1. Session 1 1 Check installations 2 Open Mplus 3 Type basic commands 4 Get data read in, spat out &read in again 5 Run an analysis 6 What has it done?

2. Session 2 1 Mplus input file command structures 2 Mplus conventions 3 Mplus punctuation CaSeS ; : (.) & green! 4 Common typos in input 5 Mplus output file structure 6 Output options inc. saves and plots

3. Session 1 1 Check installations 2 Open Mplus 3 Type basic commands 4 Get data read in, spat out &read in again 5 Run an analysis 6 What has it done?

4. Odd1 Even1 Sum1 Case1 Odd2 Even2 Sum2 Case2 7 5 12 1 7 5 12 1 4 4 8 1 4 3 7 1 12 10 22 1 12 12 24 1 5 5 10 1 7 7 14 1 3 7 10 1 3 5 8 1 4 2 6 0 3 1 4 0 3 5 8 1 2 3 5 0 2 2 4 0 3 3 6 0 7 7 14 1 6 8 14 1 3 3 6 0 2 3 5 0 0 2 2 0 3 2 5 0 11 11 22 1 8 8 16 1 12345678901234567890123456789012 12341234XXXX123412341234XXXX1234 DATA: Dunn Statistics in Psychiatry GHQ12 T1 T2 Clinical Psychology students General Health Questionnaire Short self-report questionnaire Used to screen for common mental Disorder (anxiety and depression)

5. Warning, detour ahead …

6. Getting (past) the basics … The importance of total control over data The value of learning simple FORTRAN formatting statements –LISCOMP, the predecessor to Mplus, –And Mplus itself, is written in FORTRAN Reading data in uses simple conventions F / I / G / E / X / T –34.234 could be read as F6 –92 read as F2.1 would be 9.1 »Width in columns for the real number »then number of numerals that appear after the decimal point

7. Overcoming limitations Of the Mplus demo –It has a limit on the number of variables Depending on what analysis you are doing these limits are –4 variables –6 variables We shall (largely) work within them –But we can also beat them to make life easier for you

8. FORTRAN FORMAT STATEMENTS I X T and / –I1 Integer single digit –4X skip four columns without reading anything –Can jump over data in the middle of a file this way »i.e. columns in text files can be ignored –T10 Jump from first column to and start reading at column ten, then process rest of format instructions –Can jump over data at the start of a file this way –/ is to jump to next line (when data has more “records” lines of data per individidual) 001 1 2 3 4 5 6 rather than 001 1 2 3 4 5 6

9. Dunn SiP Book GHQ12 from clinical psychology students Odd1 Even1 Sum1 Case1 Odd2 Even2 Sum2Case2 ------------------------------------------ | 7 5 12 1 7 5 12 1 | 4 4 8 1 4 3 7 1 | 12 10 22 1 12 12 24 1 | 5 5 10 1 7 7 14 1 | 3 7 10 1 3 5 8 1 | 4 2 6 0 3 1 4 0 | 3 5 8 1 2 3 5 0 | 2 2 4 0 3 3 6 0 | 7 7 14 1 6 8 14 1 | 3 3 6 0 2 3 5 0 | 0 2 2 0 3 2 5 0 | 11 11 22 1 8 8 16 1 123451234512345123456123451234561234512345 Numbered columns for field widths (guide for eye and FORTRAN SYNTAX) F5 F5 F5 F6 F5 F6 F5 F5 i.e (3F5,F6,F5,F6,2F5) Specifications for formatted input some F5 some F6

10. End of detour …

11. Analysis time Time to begin! –A first orientation to Mplus in action Data Input file syntax Output Plot Actually just doing data transformation at this stage –Not doing any analysis

