```Mplus VERSION 6
MUTHEN & MUTHEN
04/25/2010  10:58 PM

INPUT INSTRUCTIONS

TITLE: mix1

DATA: FILE IS bart.dat;

VARIABLE: NAMES ARE u1-u4;
USEV ARE  u1-u4;
CATEGORICAL = u1 - u4;
CLASSES = c(2);

ANALYSIS: TYPE=MIXTURE;
MITERATIONS = 100;

!        this is a latent class analysis of 4 binary indicators of a
!        categorical latent variable with 2 classes
!        the default number of E step iterations is reduced from 100
!        to 60 because this example converges quickly even with rough
!        starting values

MODEL:
%OVERALL%
!  c#1 BY u1*-2 u2*-2 u3*-2 u4*-2;
!  c#2 BY u1*1 u2*1 u3*1 u4*1;

[u1\$1*2 u2\$1*2 u3\$1*2 u4\$1*2];

%C#2%
[u1\$1*-1 u2\$1*-1 u3\$1*-1 u4\$1*-1];

!        the two lines above refer to the logits of the conditional
!        probabilities of u = 1 given latent class 1 and 2, respectively.
!        Starting  values are required for these parameters.
!        Starting values can for example be obtained
!        by having lower u probabilities for the first class than for the second
!        class. There is no need to provide starting values for the latent class
!        probabilities - the default is equal probabilities. As an example of
!        giving a starting value with a small probability for class 1 is as
!        follows:
!
!        [c#1*-2];
!
!        The following shows how to set starting values in the logit scale.

!        the relationship between logits and probabilities is
!
!        probability = 1/(1+exp(-logit))
!
!        logit = elog(probability/(1-probability))
!
!        which means that
!
!        Probability        Logit
!        0                -100 (approximately)
!        0.5                0
!        1                +100 (approximately)

OUTPUT:
TECH8;

!        tech8 is needed to monitor the convergence of mixture modeling

mix1

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                         142

Number of dependent variables                                    4
Number of independent variables                                  0
Number of continuous latent variables                            0
Number of categorical latent variables                           1

Observed dependent variables

Binary and ordered categorical (ordinal)
U1          U2          U3          U4

Categorical latent variables
C

Estimator                                                      MLR
Information matrix                                        OBSERVED
Optimization Specifications for the Quasi-Newton Algorithm for
Continuous Outcomes
Maximum number of iterations                                 100
Convergence criterion                                  0.100D-05
Optimization Specifications for the EM Algorithm
Maximum number of iterations                                 100
Convergence criteria
Loglikelihood change                                 0.100D-06
Relative loglikelihood change                        0.100D-06
Derivative                                           0.100D-05
Optimization Specifications for the M step of the EM Algorithm for
Categorical Latent variables
Number of M step iterations                                    1
M step convergence criterion                           0.100D-05
Basis for M step termination                           ITERATION
Optimization Specifications for the M step of the EM Algorithm for
Censored, Binary or Ordered Categorical (Ordinal), Unordered
Categorical (Nominal) and Count Outcomes
Number of M step iterations                                    1
M step convergence criterion                           0.100D-05
Basis for M step termination                           ITERATION
Maximum value for logit thresholds                            15
Minimum value for logit thresholds                           -15
Minimum expected cell size for chi-square              0.100D-01
Optimization algorithm                                         EMA
Random Starts Specifications
Number of initial stage random starts                         10
Number of final stage optimizations                            2
Number of initial stage iterations                            10
