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

INPUT INSTRUCTIONS

TITLE: mix6

Mixed logistic regression analysis

Class-varying intercepts, class-invariant slopes,
covariate does not influence the latent class variable.

Trypanosome data analyzed by Follmann & Lambert (1989)

Source: Follmann & Lambert (1989).  Generalizing logistic regression
by nonparametric mixing.  Journal of the American Statistical Association,
295-300.

DATA: FILE IS jasa.dat;

VARIABLE: NAMES ARE u x;
USEV ARE u x;
CATEGORICAL IS u;
CLASSES = c(2);
DEFINE:
x = log(x);

!        the x variable is transformed before analysis

ANALYSIS: TYPE = MIXTURE;

MODEL:
%overall%
u ON x;

!        the above statement refers to the class-invariant slope

!  c#1 BY u*-1;
!  c#2 BY u*1;

[u\$1*1];

%c#2%
[u\$1*-1];

!        the above 2 statements refer to the class-varying intercepts.
!        Note that these intercepts cannot be referred to as [u]

OUTPUT:
tech1 tech8;

SAVEDATA:
SAVE=CPROB;
FILE IS jasap.sav;

!        class probability estimates (posterior probabilities)
!        are save together with original data (USEV variables)
!        in the file called jasap.out

mix6

Mixed logistic regression analysis

Class-varying intercepts, class-invariant slopes,
covariate does not influence the latent class variable.

Trypanosome data analyzed by Follmann & Lambert (1989)

Source: Follmann & Lambert (1989).  Generalizing logistic regression
by nonparametric mixing.  Journal of the American Statistical Association,
295-300.

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                         426

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

Observed dependent variables

Binary and ordered categorical (ordinal)
U

Observed independent variables
X

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                                 500
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)
jasa.dat
Input data format  FREE

UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES

U
Category 1    0.531      226.000
Category 2    0.469      200.000

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:

-177.369  93468            3
-177.369  462953           7

THE MODEL ESTIMATION TERMINATED NORMALLY

TESTS OF MODEL FIT

Loglikelihood

H0 Value                        -177.369
H0 Scaling Correction Factor       0.948
for MLR

Information Criteria

Number of Free Parameters              4
Akaike (AIC)                     362.737
Bayesian (BIC)                   378.955
(n* = (n + 2) / 24)

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

Latent
Classes

1        280.07389          0.65745
2        145.92611          0.34255

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

Latent
Classes

1        280.07384          0.65745
2        145.92616          0.34255

CLASSIFICATION QUALITY

Entropy                         0.437

CLASSIFICATION OF INDIVIDUALS BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP

Class Counts and Proportions

Latent
Classes

1              323          0.75822
2              103          0.24178

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

1        2

1   0.800    0.200
2   0.211    0.789

MODEL RESULTS

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

Latent Class 1

U          ON
X                124.786     23.100      5.402      0.000

Thresholds
U\$1              205.684     38.215      5.382      0.000

Latent Class 2

U          ON
X                124.786     23.100      5.402      0.000

Thresholds
U\$1              196.153     36.078      5.437      0.000

Categorical Latent Variables

Means
C#1                0.652      0.199      3.282      0.001

LOGISTIC REGRESSION ODDS RATIO RESULTS

Latent Class 1

U          ON
X              *********

Latent Class 2

U          ON
X              *********

QUALITY OF NUMERICAL RESULTS

Condition Number for the Information Matrix              0.294E-05
(ratio of smallest to largest eigenvalue)

