Mplus VERSION 6.1 MUTHEN & MUTHEN 10/16/2010 1:09 AM INPUT INSTRUCTIONS title: Raw data from Holzinger-Swineford's monograph Grades VII and VIII of the Pasteur elementary school (n=156) followed by Grant-White (n=145) Gender, grade, and age information, and the 24 tests (Pasteur does not have tests 25 and 26) Sources: Holzinger, K. J. & Swineford, F. (1939). A study in Factor Analysis. The Stability of a Bi-Factor Solution. Supplementary Educational Monographs. Chicago, Ill.: The University of Chicago. Harman, H.H. (1976). Modern Factor Analysis. Third Edition. Chicago: The University of Chicago Press data: file is H-S Combined.txt; variable: names are id female grade agey agem school ! school =0/1 with Pasteur=1 visual cubes paper flags general paragrap sentence wordc wordm addition code counting straight wordr numberr figurer object numberf figurew deduct numeric problemr series arithmet; usev = visual-figurew; useobs = school eq 1; !school = 0 for Grant-White; 1 for Pasteur define: standardize visual-figurew; grade = grade - 7; !grade = 0 for Grade 7 vs 1 for Grade 8 analysis: estimator = ml; model: spatial by visual cubes paper flags; verbal by general paragrap sentence wordc wordm; speed by addition code counting straight; memory by wordr numberr figurer object numberf figurew; output: tech1 tech8 stdy; plot: type = plot2; *** WARNING in OUTPUT command TECH8 option is available only with analysis types MIXTURE, RANDOM, or TWOLEVEL with estimators ML, MLF, or MLR or ALGORITHM=INTEGRATION. Request for TECH8 is ignored. 1 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS Raw data from Holzinger-Swineford's monograph Grades VII and VIII of the Pasteur elementary school (n=156) followed by Grant-White (n=145) Gender, grade, and age information, and the 24 tests (Pasteur does not have tests 25 and 26) Sources: Holzinger, K. J. & Swineford, F. (1939). A study in Factor Analysis. The Stability of a Bi-Factor Solution. Supplementary Educational Monographs. Chicago, Ill.: The University of Chicago. Harman, H.H. (1976). Modern Factor Analysis. Third Edition. Chicago: The University of Chicago Press SUMMARY OF ANALYSIS Number of groups 1 Number of observations 156 Number of dependent variables 19 Number of independent variables 0 Number of continuous latent variables 4 Observed dependent variables Continuous VISUAL CUBES PAPER FLAGS GENERAL PARAGRAP SENTENCE WORDC WORDM ADDITION CODE COUNTING STRAIGHT WORDR NUMBERR FIGURER OBJECT NUMBERF FIGUREW Continuous latent variables SPATIAL VERBAL SPEED MEMORY Estimator ML Information matrix OBSERVED Maximum number of iterations 1000 Convergence criterion 0.500D-04 Maximum number of steepest descent iterations 20 Input data file(s) H-S Combined.txt Input data format FREE THE MODEL ESTIMATION TERMINATED NORMALLY MODEL FIT INFORMATION Number of Free Parameters 63 Loglikelihood H0 Value -3755.761 H1 Value -3625.383 Information Criteria Akaike (AIC) 