1. James G. Anderson, Ph.D. Purdue University
Model Building
James G. Anderson, Ph.D.
Purdue University

2. Causal Relationships Imply: An association between the variables
Lack of spuriousness of the relation
Evidence to support the direction of causality

3. Research Designs Experimental Designs Spuriousness
Randomization
Direction of Causality
Manipulation

4. Research Designs (2) Cross Sectional Data Specification
Direction of Causality
Not dealt with in recursive models
Nonrecursive Models
Impose restrictive constraints to identify model

5. Research Designs (3) Panel Designs Evaluate direction of causality
Estimate the stability of endogenous variables over time

6. Research Designs (4) Latent Variable Models
Disattentuated relations can be estimated by taking random error into account in the measures
Conceptualize constructs as made up of multiple indicators
The effects of fixing or constraining parameters can be examined
Better represent complex social-psychological processes

9. Recursive Model Includes directly observed variables
Presumes no measurement error
Involves one-way causal relations
The model hypothesizes that family socialization affects achievement both directly and indirectly through achievement values and self-concept

11. Parameter Estimates: Recursive Model
Effects
Parameter Z
Ethnicity on Achievement Values
0.36
4.22
Ethnicity on Self-concept
0.21
2.07
Sex on Independence Training
0.31
3.30
Father's Ed. On Independence Training
0.30
3.23
Father's Ed. On Stress on Achievement
0.17
1.68
Father's Ed. On Achievement (t1)
0.29
3.73

12. Parameter Estimates: Recursive Model (2)
Effects
Parameter Z
Independence Training on Achievement Values
0.29
3.38
Independence Training on Achievement (t1)
0.24
3.17
Stress on Achievement on Achievement Values
-0.24
-2.9
Stress on Achievement on Achievement (t1)
-0.19
-2.61
Achievement Values on Self Concept
0.20
1.93
Self-Concept on Achievement (t1)
0.45
6.07

13. Goodness of Fit: Recursive Model
Chi square:
df:
Significance: NS
Chi Square (null):
df:
Significance: Sig
Δf :
Adjusted Goodness of Fit Index: 0.92
Root Mean Square Residual: 0.05

14. Nonrecursive Model Includes directly observed variables
Assumes no measurement error
Assumes reciprocal causation between Achievement and Self-Concept of Ability

16. Parameter Estimates: Nonrecursive Model
Effects
Parameter Z
Ethnicity on Achievement Values
0.36
4.22
Ethnicity on Self-concept
0.26
1.72
Sex on Independence Training
0.31
3.30
Father's Ed. On Independence Training
0.30
3.23
Father's Ed. On Stress on Achievement
0.17
1.68
Father's Ed. On Achievement (t1)
0.21
2.18

17. Parameter Estimates: Nonrecursive Model (2)
Effects
Parameter Z
Independence Training on Achievement Values
0.29
3.38
Independence Training on Achievement (t1)
0.21
2.61
Stress on Achievement on Achievement Values
-0.24
-2.90
Stress on Achievement on Achievement (t1)
-0.17
-2.12
Achievement Values on Self Concept
0.18
1.35
Self-Concept on Achievement (t1)
0.86
2.89
Achievement (t1) on Self-concept
-0.14
-0.13

18. Goodness of Fit: Nonrecursive Model
Chi square:
df:
Significance: NS
Chi Square (null):
df:
Δf :
Adjusted Goodness of Fit Index: 0.93
Root Mean Square Residual: 0.04

19. Incremental Fit Indices
Consider hierarchically nested
models: Mk, Mt, Mo
where: Mk is the most restricted model
Mo is the null model
The models can then be evaluated relative to each other
The Normed Fit Index: Δf = Xk2 – Xt2
Xo2
0 < Δf < 1

20. Models 1 and 2 The null model involves only:
Variances and covariances of exogenous variables
Variances of the endogenous variables
No structural relations among the endogenous and exogenous variables

21. Chi Square Difference Test
To compare nested models, if M1 can be obtained from M2 by constraining one or more parameters of M2:
Χ2 = Χ12 – Χ22
df = df1 – df2

