Mplus VERSION 7.2
MUTHEN & MUTHEN
05/07/2014   2:04 PM

INPUT INSTRUCTIONS

  title:	this is an example of a SEM with continuous factor indicators

  montecarlo:
  	names = y1-y12;
  	nobs = 500;
  	nreps = 1;
  	save = ex5.12.dat;

  model montecarlo:

  	f1 by y1@1 y2-y3*1;
  	f2 by y4@1 y5-y6*.8;
  	f3 by y7@1 y8-y9*.9;
  	f4 by y10@1 y11-y12*.7;

  	y1-y12*1;
  	f1-f2*1;
  	f3-f4*.5;

  	f3 on f1*.5 f2*.7;
  	f4 on f3*.6;

  model:

  	f1 by y1@1 y2-y3*1;
  	f2 by y4@1 y5-y6*.8;
  	f3 by y7@1 y8-y9*.9;
  	f4 by y10@1 y11-y12*.7;

  	y1-y12*1;
  	f1-f2*1;
  	f3-f4*.5;

  	f3 on f1*.5 f2*.7;
  	f4 on f3*.6;

  output:
  	tech9;





INPUT READING TERMINATED NORMALLY



this is an example of a SEM with continuous factor indicators

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                         500

Number of replications
    Requested                                                    1
    Completed                                                    1
Value of seed                                                    0

Number of dependent variables                                   12
Number of independent variables                                  0
Number of continuous latent variables                            4

Observed dependent variables

  Continuous
   Y1          Y2          Y3          Y4          Y5          Y6
   Y7          Y8          Y9          Y10         Y11         Y12

Continuous latent variables
   F1          F2          F3          F4


Estimator                                                       ML
Information matrix                                        OBSERVED
Maximum number of iterations                                  1000
Convergence criterion                                    0.500D-04
Maximum number of steepest descent iterations                   20



SAMPLE STATISTICS FOR THE FIRST REPLICATION


     SAMPLE STATISTICS


           Means
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
      1         0.011         0.047         0.005         0.104         0.078


           Means
              Y6            Y7            Y8            Y9            Y10
              ________      ________      ________      ________      ________
      1         0.074         0.051         0.063         0.078        -0.008


           Means
              Y11           Y12
              ________      ________
      1         0.039         0.031


           Covariances
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
 Y1             1.917
 Y2             1.033         2.031
 Y3             0.794         1.017         1.914
 Y4            -0.038         0.015         0.033         2.039
 Y5             0.002        -0.056        -0.190         0.797         1.622
 Y6            -0.031        -0.005        -0.024         0.745         0.707
 Y7             0.574         0.502         0.330         0.742         0.550
 Y8             0.477         0.368         0.323         0.678         0.476
 Y9             0.511         0.559         0.387         0.601         0.453
 Y10            0.214         0.296         0.184         0.331         0.275
 Y11            0.236         0.267         0.138         0.204         0.138
 Y12            0.221         0.313         0.198         0.139         0.122


           Covariances
              Y6            Y7            Y8            Y9            Y10
              ________      ________      ________      ________      ________
 Y6             1.761
 Y7             0.599         2.312
 Y8             0.579         1.206         1.977
 Y9             0.624         1.178         1.034         1.954
 Y10            0.201         0.693         0.555         0.574         2.061
 Y11            0.213         0.502         0.430         0.403         0.737
 Y12            0.193         0.497         0.385         0.487         0.534


           Covariances
              Y11           Y12
              ________      ________
 Y11            1.501
 Y12            0.494         1.470


           Correlations
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
 Y1             1.000
 Y2             0.524         1.000
 Y3             0.414         0.516         1.000
 Y4            -0.019         0.008         0.017         1.000
 Y5             0.001        -0.031        -0.108         0.438         1.000
 Y6            -0.017        -0.003        -0.013         0.393         0.419
 Y7             0.273         0.232         0.157         0.342         0.284
 Y8             0.245         0.183         0.166         0.338         0.266
 Y9             0.264         0.281         0.200         0.301         0.254
 Y10            0.108         0.145         0.093         0.162         0.150
 Y11            0.139         0.153         0.082         0.116         0.088
 Y12            0.132         0.181         0.118         0.080         0.079


           Correlations
              Y6            Y7            Y8            Y9            Y10
              ________      ________      ________      ________      ________
 Y6             1.000
 Y7             0.297         1.000
 Y8             0.311         0.564         1.000
 Y9             0.337         0.554         0.526         1.000
 Y10            0.105         0.317         0.275         0.286         1.000
 Y11            0.131         0.269         0.250         0.235         0.419
 Y12            0.120         0.269         0.226         0.287         0.307


