04_TwoOccasionChange_020210

04_TwoOccasionChange_020210 - HDFS 597K Overview 1...

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1 AUTO-REGRESSIVE & DIFFERENCE SCORE MODELS of CHANGE HDFS 597K February 02, 2009 HDFS 597K Applied Longitudinal Data Analysis Overview 1. Two-occasion longitudinal data 2. Type-A Auto-Regression Model 3. Type-D difference score models 4. Some additions 2-OCCASION LONGITUDINAL DATA Two-Occasion Data are Valuable • Two-occasions are the first instance of longitudinal data – All longitudinal data collections begin with two occasions, then they get more … and more … and . .. Some basic questions of representing change over • Some basic questions of representing change over time ( see Nesselroade, 1991 ) Change in interindividual differences Interindividual differences in change Different problems seem to suggest different models and methods of analysis Example of Two-Occasion Data • Data from the RIGHT (Research Investigating Growth and Health Trajectories) Track Research Project – Focus on the development and developmental trajectories of early disruptive behavior • Participants: – N=431 children, Measured at age 2, 4, 5 & 7 years • Measures: – Attention Deficit Hyperactivity Total Scores • age 4 & age 7 assessments 5 The CORR Procedure 2 Variables: adhd_to4 adhd_to7 Simple Statistics Variable N Mean Std Dev Sum Minimum Maximum adhd_to4 376 13.78 9.29 5182 0 51.00 adhd_to7 328 12.11 10.13 3973 0 54.00 Summary Statistics from RIGHT Track Pearson Correlation Coefficients Prob > |r| under H0: Rho=0 Number of Observations adhd_to4 adhd_to7 adhd_to4 1.00000 0.60359 <.0001 376 314 adhd_to7 0.60359 1.00000 <.0001 314 328
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2 There are two approaches to the prediction of change in such analyses, and in this book (sic) we use both. The first approach involves computing a change score by subtracting the “before” measure from the “after” measure, and then using the change score as the “dependent variable.” Quotes from Bachman et al (2002, p.31) The second approach uses the “after” measure as the “dependent variable” and include the “before” measure as one of the “predictors” (i.e., as a covariate). In either case one could say that the earlier score is being “controlled,” but the means of controlling differ and the results of the analysis also can differ --- sometimes in important ways. Bivariate Scatterplot X=Age 4 vs. Y=Age 7 8 Plotting Individual “Trajectories” (n=50) 9 AUTO-REGRESSIVE MODELS MODELS FOR REPEATED MEASURES O A linear model is expressed for i=1 to N as Y[2] i = β 0 + 1 Y[1] i + e i • where 0 is the intercept term -- the predicted score of Y[2] when Y[1]=0 • where 1 is the coefficient term -- the change in the predicted score of Y[2] for a one unit change in Y[1] Most Common Linear Regression Models • where e is the residual score -- an unobserved and random score which is uncorrelated with Y[1] but forms part of the variance of Y[2] O The ratio of the variance of e to Y [ 2 ] ( σ e 2 / y 2 = 1- R 2 ) can be a useful index of forecast (in)efficiency Complete Cross-Products based Auto- Regression Model for Repeated Measures Y[1] Y[2] e e 2 =1 1 2 1 12 1 μ 1 =1 0 Note: The inclusion of constant 1 allows the intercept 0 to be part of the regression equation for Y[2].
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This note was uploaded on 01/27/2011 for the course HDFS 597 taught by Professor P during the Spring '11 term at Penn State.

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04_TwoOccasionChange_020210 - HDFS 597K Overview 1...

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