12. Odd1 Even1 Sum1 Case1 Odd2 Even2 Sum2 Case2 7 5 12 1 7 5 12 1 4 4 8 1 4 3 7 1 12 10 22 1 12 12 24 1 5 5 10 1 7 7 14 1 3 7 10 1 3 5 8 1 4 2 6 0 3 1 4 0 3 5 8 1 2 3 5 0 2 2 4 0 3 3 6 0 7 7 14 1 6 8 14 1 3 3 6 0 2 3 5 0 0 2 2 0 3 2 5 0 11 11 22 1 8 8 16 1 12345678901234567890123456789012 12341234XXXX123412341234XXXX1234 DATA: Dunn Statistics in Psychiatry GHQ12 T1 T2 Clinical Psychology students General Health Questionnaire Short self-report questionnaire Used to screen for common mental Disorder (anxiety and depression)

13. DATA: FILE IS "c:\dunn_ghqoddeven12.dat"; FORMAT IS I4 I4 4x I4 I4 I4 4x I4; Odd1 Even1 Sum1 Case1 Odd2 Even2 Sum2 Case2 7 5 12 1 7 5 12 1 3 3 6 0 2 3 5 0 11 11 22 1 8 8 16 1

14. DATA: FILE IS "c:\dunn_ghqoddeven12.dat"; FORMAT IS I4 I4 4x I4 I4 I4 4x I4; DEFINE: sum1 = odd1 + even1; diff1= odd1 - even1; !sum2 = odd2 + even2; !diff2= odd2 - even2; VARIABLE: NAMES ARE odd1 even1 case1 odd2 even2 case2; **File actually contains SUM1 & SUM2 variables** USEVARIABLES ARE sum1 diff1; Odd1 Even1 Sum1 Case1 Odd2 Even2 Sum2 Case2 7 5 12 1 7 5 12 1 3 3 6 0 2 3 5 0 11 11 22 1 8 8 16 1 This file is dunn_GHQ12_T1T2_ClinPsych_SiP.inp WARNING - more syntax below in the file estimates a correlation and produces a scatter plot

15. ANALYSIS: ESTIMATOR=ML; MODEL: sum1 with diff1; !sum1 with diff1 sum2 diff2; ! diff1 with sum2 diff2; ! sum2 with diff2; OUTPUT: STDY SAMPSTAT; PLOT: TYPE IS PLOT1; Odd1 Even1 Sum1 Case1 Odd2 Even2 Sum2 Case2 7 5 12 1 7 5 12 1 3 3 6 0 2 3 5 0 11 11 22 1 8 8 16 1 This file is dunn_GHQ12_T1T2_ClinPsych_SiP.inp

16. ANALYSIS: ESTIMATOR=ML; MODEL: sum1 with diff1; !sum1 with diff1 sum2 diff2; ! diff1 with sum2 diff2; ! sum2 with diff2; OUTPUT: STDY SAMPSTAT; PLOT: TYPE IS PLOT1; This file is dunn_GHQ12_T1T2_ClinPsych_SiP.inp

17. SUMMARY OF ANALYSIS [ dunn_GHQ12_T1T2_ClinPsych_SiP.out] Number of groups 1 Number of observations 12 Number of dependent variables 2 Number of independent variables 0 Number of continuous latent variables 0 Observed dependent variables Continuous SUM1 DIFF1

18. [ dunn_GHQ12_T1T2_ClinPsych_SiP.out] 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) c:\dunn_ghqoddeven12.dat Input data format (I4 I4 4X I4 I4 I4 4X I4) [dunn_GHQ12_T1T2_ClinPsych_SiP.out]

19. SAMPLE STATISTICS [ dunn_GHQ12_T1T2_ClinPsych_SiP.out] Means SUM1 DIFF1 ________ ________ 1 10.333 -0.167 Covariances SUM1 DIFF1 ________ ________ SUM1 37.222 DIFF1 3.389 2.972 Correlations SUM1 DIFF1 ________ ________ SUM1 1.000 DIFF1 0.322 1.000 [dunn_GHQ12_T1T2_ClinPsych_SiP.out]

20. THE MODEL ESTIMATION TERMINATED NORMALLY TESTS OF MODEL FIT Chi-Square Test of Model Fit Value 0.000 Degrees of Freedom 0 P-Value 0.0000 Chi-Square Test of Model Fit for the Baseline Model Value 1.315 Degrees of Freedom 1 P-Value 0.2515 CFI/TLI CFI 1.000 TLI 1.000 Loglikelihood H0 Value -61.634 H1 Value -61.634 [dunn_GHQ12_T1T2_ClinPsych_SiP.out]