           Correlations
              Y11           Y12
              ________      ________
 Y11            1.000
 Y12            0.333         1.000


MODEL FIT INFORMATION

Number of Free Parameters                       40

Loglikelihood

    H0 Value

        Mean                             -9646.960
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000        -9646.960      -9646.960
           0.980       0.000        -9646.960      -9646.960
           0.950       0.000        -9646.960      -9646.960
           0.900       0.000        -9646.960      -9646.960
           0.800       0.000        -9646.960      -9646.960
           0.700       0.000        -9646.960      -9646.960
           0.500       0.000        -9646.960      -9646.960
           0.300       0.000        -9646.960      -9646.960
           0.200       0.000        -9646.960      -9646.960
           0.100       0.000        -9646.960      -9646.960
           0.050       0.000        -9646.960      -9646.960
           0.020       0.000        -9646.960      -9646.960
           0.010       0.000        -9646.960      -9646.960

    H1 Value

        Mean                             -9620.108
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000        -9620.108      -9620.108
           0.980       0.000        -9620.108      -9620.108
           0.950       0.000        -9620.108      -9620.108
           0.900       0.000        -9620.108      -9620.108
           0.800       0.000        -9620.108      -9620.108
           0.700       0.000        -9620.108      -9620.108
           0.500       0.000        -9620.108      -9620.108
           0.300       0.000        -9620.108      -9620.108
           0.200       0.000        -9620.108      -9620.108
           0.100       0.000        -9620.108      -9620.108
           0.050       0.000        -9620.108      -9620.108
           0.020       0.000        -9620.108      -9620.108
           0.010       0.000        -9620.108      -9620.108

Information Criteria

    Akaike (AIC)

        Mean                             19373.920
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000        19373.920      19373.920
           0.980       0.000        19373.920      19373.920
           0.950       0.000        19373.920      19373.920
           0.900       0.000        19373.920      19373.920
           0.800       0.000        19373.920      19373.920
           0.700       0.000        19373.920      19373.920
           0.500       0.000        19373.920      19373.920
           0.300       0.000        19373.920      19373.920
           0.200       0.000        19373.920      19373.920
           0.100       0.000        19373.920      19373.920
           0.050       0.000        19373.920      19373.920
           0.020       0.000        19373.920      19373.920
           0.010       0.000        19373.920      19373.920

    Bayesian (BIC)

        Mean                             19542.505
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000        19542.505      19542.505
           0.980       0.000        19542.505      19542.505
           0.950       0.000        19542.505      19542.505
           0.900       0.000        19542.505      19542.505
           0.800       0.000        19542.505      19542.505
           0.700       0.000        19542.505      19542.505
           0.500       0.000        19542.505      19542.505
           0.300       0.000        19542.505      19542.505
           0.200       0.000        19542.505      19542.505
           0.100       0.000        19542.505      19542.505
           0.050       0.000        19542.505      19542.505
           0.020       0.000        19542.505      19542.505
           0.010       0.000        19542.505      19542.505

    Sample-Size Adjusted BIC (n* = (n + 2) / 24)

        Mean                             19415.542
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000        19415.542      19415.542
           0.980       0.000        19415.542      19415.542
           0.950       0.000        19415.542      19415.542
           0.900       0.000        19415.542      19415.542
           0.800       0.000        19415.542      19415.542
           0.700       0.000        19415.542      19415.542
           0.500       0.000        19415.542      19415.542
           0.300       0.000        19415.542      19415.542
           0.200       0.000        19415.542      19415.542
           0.100       0.000        19415.542      19415.542
           0.050       0.000        19415.542      19415.542
           0.020       0.000        19415.542      19415.542
           0.010       0.000        19415.542      19415.542

Chi-Square Test of Model Fit

        Degrees of freedom                      50

        Mean                                53.704
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       1.000           29.707         53.704
           0.980       1.000           31.664         53.704
           0.950       1.000           34.764         53.704
           0.900       1.000           37.689         53.704
           0.800       1.000           41.449         53.704
           0.700       1.000           44.313         53.704
           0.500       1.000           49.335         53.704
           0.300       0.000           54.723         53.704
           0.200       0.000           58.164         53.704
           0.100       0.000           63.167         53.704
           0.050       0.000           67.505         53.704
           0.020       0.000           72.613         53.704
           0.010       0.000           76.154         53.704

RMSEA (Root Mean Square Error Of Approximation)

