2
lab X A B C D
mod
X
A|X
B|X
C|X eq1 B|X
D|X eq2
des [1 0 0 1]
dat [20 2
6 1
9 2
4 1
38 7
25 6
24 6
23 42]
*** STATISTICS ***
Number of iterations = 60
Converge criterion = 0.0000009450
Seed random values = 5864
X-squared = 3.6029 (0.9356)
L-squared = 3.6504 (0.9329)
Cressie-Read = 3.6133 (0.9350)
Dissimilarity index = 0.0431
Degrees of freedom = 9
Log-likelihood = -504.93290
Number of parameters = 6 (+1)
Sample size = 216.0
BIC(L-squared) = -44.7271
AIC(L-squared) = -14.3496
BIC(log-likelihood) = 1042.1175
AIC(log-likelihood) = 1021.8658
Model H4: H3 + A as perfect indicator for class 2
lat 1
man 4
dim 2 2 2 2 2
lab X A B C D
mod
X
A|X eq2
B|X
C|X eq1 B|X
D|X eq2
des [1 0 0 -1
2 0 0 2]
sta A|X [.2 .8 0 1]
dat [20 2
6 1
9 2
4 1
38 7
25 6
24 6
23 42]
*** STATISTICS ***
Number of iterations = 38
Converge criterion = 0.0000009584
Seed random values = 5607
X-squared = 3.6055 (0.9634)
L-squared = 3.6586 (0.9614)
Cressie-Read = 3.6177 (0.9629)
Dissimilarity index = 0.0430
Degrees of freedom = 10
Log-likelihood = -504.93703
Number of parameters = 5 (+1)
Sample size = 216.0
BIC(L-squared) = -50.0941
AIC(L-squared) = -16.3414
BIC(log-likelihood) = 1036.7505
AIC(log-likelihood) = 1019.8741
Table 6 on page 72 based on H4:
*** LATENT CLASS OUTPUT ***
X 1 X 2
0.7574 0.2426
A 1 0.2751 0.0000
A 2 0.7249 1.0000
B 1 0.6362 0.0463
B 2 0.3638 0.9537
C 1 0.6362 0.0463
C 2 0.3638 0.9537
D 1 0.8524 0.1476
D 2 0.1476 0.8524
Table 8 on page 75 based on data presented in Table 7.
Model H1: two-class LCM
lat 1
man 4
dim 2 2 2 2 2
lab X A B C D
mod X
A|X
B|X
C|X
D|X
dat [567 11 62 32 17 10 22 38 18 13 42 62 9 11 28 719]
*** STATISTICS ***
Number of iterations = 67 Converge criterion = 0.0000008203 Seed random values = 2814
X-squared = 214.7577 (0.0000) L-squared = 179.8535 (0.0000) Cressie-Read = 199.6028 (0.0000) Dissimilarity index = 0.0963 Degrees of freedom = 6 Log-likelihood = -2773.79306 Number of parameters = 9 (+1) Sample size = 1661.0 BIC(L-squared) = 135.3624 AIC(L-squared) = 167.8535 BIC(log-likelihood) = 5614.3227 AIC(log-likelihood) = 5565.5861
Model H2: three-class model with linear restrictions
lat 1
man 4
dim 3 2 2 2 2
lab X A B C D
mod X {X}
A|X {A,spe(XA,1b)}
B|X {B,spe(XB,1b)}
C|X {C,spe(XC,1b)}
D|X {D,spe(XD,1b)}
dat [567 11 62 32 17 10 22 38 18 13 42 62 9 11 28 719]
see 12357 ite 10000 *** STATISTICS *** Number of iterations = 8587 Converge criterion = 0.0000009999 Seed random values = 12357 X-squared = 2.3618 (0.7972) L-squared = 2.3451 (0.7996) Cressie-Read = 2.3554 (0.7981) Dissimilarity index = 0.0069 Degrees of freedom = 5 Log-likelihood = -2685.03886 Number of parameters = 10 (+1) Sample size = 1661.0 BIC(L-squared) = -34.7308 AIC(L-squared) = -7.6549 BIC(log-likelihood) = 5444.2295 AIC(log-likelihood) = 5390.0777