21. MODEL RESULTS Two-Tailed Estimate S.E. Est./S.E. P-Value SUM1 WITH DIFF1 3.389 3.190 1.062 0.288 Means SUM1 10.333 1.761 5.867 0.000 DIFF1 -0.167 0.498 -0.335 0.738 Variances SUM1 37.221 15.195 2.450 0.014 DIFF1 2.972 1.213 2.449 0.014 STANDARDIZED MODEL RESULTS STDY Standardization Two-Tailed Estimate S.E. Est./S.E. P-Value SUM1 WITH DIFF1 0.322 0.259 1.245 0.213 Means SUM1 1.694 0.450 3.761 0.000 DIFF1 -0.097 0.289 -0.334 0.738 Variances SUM1 1.000 0.000 999.000 999.000 DIFF1 1.000 0.000 999.000 999.000 [dunn_GHQ12_T1T2_ClinPsych_SiP.out]

22. [dunn_GHQ12_T1T2_ClinPsych_SiP.out/gph]

23. Session 2 1 Mplus input file COMMAND STRUCTURES: 2 Mplus conventions 3 Mplus punctuation ; : (.) & green! comment 4 Common typos in input 5 Mplus output file structure 6 Output options inc. saves and plots

24. TITLE: DATA: VARIABLE: DEFINE: ANALYSIS: MODEL: OUTPUT: SAVEDATA: PLOT: Command Structures Simple command structures can be built from the GUI

25. Main command structures appear first on lines as BLOCK CAPS: OTHER COMMANDS THEN FOLLOW either IN CAPS or lowercase; All lines end with a ; but lines can run over more than one line and end with a colon; Conventions

26. We’ve seen this already … TITLE: DATA: VARIABLE: DEFINE: ANALYSIS: MODEL: OUTPUT: SAVEDATA: PLOT: Mplus does not mind which Order commands come in …. You do not need them all! Actually you can do a lot With a little!

27. Mplus is not CaSe SeNsItIvE ! Exclamations - are like comment statements, the editor turns them green

28. All lines end with a semi-colon The most common typo is probably omitting one of these or typing two;;

29. { ( [ Mplus parameters } ) } Variancesor Residual Variances –Variable name without brackets [Means]or Thresholds [catvar$1] –Variable name in square brackets (round brackets) –Variable name in round brackets {Scale factors} –Variable name in curly brackets

30. Mplus output file structure- has to be seen to be believed! OUTPUT: options here govern what you will see in the text output file; SAVEDATA: options here will determine what else is saved in new text files; PLOT: options here will enable you to view graphs of certain things;

31. OUTPUT: and PLOT: OUTPUT: !many more! SAMP STAND RES ! short for residuals) MOD (number) CINT !(three types) TECHn !(14 types-no’s 1 to 14) FSCOEFF FSDETERMINACY + a few more … don’t forget that final colon; PLOT: TYPE IS PLOT1 PLOT2 or PLOT3; ! That’s about it

32. SAVEDATA: You can save –You data (the subset of variables that you modelled only, or these variables plus some more that you want to keep even though you did not use them e.g. IDVARIABLE a subid or AUXILIARY other variables such as sex etc. You can also save –Factor scores (appended to your data) –Latent class memberships –Cook’s distances or “influence” statistics There are also other things you can save …. –These depend on what analysis you have constructed

33. Watch out for the GUI spot here ….. (if you want it)

34. Watch out for the GUI-2

35. GUI doesn’t build this part … V1 F1 V2V3V4 F2 E1 E2 E3 E4

36. GHQ T1 T2 Psychological Distress Odd 1 GHQ T1 Even 1 Odd 2 Even 2 GHQ T2 E1 E2 E3 E4 Correlation Among GHQ scores at T1 and T2 (could be regression)