Initial stage convergence criterion                    0.100D+01
Random starts scale                                    0.500D+01
Random seed for generating random starts                       0

Input data file(s)
bart.dat
Input data format  FREE

UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES

U1
Category 1    0.472       67.000
Category 2    0.528       75.000
U2
Category 1    0.514       73.000
Category 2    0.486       69.000
U3
Category 1    0.739      105.000
Category 2    0.261       37.000
U4
Category 1    0.563       80.000
Category 2    0.437       62.000

RANDOM STARTS RESULTS RANKED FROM THE BEST TO THE WORST LOGLIKELIHOOD VALUES

Final stage loglikelihood values at local maxima, seeds, and initial stage start numbers:

-331.764  unperturbed      0
-331.764  195873           6

THE MODEL ESTIMATION TERMINATED NORMALLY

TESTS OF MODEL FIT

Loglikelihood

H0 Value                        -331.764
H0 Scaling Correction Factor       1.018
for MLR

Information Criteria

Number of Free Parameters              9
Akaike (AIC)                     681.527
Bayesian (BIC)                   708.130
(n* = (n + 2) / 24)

Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes

Pearson Chi-Square

Value                              9.459
Degrees of Freedom                     6
P-Value                           0.1494

Likelihood Ratio Chi-Square

Value                              8.966
Degrees of Freedom                     6
P-Value                           0.1755

FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL

Latent
Classes

1         58.70852          0.41344
2         83.29148          0.58656

FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASS PATTERNS
BASED ON ESTIMATED POSTERIOR PROBABILITIES

Latent
Classes

1         58.70852          0.41344
2         83.29148          0.58656

CLASSIFICATION QUALITY

Entropy                         0.754

CLASSIFICATION OF INDIVIDUALS BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP

Class Counts and Proportions

Latent
Classes

1               65          0.45775
2               77          0.54225

Average Latent Class Probabilities for Most Likely Latent Class Membership (Row)
by Latent Class (Column)

1        2

1   0.875    0.125
2   0.024    0.976

MODEL RESULTS

Two-Tailed
Estimate       S.E.  Est./S.E.    P-Value

Latent Class 1

Thresholds
U1\$1               1.333      0.402      3.313      0.001
U2\$1               2.613      0.883      2.960      0.003
U3\$1               4.004      2.120      1.888      0.059
U4\$1               2.898      1.143      2.535      0.011

Latent Class 2

Thresholds
U1\$1              -1.117      0.323     -3.455      0.001
U2\$1              -1.267      0.402     -3.155      0.002
U3\$1               0.275      0.238      1.158      0.247
U4\$1              -0.883      0.306     -2.886      0.004

Categorical Latent Variables

Means
C#1               -0.350      0.271     -1.290      0.197

RESULTS IN PROBABILITY SCALE

Latent Class 1

U1
Category 1         0.791      0.066     11.911      0.000
Category 2         0.209      0.066      3.139      0.002
U2
Category 1         0.932      0.056     16.584      0.000
Category 2         0.068      0.056      1.216      0.224
U3
Category 1         0.982      0.037     26.325      0.000
Category 2         0.018      0.037      0.480      0.631
U4
Category 1         0.948      0.057     16.741      0.000
Category 2         0.052      0.057      0.923      0.356

Latent Class 2

U1
Category 1         0.247      0.060      4.105      0.000
Category 2         0.753      0.060     12.543      0.000
U2
Category 1         0.220      0.069      3.191      0.001
Category 2         0.780      0.069     11.332      0.000
U3
Category 1         0.568      0.058      9.748      0.000
Category 2         0.432      0.058      7.402      0.000
U4
Category 1         0.292      0.063      4.617      0.000
Category 2         0.708      0.063     11.169      0.000

LATENT CLASS ODDS RATIO RESULTS

Latent Class 1 Compared to Latent Class 2

U1
Category > 1       0.086      0.043      2.025      0.043
U2