TECHNICAL 1 OUTPUT

PARAMETER SPECIFICATION FOR LATENT CLASS 1

NU
X
________
1                  0

LAMBDA
X
________
X                  0

THETA
X
________
X                  0

ALPHA
X
________
1                  0

BETA
X
________
X                  0

PSI
X
________
X                  0

PARAMETER SPECIFICATION FOR LATENT CLASS 2

NU
X
________
1                  0

LAMBDA
X
________
X                  0

THETA
X
________
X                  0

ALPHA
X
________
1                  0

BETA
X
________
X                  0

PSI
X
________
X                  0

PARAMETER SPECIFICATION FOR LATENT CLASS INDICATOR MODEL PART

LAMBDA(U)
C#1           C#2
________      ________
U                  1             2

KAPPA(U) FOR LATENT CLASS 1
X
________
U                  3

KAPPA(U) FOR LATENT CLASS 2
X
________
U                  3

PARAMETER SPECIFICATION FOR LATENT CLASS REGRESSION MODEL PART

ALPHA(C)
C#1           C#2
________      ________
1                  4             0

GAMMA(C)
X
________
C#1                0
C#2                0

STARTING VALUES FOR LATENT CLASS 1

NU
X
________
1              0.000

LAMBDA
X
________
X              1.000

THETA
X
________
X              0.000

ALPHA
X
________
1              0.000

BETA
X
________
X              0.000

PSI
X
________
X              0.001

STARTING VALUES FOR LATENT CLASS 2

NU
X
________
1              0.000

LAMBDA
X
________
X              1.000

THETA
X
________
X              0.000

ALPHA
X
________
1              0.000

BETA
X
________
X              0.000

PSI
X
________
X              0.001

STARTING VALUES FOR LATENT CLASS INDICATOR MODEL PART

LAMBDA(U)
C#1           C#2
________      ________
U             -1.000         1.000

KAPPA(U) FOR LATENT CLASS 1
X
________
U              0.000

KAPPA(U) FOR LATENT CLASS 2
X
________
U              0.000

STARTING VALUES FOR LATENT CLASS REGRESSION MODEL PART

ALPHA(C)
C#1           C#2
________      ________
1              0.000         0.000

GAMMA(C)
X
________
C#1            0.000
C#2            0.000

TECHNICAL 8 OUTPUT

INITIAL STAGE ITERATIONS

TECHNICAL 8 OUTPUT FOR UNPERTURBED STARTING VALUE SET

ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE      CLASS COUNTS    ALGORITHM
1 -0.29528070D+03    0.0000000    0.0000000    219.008   206.992    EM
2 -0.19408360D+03  101.1971007    0.3427149    219.807   206.193    EM
3 -0.18800179D+03    6.0818051    0.0313360    220.148   205.852    EM
4 -0.18768933D+03    0.3124662    0.0016620    220.389   205.611    EM

TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 1

ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE      CLASS COUNTS    ALGORITHM
1 -0.44502316D+03    0.0000000    0.0000000    173.747   252.253    EM
2 -0.20671197D+03  238.3111843    0.5355029    174.885   251.115    EM
3 -0.19353091D+03   13.1810680    0.0637654    174.409   251.591    EM
4 -0.18817343D+03    5.3574791    0.0276828    174.352   251.648    EM
5 -0.18800848D+03    0.1649414    0.0008765    174.350   251.650    EM

TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 2

ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE      CLASS COUNTS    ALGORITHM
1 -0.12389653D+04    0.0000000    0.0000000    298.101   127.899    EM
2 -0.19828041D+03 1040.6848765    0.8399629    308.315   117.685    EM
3 -0.19002396D+03    8.2564519    0.0416403    307.503   118.497    EM
4 -0.18912451D+03    0.8994511    0.0047334    305.892   120.108    EM

TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 3

ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE      CLASS COUNTS    ALGORITHM
1 -0.86559584D+03    0.0000000    0.0000000    302.931   123.069    EM
2 -0.18779430D+03  677.8015407    0.7830462    303.007   122.993    EM
3 -0.18764980D+03    0.1445052    0.0007695    302.974   123.026    EM

TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 4

ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE      CLASS COUNTS    ALGORITHM
1 -0.29218610D+03    0.0000000    0.0000000    358.387    67.613    EM
2 -0.19541236D+03   96.7737384    0.3312058    359.519    66.481    EM
3 -0.18817285D+03    7.2395174    0.0370474    359.679    66.321    EM
4 -0.18779751D+03    0.3753340    0.0019946    359.581    66.419    EM

TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 5

ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE      CLASS COUNTS    ALGORITHM
1 -0.18343751D+04    0.0000000    0.0000000    253.154   172.846    EM
2 -0.18785364D+03 1646.5215060    0.8975926    253.245   172.755    EM
3 -0.18771865D+03    0.1349944    0.0007186    253.339   172.661    EM

TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 6

ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE      CLASS COUNTS    ALGORITHM
1 -0.57409037D+03    0.0000000    0.0000000    371.799    54.201    EM
2 -0.18793128D+03  386.1590851    0.6726451    371.759    54.241    EM
3 -0.18791208D+03    0.0191977    0.0001022    371.696    54.304    EM

TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 7

ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE      CLASS COUNTS    ALGORITHM
1 -0.29361257D+03    0.0000000    0.0000000    200.161   225.839    EM
2 -0.19248471D+03  101.1278532    0.3444262    198.657   227.343    EM
3 -0.18667734D+03    5.8073689    0.0301705    197.004   228.996    EM
4 -0.18600715D+03    0.6701941    0.0035901    195.218   230.782    EM

TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 8

ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE      CLASS COUNTS    ALGORITHM
1 -0.38385154D+03    0.0000000    0.0000000    252.518   173.482    EM
2 -0.19956863D+03  184.2829088    0.4800890    251.114   174.886    EM
3 -0.18840409D+03   11.1645345    0.0559433    251.214   174.786    EM
4 -0.18800741D+03    0.3966851    0.0021055    251.217   174.783    EM

TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 9

ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE      CLASS COUNTS    ALGORITHM
1 -0.30305865D+03    0.0000000    0.0000000    143.082   282.918    EM
2 -0.20182784D+03  101.2308039    0.3340304    136.896   289.104    EM
3 -0.18900921D+03   12.8186292    0.0635127    136.681   289.319    EM
4 -0.18804716D+03    0.9620543    0.0050900    137.392   288.608    EM

TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 10

ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE      CLASS COUNTS    ALGORITHM
1 -0.11043172D+04    0.0000000    0.0000000    165.072   260.928    EM
2 -0.18858185D+03  915.7353566    0.8292322    164.697   261.303    EM
3 -0.18776089D+03    0.8209625    0.0043533    165.375   260.625    EM

FINAL STAGE ITERATIONS

TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 7

4 -0.18600715D+03    0.6701941    0.0035901    195.218   230.782    EM
5 -0.18564770D+03    0.3594480    0.0019324    193.204   232.796    EM
6 -0.18521540D+03    0.4322999    0.0023286    190.926   235.074    EM
7 -0.18468446D+03    0.5309373    0.0028666    188.362   237.638    EM
8 -0.18404143D+03    0.6430342    0.0034818    185.506   240.494    EM
9 -0.18328318D+03    0.7582549    0.0041200    182.373   243.627    EM
10 -0.18242638D+03    0.8567930    0.0046747    179.008   246.992    EM
11 -0.18151465D+03    0.9117335    0.0049978    175.495   250.505    EM
12 -0.18061474D+03    0.8999119    0.0049578    171.942   254.058    EM
13 -0.17979760D+03    0.8171390    0.0045242    168.474   257.526    EM
14 -0.17911357D+03    0.6840333    0.0038045    165.199   260.801    EM
15 -0.17857955D+03    0.5340123    0.0029814    162.197   263.803    EM
16 -0.17818481D+03    0.3947384    0.0022104    159.514   266.486    EM
17 -0.17790508D+03    0.2797386    0.0015699    157.169   268.831    EM
18 -0.17771360D+03    0.1914754    0.0010763    155.156   270.844    EM
19 -0.17758647D+03    0.1271288    0.0007154    153.458   272.542    EM
20 -0.17750429D+03    0.0821770    0.0004627    152.043   273.957    EM
21 -0.17745234D+03    0.0519498    0.0002927    150.879   275.121    EM
22 -0.17742005D+03    0.0322912    0.0001820    149.928   276.072    EM
23 -0.17740020D+03    0.0198497    0.0001119    149.156   276.844    EM
24 -0.17738807D+03    0.0121337    0.0000684    148.532   277.468    EM
25 -0.17738066D+03    0.0074113    0.0000418    148.028   277.972    EM
26 -0.17737612D+03    0.0045407    0.0000256    147.623   278.377    EM
27 -0.17737332D+03    0.0027981    0.0000158    147.296   278.704    EM
28 -0.17737158D+03    0.0017373    0.0000098    147.033   278.967    EM
29 -0.17737050D+03    0.0010878    0.0000061    146.821   279.179    EM
30 -0.17736981D+03    0.0006869    0.0000039    146.651   279.349    EM
31 -0.17736937D+03    0.0004373    0.0000025    146.513   279.487    EM
32 -0.17736909D+03    0.0002804    0.0000016    146.402   279.598    EM
33 -0.17736891D+03    0.0001810    0.0000010    146.312   279.688    EM
34 -0.17736879D+03    0.0001175    0.0000007    146.239   279.761    EM
35 -0.17736872D+03    0.0000767    0.0000004    146.180   279.820    EM
36 -0.17736858D+03    0.0001349    0.0000008    145.897   280.103    FS
37 -0.17736857D+03    0.0000082    0.0000000    145.946   280.054    FS
38 -0.17736857D+03    0.0000027    0.0000000    145.914   280.086    FS
39 -0.17736857D+03    0.0000009    0.0000000    145.932   280.068    FS
40 -0.17736857D+03    0.0000003    0.0000000    145.922   280.078    FS
41 -0.17736857D+03    0.0000001    0.0000000    145.928   280.072    FS
42 -0.17736857D+03    0.0000000    0.0000000    145.924   280.076    FS

TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 3

3 -0.18764980D+03    0.1445052    0.0007695    302.974   123.026    EM
4 -0.18759481D+03    0.0549850    0.0002930    302.927   123.073    EM
5 -0.18752945D+03    0.0653576    0.0003484    302.874   123.126    EM
6 -0.18745086D+03    0.0785933    0.0004191    302.815   123.185    EM
7 -0.18735572D+03    0.0951431    0.0005076    302.746   123.254    EM
8 -0.18723974D+03    0.1159756    0.0006190    302.667   123.333    EM
9 -0.18709739D+03    0.1423566    0.0007603    302.573   123.427    EM
10 -0.18692146D+03    0.1759256    0.0009403    302.459   123.541    EM
11 -0.18670270D+03    0.2187604    0.0011703    302.319   123.681    EM
12 -0.18642931D+03    0.2733868    0.0014643    302.145   123.855    EM
13 -0.18608668D+03    0.3426307    0.0018379    301.922   124.078    EM
14 -0.18565756D+03    0.4291190    0.0023060    301.635   124.365    EM
15 -0.18512346D+03    0.5341039    0.0028768    301.261   124.739    EM
16 -0.18446823D+03    0.6552335    0.0035394    300.776   125.224    EM
17 -0.18368500D+03    0.7832262    0.0042459    300.150   125.850    EM
18 -0.18278628D+03    0.8987177    0.0048927    299.359   126.641    EM
19 -0.18181335D+03    0.9729283    0.0053228    298.384   127.616    EM
20 -0.18083652D+03    0.9768346    0.0053727    297.225   128.775    EM
21 -0.17993853D+03    0.8979899    0.0049658    295.901   130.099    EM
22 -0.17918588D+03    0.7526450    0.0041828    294.455   131.545    EM
23 -0.17860689D+03    0.5789946    0.0032313    292.944   133.056    EM
24 -0.17819142D+03    0.4154735    0.0023262    291.428   134.572    EM
25 -0.17790752D+03    0.2838967    0.0015932    289.963   136.037    EM
26 -0.17771921D+03    0.1883082    0.0010585    288.591   137.409    EM
27 -0.17759623D+03    0.1229816    0.0006920    287.340   138.660    EM
28 -0.17751645D+03    0.0797823    0.0004492    286.224   139.776    EM
29 -0.17746478D+03    0.0516625    0.0002910    285.246   140.754    EM
30 -0.17743131D+03    0.0334751    0.0001886    284.400   141.600    EM
31 -0.17740958D+03    0.0217305    0.0001225    283.676   142.324    EM
32 -0.17739544D+03    0.0141403    0.0000797    283.063   142.937    EM
33 -0.17738621D+03    0.0092253    0.0000520    282.547   143.453    EM
34 -0.17738018D+03    0.0060343    0.0000340    282.115   143.885    EM
35 -0.17737622D+03    0.0039569    0.0000223    281.755   144.245    EM
36 -0.17736961D+03    0.0066115    0.0000373    279.798   146.202    FS
37 -0.17736889D+03    0.0007176    0.0000040    280.255   145.745    FS
38 -0.17736868D+03    0.0002107    0.0000012    279.971   146.029    FS
39 -0.17736861D+03    0.0000756    0.0000004    280.134   145.866    FS
40 -0.17736858D+03    0.0000254    0.0000001    280.039   145.961    FS
41 -0.17736857D+03    0.0000089    0.0000001    280.095   145.905    FS
42 -0.17736857D+03    0.0000031    0.0000000    280.062   145.938    FS
43 -0.17736857D+03    0.0000011    0.0000000    280.082   145.918    FS
44 -0.17736857D+03    0.0000004    0.0000000    280.070   145.930    FS
45 -0.17736857D+03    0.0000001    0.0000000    280.077   145.923    FS
46 -0.17736857D+03    0.0000000    0.0000000    280.073   145.927    FS
47 -0.17736857D+03    0.0000000    0.0000000    280.075   145.925    FS

SAVEDATA INFORMATION

Order and format of variables

U              F10.3
X              F10.3
CPROB1         F10.3
CPROB2         F10.3
C              F10.3

Save file
jasap.sav

Save file format
5F10.3

Save file record length    5000

Beginning Time:  22:58:13
Ending Time:  22:58:13
Elapsed Time:  00:00:00

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