Growth Models: A Practical Guide

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2. Outline of Presentation. What are growth models?Nuts and BoltsHands-On ExampleAdditional Issues. 3. Part I: What is a Growth Model?. 4. What is a Growth Model?. A way to assess individual stability and change, both growth and decay, over time.A two-level, hierarchical model that that models (1) within individual change over time and (2) between individual differences in patterns of growth..

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Growth Models: A Practical Guide

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1. 1 Growth Models: A Practical Guide Sarah O. Meadows Center for Research on Child Wellbeing Princeton University October 15, 2007

2. 2 Outline of Presentation What are growth models? Nuts and Bolts Hands-On Example Additional Issues

3. 3 Part I: What is a Growth Model? 1. 1.

4. 4 What is a Growth Model? A way to assess individual stability and change, both growth and decay, over time. A two-level, hierarchical model that that models (1) within individual change over time and (2) between individual differences in patterns of growth.

5. 5 A Rose by Any Other Name . . . Growth Models Trajectory Models Growth Curve Models Latent GM Latent TM Latent GCM Hierarchical Models Random Intercept Models Random Coefficient Models Random Intercept/Random Slope Models Variance Component Models

6. 6 Why Latent? Because we assume that whatever process that is underlying the thing we are modeling (or the behavior we observe) is actually unobserved, or latent. The characteristics we observe are a manifestation of this latent trajectory. This language grew out of structural equation modeling (SEM).

7. 7 Why use GM’s? Everyone else is doing it! Education Criminology Psychology Sociology Public Health You have longitudinal data and are interested in change over time. You may want to explain those changes. You may also believe that not everyone follows the same path.

8. 8 How Have Others Used GMs? “Growth Trajectories of Sexual Risk Behavior in Adolescence and Young Adulthood.” Fergus, Zimmerman, & Caldwell. American Journal of Public Health. 2007. “Individual Differences in the Onset of Tense Marking: A Growth Model Example.” Hadley & Colt. Journal of Speech, Language, and Hearing Research. 2006. “Ten-Year Stability of Depressive Personality Disorder in Depressed Outpatients.” Laptook, Klein, & Dougherty. The American Journal of Psychiatry. 2006. “Verbal Learning and Everyday Functioning in Dementia: An Application of Latent Variable Growth Curve Modeling.” Mast & Allaire. The Journals of Gerontology. 2006. “You Make Me Sick: Marital Quality and Health Over the Life Course.” Umberson, Williams, & Powers. Journal of Health and Social Behavior. 2006. “Parental Divorce and Child Mental Health Trajectories.” Strohschein. 2005. Journal of Marriage and Family.

9. 9 A Detailed Example “Stability and Change in Family Structure and Maternal Health Trajectories.” Meadows, McLanahan, & Brooks-Gunn. American Sociological Review. Forthcoming. We wanted to know whether changes in family structure, including transitions into and out of coresidential relationships, had short-term impacts on health (i.e., crisis model) or long-term impacts on health (i.e., resource model).

10. 10 Example (cont.) Trajectories of maternal self-rated health and mental health problems from one year after birth to five years after birth. Two measures of family structure change: Level 1: Time-Varying Level 2: Time-Invariant

11. 11 Example (cont.) Results: Transitions, especially exits from marriages, resulted in short-term declines in physical health and short-term increases in mental health problems. Little support for the resource model; no growing gap in well-being between mothers who remained stably married and those remained stably single, as well as mothers who made transitions.

12. 12 Figure 1. Mothers’ Mental Health Trajectories

13. 13 Figure 2. Mothers’ Household Income Trajectories

14. 14 Figure 3. Fathers’ Mental Health Trajectories

15. 15 Figure 4. Fathers’ Earnings Trajectories

16. 16 Part II: Nuts and Bolts

17. 17 Where Did GM’s Come From? Time Series Models (Autoregressive) Repeated Measures ANOVA (Duncan & Duncan, 2004) SEM Multilevel Models (HLM)

18. 18 Hierarchical Models Traditional: Level 1: Students Level 2: Schools Growth Models (a type of HM): Level 1: Repeated Observations Level 2: Individuals

19. 19 Unconditional Model Level 1: Within Individual Level 2: Between Individual

20. 20 A Latent Trajectory

21. 21 Time-Invariant Covariates Level 1: Within Individual Level 2: Between Individual

22. 22 Time-Varying Variables Level 1: Within Individual Level 2: Between Individual

23. 23 Fixed vs. Random Fixed: Means of the latent trajectory parameters (i.e., intercept and slope) Random: Variance of the latent trajectory parameters (i.e., indicates individual heterogeneity around population means)

24. 24 Part III: An Example 1. 1.

25. 25 Software MPlus – SEM based HLM – Hierarchical Modeling SAS – Proc Traj STATA

26. 26 Data Requirements Three observations For polynomial curves you need d + 2 repeated measures, where d is the degree of the polynomial. Horizontal data file (i.e., one person, one row). Convert data to .dat file. Remember the order of the variables!!

27. 27 Self-Rated Health Mothers in FFCWS “In general, how is your health?” Excellent (5) Very Good (4) Good (3) Fair (2) Poor (1) Repeated measures one, three, and five years after birth.

28. 28 Setting the Trajectory

29. 29 Models Unconditional Model Fit Conditional Time-Invariant Covariates MPlus Graphs Selection and Causation Time-Varying Covariates

30. 30 Model Fit Chi-Square Not Significant, but almost always is. CFI (Comparative Fit Index) Range: 0 – 1; 1 is best. TLI (Tucker Lewis Index; or NNFI) Range: 0 – 1; 1 is best. RMSEA (Root Mean Square Error of Approximation) Under .05 is good; above .10 is bad.

31. 31 Time-Invariant Covariates Age at Baseline Education Race Biological Parents Mental Health Problem Lived with both Bio Parents at Age 15 Number of Previous Relationships Baseline SRH Considered an Abortion Positive Marriage Attitude Prenatal Variables (medical care, drug and alcohol use, smoking) Baseline Marital Status

32. 32

33. 33 Figure 5. Mothers’ Self-Rated Health Trajectories.

34. 34 Selection Issues Intercept Third factor is responsible for where people start. Slope Third factor is responsible for where people go.

35. 35 Time-Varying Covariate Mental Health Problems Range 0-3 Includes CIDI Major depressive episode, binge drinking, and drug use. All occurred in the past 12-months.

36. 36

37. 37 Part IV: Additional Issues 1. 1.

38. 38 Multi-Models Multi-Group Growth process may vary for each group. Multi-Process Models more than one trajectory.

39. 39 Measurement Latent Measures (Multiple Indicators) Dichotomous/Categorical Variables Count Variables ZIP Models Skewness Transform Variable Semi-Continuous Growth Model

40. 40 Age-Based Growth Model Synthetic cohort Sample members may contribute different amounts of information at different times. Missing Data Drop Cases (default) Multiple Imputation Full Information Maximum Likelihood (FIML) Analysis: MISSING

41. 41 Mixture Models Latent Class Models (LCM/LCA) Group membership not known. Latent Class Growth Models (LCGM/LCGA) Group membership not known and is based on trajectory patterns. No variation is allowed within latent classes. Growth Mixture Models (GMM) Group membership is not known and is based on trajectory patterns. Allows for variation within latent classes.

42. 42 Contact Info 1. 1.

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