the table and compare the MF, MV, FVmodel with each of the models that include two-
way interactions. If we compare chi-square for the MF, MV, FVmodel with chi-square
for the FV, MF model, the difference in chi-square values is 8.66 2 0.26 5 .8.40, which
is a chi-square on 4 – 2 52 df. This decrement is statistically significant, indicating that
we have lost real interpretive power by dropping MVfrom the model. So we don’t want
to do that. But if we now compare the MF, MV, FVmodel with the MV, FVmodel we
have 5 2.81 – 0.26 5 2.55 on 4 – 2 df, which is not statistically significant. This sug-
gests that we do not need MFin our model. Moving up one additional row we see that
dropping FVfrom our model would lead to a significant decrement. This leaves us with
MV, FVas our best model to date. If you compare the likelihood ratio chi-square for that
model with the likelihood ratio chi-square for any of the models above it, you see that
dropping any other components of the model would lead to a statistically significant decre-
ment. For example, although the model M, FV is not statistically significant
(p 5 .0720), and therefore fits the data at least adequately, it is significantly different from
MV, FV(11.58 – 2.81 5 8.77 on 6 – 4 52 df. As a result of these tests we are left with
the model (MV, FV). (One very good reason for using hierarchical models is that they al-
low us to test differences between models in this way. If we don’t have hierarchical mod-
els we cannot always test the decrement in chi-square resulting from omitting a term
from the model.)Stepwise Procedures
Just as with multiple regression, there are stepwise procedures for model building. SPSS
HILOGLINEAR includes just such a procedure, which starts with the saturated model and
shows what would happen if various parts of the model were eliminated. An example of
such an approach can be seen in Exhibit 17.4.x^2650 Chapter 17 Log-Linear Analysis
LIKELIHOOD- PEARSON
MODEL D.F. RATIO CHISQ PROB. CHISQ PROB.
----------- ---- ------------------- -------- --------- ----------
M 9 121.17 .0000 109.51 .0000
F 10 191.88 .0000 201.66 .0000
V 10 119.73 .0000 125.38 .0000
M, F 8 121.12 .0000 110.43 .0000
F, V 9 119.68 .0000 125.03 .0000
V, M 8 48.98 .0000 49.13 .0000
M, F, V 7 48.93 .0000 49.02 .0000
MF 6 118.21 .0000 105.99 .0000
MV 6 40.21 .0000 38.64 .0000
FV 8 82.33 .0000 84.99 .0000
M, FV 6 11.58 .0720 11.63 .0709
F, MV 5 40.16 .0000 38.60 .0000
V, MF 5 46.01 .0000 45.02 .0000
MF, MV 3 37.25 .0000 35.94 .0000
MV, FV 4 2.81 .5898 2.80 .5921
FV, MF 4 8.66 .0701 8.74 .0680
MF, MV, FV 2 .26 .8801 .26 .8802
MVF 0 0.00 1.000 0.00 1.000
Exhibit 17.3 Test of all possible models