22. Chi Square Difference Test (3)
XR2 = 10.93
XNR2 = 8.32
Xo2 =
For the recursive model: Δf = – = 0.92
149.39
For the nonrecursive model: Δf = – 8.32 = 0.93
To compare the two models: Δf = – 8.32 = 0.017

23. Longitudinal Model Includes directly observed variables
Assumes no measurement error
Includes Achievement measures at two points in time
Assume time lagged effects of Achievement on Self-concept of Ability and Self-concept on Achievement

25. Parameter Estimates: Longitudinal Model
Effects
Parameter Z
Ethnicity on Achievement Values
0.32
3.75
Ethnicity on Self-concept
0.18
1.84
Sex on Independence Training
0.31
3.3
Father's Ed. On Independence Training
0.3
3.23
Father's Ed. On Stress on Achievement
0.17
1.68
Father's Ed. On Achievement (t0)
0.33
3.43
Father's Ed. On Achievement (t1)
0.14
1.87

26. Parameter Estimates: Longitudinal Model (2)
Effects
Parameter Z
Independence Training on Achievement Values
0.26
3.02
Independence Training on Achievement (t0)
0.13
1.42
Independence Training on Achievement (t1)
0.17
2.94
Stress on Achievement on Achievement Values
-0.20
-2.29
Stress on Achievement on Achievement (t1)
-0.30
-3.27
Achievement Values on Self Concept
0.11
1.07
Self-Concept on Achievement (t1)
0.27
4.79
Achievement (t0) on Achievement Values
0.20
2.22
Achievement (t0) on Self-Concept
2.73
Achievement (t0) on Achievement (t1)
0.60
3.42

27. Goodness of Fit: Longitudinal Model
Chi square:
df:
Significance: NS
Chi Square (null):
df:
Δf :
Adjusted Goodness of Fit Index: 0.86
Root Mean Square Residual: 0.05

28. Latent Variable Model
Assumes that a latent variable, control, underlies the two observed variables: Achievement values and Self-concept of Ability
Both measures of Achievement are adjusted for unreliability
It is assumed that the errors in the measurement of Achievement at Time 1 and Time 2 are correlated.

30. Parameter Estimates: Latent Variable Model
Effects
Parameter Z
Ethnicity on Control
0.52
4.28
Sex on Independence Training
0.31
3.30
Father's Ed. On Independence Training
0.30
3.23
Father's Ed. On Stress on Achievement
0.17
1.68
Father's Ed. On Achievement (t0)
0.34
3.43

31. Parameter Estimates: Latent Variable Model (2)
Effects
Parameter Z
Independence Training on Control
0.37
3.56
Independence Training on Achievement (t0)
0.14
1.43
Stress on Achievement on Achievement (t0)
-0.32
-3.33
Control on Achievement (t1)
0.59
3.86
Achievement (t0) on Control
0.61
4.06
Achievement (t0) on Achievement (t1)
0.23
1.19

32. Goodness of Fit: Latent Variable Model
Chi square:
df:
Significance: NS
Chi Square (null):
df:
Δf :
Adjusted Goodness of Fit Index: 0.88
Root Mean Square Residual: 0.06

33. Model 4 The null model involves only:
Variances and covariances of exogenous variables
Variances of exogenous variables
No structural relations among the exogenous and endogenous variables

34. Model 4 (2) Factor loadings equal to 1 XLV2 = 22.27 X02 = 255.37

36. Results Several variables have larger effects than previous models:
Ethnicity Control
Lagged effects of Family Socialization:
Ind. Training
Ach (t0) Control Ach (t1)
Stress on Ach.

37. Results (2)
Stability coefficients β73 is much smaller than earlier estimates:
Achievement (t0) Achievement (t1)
Lagged effects of Achievement on Control is larger than its effect on
(Y4) Achievement Values
(Y5) Self-Concept
than in the previous model.

38. Results (3)
Control has a stronger effect on Achievement (t1) than Self-Concept in the previous model.

39. Inferences Control has a direct effect (0.59):
Control Ach(t1)
Ethnicity has an indirect effect (0.31):
Ethnicity Control Ach(t1)
Father’s education has an indirect effect (0.26):
Father’s Ed Ach Train Ach(t0) Ach(t1)
Control

40. Inferences (2)
Achievement has a lagged feedback effect through Control