        Mean                                 0.012
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000            0.012          0.012
           0.980       0.000            0.012          0.012
           0.950       0.000            0.012          0.012
           0.900       0.000            0.012          0.012
           0.800       0.000            0.012          0.012
           0.700       0.000            0.012          0.012
           0.500       0.000            0.012          0.012
           0.300       0.000            0.012          0.012
           0.200       0.000            0.012          0.012
           0.100       0.000            0.012          0.012
           0.050       0.000            0.012          0.012
           0.020       0.000            0.012          0.012
           0.010       0.000            0.012          0.012

SRMR (Standardized Root Mean Square Residual)

        Mean                                 0.027
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000            0.027          0.027
           0.980       0.000            0.027          0.027
           0.950       0.000            0.027          0.027
           0.900       0.000            0.027          0.027
           0.800       0.000            0.027          0.027
           0.700       0.000            0.027          0.027
           0.500       0.000            0.027          0.027
           0.300       0.000            0.027          0.027
           0.200       0.000            0.027          0.027
           0.100       0.000            0.027          0.027
           0.050       0.000            0.027          0.027
           0.020       0.000            0.027          0.027
           0.010       0.000            0.027          0.027


MODEL RESULTS

                              ESTIMATES              S. E.     M. S. E.  95%  % Sig
                 Population   Average   Std. Dev.   Average             Cover Coeff
 F1       BY
  Y1                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y2                  1.000     1.1825     0.0000     0.1039     0.0333 1.000 1.000
  Y3                  1.000     0.9376     0.0000     0.0867     0.0039 1.000 1.000

 F2       BY
  Y4                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y5                  0.800     0.8695     0.0000     0.0852     0.0048 1.000 1.000
  Y6                  0.800     0.8906     0.0000     0.0915     0.0082 1.000 1.000

 F3       BY
  Y7                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y8                  0.900     0.8717     0.0000     0.0593     0.0008 1.000 1.000
  Y9                  0.900     0.8825     0.0000     0.0604     0.0003 1.000 1.000

 F4       BY
  Y10                 1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y11                 0.700     0.8259     0.0000     0.0937     0.0159 1.000 1.000
  Y12                 0.700     0.6820     0.0000     0.0886     0.0003 1.000 1.000

 F3       ON
  F1                  0.500     0.5629     0.0000     0.0701     0.0040 1.000 1.000
  F2                  0.700     0.7901     0.0000     0.0856     0.0081 1.000 1.000

 F4       ON
  F3                  0.600     0.4730     0.0000     0.0570     0.0161 0.000 1.000

 F2       WITH
  F1                  0.000    -0.0301     0.0000     0.0553     0.0009 1.000 0.000

 Intercepts
  Y1                  0.000     0.0113     0.0000     0.0619     0.0001 1.000 0.000
  Y2                  0.000     0.0470     0.0000     0.0637     0.0022 1.000 0.000
  Y3                  0.000     0.0048     0.0000     0.0619     0.0000 1.000 0.000
  Y4                  0.000     0.1039     0.0000     0.0639     0.0108 1.000 0.000
  Y5                  0.000     0.0775     0.0000     0.0570     0.0060 1.000 0.000
  Y6                  0.000     0.0736     0.0000     0.0593     0.0054 1.000 0.000
  Y7                  0.000     0.0513     0.0000     0.0680     0.0026 1.000 0.000
  Y8                  0.000     0.0628     0.0000     0.0629     0.0039 1.000 0.000
  Y9                  0.000     0.0780     0.0000     0.0625     0.0061 1.000 0.000
  Y10                 0.000    -0.0082     0.0000     0.0642     0.0001 1.000 0.000
  Y11                 0.000     0.0392     0.0000     0.0548     0.0015 1.000 0.000
  Y12                 0.000     0.0305     0.0000     0.0542     0.0009 1.000 0.000

 Variances
  F1                  1.000     0.8838     0.0000     0.1222     0.0135 1.000 1.000
  F2                  1.000     0.8883     0.0000     0.1300     0.0125 1.000 1.000

 Residual Variances
  Y1                  1.000     1.0331     0.0000     0.0936     0.0011 1.000 1.000
  Y2                  1.000     0.7955     0.0000     0.1012     0.0418 0.000 1.000
  Y3                  1.000     1.1369     0.0000     0.0918     0.0187 1.000 1.000
  Y4                  1.000     1.1512     0.0000     0.1043     0.0228 1.000 1.000
  Y5                  1.000     0.9502     0.0000     0.0829     0.0025 1.000 1.000
  Y6                  1.000     1.0563     0.0000     0.0905     0.0032 1.000 1.000
  Y7                  1.000     0.9542     0.0000     0.0887     0.0021 1.000 1.000
  Y8                  1.000     0.9448     0.0000     0.0789     0.0031 1.000 1.000
  Y9                  1.000     0.8962     0.0000     0.0774     0.0108 1.000 1.000
  Y10                 1.000     1.2025     0.0000     0.1179     0.0410 1.000 1.000
  Y11                 1.000     0.9155     0.0000     0.0850     0.0071 1.000 1.000
  Y12                 1.000     1.0708     0.0000     0.0834     0.0050 1.000 1.000
  F3                  0.500     0.5501     0.0000     0.0923     0.0025 1.000 1.000
  F4                  0.500     0.5546     0.0000     0.1023     0.0030 1.000 1.000