7637.521 Bayesian (BIC) 7829.662 Sample-Size Adjusted BIC 7630.247 (n* = (n + 2) / 24) Chi-Square Test of Model Fit Value 260.755 Degrees of Freedom 146 P-Value 0.0000 RMSEA (Root Mean Square Error Of Approximation) Estimate 0.071 90 Percent C.I. 0.057 0.085 Probability RMSEA <= .05 0.009 CFI/TLI CFI 0.882 TLI 0.862 Chi-Square Test of Model Fit for the Baseline Model Value 1141.640 Degrees of Freedom 171 P-Value 0.0000 SRMR (Standardized Root Mean Square Residual) Value 0.081 MODEL RESULTS Two-Tailed Estimate S.E. Est./S.E. P-Value SPATIAL BY VISUAL 1.000 0.000 999.000 999.000 CUBES 0.476 0.140 3.405 0.001 PAPER 0.546 0.129 4.229 0.000 FLAGS 0.716 0.154 4.644 0.000 VERBAL BY GENERAL 1.000 0.000 999.000 999.000 PARAGRAP 0.975 0.084 11.630 0.000 SENTENCE 1.054 0.081 13.062 0.000 WORDC 0.874 0.087 10.042 0.000 WORDM 1.008 0.081 12.418 0.000 SPEED BY ADDITION 1.000 0.000 999.000 999.000 CODE 1.410 0.260 5.412 0.000 COUNTING 0.923 0.192 4.797 0.000 STRAIGHT 0.984 0.207 4.748 0.000 MEMORY BY WORDR 1.000 0.000 999.000 999.000 NUMBERR 0.840 0.162 5.181 0.000 FIGURER 0.944 0.180 5.255 0.000 OBJECT 0.885 0.171 5.168 0.000 NUMBERF 0.742 0.167 4.430 0.000 FIGUREW 0.738 0.168 4.384 0.000 VERBAL WITH SPATIAL 0.302 0.082 3.686 0.000 SPEED WITH SPATIAL 0.163 0.055 2.946 0.003 VERBAL 0.222 0.057 3.883 0.000 MEMORY WITH SPATIAL 0.187 0.062 3.009 0.003 VERBAL 0.092 0.053 1.738 0.082 SPEED 0.159 0.048 3.322 0.001 Intercepts VISUAL 0.000 0.080 0.000 1.000 CUBES 0.000 0.080 0.000 1.000 PAPER 0.000 0.080 0.000 1.000 FLAGS 0.000 0.080 0.000 1.000 GENERAL 0.000 0.080 0.000 1.000 PARAGRAP 0.000 0.080 0.000 1.000 SENTENCE 0.000 0.080 0.000 1.000 WORDC 0.000 0.080 0.000 1.000 WORDM 0.000 0.080 0.000 1.000 ADDITION 0.000 0.080 0.000 1.000 CODE 0.000 0.080 0.000 1.000 COUNTING 0.000 0.080 0.000 1.000 STRAIGHT 0.000 0.080 0.000 1.000 WORDR 0.000 0.080 0.000 1.000 NUMBERR 0.000 0.080 0.000 1.000 FIGURER 0.000 0.080 0.000 1.000 OBJECT 0.000 0.080 0.000 1.000 NUMBERF 0.000 0.080 0.000 1.000 FIGUREW 0.000 0.080 0.000 1.000 Variances SPATIAL 0.652 0.154 4.245 0.000 VERBAL 0.681 0.110 6.181 0.000 SPEED 0.306 0.096 3.192 0.001 MEMORY 0.398 0.108 3.673 0.000 Residual Variances VISUAL 0.342 0.118 2.894 0.004 CUBES 0.846 0.105 8.027 0.000 PAPER 0.799 0.100 8.013 0.000 FLAGS 0.659 0.101 6.506 0.000 GENERAL 0.312 0.045 6.989 0.000 PARAGRAP 0.346 0.048 7.269 0.000 SENTENCE 0.236 0.039 6.130 0.000 WORDC 0.473 0.060 7.910 0.000 WORDM 0.301 0.044 6.867 0.000 ADDITION 0.688 0.093 7.398 0.000 CODE 0.386 0.092 4.194 0.000 COUNTING 0.733 0.098 7.510 0.000 STRAIGHT 0.698 0.094 7.457 0.000 WORDR 0.595 0.090 6.579 0.000 NUMBERR 0.713 0.096 7.406 0.000 FIGURER 0.639 0.094 6.833 0.000 OBJECT 0.682 0.094 7.223 0.000 NUMBERF 0.775 0.098 7.869 0.000 FIGUREW 0.777 0.099 7.877 0.000 STANDARDIZED MODEL RESULTS STDY Standardization Two-Tailed Estimate S.E. Est./S.E. P-Value SPATIAL BY VISUAL 0.810 0.075 10.870 0.000 CUBES 0.386 0.089 4.336 