1. Dynamic Factor Models: A Tool for Analyzing Longitudinal Public Health and Medical Databases Presentation for the 135 th Annual Program Meeting of the American Public Health Association November 7 th, 2007 Ruth L Eudy, PhD Associate Professor, Health Policy and Management Fay W Boozman College of Public Health University of Arkansas for Medical Sciences

2. Purpose of the Presentation Describe the purpose of dynamic factor models for longitudinal data analysis Describe the purpose of dynamic factor models for longitudinal data analysis Illustrate how to set up models and how to interpret results Illustrate how to set up models and how to interpret results Demonstrate the potential of dynamic factor models as a statistical tool for public health research. Demonstrate the potential of dynamic factor models as a statistical tool for public health research.

3. Definition “A class of structural equation modeling applications that involve stationary and non-stationary latent variables across time with lagged (correlated) measurement error.” Randall Schumacker, 2006.

4. Measurement Models   Greek letter Ksi. Latent variable (construct or factor). x i : Indicators of latent variable. Also called observed variables.  : Greek letter lambda. Factor loadings. Parameter estimate of x i regressed on  controlling for measurement error.  i : Greek letter delta. Error term associated with indicator x i. 11 x1x1 x2x2 x3x3 x4x4 x5x5          

5. The Data for Our Example National Longitudinal Survey of Youth 1979 (NLSY79) Over 40 Health Module Answered CESD at 3 points in time Random sample of 500

6. The CES-D Center for Epidemiologic Studies Depressed Mood Scale Designed for population-based studies Summative scale – 7 items included in NLSY questionnaire Has had varied levels of correlation with clinical diagnoses Reliability using coefficient alpha high (0.75 – 0.90)

7. Observed Variables (Indicators) Poor appetite (Appetite) Trouble keeping mind on tasks (Concentrate) Depressed (Depressed) Everything took extra effort (Effort) Restless sleep (Restless) Sad (Sad) Could not get going (Nogo)

8. Cronbach Coefficient Alpha 199219942004 Alpha0.780.820.84 Item-Total Correlation Appetite0.450.460.47 Concentrate0.510.580.61 Depressed0.660.680.72 Effort0.350.440.50 Restless0.470.540.57 Sad0.610.650.67 NoGo0.520.560.63

9. Models for Individual Years CESD 1992 A CD E R S N A CD E R S N A CD E R S N 0.58 0.63 0.89 0.50 0.57 0.85 0.64 0.66 0.60 0.200.75 0.67 0.29 0.59  2 = 24.3, p>0.04 RMSEA = 0.04 NFI = 0.97 CFI = 0.98 0.67 0.58 0.92 0.58 0.60 0.90 0.60 0.650.550.660.150.200.640.62  2 = 14.2, p>0.12 RMSEA = 0.03 NFI = 0.97 CFI = 0.98  2 = 16.7, p>0.17 RMSEA = 0.03 NFI = 0.97 CFI = 0.98 0.72 0.57 0.92 0.87 0.69 0.63 0.70 0.680.490.530.160.240.610.52

10. Hypothesized Dynamic Factor Model CESD 1992 CESD 1994 CESD 2004 ACD ERS N A CE N D RSD A CE R SN

11. Dynamic Factor Model Results: 1992 and 1994 0.63 0.88 CESD 1992 CESD 1994 ACD ERS N N D A CE R S 0.43 0.64 0.63 0.58 0.89 0.63 0.84 0.45 0.66 0.88 0.91 0.73 0.58 0.74 0.67  2 = 39.6, p=0.77 RMSEA = 0.00 NFI = 0.97 CFI = 0.98

12. Dynamic Factor Model Results: 1992, 1994 and 2004 0.69 0.92 CESD 1992 CESD 1994 CESD 2004 ACD ERS N A CE N D RSD A CE R SN 0.630.58 0.90 0.50 0.64 0.80 0.57 0.59 0.66 0.88 0.63 0.62 0.91 0.70 0.58 0.72 0.86 0.65 0.71 0.90 0.72 0.850.56 -0.38  2 = 159.0, p=0.77 RMSEA = 0.00 NFI = 0.97 CFI = 0.98

13. Conclusions Depression in 1992 was significant predictor of depression in 1994 Depression in 1994 was significant predictor of depression in 2004 Autocorrelation of errors was present between both time periods Indicators with higher reliabilities had non-significant error autocorrelations

14. Resources for SEM Bollen, KA (1989). Structural Equation Models with Latent Variables. Wiley Series in Probability and Mathematical Statistics. New York: Wiley and Sons Bollen, KA & Long, JS (Eds.) (1993). Testing Structural Equation Models. Newbury Park, CA: Sage Publication Marcoulides, G.A. & Schumacker, RE (Eds) (2001) New Developments and Techniques in Structural Equation Modeling. Mawah, NJ: Lawrence Erlbaum Associates, Publishers. Scientific Software International: http://www.ssicentral.com Schumacker, RE & Lomax, RG (2004). A Beginner’s Guide to Structural Equation Modeling. 2 nd Ed. Mawah, NJ: Lawrence Erlbaum Associates Structural Equation Modeling: A Multidisciplinary Journal. Mawah, NJ: Lawrence Erlbaum Associates, Publishers.