QUALITY OF NUMERICAL RESULTS

     Average Condition Number for the Information Matrix      0.448E-01
       (ratio of smallest to largest eigenvalue)


TECHNICAL OUTPUT


     PARAMETER SPECIFICATION


           NU
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
      1           1             2             3             4             5


           NU
              Y6            Y7            Y8            Y9            Y10
              ________      ________      ________      ________      ________
      1           6             7             8             9            10


           NU
              Y11           Y12
              ________      ________
      1          11            12


           LAMBDA
              F1            F2            F3            F4
              ________      ________      ________      ________
 Y1                 0             0             0             0
 Y2                13             0             0             0
 Y3                14             0             0             0
 Y4                 0             0             0             0
 Y5                 0            15             0             0
 Y6                 0            16             0             0
 Y7                 0             0             0             0
 Y8                 0             0            17             0
 Y9                 0             0            18             0
 Y10                0             0             0             0
 Y11                0             0             0            19
 Y12                0             0             0            20


           THETA
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
 Y1                21
 Y2                 0            22
 Y3                 0             0            23
 Y4                 0             0             0            24
 Y5                 0             0             0             0            25
 Y6                 0             0             0             0             0
 Y7                 0             0             0             0             0
 Y8                 0             0             0             0             0
 Y9                 0             0             0             0             0
 Y10                0             0             0             0             0
 Y11                0             0             0             0             0
 Y12                0             0             0             0             0


           THETA
              Y6            Y7            Y8            Y9            Y10
              ________      ________      ________      ________      ________
 Y6                26
 Y7                 0            27
 Y8                 0             0            28
 Y9                 0             0             0            29
 Y10                0             0             0             0            30
 Y11                0             0             0             0             0
 Y12                0             0             0             0             0


           THETA
              Y11           Y12
              ________      ________
 Y11               31
 Y12                0            32


           ALPHA
              F1            F2            F3            F4
              ________      ________      ________      ________
      1           0             0             0             0


           BETA
              F1            F2            F3            F4
              ________      ________      ________      ________
 F1                 0             0             0             0
 F2                 0             0             0             0
 F3                33            34             0             0
 F4                 0             0            35             0


           PSI
              F1            F2            F3            F4
              ________      ________      ________      ________
 F1                36
 F2                37            38
 F3                 0             0            39
 F4                 0             0             0            40


     STARTING VALUES


           NU
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
      1         0.000         0.000         0.000         0.000         0.000


           NU
              Y6            Y7            Y8            Y9            Y10
              ________      ________      ________      ________      ________
      1         0.000         0.000         0.000         0.000         0.000


           NU
              Y11           Y12
              ________      ________
      1         0.000         0.000


           LAMBDA
              F1            F2            F3            F4
              ________      ________      ________      ________
 Y1             1.000         0.000         0.000         0.000
 Y2             1.281         0.000         0.000         0.000
 Y3             0.984         0.000         0.000         0.000
 Y4             0.000         1.000         0.000         0.000
 Y5             0.000         0.800         0.000         0.000
 Y6             0.000         0.800         0.000         0.000
 Y7             0.000         0.000         1.000         0.000
 Y8             0.000         0.000         0.900         0.000
 Y9             0.000         0.000         0.900         0.000
 Y10            0.000         0.000         0.000         1.000
 Y11            0.000         0.000         0.000         0.700
 Y12            0.000         0.000         0.000         0.700


           THETA
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
 Y1             1.000
 Y2             0.000         1.000
 Y3             0.000         0.000         1.000
 Y4             0.000         0.000         0.000         1.000
 Y5             0.000         0.000         0.000         0.000         1.000
 Y6             0.000         0.000         0.000         0.000         0.000
 Y7             0.000         0.000         0.000         0.000         0.000
 Y8             0.000         0.000         0.000         0.000         0.000
 Y9             0.000         0.000         0.000         0.000         0.000
 Y10            0.000         0.000         0.000         0.000         0.000
 Y11            0.000         0.000         0.000         0.000         0.000
 Y12            0.000         0.000         0.000         0.000         0.000