0.000 PAPER 0.443 0.080 5.526 0.000 FLAGS 0.580 0.080 7.279 0.000 VERBAL BY GENERAL 0.828 0.030 27.482 0.000 PARAGRAP 0.808 0.033 24.825 0.000 SENTENCE 0.873 0.025 35.070 0.000 WORDC 0.724 0.042 17.071 0.000 WORDM 0.835 0.029 28.349 0.000 SPEED BY ADDITION 0.555 0.072 7.694 0.000 CODE 0.782 0.061 12.877 0.000 COUNTING 0.512 0.078 6.579 0.000 STRAIGHT 0.546 0.073 7.498 0.000 MEMORY BY WORDR 0.633 0.068 9.331 0.000 NUMBERR 0.532 0.076 7.001 0.000 FIGURER 0.597 0.072 8.330 0.000 OBJECT 0.560 0.073 7.626 0.000 NUMBERF 0.470 0.079 5.967 0.000 FIGUREW 0.467 0.079 5.919 0.000 VERBAL WITH SPATIAL 0.453 0.085 5.331 0.000 SPEED WITH SPATIAL 0.366 0.100 3.644 0.000 VERBAL 0.486 0.081 6.038 0.000 MEMORY WITH SPATIAL 0.368 0.105 3.505 0.000 VERBAL 0.177 0.098 1.811 0.070 SPEED 0.456 0.099 4.607 0.000 Intercepts VISUAL 0.000 0.080 0.000 1.000 CUBES 0.000 0.080 0.000 1.000 PAPER 0.000 0.080 0.000 1.000 FLAGS 0.000 0.080 0.000 1.000 GENERAL 0.000 0.080 0.000 1.000 PARAGRAP 0.000 0.080 0.000 1.000 SENTENCE 0.000 0.080 0.000 1.000 WORDC 0.000 0.080 0.000 1.000 WORDM 0.000 0.080 0.000 1.000 ADDITION 0.000 0.080 0.000 1.000 CODE 0.000 0.080 0.000 1.000 COUNTING 0.000 0.080 0.000 1.000 STRAIGHT 0.000 0.080 0.000 1.000 WORDR 0.000 0.080 0.000 1.000 NUMBERR 0.000 0.080 0.000 1.000 FIGURER 0.000 0.080 0.000 1.000 OBJECT 0.000 0.080 0.000 1.000 NUMBERF 0.000 0.080 0.000 1.000 FIGUREW 0.000 0.080 0.000 1.000 Variances SPATIAL 1.000 0.000 999.000 999.000 VERBAL 1.000 0.000 999.000 999.000 SPEED 1.000 0.000 999.000 999.000 MEMORY 1.000 0.000 999.000 999.000 Residual Variances VISUAL 0.344 0.121 2.847 0.004 CUBES 0.851 0.069 12.388 0.000 PAPER 0.804 0.071 11.340 0.000 FLAGS 0.663 0.092 7.173 0.000 GENERAL 0.314 0.050 6.295 0.000 PARAGRAP 0.348 0.053 6.618 0.000 SENTENCE 0.238 0.043 5.477 0.000 WORDC 0.476 0.061 7.764 0.000 WORDM 0.303 0.049 6.173 0.000 ADDITION 0.692 0.080 8.658 0.000 CODE 0.389 0.095 4.092 0.000 COUNTING 0.738 0.080 9.275 0.000 STRAIGHT 0.702 0.079 8.839 0.000 WORDR 0.599 0.086 6.973 0.000 NUMBERR 0.717 0.081 8.889 0.000 FIGURER 0.643 0.086 7.506 0.000 OBJECT 0.686 0.082 8.335 0.000 NUMBERF 0.780 0.074 10.551 0.000 FIGUREW 0.782 0.074 10.605 0.000 R-SQUARE Observed Two-Tailed Variable Estimate S.E. Est./S.E. P-Value VISUAL 0.656 0.121 5.435 0.000 CUBES 0.149 0.069 2.168 0.030 PAPER 0.196 0.071 2.763 0.006 FLAGS 0.337 0.092 3.640 0.000 GENERAL 0.686 0.050 13.741 0.000 PARAGRAP 0.652 0.053 12.413 0.000 SENTENCE 0.762 0.043 17.535 0.000 WORDC 0.524 0.061 8.536 0.000 WORDM 0.697 0.049 14.175 0.000 ADDITION 0.308 0.080 3.847 0.000 CODE 0.611 0.095 6.439 0.000 COUNTING 0.262 0.080 3.290 0.001 STRAIGHT 0.298 0.079 3.749 0.000 WORDR 0.401 0.086 4.666 0.000 NUMBERR 0.283 0.081 3.501 0.000 FIGURER 0.357 0.086 4.165 0.000 OBJECT 0.314 0.082 3.813 0.000 NUMBERF 0.220 0.074 2.984 0.003 FIGUREW 0.218 0.074 2.959 0.003 QUALITY OF NUMERICAL RESULTS Condition Number for the Information Matrix 0.504E-02 (ratio