Statistical Methods for Psychology

2. Can the pattern of cell frequencies be explained by differences in the number of people
   judged Guilty and Not guilty?


3. Can the pattern be explained by a combination of the number of participants in the three
   Moral conditions and a higher incidence of Guilty over Not guilty?


4. Can the pattern be explained by an interaction of Moral and Verdict—for example,
   are there more judgments of Guilty when the victim is seen as being of “high moral
   character” and fewer when she is seen as being of “low moral character” or “neutral
   moral character”?


5. Can the pattern be explained by both the Moral 3 Verdict interaction andthe difference
   in the number of cases where the victim was seen as high or low in Fault?


6. Can the pattern be explained by both a Moral 3 Verdict interaction anda Moral 3 Fault
   interaction?


7. Can the pattern be explained by a three-way interaction involving Fault, Moral, and
   Verdict?
   Each of these possibilities—and there are a total of 18 if you count the hypothesis that
   the cell frequencies are random (equiprobable)—represents a possible underlying model.
   Our task will be to decide which of these models both fits the data and is parsimonious.
   (I already know that the saturated model, which by definition involves the highest-order
   interaction, will fit the data perfectly—but it is certainly not parsimonious.)
   This list of questions corresponds directly to a list of different models. Letting F, M,
   and Vstand for Fault, Moral, and Verdict, we can associate the first question with a model
   specified as M. To be more precise, our underlying structural model, which is almost cer-
   tainly much too simple, would be

In the same way we can write out the other models, as shown in Table 17.9.

Notice once again that this is notan analysis of variance—that is, we are not trying to

explain variability in a single dependent variable (Verdict) on the basis of two independent

variables (Fault and Moral). It is easy to keep falling into that trap. We are trying to explain

a pattern of observed cell frequencies, and the explanation may involve any or all of the

variables (dependent or independent) and their interactions. Even where you have one

clearly defined dependent variable and two clearly defined independent variables, part of

the variability may involve just the independent variables—for example, higher frequen-

cies in the Group 1 cells may be due to the often inconsequential fact that you assigned

more participants to Group 1.

ln(Fijk)=l1lM

646 Chapter 17 Log-Linear Analysis

Table 17.9 Some possible models for data in Table 17.8

Question Model Specification

1 M

2 V

3 M, V

4 MV

5 MV, F

6 FM, MV

7 ln(Fij)=l 1 lF 1 lM 1 lV 1 lMV 1 lFM 1 lFV 1 lFMV FMV

ln(Fij)=l 1 lF 1 lM 1 lV 1 lMV 1 lFM

ln(Fij)=l 1 lF 1 lM 1 lV 1 lMV

ln(Fij)=l 1 lM 1 lV 1 lMV

ln(Fij)=l1lM1lV

ln(Fij)=l1lV

ln(Fij)=l1lM