37. Acronyms / Abbreviations / Fit Chi-Square [Pearson and Likelihood Ratio] CFI/TLI Loglikelihood H0 Value H1 Value Information Criteria Akaike (AIC) Bayesian (BIC) Sample-Size Adjusted BIC (n* = (n + 2) / 24) RMSEA Root Mean Square Error Of Approximation SRMR Standardized Root Mean Square Residual

38. TITLE: Dunn SiP Book GHQ12 from clinical psychology students Odd1 Even1 Sum1 Case1 Odd2 Even2 Sum2 Case2 7 5 12 1 7 5 12 1 4 4 8 1 4 3 7 1 12 10 22 1 12 12 24 1 5 5 10 1 7 7 14 1 3 7 10 1 3 5 8 1 4 2 6 0 3 1 4 0 3 5 8 1 2 3 5 0 2 2 4 0 3 3 6 0 7 7 14 1 6 8 14 1 3 3 6 0 2 3 5 0 0 2 2 0 3 2 5 0 11 11 22 1 8 8 16 1 DATA: FILE IS "c:\dunn_ghqoddeven12.dat"; FORMAT IS I4 I4 4x I4 I4 I4 4x I4; VARIABLE: NAMES ARE odd1 even1 case1 odd2 even2 case2; USEVARIABLES ARE odd1 even1 odd2 even2;

39. ANALYSIS: ESTIMATOR=ML; MODEL: GHQ_T1 by Odd1*1 (1) Even1 (1); GHQ_T1@1; GHQ_T2 by Odd2*1 (1) Even2 (1); GHQ_T2@1; GHQ_T1 with GHQ_T2; Odd1 Even1 Odd2 Even2 (2); OUTPUT: SAMPSTAT RESIDUAL; PLOT: TYPE IS PLOT3; INPUT READING TERMINATED NORMALLY

40. The MODEL statement: Basic commands for modelling BY As in “latent construct measured BY variable” An example would be Depression BY BDI1-BDI3; ! first loading constrained to 1 by default – else can free it and fix var=1 …. which can be read as “measure the latent factor Depression by three variables from the Beck Depression Inventory” [BDI1-BDI3] NB. “through” = hyphen & numbering goes 1-3 not 01-03 ON As in “regression of y ON x” An example would be Depression ON Sex Age; ….. which can be read as “regress the latent construct Depression (y) on the 1st covariate Sex (x1) and 2nd covariate Age (x2)” WITH As in “x1 correlated with y” or “y2 correlated with y3” An example would be Age WITH Depression or Mental WITH Physical

41. MODEL: WITH ON BY WITH –correlated with ON –regressed on BY –measured by

42. SUMMARY OF ANALYSIS Number of groups 1 Number of observations 12 Number of dependent variables 4 Number of independent variables 0 Number of continuous latent variables 2 Observed dependent variables Continuous ODD1 EVEN1 ODD2 EVEN2 Continuous latent variables GHQ_T1 GHQ_T2

43. SAMPLE STATISTICS SAMPLE STATISTICS Means ODD1 EVEN1 ODD2 EVEN2 ________ ________ ________ ________ 1 5.083 5.250 5.000 5.000 Covariances ODD1 EVEN1 ODD2 EVEN2 ________ ________ ________ ________ ODD1 11.743 EVEN1 8.562 8.354 ODD2 9.000 6.333 8.500 EVEN2 9.000 7.667 8.083 9.333 Correlations ODD1 EVEN1 ODD2 EVEN2 ________ ________ ________ ________ ODD1 1.000 EVEN1 0.864 1.000 ODD2 0.901 0.752 1.000 EVEN2 0.860 0.868 0.908 1.000

44. TESTS OF MODEL FIT Chi-Square Test of Model Fit Value 11.920 Degrees of Freedom 7 P-Value 0.1032 Chi-Square Test of Model Fit for the Baseline Model Value 66.542 Degrees of Freedom 6 P-Value 0.0000 CFI/TLI CFI 0.919 TLI 0.930 Loglikelihood H0 Value -94.556 H1 Value -88.596 Information Criteria Number of Free Parameters 7 Akaike (AIC) 203.112 Bayesian (BIC) 206.507 Sample-Size Adjusted BIC 185.339 (n* = (n + 2) / 24) RMSEA (Root Mean Square Error Of Approximation) Estimate 0.242 90 Percent C.I. 0.000 0.471 Probability RMSEA <=.05 0.115 SRMR (Standardized Root Mean Square Residual) Value 0.097