Model H3: H2 + A, B, C restricted to equal association
lat 1
man 4
dim 3 2 2 2 2
lab X A B C D
mod X {X}
ABC|X {A,B,C,spe(XA,XB,XC,1b)}
D|X {D,spe(XD,1b)}
dat [567 11 62 32 17 10 22 38 18 13 42 62 9 11 28 719]
ite 10000
*** STATISTICS ***
Number of iterations = 9128
Converge criterion = 0.0000009999
Seed random values = 1532
X-squared = 3.5802 (0.8267)
L-squared = 3.5897 (0.8256)
Cressie-Read = 3.5816 (0.8265)
Dissimilarity index = 0.0089
Degrees of freedom = 7
Log-likelihood = -2685.66117
Number of parameters = 8 (+1)
Sample size = 1661.0
BIC(L-squared) = -48.3165
AIC(L-squared) = -10.4103
BIC(log-likelihood) = 5430.6437
AIC(log-likelihood) = 5387.3223
Table 9 on page 77 based on model H3 in previous table
lat 1
man 4
dim 3 2 2 2 2
lab X A B C D
mod X {X}
ABC|X {A,B,C,spe(XA,XB,XC,1b)}
D|X {D,spe(XD,1b)}
dat [567 11 62 32 17 10 22 38 18 13 42 62 9 11 28 719]
ite 10000
*** LOG-LINEAR PARAMETERS ***
* TABLE X [or P(X)] *
effect beta std err z-value exp(beta) Wald df prob
X
1 0.3024 0.0489 6.186 1.3531
2 -0.4448 0.0613 -7.255 0.6409
3 0.1424 1.1531 55.16 2 0.000
* TABLE XABC [or P(ABC|X)] *
effect beta std err z-value exp(beta) Wald df prob
A
1 -0.0969 0.0827 -1.172 0.9077
2 0.0969 1.1017 1.37 1 0.241
B
1 0.1306 0.0839 1.558 1.1395
2 -0.1306 0.8776 2.43 1 0.119
C
1 -0.6152 0.0899 -6.841 0.5405
2 0.6152 1.8501 46.80 1 0.000
spe(XA,.,XC,1b)
1 -4.1065 0.2247 -18.279 0.0165 334.13 1 0.000
* TABLE XD [or P(D|X)] *
effect beta std err z-value exp(beta) Wald df prob
D
1 -0.0749 0.1008 -0.743 0.9279
2 0.0749 1.0777 0.55 1 0.458
spe(XD,1b)
1 -7.2381 ****** ***** 7.19E-0004 0.00 1 1.000
Table 10 on page 79
Model H1: {AXG, BXG, CXG, DXG}
lat 1
man 5
dim 2 2 2 2 2 2
lab X G A B C D
mod G
X|G
A|XG
B|XG
C|XG
D|XG
dat [20 2 6 1 9 2 4 1 38 7 25 6 24 6 23 42
20 3 4 3 23 3 4 2 25 6 15 6 29 5 31 37]
*** STATISTICS ***
Number of iterations = 341 Converge criterion = 0.0000009878 Seed random values = 3036
X-squared = 9.0628 (0.6976) L-squared = 8.2533 (0.7650) Cressie-Read = 8.7323 (0.7256) Dissimilarity index = 0.0443 Degrees of freedom = 12 Log-likelihood = -1324.98883 Number of parameters = 19 (+1) Sample size = 432.0 BIC(L-squared) = -64.5678 AIC(L-squared) = -15.7467 BIC(log-likelihood) = 2765.2777 AIC(log-likelihood) = 2687.9777
Model H2: {XG, AX, BX, CX, DX}
lat 1
man 5
dim 2 2 2 2 2 2
lab X G A B C D
mod G
X|G
A|X
B|X
C|X
D|X
dat [20 2 6 1 9 2 4 1 38 7 25 6 24 6 23 42
20 3 4 3 23 3 4 2 25 6 15 6 29 5 31 37]
*** STATISTICS ***
Number of iterations = 135
Converge criterion = 0.0000009252
Seed random values = 3122
X-squared = 24.7761 (0.2101)
L-squared = 23.4693 (0.2663)
Cressie-Read = 24.2359 (0.2322)
Dissimilarity index = 0.0871
Degrees of freedom = 20
Log-likelihood = -1332.59683
Number of parameters = 11 (+1)