Category > 1       0.021      0.019      1.084      0.278
U3
Category > 1       0.024      0.051      0.468      0.639
U4
Category > 1       0.023      0.026      0.875      0.382

QUALITY OF NUMERICAL RESULTS

Condition Number for the Information Matrix              0.842E-02
(ratio of smallest to largest eigenvalue)

TECHNICAL 8 OUTPUT

INITIAL STAGE ITERATIONS

TECHNICAL 8 OUTPUT FOR UNPERTURBED STARTING VALUE SET

ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE      CLASS COUNTS    ALGORITHM
1 -0.35341784D+03    0.0000000    0.0000000     67.571    74.429    EM
2 -0.33273204D+03   20.6858009    0.0585307     66.296    75.704    EM
3 -0.33232989D+03    0.4021470    0.0012086     65.255    76.745    EM

TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 1

ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE      CLASS COUNTS    ALGORITHM
1 -0.48417716D+03    0.0000000    0.0000000     90.980    51.020    EM
2 -0.34687327D+03  137.3038923    0.2835819     88.175    53.825    EM
3 -0.34063962D+03    6.2336522    0.0179710     85.917    56.083    EM
4 -0.33840420D+03    2.2354233    0.0065624     83.463    58.537    EM
5 -0.33645180D+03    1.9523944    0.0057694     80.938    61.062    EM
6 -0.33504185D+03    1.4099537    0.0041907     78.685    63.315    EM
7 -0.33423040D+03    0.8114423    0.0024219     76.797    65.203    EM

TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 2

ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE      CLASS COUNTS    ALGORITHM
1 -0.77768249D+03    0.0000000    0.0000000     46.971    95.029    EM
2 -0.36949672D+03  408.1857690    0.5248746     48.542    93.458    EM
3 -0.35165377D+03   17.8429484    0.0482899     52.522    89.478    EM
4 -0.34077280D+03   10.8809669    0.0309423     55.474    86.526    EM
5 -0.33731967D+03    3.4531338    0.0101332     57.798    84.202    EM
6 -0.33570616D+03    1.6135105    0.0047833     59.878    82.122    EM
7 -0.33481833D+03    0.8878320    0.0026447     61.695    80.305    EM

TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 3

ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE      CLASS COUNTS    ALGORITHM
1 -0.61820111D+03    0.0000000    0.0000000     47.935    94.065    EM
2 -0.37843203D+03  239.7690785    0.3878496     46.882    95.118    EM
3 -0.37601374D+03    2.4182954    0.0063903     46.636    95.364    EM
4 -0.37542767D+03    0.5860713    0.0015586     46.593    95.407    EM

TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 4

ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE      CLASS COUNTS    ALGORITHM
1 -0.48659193D+03    0.0000000    0.0000000     44.898    97.102    EM
2 -0.37742247D+03  109.1694573    0.2243553     44.122    97.878    EM
3 -0.37598331D+03    1.4391617    0.0038131     43.868    98.132    EM
4 -0.37555870D+03    0.4246111    0.0011293     43.774    98.226    EM

TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 5

ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE      CLASS COUNTS    ALGORITHM
1 -0.41231589D+03    0.0000000    0.0000000     45.822    96.178    EM
2 -0.33561386D+03   76.7020372    0.1860274     49.722    92.278    EM
3 -0.33293099D+03    2.6828640    0.0079939     51.046    90.954    EM
4 -0.33258677D+03    0.3442275    0.0010339     51.626    90.374    EM

TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 6

ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE      CLASS COUNTS    ALGORITHM
1 -0.79307525D+03    0.0000000    0.0000000     68.408    73.592    EM
2 -0.33398857D+03  459.0866854    0.5788690     67.718    74.282    EM
3 -0.33273698D+03    1.2515866    0.0037474     66.925    75.075    EM
4 -0.33243624D+03    0.3007386    0.0009038     66.093    75.907    EM

TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 7

ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE      CLASS COUNTS    ALGORITHM
1 -0.52760607D+03    0.0000000    0.0000000    109.495    32.505    EM
2 -0.36030670D+03  167.2993712    0.3170914    107.529    34.471    EM
3 -0.35139501D+03    8.9116866    0.0247336    102.010    39.990    EM
4 -0.34404878D+03    7.3462369    0.0209059     95.968    46.032    EM
