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The data set can be downloaded following the link here.
Expected frequencies of Table 1 on page 310 based on the simple Markov model with time homogeneous transition probabilities.
data: file is chap11.dat;
variable: names are u1 u2 u3 u4 u5 count group; missing are all (-9999) ; usevariables are u1 u2 u3 u4 u5 count; weight is count (freq); categorical are u1 u2 u3 u4 u5; classes = c1(2) c2(2) c3(2) c4(2) c5(2);
analysis: type = mixture;
model:
%overall%
c2#1 on c1#1 (1);
c3#1 on c2#1 (1);
c4#1 on c3#1 (1);
c5#1 on c4#1 (1);
[c1#1];
[c2#1 c3#1 c4#1 c5#1] (2);
model c1:
%c1#1%
[u1$1@-15];
%c1#2%
[u1$1@15];
model c2:
%c2#1%
[u2$1@-15];
%c2#2%
[u2$1@15];
model c3:
%c3#1%
[u3$1@-15];
%c3#2%
[u3$1@15];
model c4:
%c4#1%
[u4$1@-15];
%c4#2%
[u4$1@15];
model c5:
%c5#1%
[u5$1@-15];
%c5#2%
[u5$1@15];
output: tech10;
RESPONSE PATTERN FREQUENCIES AND CHI-SQUARE CONTRIBUTIONS
Response Frequency Standard Chi-square Contribution
Pattern Observed Estimated Residual Pearson Loglikelihood Deleted
1 891.00 553.84 15.17 205.25 847.29
2 237.00 288.85 3.14 9.31 -93.79
3 120.00 92.85 2.84 7.94 61.56
4 136.00 293.64 9.47 84.63 -209.36
5 111.00 92.85 1.90 3.55 39.64
6 80.00 48.43 4.56 20.59 80.32
7 54.00 94.39 4.20 17.28 -60.31
8 99.00 298.50 11.90 133.34 -218.53
9 119.00 92.85 2.74 7.37 59.06
10 68.00 48.43 2.83 7.91 46.17
11 51.00 15.57 8.99 80.66 121.05
12 64.00 49.23 2.12 4.43 33.59
13 52.00 94.39 4.40 19.04 -62.00
14 51.00 49.23 0.25 0.06 3.61
15 49.00 95.95 4.84 22.97 -65.86
16 172.00 303.45 7.78 56.94 -195.30
17 176.00 231.40 3.73 13.26 -96.33
18 107.00 120.69 1.26 1.55 -25.76
19 64.00 38.79 4.06 16.38 64.08
20 95.00 122.69 2.53 6.25 -48.59
21 60.00 38.79 3.42 11.59 52.33
22 75.00 20.23 12.20 148.25 196.53
23 50.00 39.44 1.69 2.83 23.73
24 165.00 124.72 3.65 13.01 92.36
25 106.00 235.23 8.63 71.00 -168.99
26 107.00 122.69 1.43 2.01 -29.28
27 67.00 39.44 4.41 19.27 71.02
28 187.00 124.72 5.65 31.10 151.49
29 92.00 239.13 9.74 90.53 -175.76
30 200.00 124.72 6.82 45.44 188.90
31 176.00 243.09 4.41 18.52 -113.68
32 1066.00 768.79 11.62 114.90 696.84
Table 2 based on the simple Markov chain model with time heterogeneous transition probabilities.
data: file is chap11.dat ;
variable: names are u1 u2 u3 u4 u5 count group; missing are all (-9999) ; usevariables are u1 u2 u3 u4 u5 count; weight is count (freq); categorical are u1 u2 u3 u4 u5; classes = c1(2) c2(2) c3(2) c4(2) c5(2);
analysis: type = mixture;
model:
%overall%
c2#1 on c1#1 ;
c3#1 on c2#1 ;
c4#1 on c3#1 ;
c5#1 on c4#1 ;
[c1#1 c2#1 c3#1 c4#1 c5#1] ;
model c1:
%c1#1%
[u1$1@-15];
%c1#2%
[u1$1@15];
model c2:
%c2#1%
[u2$1@-15];
%c2#2%
[u2$1@15];
model c3:
%c3#1%
[u3$1@-15];
%c3#2%
[u3$1@15];
model c4:
%c4#1%
[u4$1@-15];
%c4#2%
[u4$1@15];
model c5:
%c5#1%
[u5$1@-15];
%c5#2%
[u5$1@15];
FINAL CLASS COUNTS AND PROPORTIONS FOR EACH LATENT CLASS VARIABLE BASED ON THE ESTIMATED MODEL
Latent Class
Variable Class
C1 1 2908.99976 0.56518
2 2237.99976 0.43482
C2 1 2615.00000 0.50806
2 2532.00000 0.49194
C3 1 2551.99976 0.49582
2 2595.00000 0.50418
C4 1 2627.00000 0.51039
2 2520.00000 0.48961
C5 1 2793.00000 0.54265
2 2353.99976 0.45735
LATENT TRANSITION PROBABILITIES BASED ON THE ESTIMATED MODEL
C1 Classes (Rows) by C2 Classes (Columns)
1 2
1 0.682 0.318 2 0.282 0.718
C2 Classes (Rows) by C3 Classes (Columns)
1 2
1 0.700 0.300 2 0.285 0.715
C3 Classes (Rows) by C4 Classes (Columns)
1 2
1 0.728 0.272 2 0.296 0.704
C4 Classes (Rows) by C5 Classes (Columns)
1 2
1 0.762 0.238 2 0.314 0.686
Table 3 on page 315.
