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1. Latent Growth Curve Modeling In Mplus: An Introduction and Practice Examples Part I Edward D. Barker, Ph.D. Social, Genetic, and Developmental Psychiatry Centre Institute of Psychiatry, King’s College London

2. Bength & Linda Muthén Mplus: http://www.statmodel.com/ Alan A. Acock Department of HDFS Oregon State University Brigitte Wanner GRIP University of Montréal Acknowledgements

3. Introduction to Mplus Mplus & prog. language Preparing data Descriptive statistics Basic growth Curve Model Basic Model and Assumption Mplus code Interpreting Output & Graphs Quadratic terms Mplus program Interpreting Output & Graphs Missing values in growth models Introduction Mplus code Output Multiple group models At the same time As categorical predictors to show differences in intercept and/or slope Additional models There are many . . . Outline

4. Introduction to Mplus

5. Input and output windows

6. Different commands divided into a series of sections TITLE DATA (required) VARIABLE (required) DEFINE ANALYSIS MODEL OUTPUT SAVEDATA MONTECARLO Mplus Command Language (code, script, etc.)

7. TITLE: Everything after “Title:” is the title and the title ends when “Data:” appears DATA: Tells Mplus where to find the file containing the data. “E:\Growth_Curves\ClassData.dat” Without a specific path, Mplus will look in the same folder where the Mplus code is saved Mplus Command Language (code, script, etc.)

8. VARIABLE: Series of subcommands that tell Mplus . . . Names are names of variables (8 characters max; case sensitive in certain versions) Missing are all (-99) ; tells Mplus user defined missing values Use variables arenames variables to use in the analysis. Useful if have larger data file for multiple purposes/analysis. IMPORTANT ANALYSIS: Tells Mplus what type of analysis and estimator will be used Type = basic ; (default) Mplus Command Language (code, script, etc.)

9. MODEL: This contains the basic model statements Y ON X ; ! regression F1 BY var1@1 var2 var3 var4 ; ! Latent factors var1 WITH var2 ; !correlation OUTPUT: Lists specific statistical and graphical output wanted Will get to this in the next section Mplus Command Language (code, script, etc.)

10. Data and data preparation: SPSS to Mplus

11. Basic Analysis

12. Create Mplus data file from SPSS Write the translation file in SPSS Check to make sure your data is correctly created Conduct basic Mplus analysis Write the Mplus code Practice 1

13. Introduction to Mplus Mplus & prog. language Preparing data Descriptive statistics Basic growth Curve Model Basic Model and Assumption Mplus code Interpreting Output & Graphs Quadratic terms Mplus program Interpreting Output & Graphs Missing values in growth models Introduction Mplus code Output Multiple group models At the same time As categorical predictors to show differences in intercept and/or slope Additional models There are many . . . Outline

14. General latent variable framework Implemented in Mplus program Muthén and Muthén (1998-2007) Latent Growth Curve modeling / Structural Equation Modeling (SEM) is linked to Random Coefficient Growth Modeling / Multilevel modeling Latent Growth Curve modeling (single population) is a “case“ of Growth Mixture Modeling (we cover this tomorrow) Basic Growth Curve Analysis

15. Average growth within a population and its variation Continuous latent variables (growth factors) capture individual differences in development Intercept (mean starting value) Slope (rate of growth) Quadratic term (leveling off, or coming down) Basic Growth Curve Analysis

16. observed variables continuous censored binary ordinal count combinations continuous latent variables measurement models (show an example later today) Basic Growth Curve Analysis

17. Estimating a basic growth curve using Mplus is quite easy. In general, start simple, move to more complex Basic Growth Curve Analysis

18. Basic Growth Curve Analysis Slope Intercept 1.0 1.0 1.0 1.0 1.0 1.0 5.0 2.0 4.0 3.0 1.0 0.0 D12 D13 D14 D15 D16 D17

19. Mplus code for basic growth model

20. Selected growth curve output

21. Selected growth curve output

22. Selected growth curve output

23. Selected growth curve output

24. Selected growth curve output

25. Selected growth curve output

26. Selected growth curve output

27. Run basic growth curve model in Mplus Write Mplus code Go through results and annotate the meaning of different parts of the results Examine 2 graphs Individual observed values Sample estimated means based on model Practice 2

28. Introduction to Mplus Mplus & prog. language Preparing data Descriptive statistics Basic growth Curve Model Basic Model and Assumption Mplus code Interpreting Output & Graphs Quadratic terms Mplus program Interpreting Output & Graphs Missing values in growth models Introduction Mplus code Output Multiple group models At the same time As categorical predictors to show differences in intercept and/or slope Additional models There are many . . . Outline

29. Growth Curve with a Quadratic Term Slope Quadratic Intercept 0.0 4.0 9.0 1.0 16.0 25.0 1.0 0.0 1.0 1.0 1.0 1.0 1.0 5.0 2.0 4.0 3.0 1.0 0.0 D12 D13 D14 D15 D16 D17

30. Mplus code for basic growth model with Quadratic Term

31. Selected output for quadratic model

32. Selected output for quadratic model

33. Selected output for quadratic model

34. Selected output for quadratic model

35. Run growth curve model with quradratic term Write Mplus code Go through results and annotate the meaning of different parts of the results Examine 2 graphs Estimated means based on model Sample individual values Practice 3

36. Introduction to Mplus Mplus & prog. language Preparing data Descriptive statistics Basic growth Curve Model Basic Model and Assumption Mplus code Interpreting Output & Graphs Quadratic terms Mplus program Interpreting Output & Graphs Missing values in growth models Introduction Mplus code Output Multiple group models At the same time As categorical predictors to show differences in intercept and/or slope Additional models There are many . . . Outline

37. Mplus has two ways of working with missing values full information maximum likelihood estimation with missing values (FIML) Multiple imputations. Imputing multiple datasets Estimating the model for each of these datasets Then pooling the estimates and standard errors Missing values

38. Mplus code with missing data

39. Selected output for missing model

40. Selected output for missing model

41. Selected output for missing model

42. Selected output for missing model

43. Run growth curve model with missing analysis Write Mplus code Go through results and annotate how the results change when using missing data analysis Practice 4

44. Introduction to Mplus Mplus & prog. language Preparing data Descriptive statistics Basic growth Curve Model Basic Model and Assumption Mplus code Interpreting Output & Graphs Quadratic terms Mplus program Interpreting Output & Graphs Missing values in growth models Introduction Mplus code Output Multiple group models At the same time As categorical predictors to show differences in intercept and/or slope Additional models There are many . . . Outline

45. Gender Boys higher in delinquency Several ways Compare models Step 1: fit multiple model group and allow estimated parameters to vary Step 2: constrain, at least intercept and slope Multiple group models

46. Multiple group models

47. Selected output: Multiple group models

48. Selected output: Multiple group models

49. Selected output: Multiple group models

50. Selected output: Multiple group models