45. MODEL RESULTS Two-Tailed Estimate S.E. Est./S.E. P-Value GHQ_T1 BY ODD1 2.885 0.600 4.812 0.000 EVEN1 2.885 0.600 4.812 0.000 GHQ_T2 BY ODD2 2.885 0.600 4.812 0.000 EVEN2 2.885 0.600 4.812 0.000 GHQ_T1 WITH GHQ_T2 0.961 0.050 19.155 0.000 Intercepts ODD1 5.083 0.889 5.718 0.000 EVEN1 5.250 0.889 5.906 0.000 ODD2 5.000 0.889 5.625 0.000 EVEN2 5.000 0.889 5.625 0.000 Variances GHQ_T1 1.000 0.000 999.000 999.000 GHQ_T2 1.000 0.000 999.000 999.000 Residual Variances ODD1 1.160 0.335 3.464 0.001 EVEN1 1.160 0.335 3.464 0.001 ODD2 1.160 0.335 3.464 0.001 EVEN2 1.160 0.335 3.464 0.001 Ratio of estimate to std error is an approximate z test

46. RESIDUAL OUTPUT ESTIMATED MODEL AND RESIDUALS (OBSERVED - ESTIMATED) Model Estimated Means/Intercepts/Thresholds ODD1 EVEN1 ODD2 EVEN2 ________ ________ ________ ________ 1 5.083 5.250 5.000 5.000 Standardized Residuals (z-scores) for Means/Intercepts/Thresholds ODD1 EVEN1 ODD2 EVEN2 ________ ________ ________ ________ 1 0.000 0.000 0.000 0.000 Model Estimated Covariances/Correlations/Residual Correlations ODD1 EVEN1 ODD2 EVEN2 ________ ________ ________ ________ ODD1 9.483 EVEN1 8.323 9.483 ODD2 8.000 8.000 9.483 EVEN2 8.000 8.000 8.323 9.483 Residuals for Covariances/Correlations/Residual Correlations ODD1 EVEN1 ODD2 EVEN2 ________ ________ ________ ________ ODD1 2.260 EVEN1 0.240 -1.128 ODD2 1.000 -1.667 -0.983 EVEN2 1.000 -0.333 -0.240 -0.149

47. A structural model Measurement and structural relations ABBREVIATIONS & FIT STATISTICS

48. We will see more like that tomorrow, and later today Now for some simple syntax steps INCLUDING REGRESSION CLARIFICATIONS each TYPE

49. Using Mplus to estimate different types of regression model Output gives Odds ratios

50. Mplus regressions (1) Y ON X Linear Regression ANALYSIS: TYPE IS GENERAL; ESTIMATOR=ML; MODEL: Y ON X; Probit regression VARIABLE: CATEGORICAL ARE Y1234; ANALYSIS: TYPE IS GENERAL; ESTIMATOR=WLS; MODEL: Y1234 ON X;

51. Mplus regressions (2) Y ON X Binary Logistic Regression VARIABLE: CATEGORICAL ARE U01; ANALYSIS: TYPE IS GENERAL; ESTIMATOR=ML; MODEL: U01 ON X; Ordinal Logistic Regression VARIABLE: CATEGORICAL ARE U123; ANALYSIS: TYPE IS GENERAL; ESTIMATOR=ML; MODEL: U123 ON X;

52. Out and back: Bob the (re)-builder walk through Reading data with a fixed format –Same kind of data now, bigger dataset –Do an analysis and save data –Then read back in formatted –hals_ighq.inp Then –read_savehalstxt.inp