of smallest to largest eigenvalue) TECHNICAL 1 OUTPUT PARAMETER SPECIFICATION NU VISUAL CUBES PAPER FLAGS GENERAL ________ ________ ________ ________ ________ 1 1 2 3 4 5 NU PARAGRAP SENTENCE WORDC WORDM ADDITION ________ ________ ________ ________ ________ 1 6 7 8 9 10 NU CODE COUNTING STRAIGHT WORDR NUMBERR ________ ________ ________ ________ ________ 1 11 12 13 14 15 NU FIGURER OBJECT NUMBERF FIGUREW ________ ________ ________ ________ 1 16 17 18 19 LAMBDA SPATIAL VERBAL SPEED MEMORY ________ ________ ________ ________ VISUAL 0 0 0 0 CUBES 20 0 0 0 PAPER 21 0 0 0 FLAGS 22 0 0 0 GENERAL 0 0 0 0 PARAGRAP 0 23 0 0 SENTENCE 0 24 0 0 WORDC 0 25 0 0 WORDM 0 26 0 0 ADDITION 0 0 0 0 CODE 0 0 27 0 COUNTING 0 0 28 0 STRAIGHT 0 0 29 0 WORDR 0 0 0 0 NUMBERR 0 0 0 30 FIGURER 0 0 0 31 OBJECT 0 0 0 32 NUMBERF 0 0 0 33 FIGUREW 0 0 0 34 THETA VISUAL CUBES PAPER FLAGS GENERAL ________ ________ ________ ________ ________ VISUAL 35 CUBES 0 36 PAPER 0 0 37 FLAGS 0 0 0 38 GENERAL 0 0 0 0 39 PARAGRAP 0 0 0 0 0 SENTENCE 0 0 0 0 0 WORDC 0 0 0 0 0 WORDM 0 0 0 0 0 ADDITION 0 0 0 0 0 CODE 0 0 0 0 0 COUNTING 0 0 0 0 0 STRAIGHT 0 0 0 0 0 WORDR 0 0 0 0 0 NUMBERR 0 0 0 0 0 FIGURER 0 0 0 0 0 OBJECT 0 0 0 0 0 NUMBERF 0 0 0 0 0 FIGUREW 0 0 0 0 0 THETA PARAGRAP SENTENCE WORDC WORDM ADDITION ________ ________ ________ ________ ________ PARAGRAP 40 SENTENCE 0 41 WORDC 0 0 42 WORDM 0 0 0 43 ADDITION 0 0 0 0 44 CODE 0 0 0 0 0 COUNTING 0 0 0 0 0 STRAIGHT 0 0 0 0 0 WORDR 0 0 0 0 0 NUMBERR 0 0 0 0 0 FIGURER 0 0 0 0 0 OBJECT 0 0 0 0 0 NUMBERF 0 0 0 0 0 FIGUREW 0 0 0 0 0 THETA CODE COUNTING STRAIGHT WORDR NUMBERR ________ ________ ________ ________ ________ CODE 45 COUNTING 0 46 STRAIGHT 0 0 47 WORDR 0 0 0 48 NUMBERR 0 0 0 0 49 FIGURER 0 0 0 0 0 OBJECT 0 0 0 0 0 NUMBERF 0 0 0 0 0 FIGUREW 0 0 0 0 0 THETA FIGURER OBJECT NUMBERF FIGUREW ________ ________ ________ ________ FIGURER 50 OBJECT 0 51 NUMBERF 0 0 52 FIGUREW 0 0 0 53 ALPHA SPATIAL VERBAL SPEED MEMORY ________ ________ ________ ________ 1 0 0 0 0 BETA SPATIAL VERBAL SPEED MEMORY ________ ________ ________ ________ SPATIAL 0 0 0 0 VERBAL 0 0 0 0 SPEED 0 0 0 0 MEMORY 0 0 0 0 PSI SPATIAL VERBAL SPEED MEMORY ________ ________ ________ ________ SPATIAL 54 VERBAL 55 56 SPEED 57 58 59 MEMORY 60 61 62 63 STARTING VALUES NU VISUAL CUBES PAPER FLAGS GENERAL ________ ________ ________ ________ ________ 1 0.000 0.000 0.000 0.000 0.000 NU PARAGRAP SENTENCE WORDC WORDM ADDITION ________ ________ ________ ________ ________ 1 0.000 0.000 0.000 0.000 0.000 NU CODE COUNTING STRAIGHT WORDR NUMBERR ________ ________ ________ ________ ________ 1 0.000 0.000 0.000 0.000 0.000 NU FIGURER OBJECT NUMBERF FIGUREW ________ ________ ________ ________ 1 0.000 0.000 0.000 0.000 LAMBDA SPATIAL VERBAL SPEED MEMORY ________ ________ ________ ________ VISUAL 1.000 0.000 0.000 0.000 CUBES 0.759 0.000 0.000 0.000 PAPER 0.690 0.000 0.000 0.000 FLAGS 0.922 0.000 0.000 0.000 GENERAL 0.000 1.000 0.000 0.000 