Statistical Methods for Psychology

a change in chi-square of 2.556 on 2 df, which is not significant. This leaves us with the

more optimal model of (Verdict 3 Fault Verdict 3 Moral). The program looks to see if ei-

ther of the remaining two-way interactions can be deleted, and finds that both would result

in a significant decrement.

You might expect the program to then see what happens if we were to drop one of the

main effects, but that won’t do. Remember that for a hierarchical model any effect that

appears in an interaction must also appear as a main effect. Thus if our model contains

Verdict 3 Fault, both Verdict and Fault must also appear. And if it also contains Verdict 3

Moral, Moral must also appear. Therefore the simplest possible model is (Verdict 3 Fault

Verdict 3 Moral), which is the same conclusion we came to earlier.

17.8 Treatment Effects

Now that we have chosen a model, we can return to the treatment effect statistics that were

discussed in conjunction with two-dimensional tables. Here we can see how they add to our

understanding of the data. We can ask SPSS GENLOG to fit our model, produce observed

and expected frequencies, and calculate treatment effects (lambdas). Exhibit 17.5 contains

this information for the model

It is important to understand that estimates of depend on the way the program you

are using codes the data internally. For example I entered 1s, 2s, and 3s as the values for

Moral. SPSS GENLOG takes my codes and converts them to dummy variables, where

Moral 2 is coded 1 if the observation came from the second level of Moral, and 0 otherwise.

l

ln(Fijk)=l1lF1lM1lV1lFV1lMV

652 Chapter 17 Log-Linear Analysis

Parameter Estimatesc,d

Parameter

Constant

[Fault = 1]

[Fault = 2]

[Moral = 1]

[Moral = 2]

[Moral = 3]

[Verdict = 1]

[Verdict = 2]

[Verdict = 1] * [Fault = 1]

[Verdict = 1] * [Fault = 2]

[Verdict = 2] * [Fault = 1]

[Verdict = 2] * [Fault = 2]

[Verdict = 1] * [Moral = 1]

[Verdict = 1] * [Moral = 2]

[Verdict = 1] * [Moral = 3]

[Verdict = 2] * [Moral = 1]

[Verdict = 2] * [Moral = 2]

[Verdict = 2] * [Moral = 3]

Estimate

3.191a

–1.153

0 b

–.758

.505

0 b

–.198

0 b

1.529

0 b

0 b

0 b

1.040

.573

0 b

0 b

0 b

0 b

Std. Error

.234

.

.313

.224

.

.246

.

.266

.

.

.

.366

.278

.

.

.

.

Z

–4.923

.

–2.422

2.254

.

–.807

.

5.744

.

.

.

2.845

2.060

.

.

.

.

Sig.

.000

.

.015

.024

.

.420

.

.000

.

.

.

.004

.039

.

.

.

.

Lower Bound

–1.612

.

–1.371

.066

.

–.680

.

1.007

.

.

.

.324

.028

.

.

.

.

Upper Bound

–.694

.

–.145

.943

.

.283

.

2.051

.

.

.

1.757

1.119

.

.

.

.

aConstants are not parameters under the multinomial assumption. Therefore, their standard errors are not calculated.

bThis parameter is set to zero because it is redundant.

cModel: Multinomial

dDesign: Constant 1 Fault 1 Moral 1 Verdict 1 Verdict*Fault 1 Verdict*Moral

95% Confidence Interval

Exhibit 17.5 Parameter estimates for the model VFVM