05b_Model Building.ppt 1430KB Jan 10 2009 11:10:28 AM
Model Building
James G. Anderson, Ph.D.
Purdue University
Causal Relationships
Imply:
• An association between the variables
• Lack of spuriousness of the relation
• Evidence to support the direction of
causality
Research Designs
Experimental Designs
• Spuriousness
– Randomization
• Direction of Causality
– Manipulation
Research Designs (2)
Cross Sectional Data
• Specification
• Direction of Causality
– Not dealt with in recursive models
• Nonrecursive Models
– Impose restrictive constraints to identify
model
Research Designs (3)
Panel Designs
• Evaluate direction of causality
• Estimate the stability of endogenous
variables over time
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
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
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
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
Goodness of Fit:
Recursive Model
Chi square: 10.93
df:12
Significance: NS
Chi Square (null):
df:20
Significance:
Δf :
0.93
149.39
Sig
Adjusted Goodness of Fit Index: 0.92
Root Mean Square Residual:
0.05
Nonrecursive Model
• Includes directly observed variables
• Assumes no measurement error
• Assumes reciprocal causation between
Achievement and Self-Concept of Ability
Parameter Estimates:
Nonrecursive Model
Paramet
er
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
Effects
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
Goodness of Fit:
Nonrecursive Model
Chi square:
df:
Significance:
8.32
10
NS
Chi Square (null):
df:
Δf :
149.39
20
0.94
Adjusted Goodness of Fit Index: 0.93
Root Mean Square Residual:0.04
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
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
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
Chi Square Difference Test (3)
XR2 = 10.93
XNR2 = 8.32
Xo2 = 149.39
For the recursive model:
Δf = 149.39 – 10.93 = 0.92
For the nonrecursive model:
149.39
Δf = 149.39 – 8.32 = 0.93
To compare the two models:
149.39
Δf = 10.93 – 8.32 = 0.017
149.39
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
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
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
0.27
2.73
Achievement (t0) on Achievement (t1)
0.60
3.42
Goodness of Fit:
Longitudinal Model
Chi square:
df:
Significance:
23.21
14
NS
Chi Square (null):
df:
Δf :
264.44
27
0.91
Adjusted Goodness of Fit Index: 0.86
Root Mean Square Residual:0.05
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.
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
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
Goodness of Fit:
Latent Variable Model
Chi square:
df:
Significance:
22.27
17
NS
Chi Square (null):
df:
Δf :
255.37
28
0.91
Adjusted Goodness of Fit Index: 0.88
Root Mean Square Residual:0.06
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
Model 4 (2)
• Factor loadings equal to 1
• XLV2 = 22.27
• X02 = 255.37
• Δf = 255.37 – 22.27 = 0.91
255.37
Results
• Several variables have larger effects than
previous models:
Ethnicity
Control
• Lagged effects of Family Socialization:
Ind. Training
Ach (t0)
Stress on Ach.
Control
Ach (t 1)
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.
Results (3)
• Control has a stronger effect on
Achievement (t1) than Self-Concept in the
previous model.
Inferences
• Control has a direct effect (0.59):
Control
Ach(t1)
• Ethnicity has an indirect effect (0.31):
Ethnicity
Control
Ach(t 1)
• Father’s education has an indirect effect
(0.26):
Father’s Ed
Ach Train.
Ach(t 0)
Ach(t1)
Control
Inferences (2)
• Achievement has a lagged feedback effect
through Control
James G. Anderson, Ph.D.
Purdue University
Causal Relationships
Imply:
• An association between the variables
• Lack of spuriousness of the relation
• Evidence to support the direction of
causality
Research Designs
Experimental Designs
• Spuriousness
– Randomization
• Direction of Causality
– Manipulation
Research Designs (2)
Cross Sectional Data
• Specification
• Direction of Causality
– Not dealt with in recursive models
• Nonrecursive Models
– Impose restrictive constraints to identify
model
Research Designs (3)
Panel Designs
• Evaluate direction of causality
• Estimate the stability of endogenous
variables over time
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
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
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
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
Goodness of Fit:
Recursive Model
Chi square: 10.93
df:12
Significance: NS
Chi Square (null):
df:20
Significance:
Δf :
0.93
149.39
Sig
Adjusted Goodness of Fit Index: 0.92
Root Mean Square Residual:
0.05
Nonrecursive Model
• Includes directly observed variables
• Assumes no measurement error
• Assumes reciprocal causation between
Achievement and Self-Concept of Ability
Parameter Estimates:
Nonrecursive Model
Paramet
er
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
Effects
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
Goodness of Fit:
Nonrecursive Model
Chi square:
df:
Significance:
8.32
10
NS
Chi Square (null):
df:
Δf :
149.39
20
0.94
Adjusted Goodness of Fit Index: 0.93
Root Mean Square Residual:0.04
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
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
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
Chi Square Difference Test (3)
XR2 = 10.93
XNR2 = 8.32
Xo2 = 149.39
For the recursive model:
Δf = 149.39 – 10.93 = 0.92
For the nonrecursive model:
149.39
Δf = 149.39 – 8.32 = 0.93
To compare the two models:
149.39
Δf = 10.93 – 8.32 = 0.017
149.39
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
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
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
0.27
2.73
Achievement (t0) on Achievement (t1)
0.60
3.42
Goodness of Fit:
Longitudinal Model
Chi square:
df:
Significance:
23.21
14
NS
Chi Square (null):
df:
Δf :
264.44
27
0.91
Adjusted Goodness of Fit Index: 0.86
Root Mean Square Residual:0.05
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.
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
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
Goodness of Fit:
Latent Variable Model
Chi square:
df:
Significance:
22.27
17
NS
Chi Square (null):
df:
Δf :
255.37
28
0.91
Adjusted Goodness of Fit Index: 0.88
Root Mean Square Residual:0.06
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
Model 4 (2)
• Factor loadings equal to 1
• XLV2 = 22.27
• X02 = 255.37
• Δf = 255.37 – 22.27 = 0.91
255.37
Results
• Several variables have larger effects than
previous models:
Ethnicity
Control
• Lagged effects of Family Socialization:
Ind. Training
Ach (t0)
Stress on Ach.
Control
Ach (t 1)
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.
Results (3)
• Control has a stronger effect on
Achievement (t1) than Self-Concept in the
previous model.
Inferences
• Control has a direct effect (0.59):
Control
Ach(t1)
• Ethnicity has an indirect effect (0.31):
Ethnicity
Control
Ach(t 1)
• Father’s education has an indirect effect
(0.26):
Father’s Ed
Ach Train.
Ach(t 0)
Ach(t1)
Control
Inferences (2)
• Achievement has a lagged feedback effect
through Control