5 -0.33924135D+03    4.8074202    0.0139731     91.281    50.719    EM
6 -0.33699025D+03    2.2511054    0.0066357     87.893    54.107    EM
7 -0.33587049D+03    1.1197547    0.0033228     85.335    56.665    EM
8 -0.33522041D+03    0.6500896    0.0019355     83.323    58.677    EM

TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 8

ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE      CLASS COUNTS    ALGORITHM
1 -0.51298960D+03    0.0000000    0.0000000     95.411    46.589    EM
2 -0.34268810D+03  170.3014993    0.3319785     93.883    48.117    EM
3 -0.34021089D+03    2.4772094    0.0072288     91.611    50.389    EM
4 -0.33840223D+03    1.8086548    0.0053163     88.867    53.133    EM
5 -0.33677031D+03    1.6319190    0.0048224     86.145    55.855    EM
6 -0.33563440D+03    1.1359109    0.0033730     83.786    58.214    EM
7 -0.33495725D+03    0.6771488    0.0020175     81.836    60.164    EM

TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 9

ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE      CLASS COUNTS    ALGORITHM
1 -0.65538774D+03    0.0000000    0.0000000    100.101    41.899    EM
2 -0.35243394D+03  302.9537974    0.4622512     95.169    46.831    EM
3 -0.34659260D+03    5.8413457    0.0165743     89.437    52.563    EM
4 -0.34049161D+03    6.1009858    0.0176028     84.429    57.571    EM
5 -0.33642426D+03    4.0673504    0.0119455     80.936    61.064    EM
6 -0.33469993D+03    1.7243285    0.0051255     78.538    63.462    EM
7 -0.33404244D+03    0.6574908    0.0019644     76.742    65.258    EM

TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 10

ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE      CLASS COUNTS    ALGORITHM
1 -0.61777512D+03    0.0000000    0.0000000    126.981    15.019    EM
2 -0.36283884D+03  254.9362853    0.4126684    123.421    18.579    EM
3 -0.35935476D+03    3.4840776    0.0096023    120.617    21.383    EM
4 -0.35742723D+03    1.9275333    0.0053639    117.671    24.329    EM
5 -0.35482527D+03    2.6019530    0.0072797    113.446    28.554    EM
6 -0.35057447D+03    4.2508072    0.0119800    107.466    34.534    EM
7 -0.34500864D+03    5.5658275    0.0158763    100.907    41.093    EM
8 -0.34044954D+03    4.5590949    0.0132144     95.655    46.345    EM
9 -0.33805236D+03    2.3971878    0.0070412     91.960    50.040    EM
10 -0.33683591D+03    1.2164475    0.0035984     89.280    52.720    EM

FINAL STAGE ITERATIONS

TECHNICAL 8 OUTPUT FOR UNPERTURBED STARTING VALUE SET

3 -0.33232989D+03    0.4021470    0.0012086     65.255    76.745    EM
4 -0.33216130D+03    0.1685907    0.0005073     64.365    77.635    EM
5 -0.33206162D+03    0.0996882    0.0003001     63.596    78.404    EM
6 -0.33199055D+03    0.0710615    0.0002140     62.931    79.069    EM
7 -0.33193654D+03    0.0540137    0.0001627     62.355    79.645    EM
8 -0.33189488D+03    0.0416624    0.0001255     61.855    80.145    EM
9 -0.33186280D+03    0.0320784    0.0000967     61.423    80.577    EM
10 -0.33183826D+03    0.0245411    0.0000739     61.050    80.950    EM
11 -0.33181961D+03    0.0186462    0.0000562     60.728    81.272    EM
12 -0.33180553D+03    0.0140837    0.0000424     60.449    81.551    EM
13 -0.33179494D+03    0.0105887    0.0000319     60.210    81.790    EM
14 -0.33178700D+03    0.0079344    0.0000239     60.003    81.997    EM
15 -0.33178107D+03    0.0059317    0.0000179     59.825    82.175    EM
16 -0.33177665D+03    0.0044279    0.0000133     59.672    82.328    EM
17 -0.33177334D+03    0.0033023    0.0000100     59.540    82.460    EM
18 -0.33177088D+03    0.0024618    0.0000074     59.426    82.574    EM
19 -0.33176905D+03    0.0018349    0.0000055     59.328    82.672    EM
20 -0.33176768D+03    0.0013678    0.0000041     59.243    82.757    EM
21 -0.33176666D+03    0.0010197    0.0000031     59.171    82.829    EM
22 -0.33176590D+03    0.0007604    0.0000023     59.108    82.892    EM
23 -0.33176533D+03    0.0005673    0.0000017     59.053    82.947    EM
24 -0.33176491D+03    0.0004233    0.0000013     59.007    82.993    EM
