05b_Model Building.ppt 1430KB Jan 10 2009 11:10:28 AM

Model Building

Causal Relationships

Imply:

• An association between the variables • Lack of spuriousness of the relation • Evidence to support the direction of

Research Designs

Experimental Designs • Spuriousness

– Randomization

• Direction of Causality

Research Designs (2)

Cross Sectional Data • Specification

• Direction of Causality

– Not dealt with in recursive models

• Nonrecursive Models

Research Designs (3)

Panel Designs

• Evaluate direction of causality

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

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

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

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

Goodness of Fit:

Nonrecursive Model

• Includes directly observed variables • Assumes no measurement error

Parameter Estimates:

Nonrecursive Model

Effects

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

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

Goodness of Fit:

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

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

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

Longitudinal Model

• Includes directly observed variables • Assumes no measurement error

• Includes Achievement measures at two points in time

• Assume time lagged effects of

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

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}

Goodness of Fit:

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

Parameter Estimates:

Latent Variable Model

Effects Parameter Z

Ethnicity on Control 0.52 4.28

Sex on Independence Training 0.31 3.30

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}

Goodness of Fit:

Model 4

The null model involves only:

• Variances and covariances of exogenous variables

• Variances of exogenous variables No structural relations among the

Model 4 (2)

• Factor loadings equal to 1 • XLV2 = 22.27

• X02 = 255.37

• Δf = 255.37 – 22.27 = 0.91

Results

• Several variables have larger effects than previous models:

Ethnicity Control

• Lagged effects of Family Socialization:

Ind. Training

Ach (t0) Control Ach (t1)

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

Results (3)

• Control has a stronger effect on

Achievement (t1) than Self-Concept in the

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)

Inferences (2)