           THETA
              Y6            Y7            Y8            Y9            Y10
              ________      ________      ________      ________      ________
 Y6             1.000
 Y7             0.000         1.000
 Y8             0.000         0.000         1.000
 Y9             0.000         0.000         0.000         1.000
 Y10            0.000         0.000         0.000         0.000         1.000
 Y11            0.000         0.000         0.000         0.000         0.000
 Y12            0.000         0.000         0.000         0.000         0.000


           THETA
              Y11           Y12
              ________      ________
 Y11            1.000
 Y12            0.000         1.000


           ALPHA
              F1            F2            F3            F4
              ________      ________      ________      ________
      1         0.000         0.000         0.000         0.000


           BETA
              F1            F2            F3            F4
              ________      ________      ________      ________
 F1             0.000         0.000         0.000         0.000
 F2             0.000         0.000         0.000         0.000
 F3             0.500         0.700         0.000         0.000
 F4             0.000         0.000         0.600         0.000


           PSI
              F1            F2            F3            F4
              ________      ________      ________      ________
 F1             1.000
 F2             0.000         1.000
 F3             0.000         0.000         0.500
 F4             0.000         0.000         0.000         0.500


     POPULATION VALUES


           NU
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           NU
              Y6            Y7            Y8            Y9            Y10
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           NU
              Y11           Y12
              ________      ________
 1              0.000         0.000


           LAMBDA
              F1            F2            F3            F4
              ________      ________      ________      ________
 Y1             1.000         0.000         0.000         0.000
 Y2             1.000         0.000         0.000         0.000
 Y3             1.000         0.000         0.000         0.000
 Y4             0.000         1.000         0.000         0.000
 Y5             0.000         0.800         0.000         0.000
 Y6             0.000         0.800         0.000         0.000
 Y7             0.000         0.000         1.000         0.000
 Y8             0.000         0.000         0.900         0.000
 Y9             0.000         0.000         0.900         0.000
 Y10            0.000         0.000         0.000         1.000
 Y11            0.000         0.000         0.000         0.700
 Y12            0.000         0.000         0.000         0.700


           THETA
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
 Y1             1.000
 Y2             0.000         1.000
 Y3             0.000         0.000         1.000
 Y4             0.000         0.000         0.000         1.000
 Y5             0.000         0.000         0.000         0.000         1.000
 Y6             0.000         0.000         0.000         0.000         0.000
 Y7             0.000         0.000         0.000         0.000         0.000
 Y8             0.000         0.000         0.000         0.000         0.000
 Y9             0.000         0.000         0.000         0.000         0.000
 Y10            0.000         0.000         0.000         0.000         0.000
 Y11            0.000         0.000         0.000         0.000         0.000
 Y12            0.000         0.000         0.000         0.000         0.000


           THETA
              Y6            Y7            Y8            Y9            Y10
              ________      ________      ________      ________      ________
 Y6             1.000
 Y7             0.000         1.000
 Y8             0.000         0.000         1.000
 Y9             0.000         0.000         0.000         1.000
 Y10            0.000         0.000         0.000         0.000         1.000
 Y11            0.000         0.000         0.000         0.000         0.000
 Y12            0.000         0.000         0.000         0.000         0.000


           THETA
              Y11           Y12
              ________      ________
 Y11            1.000
 Y12            0.000         1.000


           ALPHA
              F1            F2            F3            F4
              ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000


           BETA
              F1            F2            F3            F4
              ________      ________      ________      ________
 F1             0.000         0.000         0.000         0.000
 F2             0.000         0.000         0.000         0.000
 F3             0.500         0.700         0.000         0.000
 F4             0.000         0.000         0.600         0.000


           PSI
              F1            F2            F3            F4
              ________      ________      ________      ________
 F1             1.000
 F2             0.000         1.000
 F3             0.000         0.000         0.500
 F4             0.000         0.000         0.000         0.500


TECHNICAL 9 OUTPUT

  Error messages for each replication (if any)



SAVEDATA INFORMATION

  Order of variables

    Y1
    Y2
    Y3
    Y4
    Y5
    Y6
    Y7
    Y8
    Y9
    Y10
    Y11
    Y12

  Save file
    ex5.12.dat

  Save file format           Free
  Save file record length    10000


     Beginning Time:  14:04:06
        Ending Time:  14:04:06
       Elapsed Time:  00:00:00



MUTHEN & MUTHEN
3463 Stoner Ave.
Los Angeles, CA  90066

Tel: (310) 391-9971
Fax: (310) 391-8971
Web: www.StatModel.com
Support: Support@StatModel.com

Copyright (c) 1998-2014 Muthen & Muthen

Back to examples