soc 681 – causal models with directly observed variables

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SOC 681 – Causal Models with Directly Observed Variables James G. Anderson, Ph.D. Purdue University

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SOC 681 – Causal Models with Directly Observed Variables. James G. Anderson, Ph.D. Purdue University. Types of SEMs. Regression Models Path Models Recursive Nonrecursive. Class Exercise: Example 7 SEMs with Directly Observed Variables. - PowerPoint PPT Presentation

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Page 1: SOC 681 – Causal Models with Directly Observed Variables

SOC 681 – Causal Models with Directly Observed Variables

James G. Anderson, Ph.D.Purdue University

Page 2: SOC 681 – Causal Models with Directly Observed Variables

Types of SEMs

Regression Models Path Models

Recursive Nonrecursive

Page 3: SOC 681 – Causal Models with Directly Observed Variables

Class Exercise: Example 7SEMs with Directly Observed Variables

Felson and Bohrnstedt’s study of 209 girls from 6th through 8th grade

Variables Academic: Perceived academic ability Attract: Perceived attractiveness GPA: Grade point average Height: Deviation of height from the mean

height Weight: Weight adjusted for height Rating: Rating of physical attractiveness

Page 4: SOC 681 – Causal Models with Directly Observed Variables

GPA

HEIGHT

WEIGHT

RATING

ACADEMIC

ATTRACT

e1

e2

1

1

Page 5: SOC 681 – Causal Models with Directly Observed Variables

GPA

HEIGHT

WEIGHT

RATING

ACADEMIC

ATTRACT

e1

e2

1

1

Page 6: SOC 681 – Causal Models with Directly Observed Variables

Assumptions

Relations among variables in the model are linear, additive and causal.

Curvilinear, multiplicative and interaction relations are excluded.

Variables not included in the model but subsumed under the residuals are assumed to be not correlated with the model variables.

Page 7: SOC 681 – Causal Models with Directly Observed Variables

Assumptions

Variables are measured on an interval scale.

Variables are measured without error.

Page 8: SOC 681 – Causal Models with Directly Observed Variables

Objectives

Estimate the effect parameters (i.e., path coefficients). These parameters indicate the direct effects of a variable hypothesized as a cause of a variable taken as an effect.

Decompose the correlations between an exogenous and endogenous or two endogenous variables into direct and indirect effects.

Determine the goodness of fit of the model to the data (i.e., how well the model reproduces the observed covariances/correlations among the observed variable).

Page 9: SOC 681 – Causal Models with Directly Observed Variables

AMOS Input

ASCII SPSS Microsoft Excel Microsoft Access Microsoft FoxPro dBase Lotus

Page 10: SOC 681 – Causal Models with Directly Observed Variables

AMOS Output

Path diagram Structural equations effect

coefficients, standard errors, t-scores, R2 values

Goodness of fit statistics Direct and Indirect Effects Modification Indices.

Page 11: SOC 681 – Causal Models with Directly Observed Variables

Model One

Page 12: SOC 681 – Causal Models with Directly Observed Variables

Decomposing the Effects of Variables on Achievement

Variables Direct Indirect Total

Sex -.03 - -.03

FatherEd .17 - .17

Ethnic .17 - .17

IndTrng .23* - .23*

AStress -.17* - -.17*

ActMast .02 - .02

SelfCon .42* - .42*

Page 13: SOC 681 – Causal Models with Directly Observed Variables

Model Two

Page 14: SOC 681 – Causal Models with Directly Observed Variables

Goodness of Fit: Model 2

Chi-Square = 29.07df = 15

p < 0.06 Chi-Square/df = 1.8 RMSEA = 0.086 GFI = 0.94 AGFI = 0.85 AIC = 67.82

Page 15: SOC 681 – Causal Models with Directly Observed Variables

Chi Square: 2

Best for models with N=75 to N=100 For N>100, chi square is almost always

significant since the magnitude is affected by the sample size

Chi square is also affected by the size of correlations in the model: the larger the correlations, the poorer the fit

Page 16: SOC 681 – Causal Models with Directly Observed Variables

Chi Square to df Ratio: 2/df

There are no consistent standards for what is considered an acceptable model

Some authors suggest a ratio of 2 to 1 In general, a lower chi square to df ratio

indicates a better fitting model

Page 17: SOC 681 – Causal Models with Directly Observed Variables

Root Mean Square Error of Approximation (RMSEA)

Value: [ (2/df-1)/(N-1) ] If 2 < df for the model, RMSEA is set to

0 Good models have values of < .05;

values of > .10 indicate a poor fit.

Page 18: SOC 681 – Causal Models with Directly Observed Variables

GFI and AGFI (LISREL measures)

Values close to .90 reflect a good fit. These indices are affected by sample

size and can be large for poorly specified models.

These are usually not the best measures to use.

Page 19: SOC 681 – Causal Models with Directly Observed Variables

Akaike Information Criterion (AIC)

Value: 2 + k(k-1) - 2(df)

where k= number of variables in the model A better fit is indicated when AIC is smaller Not standardized and not interpreted for a

given model. For two models estimated from the same

data, the model with the smaller AIC is preferred.

Page 20: SOC 681 – Causal Models with Directly Observed Variables

Model Building

Standardized ResidualsACH – Ethnic = 3.93

Modification IndexACH – Ethnic = 10.05

Page 21: SOC 681 – Causal Models with Directly Observed Variables

Model Three

Page 22: SOC 681 – Causal Models with Directly Observed Variables

Goodness of Fit: Model 3

Chi-Square = 16.51df = 14

p < 0.32 Chi-Square/df = 1.08 RMSEA = 0.037 GFI = 0.96 AGFI = 0.90 AIC = 59.87

Page 23: SOC 681 – Causal Models with Directly Observed Variables

Comparing Models

Chi-Square Difference = 12.56df Difference = 1

p < .0005 AIC Difference = 7.95

Page 24: SOC 681 – Causal Models with Directly Observed Variables

Difference in Chi Square

Value: X2diff = X2 model 1 -X2

model 2

DFdiff = DF model 1 –DFmodel 2

Page 25: SOC 681 – Causal Models with Directly Observed Variables

Decomposing the Effects of Variables on Achievement

Variables Direct Indirect Total

Sex - .09 .09

FatherEd .- .06 .06

Ethnic .29 .05 .34

IndTrng .25 .04 .29

AStress -.14 -.03 -.17

ActMast - .13 .13

SelfCon .44 - .44

Page 26: SOC 681 – Causal Models with Directly Observed Variables

Class Exercise: Example 7SEMs with Directly Observed Variables

Attach the data for female subjects from the Felson and Bohrnstedt study (SPSS file Fels_fem.sav)

Fit the non-recursive model Delete the non-significant path

between Attract and Academic and refit the model

Compare the chi square values and the AIC values for the two models

Page 27: SOC 681 – Causal Models with Directly Observed Variables

Class Exercise: Example 7SEMs with Directly Observed Variables

Felson and Bohrnstedt’s study of 209 girls from 6th through 8th grade

Variables Academic: Perceived academic ability Attract: Perceived attractiveness GPA: Grade point average Height: Deviation of height from the mean

height Weight: Weight adjusted for height Rating: Rating of physical attractiveness

Page 28: SOC 681 – Causal Models with Directly Observed Variables

GPA

HEIGHT

WEIGHT

RATING

ACADEMIC

ATTRACT

e1

e2

1

1

Page 29: SOC 681 – Causal Models with Directly Observed Variables

GPA

HEIGHT

WEIGHT

RATING

ACADEMIC

ATTRACT

e1

e2

1

1