PARAGRAP 0.000 0.961 0.000 0.000 SENTENCE 0.000 1.046 0.000 0.000 WORDC 0.000 0.846 0.000 0.000 WORDM 0.000 0.995 0.000 0.000 ADDITION 0.000 0.000 1.000 0.000 CODE 0.000 0.000 1.008 0.000 COUNTING 0.000 0.000 0.896 0.000 STRAIGHT 0.000 0.000 0.947 0.000 WORDR 0.000 0.000 0.000 1.000 NUMBERR 0.000 0.000 0.000 0.797 FIGURER 0.000 0.000 0.000 0.809 OBJECT 0.000 0.000 0.000 0.728 NUMBERF 0.000 0.000 0.000 0.747 FIGUREW 0.000 0.000 0.000 0.562 THETA VISUAL CUBES PAPER FLAGS GENERAL ________ ________ ________ ________ ________ VISUAL 0.500 CUBES 0.000 0.500 PAPER 0.000 0.000 0.500 FLAGS 0.000 0.000 0.000 0.500 GENERAL 0.000 0.000 0.000 0.000 0.500 PARAGRAP 0.000 0.000 0.000 0.000 0.000 SENTENCE 0.000 0.000 0.000 0.000 0.000 WORDC 0.000 0.000 0.000 0.000 0.000 WORDM 0.000 0.000 0.000 0.000 0.000 ADDITION 0.000 0.000 0.000 0.000 0.000 CODE 0.000 0.000 0.000 0.000 0.000 COUNTING 0.000 0.000 0.000 0.000 0.000 STRAIGHT 0.000 0.000 0.000 0.000 0.000 WORDR 0.000 0.000 0.000 0.000 0.000 NUMBERR 0.000 0.000 0.000 0.000 0.000 FIGURER 0.000 0.000 0.000 0.000 0.000 OBJECT 0.000 0.000 0.000 0.000 0.000 NUMBERF 0.000 0.000 0.000 0.000 0.000 FIGUREW 0.000 0.000 0.000 0.000 0.000 THETA PARAGRAP SENTENCE WORDC WORDM ADDITION ________ ________ ________ ________ ________ PARAGRAP 0.500 SENTENCE 0.000 0.500 WORDC 0.000 0.000 0.500 WORDM 0.000 0.000 0.000 0.500 ADDITION 0.000 0.000 0.000 0.000 0.500 CODE 0.000 0.000 0.000 0.000 0.000 COUNTING 0.000 0.000 0.000 0.000 0.000 STRAIGHT 0.000 0.000 0.000 0.000 0.000 WORDR 0.000 0.000 0.000 0.000 0.000 NUMBERR 0.000 0.000 0.000 0.000 0.000 FIGURER 0.000 0.000 0.000 0.000 0.000 OBJECT 0.000 0.000 0.000 0.000 0.000 NUMBERF 0.000 0.000 0.000 0.000 0.000 FIGUREW 0.000 0.000 0.000 0.000 0.000 THETA CODE COUNTING STRAIGHT WORDR NUMBERR ________ ________ ________ ________ ________ CODE 0.500 COUNTING 0.000 0.500 STRAIGHT 0.000 0.000 0.500 WORDR 0.000 0.000 0.000 0.500 NUMBERR 0.000 0.000 0.000 0.000 0.500 FIGURER 0.000 0.000 0.000 0.000 0.000 OBJECT 0.000 0.000 0.000 0.000 0.000 NUMBERF 0.000 0.000 0.000 0.000 0.000 FIGUREW 0.000 0.000 0.000 0.000 0.000 THETA FIGURER OBJECT NUMBERF FIGUREW ________ ________ ________ ________ FIGURER 0.500 OBJECT 0.000 0.500 NUMBERF 0.000 0.000 0.500 FIGUREW 0.000 0.000 0.000 0.500 ALPHA SPATIAL VERBAL SPEED MEMORY ________ ________ ________ ________ 1 0.000 0.000 0.000 0.000 BETA SPATIAL VERBAL SPEED MEMORY ________ ________ ________ ________ SPATIAL 0.000 0.000 0.000 0.000 VERBAL 0.000 0.000 0.000 0.000 SPEED 0.000 0.000 0.000 0.000 MEMORY 0.000 0.000 0.000 0.000 PSI SPATIAL VERBAL SPEED MEMORY ________ ________ ________ ________ SPATIAL 0.050 VERBAL 0.000 0.050 SPEED 0.000 0.000 0.050 MEMORY 0.000 0.000 0.000 0.050 PLOT INFORMATION The following plots are available: No plots are available Beginning Time: 01:09:08 Ending Time: 01:09:09 Elapsed Time: 00:00:01 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) 1998-2010 Muthen & Muthen