The STARTS Model David A. Kenny December 15, 2013.

Slides:



Advertisements
Similar presentations
Growth Curve Models (being revised)
Advertisements

TWO STEP EQUATIONS 1. SOLVE FOR X 2. DO THE ADDITION STEP FIRST
LEUCEMIA MIELOIDE AGUDA TIPO 0
Bellwork If you roll a die, what is the probability that you roll a 2 or an odd number? P(2 or odd) 2. Is this an example of mutually exclusive, overlapping,
1 Copyright © 2010, Elsevier Inc. All rights Reserved Fig 2.1 Chapter 2.
1 Copyright © 2013 Elsevier Inc. All rights reserved. Chapter 38.
1 Chapter 40 - Physiology and Pathophysiology of Diuretic Action Copyright © 2013 Elsevier Inc. All rights reserved.
Working with Under-identified Structural Equation Models
By D. Fisher Geometric Transformations. Reflection, Rotation, or Translation 1.
Business Transaction Management Software for Application Coordination 1 Business Processes and Coordination.
SMA 6304 / MIT / MIT Manufacturing Systems Lecture 11: Forecasting Lecturer: Prof. Duane S. Boning Copyright 2003 © Duane S. Boning. 1.
Jeopardy Q 1 Q 6 Q 11 Q 16 Q 21 Q 2 Q 7 Q 12 Q 17 Q 22 Q 3 Q 8 Q 13
Jeopardy Q 1 Q 6 Q 11 Q 16 Q 21 Q 2 Q 7 Q 12 Q 17 Q 22 Q 3 Q 8 Q 13
Title Subtitle.
0 - 0.
ALGEBRAIC EXPRESSIONS
DIVIDING INTEGERS 1. IF THE SIGNS ARE THE SAME THE ANSWER IS POSITIVE 2. IF THE SIGNS ARE DIFFERENT THE ANSWER IS NEGATIVE.
MULTIPLYING MONOMIALS TIMES POLYNOMIALS (DISTRIBUTIVE PROPERTY)
ADDING INTEGERS 1. POS. + POS. = POS. 2. NEG. + NEG. = NEG. 3. POS. + NEG. OR NEG. + POS. SUBTRACT TAKE SIGN OF BIGGER ABSOLUTE VALUE.
MULTIPLICATION EQUATIONS 1. SOLVE FOR X 3. WHAT EVER YOU DO TO ONE SIDE YOU HAVE TO DO TO THE OTHER 2. DIVIDE BY THE NUMBER IN FRONT OF THE VARIABLE.
SUBTRACTING INTEGERS 1. CHANGE THE SUBTRACTION SIGN TO ADDITION
MULT. INTEGERS 1. IF THE SIGNS ARE THE SAME THE ANSWER IS POSITIVE 2. IF THE SIGNS ARE DIFFERENT THE ANSWER IS NEGATIVE.
FACTORING Think Distributive property backwards Work down, Show all steps ax + ay = a(x + y)
Addition Facts
ALGEBRAIC EXPRESSIONS
Latent Growth Curve Models
1 What is? Structural Equation Modeling (A Very Brief Introduction) Patrick Sturgis University of Surrey.
ZMQS ZMQS
STATISTICAL INFERENCE ABOUT MEANS AND PROPORTIONS WITH TWO POPULATIONS
BT Wholesale October Creating your own telephone network WHOLESALE CALLS LINE ASSOCIATED.
Stationary Time Series
Notes 15 ECE Microwave Engineering
ABC Technology Project
O X Click on Number next to person for a question.
© S Haughton more than 3?
1 Directed Depth First Search Adjacency Lists A: F G B: A H C: A D D: C F E: C D G F: E: G: : H: B: I: H: F A B C G D E H I.
Twenty Questions Subject: Twenty Questions
Linking Verb? Action Verb or. Question 1 Define the term: action verb.
Squares and Square Root WALK. Solve each problem REVIEW:
Energy & Green Urbanism Markku Lappalainen Aalto University.
Past Tense Probe. Past Tense Probe Past Tense Probe – Practice 1.
This, that, these, those Number your paper from 1-10.
GG Consulting, LLC I-SUITE. Source: TEA SHARS Frequently asked questions 2.
Mediation: Multiple Variables David A. Kenny. 2 Mediation Webinars Four Steps Indirect Effect Causal Assumptions.
1 First EMRAS II Technical Meeting IAEA Headquarters, Vienna, 19–23 January 2009.
Event 4: Mental Math 7th/8th grade Math Meet ‘11.
Addition 1’s to 20.
25 seconds left…...
Test B, 100 Subtraction Facts
11 = This is the fact family. You say: 8+3=11 and 3+8=11
Week 1.
We will resume in: 25 Minutes.
1 MADE Why do we need econometrics? If there are two points and we want to know what relation describes that? X Y.
A SMALL TRUTH TO MAKE LIFE 100%
1 Unit 1 Kinematics Chapter 1 Day
O X Click on Number next to person for a question.
IP, IST, José Bioucas, Probability The mathematical language to quantify uncertainty  Observation mechanism:  Priors:  Parameters Role in inverse.
Growth Curve Model Using SEM
Structural Equation Modeling
The Autoregressive Model of Change David A. Kenny.
LECTURE 16 STRUCTURAL EQUATION MODELING.
Change Score Analysis David A. Kenny December 15, 2013.
Example Models for Multi-wave Data David A. Kenny December 15, 2013.
Cross-lagged Panel Correlation (CLPC) David A. Kenny December 25, 2013.
Confirmatory Factor Analysis Psych 818 DeShon. Construct Validity: MTMM ● Assessed via convergent and divergent evidence ● Convergent – Measures of the.
Controlling for Baseline
Confirmatory Factor Analysis of Longitudinal Data David A. Kenny December
Testing the Equality of Means and Variances in Over-Time Data David A. Kenny.
The Trait Model of Change
Presentation transcript:

The STARTS Model David A. Kenny December 15, 2013

2 Overview u STARTS Model u Stationarity Assumption u Multivariate Generalization

3 The STARTS Components u Stable Trait or ST (trait) u Unchanging component u Autocorrelations of one u Autoregressive Trait or ART (state) u Slow-changing component u State or S (error) u Fast-changing, random component

4 Over-Time Correlations Assuming Equal Variances

5 Over-Time Correlations Large Stable Trait Variance

6 Over-Time Correlations Large ART Variance

7 Over-Time Correlations Large State Variance

8 The STARTS Model b b b

9 Complexity Mixed with Simplicity Complexity More latent variables (11) than variances and covariances (10) Simplicity Only 5 parameters (regardless of the number of waves) 4 variances: ST, ART, S, and U 1 path: ART path all loadings fixed to 1

10 Ensuring Stationarity Variance of ART at time 2 equals Var(ART 2 ) = b 2 [Var(ART 1 )] + Var(U 2 ) Note for the ART variances to be stationarity, it follows that: Var(U 2 ) = Var(ART 1 )[1 - b 2 ] This nonlinear constraint must be made and an SEM program is needed to do so. Thus the total number of parameters for STARTS is four, regardless what the number of waves are.

11 Unequally Spaced Measurement Assume age at each wave is denoted as A t. ART Model for time t-1 to t: ART t = b (At-At-1) ART t-1 + U t For the self-esteem study, we can use in the actual ages and set the time unit for b as one year (autocorrelation for one year).

12 Identification See Cole, Martin, and Steiger (Psychological Methods, 2005). Four waves is the very minimum, but many more (perhaps at least six) are necessary. Estimation is much better with many waves and large N.

13 Problems in Estimation if the AR coefficient is too small (looks like State) or too large (looks like Stable Trait) if a variance component small (explains less than 10% of the variance)

14 Stability of the ART Component There can be a high one-year stability of the ART component but the stability over a long period of time. For example, if the.766 is the year to year stability, the correlation across 11 years is only.053 ( ).

15 Relaxing the Stationarity Assumption All of the equality assumptions require that the variances of the measures not change over time. Seems rather implausible. Model can be modified to allow for latent stationarity with T – 1 parameters and so T + 3 parameters in total.

16 Differential Variances

17 Multivariate Generalization TSO Model (Trait, State, and Occasion) of Cole, Martin, and Steiger Create a latent variable for each time Two factors cause the latent variable Stable Trait (Trait) Autoregressive Trait (Occasion) State: Error Variance of each measure Really a START not a STARTS model Can be estimated with 3 waves.

18

19 Multivariate STARTS Implemented by Donnellan et al. in a study of self-esteem. Add the true State Factor (S). Correlate errors of the same indicator at different times. Requires at least four waves of data.

20