Model 1a (M): Simple Markov model with time homogeneous transition probabilities
data: file is chap11.dat ; variable: names are u1 u2 u3 u4 u5 count group; missing are all (-9999) ; usevariables are u1 u2 u3 u4 u5 count; weight is count (freq); categorical are u1 u2 u3 u4 u5; classes = c1(2) c2(2) c3(2) c4(2) c5(2);
analysis:
type = mixture;
model:
%overall%
c2#1 on c1#1 (1);
c3#1 on c2#1 (1);
c4#1 on c3#1 (1);
c5#1 on c4#1 (1);
[c1#1];
[c2#1 c3#1 c4#1 c5#1] (2);
model c1:
%c1#1%
[u1$1@-15];
%c1#2%
[u1$1@15]; !for variable a;
model c2:
%c2#1%
[u2$1@-15];
%c2#2%
[u2$1@15]; !for variable b;
model c3:
%c3#1%
[u3$1@-15];
%c3#2%
[u3$1@15]; !for variable c;
model c4:
%c4#1%
[u4$1@-15];
%c4#2%
[u4$1@15]; !for variable d;
model c5:
%c5#1%
[u5$1@-15];
%c5#2%
[u5$1@15]; !for variable e;
TESTS OF MODEL FIT
Loglikelihood
H0 Value -15893.523
Information Criteria
Number of Free Parameters 3
Akaike (AIC) 31793.046
Bayesian (BIC) 31812.685
Sample-Size Adjusted BIC 31803.152
(n* = (n + 2) / 24)
Entropy 1.000
Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes
Pearson Chi-Square
Value 1287.146
Degrees of Freedom 28
P-Value 0.0000
Likelihood Ratio Chi-Square
Value 1266.023
Degrees of Freedom 28
P-Value 0.0000
Model 1b (M): Simple Markov model with time heterogeneous transition probabilities
data: file is chap11.dat ;
variable: names are u1 u2 u3 u4 u5 count group; missing are all (-9999) ; usevariables are u1 u2 u3 u4 u5 count; weight is count (freq); categorical are u1 u2 u3 u4 u5; classes = c1(2) c2(2) c3(2) c4(2) c5(2);
analysis: type = mixture;
model:
%overall%
c2#1 on c1#1 ;
c3#1 on c2#1 ;
c4#1 on c3#1 ;
c5#1 on c4#1 ;
[c1#1 c2#1 c3#1 c4#1 c5#1] ;
model c1:
%c1#1%
[u1$1@-15];
%c1#2%
[u1$1@15];
model c2:
%c2#1%
[u2$1@-15];
%c2#2%
[u2$1@15];
model c3:
%c3#1%
[u3$1@-15];
%c3#2%
[u3$1@15];
model c4:
%c4#1%
[u4$1@-15];
%c4#2%
[u4$1@15];
model c5:
%c5#1%
[u5$1@-15];
%c5#2%
[u5$1@15];
TESTS OF MODEL FIT
Loglikelihood
H0 Value -15865.184
Information Criteria
Number of Free Parameters 9
Akaike (AIC) 31748.367
Bayesian (BIC) 31807.283
Sample-Size Adjusted BIC 31778.684
(n* = (n + 2) / 24)
Entropy 1.000
Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes
Pearson Chi-Square
Value 1239.474
Degrees of Freedom 22
P-Value 0.0000
Likelihood Ratio Chi-Square
Value 1209.345
Degrees of Freedom 22
P-Value 0.0000
Model 2a (MS): MS Mover-Stayer with time homogenous transition probabilities.