25 -0.33176459D+03    0.0003160    0.0000010     58.966    83.034    EM
26 -0.33176436D+03    0.0002359    0.0000007     58.931    83.069    EM
27 -0.33176418D+03    0.0001762    0.0000005     58.901    83.099    EM
28 -0.33176405D+03    0.0001317    0.0000004     58.875    83.125    EM
29 -0.33176395D+03    0.0000984    0.0000003     58.852    83.148    EM
30 -0.33176388D+03    0.0000735    0.0000002     58.833    83.167    EM
31 -0.33176382D+03    0.0000550    0.0000002     58.816    83.184    EM
32 -0.33176378D+03    0.0000411    0.0000001     58.802    83.198    EM
33 -0.33176375D+03    0.0000307    0.0000001     58.789    83.211    EM
34 -0.33176373D+03    0.0000230    0.0000001     58.778    83.222    EM
35 -0.33176371D+03    0.0000172    0.0000001     58.769    83.231    EM
36 -0.33176366D+03    0.0000477    0.0000001     58.719    83.281    FS
37 -0.33176366D+03    0.0000031    0.0000000     58.713    83.287    FS
38 -0.33176366D+03    0.0000003    0.0000000     58.709    83.291    FS
39 -0.33176366D+03    0.0000000    0.0000000     58.709    83.291    FS
40 -0.33176366D+03    0.0000000    0.0000000     58.709    83.291    FS

TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 6

4 -0.33243624D+03    0.3007386    0.0009038     66.093    75.907    EM
5 -0.33229059D+03    0.1456529    0.0004381     65.280    76.720    EM
6 -0.33218415D+03    0.1064426    0.0003203     64.513    77.487    EM
7 -0.33209672D+03    0.0874278    0.0002632     63.807    78.193    EM
8 -0.33202424D+03    0.0724758    0.0002182     63.165    78.835    EM
9 -0.33196514D+03    0.0591075    0.0001780     62.591    79.409    EM
10 -0.33191788D+03    0.0472563    0.0001424     62.081    79.919    EM
11 -0.33188077D+03    0.0371104    0.0001118     61.631    80.369    EM
12 -0.33185205D+03    0.0287177    0.0000865     61.238    80.762    EM
13 -0.33183008D+03    0.0219701    0.0000662     60.895    81.105    EM
14 -0.33181342D+03    0.0166642    0.0000502     60.597    81.403    EM
15 -0.33180086D+03    0.0125612    0.0000379     60.339    81.661    EM
16 -0.33179143D+03    0.0094270    0.0000284     60.116    81.884    EM
17 -0.33178438D+03    0.0070539    0.0000213     59.924    82.076    EM
18 -0.33177911D+03    0.0052681    0.0000159     59.757    82.243    EM
19 -0.33177518D+03    0.0039298    0.0000118     59.614    82.386    EM
20 -0.33177225D+03    0.0029296    0.0000088     59.490    82.510    EM
21 -0.33177006D+03    0.0021834    0.0000066     59.383    82.617    EM
22 -0.33176844D+03    0.0016272    0.0000049     59.291    82.709    EM
23 -0.33176722D+03    0.0012129    0.0000037     59.212    82.788    EM
24 -0.33176632D+03    0.0009043    0.0000027     59.143    82.857    EM
25 -0.33176565D+03    0.0006744    0.0000020     59.084    82.916    EM
26 -0.33176514D+03    0.0005032    0.0000015     59.033    82.967    EM
27 -0.33176477D+03    0.0003755    0.0000011     58.989    83.011    EM
28 -0.33176449D+03    0.0002803    0.0000008     58.951    83.049    EM
29 -0.33176428D+03    0.0002093    0.0000006     58.918    83.082    EM
30 -0.33176412D+03    0.0001564    0.0000005     58.890    83.110    EM
31 -0.33176400D+03    0.0001168    0.0000004     58.865    83.135    EM
32 -0.33176392D+03    0.0000873    0.0000003     58.844    83.156    EM
33 -0.33176385D+03    0.0000653    0.0000002     58.826    83.174    EM
34 -0.33176380D+03    0.0000488    0.0000001     58.810    83.190    EM
35 -0.33176377D+03    0.0000365    0.0000001     58.796    83.204    EM
36 -0.33176374D+03    0.0000273    0.0000001     58.784    83.216    EM
37 -0.33176366D+03    0.0000756    0.0000002     58.721    83.279    FS
38 -0.33176366D+03    0.0000050    0.0000000     58.714    83.286    FS
39 -0.33176366D+03    0.0000005    0.0000000     58.710    83.290    FS
40 -0.33176366D+03    0.0000000    0.0000000     58.709    83.291    FS
41 -0.33176366D+03    0.0000000    0.0000000     58.709    83.291    FS

Beginning Time:  22:58:10
Ending Time:  22:58:10
Elapsed Time:  00:00:00

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Copyright (c) 1998-2010 Muthen & Muthen
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