Statistical Methods for Psychology

are again specified by their “generating class” or “defining set“, meaning that if there are

interactions the main effects are assumed and not listed. Thus the generating class MV,

FMimplies that M, V, and Fare part of the model because they are part of the interac-

tion. If the generating class were MF, the model would contain M, F, and MF, but not V

or any of its interactions. (As I stated before, you cannot use generating classes in SPSS

GENLOG, but have to list each main effect and interaction that you want. This is not true

with SPSS HILOGLINEAR or SAS PROC CATMOD, which automatically create hier-

archical models.)

From this table you can see that four models are nonsignificant at a5.05, meaning

that they produce estimated cell frequencies that are not significantly different from the

obtained frequencies. These are models that we should consider. (The corresponding

rows are shaded.) These are (MF, MV, FV), (FV, MF), (MV, FV), and (M, FV). I am ig-

noring the saturated model because we know that it fits perfectly. Because our models

are hierarchical, the difference in the log-likelihood chi-square values attached to the

models is itself a test on whether we would lose a significant amount of predictability by

going to the simpler model. The difference between the chi-square for the model con-

taining (MF, MV, FV) and the complete model is 0.26 – 0.00 5 0.26, which is a chi-

square statistic on 2 – 0 52 df, which is a nonsignificant decrease. So we are as well off

with the MF, MV, FV model as we were with the saturated model. Now we can move up

Section 17.7 Deriving Models 649

aModel: Poisson

bDesign: Constant 1 Fault 1 Moral 1 Verdict 1 Verdict*Moral

Goodness-of-Fit Testsa,b

Likelihood Ratio

Pearson Chi-Square

Value

40.163

38.602

df

5

5

Sig.

.000

.000

Cell Counts and Residualsa,b

Verdict Fault Moral

111

2

3

21

2

3

211

2

3

21

2

3

Observed

Count

42

79

32

23

65

17

4

12

8

11

41

24

%

11.7%

22.1%

8.9%

6.4%

18.2%

4.7%

1.1%

3.4%

2.2%

3.1%

11.5%

6.7%

Count

32.137

71.196

24.226

32.863

72.804

24.774

7.416

26.204

15.821

7.584

26.796

16.179

%

9.0%

19.9%

6.8%

9.2%

20.3%

6.9%

2.1%

7.3%

4.4%

2.1%

7.5%

4.5%

Residual

9.863

7.804

7.774

–9.863

–7.804

–7.774

–3.416

–14.204

–7.821

3.416

14.204

7.821

Standardized

Residual

1.740

.925

1.579

–1.721

–.915

–1.562

–1.254

–2.775

–1.966

1.241

2.744

1.944

Adjusted

Residual

2.705

1.682

2.391

–2.705

–1.682

–2.391

–1.802

–4.228

–2.898

1.802

4.228

2.898

Deviance

1.661

.909

1.505

–1.820

–.932

–1.657

–1.376

–3.109

–2.175

1.161

2.543

1.813

Expected

aModel: Poisson

bDesign: Constant 1 Fault 1 Moral 1 Verdict 1 Verdict*Moral

Exhibit 17.2 Test of simplified model F, MV