53. “Passing out” variables [ quick2_rebuild2.inp ] DATA: FILE IS c:\halsghq3.dat; VARIABLE: NAMES ARE GHQ22 GHQ24 GHQ28 AGEYRS IDNUM SEXM1F2; USEVARIABLES ARE AGEYRS GHQ22 GHQ24 GHQ28; CATEGORICAL ARE GHQ22 GHQ24 GHQ28; IDVARIABLE = IDNUM; AUXILIARY = SEXM1F2; MODEL: IGHQ BY GHQ22 GHQ24 GHQ28;!define IGHQ measured BY 3vars IGHQ ON AGEYRS; !Here regressing latent factor ON age SAVEDATA: FILE IS savedata.txt; Little words IS/ARE are optional

54. HALSGHQ3.DAT "halsGHQ3.dat“ 1.000 0.000 0.000 65.000 8514 2.000 0.000 0.000 0.000 74.000 7642 1.000 0.000 1.000 0.000 62.000 12249 2.000 2.000 0.000 2.000 46.000 12024 1.000 0.000 0.000 0.000 44.000 8808 2.000 0.000 0.000 1.000 32.000 4863 2.000 1.000 0.000 0.000 22.000 4849 1.000 0.000 0.000 0.000 60.000 8005 2.000 0.000 1.000 0.000 36.000 5923 1.000 0.000 0.000 0.000 58.000 3080 1.000 1.000 0.000 1.000 63.000 4446 1.000 0.000 0.000 0.000 69.000 6357 1.000 GHQ22 GHQ24 GHQ28 AGEYRS IDNUM SEXM1F2

55. Output. SUMMARY OF ANALYSIS Number of groups 1 Number of observations 6553 Number of dependent variables 3 Number of independent variables 1 Number of continuous latent variables 1 Observed dependent variables Binary and ordered categorical (ordinal) GHQ22 GHQ24 GHQ28 Observed independent variables AGEYRS Observed auxiliary variables SEXM1F2 Continuous latent variables IGHQ Variables with special functions ID variable IDNUM

56. SAVEDATA INFORMATION Order and format of variables GHQ22 F10.3 GHQ24 F10.3 GHQ28 F10.3 AGEYRS F10.3 IDNUM I6 SEXM1F2 F10.3 Save file savedata.txt Save file format 4F10.3 I6 F10.3 Save file record length 5000 Output.. 1.000 0.000 0.000 65.000 8514 2.000 0.000 0.000 0.000 74.000 7642 1.000 0.000 1.000 0.000 62.000 12249 2.000 2.000 0.000 2.000 46.000 12024 1.000 0.000 0.000 0.000 44.000 8808 2.000 0.000 0.000 1.000 32.000 4863 2.000 1.000 0.000 0.000 22.000 4849 1.000 0.000 0.000 0.000 60.000 8005 2.000 0.000 1.000 0.000 36.000 5923 1.000 0.000 0.000 0.000 58.000 3080 1.000 1.000 0.000 1.000 63.000 4446 1.000 0.000 0.000 0.000 69.000 6357 1.000

57. Quick2rebuildout.out INPUT READING TERMINATED NORMALLY SUMMARY OF ANALYSIS Number of groups 1 Number of observations 6553 Number of dependent variables 3 Number of independent variables 1 Number of continuous latent variables 1 Observed dependent variables Binary and ordered categorical (ordinal) GHQ22 GHQ24 GHQ28 Observed independent variables AGEYRS Observed auxiliary variables SEXM1F2 Continuous latent variables IGHQ Variables with special functions ID variable IDNUM

58. Quick2rebuildout.out (cont) Estimator WLSMV Maximum number of iterations 1000 Convergence criterion 0.500D-04 Maximum number of steepest descent iterations 20 Parameterization DELTA Input data file(s) c:\halsghq3.dat Input data format FREE

59. Quick2rebuildout.out SUMMARY OF CATEGORICAL DATA PROPORTIONS GHQ22 Category 1 0.444 Category 2 0.343 Category 3 0.167 Category 4 0.046 GHQ24 Category 1 0.713 Category 2 0.202 Category 3 0.062 Category 4 0.023 GHQ28 Category 1 0.523 Category 2 0.329 Category 3 0.120 Category 4 0.027