data:
file is chap11_dat.txt ;
variable:
names are
u1 u2 u3 u4 u5 count group;
missing are all (-9999) ;
usevariables are u1 u2 u3 u4 u5 count;
weight is count (freq);
categorical are u1 u2 u3 u4 u5;
classes = c(2) c1(2) c2(2) c3(2) c4(2) c5(2);
analysis:
type = mixture;
model:
%overall%
!c#1 is the mover class
!c#2 is the stayer class
[c#1]; ! estimates prob of being in the mover class
[c1#1]; ! estimates prob of being in unsatisfied class
c1#1 on c#1; ! adding this to [c1#1] estimates prob of being
! in the unsatisfied c1 class for movers (c#1)
[c2#1@-10]; ! fixes prob=0 for unsatisfied c2#1 class
! in the stayer class (c#2),
! for satisfied c1#2 class (see ~ on c1 below
! in model c statement)
[c3#1@-10]; ! same as above for c3#1
[c4#1@-10]; ! same as above for c4#1
[c5#1@-10]; ! same as above for c5#1
c2#1 on c#1 (2); ! adding this to [c2#1@-10] estimates prob
! of being in the unsatisfied c2#1 class
! in the mover class (c#1),
! for the unsatisfied c1#1 class
c3#1 on c#1 (2);
c4#1 on c#1 (2);
c5#1 on c#1 (2);
model c:
%c#1%
c2#1 on c1#1 (3);
c3#1 on c2#1 (3);
c4#1 on c3#1 (3);
c5#1 on c4#1 (3);
%c#2%
c2#1 on c1#1@20;
c3#1 on c2#1@20;
c4#1 on c3#1@20;
c5#1 on c4#1@20;
model c1:
%c1#1%
[u1$1@15];
%c1#2%
[u1$1@-15];
model c2:
%c2#1%
[u2$1@15];
%c2#2%
[u2$1@-15];
model c3:
%c3#1%
[u3$1@15];
%c3#2%
[u3$1@-15];
model c4:
%c4#1%
[u4$1@15];
%c4#2%
[u4$1@-15];
model c5:
%c5#1%
[u5$1@15];
%c5#2%
[u5$1@-15];
TESTS OF MODEL FIT
Loglikelihood
H0 Value -15422.306
Information Criteria
Number of Free Parameters 5
Akaike (AIC) 30854.613
Bayesian (BIC) 30887.343
Sample-Size Adjusted BIC 30871.455
(n* = (n + 2) / 24)
Entropy 0.951
Chi-Square Test of Model Fit for the Binary and Ordered Categorical (Ordinal) Outcomes
Pearson Chi-Square
Value 322.878
Degrees of Freedom 26
P-Value 0.0000
Likelihood Ratio Chi-Square
Value 323.590
Degrees of Freedom 26
P-Value 0.0000
Model 2b (MS): MS Mover-Stayer with time heterogeneous transition probabilities.
data:
file is chap11_dat.txt ;
variable:
names are
u1 u2 u3 u4 u5 count group;
missing are all (-9999) ;
usevariables are u1 u2 u3 u4 u5 count;
weight is count (freq);
categorical are u1 u2 u3 u4 u5;
classes = c(2) c1(2) c2(2) c3(2) c4(2) c5(2);
analysis:
type = mixture;
model:
%overall%
!c#1 is the mover class
!c#2 is the stayer class
[c#1]; ! estimates prob of being in the mover class
[c1#1]; ! estimates prob of being in unsatisfied class
c1#1 on c#1; ! adding this to [c1#1] estimates prob of being
! in the unsatisfied c1 class for movers (c#1)
[c2#1@-10]; ! fixes prob=0 for unsatisfied c2#1 class
! in the stayer class (c#2),
! for satisfied c1#2 class
[c3#1@-10]; ! same as above for c3#1
[c4#1@-10]; ! same as above for c4#1
[c5#1@-10]; ! same as above for c5#1
c2#1 on c#1 ;
c3#1 on c#1 ;
c4#1 on c#1 ;
c5#1 on c#1 ;
model c:
%c#1%
c2#1 on c1#1 ;
c3#1 on c2#1 ;
c4#1 on c3#1 ;
c5#1 on c4#1 ;
%c#2%
c2#1 on c1#1@20;
c3#1 on c2#1@20;
c4#1 on c3#1@20;
c5#1 on c4#1@20;
model c1:
%c1#1%
[u1$1@15];
%c1#2%
[u1$1@-15];
model c2:
%c2#1%
[u2$1@15];
%c2#2%
[u2$1@-15];
model c3:
%c3#1%
[u3$1@15];
%c3#2%
[u3$1@-15];
model c4:
%c4#1%
[u4$1@15];
%c4#2%
[u4$1@-15];
model c5:
%c5#1%
[u5$1@15];
%c5#2%
[u5$1@-15];
TESTS OF MODEL FIT
Loglikelihood
H0 Value -15395.927
Information Criteria
Number of Free Parameters 11
Akaike (AIC) 30813.853
Bayesian (BIC) 30885.861
Sample-Size Adjusted BIC 30850.907
(n* = (n + 2) / 24)
Entropy 0.951
Chi-Square Test of Model Fit for the Binary and Ordered Categorical (Ordinal) Outcomes
Pearson Chi-Square
Value 272.340
Degrees of Freedom 20
P-Value 0.0000
Likelihood Ratio Chi-Square
Value 270.830
Degrees of Freedom 20
P-Value 0.0000
Model 3a (MM): Two-chain mixed Markov with time homogeneous transition probabilities.