Sample size = 432.0
BIC(L-squared) = -97.8992
AIC(L-squared) = -16.5307
BIC(log-likelihood) = 2731.9463
AIC(log-likelihood) = 2687.1937
Model H3: {G, AX, BX, CX, DX}
lat 1
man 5
dim 2 2 2 2 2 2
lab X G A B C D
mod G
X
A|X
B|X
C|X
D|X
dat [20 2 6 1 9 2 4 1 38 7 25 6 24 6 23 42
20 3 4 3 23 3 4 2 25 6 15 6 29 5 31 37]
*** STATISTICS ***
Number of iterations = 133
Converge criterion = 0.0000009886
Seed random values = 4424
X-squared = 24.8170 (0.2552)
L-squared = 23.4808 (0.3189)
Cressie-Read = 24.2661 (0.2803)
Dissimilarity index = 0.0875
Degrees of freedom = 21
Log-likelihood = -1332.60258
Number of parameters = 10 (+1)
Sample size = 432.0
BIC(L-squared) = -103.9561
AIC(L-squared) = -18.5192
BIC(log-likelihood) = 2725.8894
AIC(log-likelihood) = 2685.2052
Table 11 on page 80 based on Model H3 from previous table
lat 1
man 5
dim 2 2 2 2 2 2
lab X G A B C D
mod G
X
A|X
B|X
C|X
D|X
dat [20 2 6 1 9 2 4 1 38 7 25 6 24 6 23 42
20 3 4 3 23 3 4 2 25 6 15 6 29 5 31 37]
*** LATENT CLASS OUTPUT ***
X 1 X 2
0.2917 0.7083
G 1 0.5000 0.5000
G 2 0.5000 0.5000
A 1 0.0105 0.3454
A 2 0.9895 0.6546
B 1 0.1077 0.5668
B 2 0.8923 0.4332
C 1 0.0208 0.7170
C 2 0.9792 0.2830
D 1 0.3189 0.8491
D 2 0.6811 0.1509
Table 12 on page 81 based on Model H3 from the previous example
lat 1
man 5
dim 2 2 2 2 2 2
lab X G A B C D
mod G
X
A|X
B|X
C|X
D|X
dat [20 2 6 1 9 2 4 1 38 7 25 6 24 6 23 42
20 3 4 3 23 3 4 2 25 6 15 6 29 5 31 37]
*** LOG-LINEAR PARAMETERS *** * TABLE G [or P(G)] * effect beta std err z-value exp(beta) Wald df prob G 1 0.0000 0.0481 0.000 1.0000 2 -0.0000 1.0000 0.00 1 1.000 * TABLE X [or P(X)] * effect beta std err z-value exp(beta) Wald df prob X 1 -0.4435 0.1145 -3.874 0.6418 2 0.4435 1.5582 15.01 1 0.000 * TABLE XA [or P(A|X)] * effect beta std err z-value exp(beta) Wald df prob A 1 -1.2959 0.5554 -2.333 0.2737 2 1.2959 3.6542 5.44 1 0.020 XA 1 1 -0.9761 0.5542 -1.761 0.3768 1 2 0.9761 2.6542 2 1 0.9761 2.6542 2 2 -0.9761 0.3768 3.10 1 0.078 * TABLE XB [or P(B|X)] * effect beta std err z-value exp(beta) Wald df prob B 1 -0.4614 0.1398 -3.301 0.6304 2 0.4614 1.5863 10.90 1 0.001 XB 1 1 -0.5958 0.1376 -4.330 0.5511 1 2 0.5958 1.8146 2 1 0.5958 1.8146 2 2 -0.5958 0.5511 18.75 1 0.000 * TABLE XC [or P(C|X)] * effect beta std err z-value exp(beta) Wald df prob C 1 -0.7306 0.7089 -1.031 0.4816 2 0.7306 2.0764 1.06 1 0.303 XC 1 1 -1.1954 0.6980 -1.712 0.3026 1 2 1.1954 3.3049 2 1 1.1954 3.3049 2 2 -1.1954 0.3026 2.93 1 0.087 * TABLE XD [or P(D|X)] * effect beta std err z-value exp(beta) Wald df prob D 1 0.2422 0.0983 2.464 1.2741 2 -0.2422 0.7849 6.07 1 0.014 XD 1 1 -0.6216 0.0916 -6.784 0.5371 1 2 0.6216 1.8620 2 1 0.6216 1.8620 2 2 -0.6216 0.5371 46.02 1 0.000
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