60. Quick2rebuildout.out MODEL ESTIMATION TERMINATED NORMALLY :TESTS OF MODELFIT Chi-Square Test of Model Fit Value 20.172* Degrees of Freedom 2** P-Value 0.0000 Chi-Square Test of Model Fit for the Baseline Model Value 12807.273 Degrees of Freedom 4 P-Value 0.0000 CFI/TLI CFI 0.999 TLI 0.997 Number of Free Parameters 13 RMSEA (Root Mean Square Error Of Approximation) Estimate 0.037 WRMR (Weighted Root Mean Square Residual) Value 0.812

61. Quick2rebuildout.out MODEL RESULTS Two-Tailed Estimate S.E. Est./S.E. P-Value IGHQ BY GHQ22 1.000 0.000 999.000 999.000 GHQ24 0.846 0.013 63.991 0.000 GHQ28 0.946 0.014 66.696 0.000 IGHQ ON AGEYRS -0.003 0.001 -3.608 0.000 Thresholds GHQ22$1 -0.344 0.040 -8.706 0.000 GHQ22$2 0.595 0.040 14.912 0.000 GHQ22$3 1.490 0.046 32.627 0.000 GHQ24$1 0.480 0.045 10.725 0.000 GHQ24$2 1.289 0.046 27.834 0.000 GHQ24$3 1.913 0.053 35.945 0.000 GHQ28$1 0.023 0.041 0.551 0.582 GHQ28$2 1.011 0.042 23.950 0.000 GHQ28$3 1.885 0.049 38.205 0.000 Residual Variances IGHQ 0.793 0.013 61.372 0.000

62. Quick2rebuildout.out R-SQUARE Observed Residual Variable Estimate Variance GHQ22 0.794 0.207 GHQ24 0.568 0.433 GHQ28 0.710 0.291 Latent Variable Estimate IGHQ 0.003 QUALITY OF NUMERICAL RESULTS Condition Number for the Information Matrix 0.967E-04 (ratio of smallest to largest eigenvalue) Beginning Time: 05:51:15 Ending Time: 05:51:17 Elapsed Time: 00:00:02

63. Day 1 Tuesday afternoon Session 3 1 Amos 1 and 2 2 Amos 3 and 4 3 Amos 5 and 6 4 Amos 7 and 8 5 Amos 9 and 10 6 Amos 11 and 12

64. Time for some constraints & * @ F by y1*1 (1) y2 (1); F1 by i1 i2 (10) i3 i4 (11); … can be words not numbers

65. Some fun to finish … after Jacque Tacq

66. EFA! DATA: FILE IS datafile.dat; NOBSERVATIONS = 145; TYPE=CORRELATION; … ANALYSIS: TYPE IS EFA 1 3;

67. Easy – eh!

68. Easier!

69. The Formal Structure of Techniques of Multivariate Analysis

70. X1 Y Convergent Causal Structure: Multiple regression analysis X3 X2

71. X Y Bivariate Causal Structure: Test of association between two variables

72. Partial Correlation Analysis Spurious Causality XY ? Z Indirect Causality ? XY Z

73. X1 Y X2 Interactive Structure: Analysis of variance and covariance

74. Latent Structure: Factor analysis... X1X2Xn

75. Canonical Structure: Canonical correlation analysis X1 Xp X2 Y1 Yq Y2...

76. X1X2XnX3 - - - Latent Structure of Similarities: Multi-dimensional scale analysis

77. Multiple regression analysis (convergent causal structure)

78. Analysis of variance (ANOVA) (the interactive structure)

79. Analysis of covariance (ANCOVA) (interactive structure)

80. Partial correlation analysis (spurious or indirect causality) ?

81. Discriminant analysis (discriminant structure)

82. Canonical correlation analysis (the canonical structure)

83. Multivariate multiple regression (convergent causal structure two or several times)

84. Multivariate analysis of variance (interactive structure two or several times)

86. Multivariate discriminate analysis (discrimination structure with more than two population groups)