data:
file is chap11_dat.txt ;
variable:
names are
u1 u2 u3 u4 u5 count group;
missing are all (-9999) ;
usevariables are u1 u2 u3 u4 u5 count;
weight is count (freq);
categorical are u1 u2 u3 u4 u5;
classes = c(2) c1(2) c2(2) c3(2) c4(2) c5(2);
analysis:
type = mixture;
model:
%overall%
[c#1];
[c1#1];
c1#1 on c#1;
[c2#1 c3#1 C4#1 C5#1] (1);
c2#1 on c#1 (2);
c3#1 on c#1 (2);
c4#1 on c#1 (2);
c5#1 on c#1 (2);
model c:
%c#1%
c2#1 on c1#1 (3);
c3#1 on c2#1 (3);
c4#1 on c3#1 (3);
c5#1 on c4#1 (3);
%c#2%
c2#1 on c1#1 (4);
c3#1 on c2#1 (4);
c4#1 on c3#1 (4);
c5#1 on c4#1 (4);
model c1:
%c1#1%
[u1$1@15];
%c1#2%
[u1$1@-15];
model c2:
%c2#1%
[u2$1@15];
%c2#2%
[u2$1@-15];
model c3:
%c3#1%
[u3$1@15];
%c3#2%
[u3$1@-15];
model c4:
%c4#1%
[u4$1@15];
%c4#2%
[u4$1@-15];
model c5:
%c5#1%
[u5$1@15];
%c5#2%
[u5$1@-15];
TESTS OF MODEL FIT
Loglikelihood
H0 Value -15333.600
Information Criteria
Number of Free Parameters 7
Akaike (AIC) 30681.201
Bayesian (BIC) 30727.024
Sample-Size Adjusted BIC 30704.780
(n* = (n + 2) / 24)
Entropy 0.943
Chi-Square Test of Model Fit for the Binary and Ordered Categorical (Ordinal) Outcomes
Pearson Chi-Square
Value 148.901
Degrees of Freedom 24
P-Value 0.0000
Likelihood Ratio Chi-Square
Value 146.176
Degrees of Freedom 24
P-Value 0.0000
Model 3b (MM): Two-chain mixed Markov with time heterogeneous transition probabilities.
data:
file is chap11_dat.txt ;
variable:
names are
u1 u2 u3 u4 u5 count group;
missing are all (-9999) ;
usevariables are u1 u2 u3 u4 u5 count;
weight is count (freq);
categorical are u1 u2 u3 u4 u5;
classes = c(2) c1(2) c2(2) c3(2) c4(2) c5(2);
analysis:
type = mixture;
model:
%overall%
[c#1];
[c1#1];
c1#1 on c#1;
[c2#1 c3#1 C4#1 C5#1] ;
c2#1 on c#1 ;
c3#1 on c#1 ;
c4#1 on c#1 ;
c5#1 on c#1 ;
model c:
%c#1%
c2#1 on c1#1 ;
c3#1 on c2#1 ;
c4#1 on c3#1 ;
c5#1 on c4#1 ;
%c#2%
c2#1 on c1#1 ;
c3#1 on c2#1 ;
c4#1 on c3#1 ;
c5#1 on c4#1 ;
model c1:
%c1#1%
[u1$1@15];
%c1#2%
[u1$1@-15];
model c2:
%c2#1%
[u2$1@15];
%c2#2%
[u2$1@-15];
model c3:
%c3#1%
[u3$1@15];
%c3#2%
[u3$1@-15];
model c4:
%c4#1%
[u4$1@15];
%c4#2%
[u4$1@-15];
model c5:
%c5#1%
[u5$1@15];
%c5#2%
[u5$1@-15];
TESTS OF MODEL FIT
Loglikelihood
H0 Value -15307.952
Information Criteria
Number of Free Parameters 19
Akaike (AIC) 30653.903
Bayesian (BIC) 30778.280
Sample-Size Adjusted BIC 30717.905
(n* = (n + 2) / 24)
Entropy 0.944
Chi-Square Test of Model Fit for the Binary and Ordered Categorical (Ordinal) Outcomes
Pearson Chi-Square
Value 97.495
Degrees of Freedom 12
P-Value 0.0000
Likelihood Ratio Chi-Square
Value 94.879
Degrees of Freedom 12
P-Value 0.0000
Model 4a (MMS): 2 Markov and 2 Stayer chains with time homogeneous transition probabilities.
Model 7a (LM): Latent Markov with time homogeneous transition probabilities.
data: file is chap11.dat ;
variable: names are u1 u2 u3 u4 u5 count group; missing are all (-9999) ; usevariables are u1 u2 u3 u4 u5 count; weight is count (freq); categorical are u1 u2 u3 u4 u5; classes = c1(2) c2(2) c3(2) c4(2) c5(2);
analysis: type = mixture;
model:
%overall%
c2#1 on c1#1 (1);
c3#1 on c2#1 (1);
c4#1 on c3#1 (1);
c5#1 on c4#1 (1);
[c2#1 c3#1 c4#1 c5#1] (2);
model c1:
%c1#1%
[u1$1] (3);
%c1#2%
[u1$1] (4);
model c2:
%c2#1%
[u2$1] (3);
%c2#2%
[u2$1] (4);
model c3:
%c3#1%
[u3$1] (3);
%c3#2%
[u3$1] (4);
model c4:
%c4#1%
[u4$1] (3);
%c4#2%
[u4$1] (4);
model c5:
%c5#1%
[u5$1] (3);
%c5#2%
[u5$1] (4);
TESTS OF MODEL FIT
Loglikelihood
H0 Value -15378.476
Information Criteria
Number of Free Parameters 5
Akaike (AIC) 30766.952
Bayesian (BIC) 30799.683
Sample-Size Adjusted BIC 30783.795
(n* = (n + 2) / 24)
Entropy 0.777
Chi-Square Test of Model Fit for the Binary and Ordered Categorical (Ordinal) Outcomes
Pearson Chi-Square
Value 243.841
Degrees of Freedom 26
P-Value 0.0000
Likelihood Ratio Chi-Square
Value 235.928
Degrees of Freedom 26
P-Value 0.0000
Model 7b (LM): Latent Markov with time heterogeneous transition probabilities.
data: file is chap11.dat ;
variable: names are u1 u2 u3 u4 u5 count group; missing are all (-9999) ; usevariables are u1 u2 u3 u4 u5 count; weight is count (freq); categorical are u1 u2 u3 u4 u5; classes = c1(2) c2(2) c3(2) c4(2) c5(2);
analysis:
type = mixture;
starts = 50 5;
model:
%overall%
c2#1 on c1#1 ;
c3#1 on c2#1 ;
c4#1 on c3#1 ;
c5#1 on c4#1 ;
[c2#1 c3#1 c4#1 c5#1] ;
model c1:
%c1#1%
[u1$1] (3);
%c1#2%
[u1$1] (4);
model c2:
%c2#1%
[u2$1] (3);
%c2#2%
[u2$1] (4);
model c3:
%c3#1%
[u3$1] (3);
%c3#2%
[u3$1] (4);
model c4:
%c4#1%
[u4$1] (3);
%c4#2%
[u4$1] (4);
model c5:
%c5#1%
[u5$1] (3);
%c5#2%
[u5$1] (4);
TESTS OF MODEL FIT
Loglikelihood
H0 Value -15325.635
Information Criteria
Number of Free Parameters 11
Akaike (AIC) 30673.271
Bayesian (BIC) 30745.279
Sample-Size Adjusted BIC 30710.324
(n* = (n + 2) / 24)
Entropy 0.802
Chi-Square Test of Model Fit for the Binary and Ordered Categorical (Ordinal) Outcomes
Pearson Chi-Square
Value 131.025
Degrees of Freedom 20
P-Value 0.0000
Likelihood Ratio Chi-Square
Value 130.246
Degrees of Freedom 20
P-Value 0.0000
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